diff --git "a/designv11-7.json" "b/designv11-7.json" new file mode 100644--- /dev/null +++ "b/designv11-7.json" @@ -0,0 +1,8947 @@ +[ + { + "image_filename": "designv11_7_0003088_j.jmatprotec.2011.09.010-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003088_j.jmatprotec.2011.09.010-Figure1-1.png", + "caption": "Fig. 1. A general deformation zone.", + "texts": [ + " The thermal-rigid-viscoplastic constitutive model was used for modeling the billet. The results were in good agreement with fundamental guidelines. Bastani et al. (2011) studied the material flow and the temperature evolution inside the container and the die in order to minimize the change in shape and mechanical properties of the extruded s Proc m p a t t t t p i E d ( d s p i l v t e n T i b a t o t i a m r t b fl e c m T a A m v e o e a f t o T s i b 0 t m s slope in the entry and exit sections can be controlled by adjusting Bezier coefficients (c1, c2). Fig. 1 shows an arbitrary deformation from the inlet section \u2032 \u2032 A.K. Meybodi et al. / Journal of Material aterial. In their paper, they investigated the effect of various arameters, including ram speed, initial temperature distribution, nd container cooling condition on material flow and temperaure evolution. They studied the mentioned parameters in order o: (1) minimize temperature and velocity field radial distribuion, (2) achieve isothermal extrusion process, and (3) investigate he effect of undesirable temperature distribution on exit velocity rofile", + " A kinematically admissible parametric velocity field has been obtained by differentiating the position vector and applying the volume constancy condition. To derive the velocity field, the following assumptions were considered and applied to the Bezier relations (Chitkara and Celik, 2000): 1. The plastically deforming zone is bounded by the entry and the exit planes. 2. Both the entry and exit cross-sections are each assumed perpendicular to the extrusion axis. 3. The proportionality of AF/AC = A\u2032F\u2032/A\u2032C\u2032 in Fig. 1 is constant on every stream surface. 4. The extrusion ratios (area of a segment at the final crosssection/area of the corresponding segment in the billet) equal to the overall extrusion ratio. 5. The material is incompressible. However, Bezier formulation fails to describe the experimental evidence. The formulation provides a constant axial velocity at a given cross-section, while in practice, the velocity decreases in radial direction from the center of die to the outer surface. To improve the velocity field, Chitkara and Celik (2000) introduced the corrective function G(u, q, t) which obeyed the boundary conditions" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000037_811309-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000037_811309-Figure3-1.png", + "caption": "Fig. 3 \u2014 Torque To vs twist tGa for final stretch ratio X, = 0.785.", + "texts": [], + "surrounding_texts": [ + "T*\n[k*NN\nk* k* CrTN TT\n14,1 r\n86\nstatic pre-load deformation as well as frequency since Stj is a parameter and g * (w) is frequency-dependent.\nCOMPUTER CODE IMPLEMENTATION\nThe constitutive laws and associated matrix formulations presented herein have been implanted in the finite element code, MARC (7). This code has the capabilities to model both the material and geometric non-linearities of elastomeric components, and utilizes 8 noded plane strain and axisymmetric isoparametric elements and a 20-node solid brick element.\nA variety of potential functions W(I 1 ,1 1) applicable to incompressible materials has been listed in Ref. 8. It was chosen to implement a form investigated by James and Green (9) and James, Green, and Simpson (10), termed the third order invariant form,\nW (1 1 ,1 2) = C o, (1, -3) + Co , (1,-3) + C\u201e (1,-3) (1 2-3) (30)\n+ C 20 + C,0 (11-3)3\nwhere the Co are parameters to be determined by fitting experimental data.\nThe solution procedure consists of the following steps:\nI. Calculation of the non-linear elastic response of the elastomeric component to a static pre load. The solution based on the potential function given by Eq. (30) is obtained by incremental application of the applied loads/displacements and a Newton-Raphson iteration within each increment to obtain static equilibrium.\n2. Calculation of the complex-valued amplitudes Au*/, AS * at each given frequency w and amplitude for theAB boundary tractions Ail and/or boundary displace-\n-* ments AuI. This portion of the analysis involves the assembly and solution of a symmetric complex-valued stiffness matrix.\nAll information calculated during the analysis can be displayed graphically: this includes deformed plots for both inand out-of-phase displacements and contour plots of the inand out-of-phase components of the incremental stresses AS*AB'\nWe will not attempt here to describe the implementation of the geometric non-linearity capability. This capability is described in volumes F and G of the MARC program [7].\nNUMERICAL EXAMPLES AND DISCUSSION\nI. VIBRATIONS IN A STATICALLY STRETCHED AND TWISTED CYLINDER. \u2014 The first example demonstrates the numerical accuracy of the code by comparing code computations with closed-form solutions for the titled problem. Here we consider a circular cylinder of undeformed length 9, and radius \"a\" comprised of an incompressible viscoelastic solid which is stretched axially to a length X012, and twisted through an angle ifrokl2o by application of forces and torques at the cylinder ends. When the stresses in the material have relaxed to constant equilibrium values, small-amplitude time harmonic torsional vibrations and extensional vibrations of frequency 0.) are applied to the pre-strained cylinder. We wish to compare finite element computations with closed-form solu-\ntions (11) for both the static pre-strain response and the lowfrequency steady-state vibrations of the cylinder, after the decay of any transients. Inertia effects in the rubber were neglected.\nThe experimental data on an unfilled SBR material at 0\u00b0C (12) was used. The static material properties are as follows:\n= 1.008 x 10\" t MPa Co, = 1.612 x 107/ C\u201e = 1.338 x 1073 C1, = 6.206 x 10-4\n= 6.206 x 10-9 The steady-state dynamic material parameters gc(w), gs(w) defined in Eq. (19) were determined from experimental test data for uni-axial storage and loss modulus and the results were fitted to the following:\ngc(w) Acw be' gs (w) = Asw-bs\nThe fitted parameters are as follows: As = 0.192940 Ac = 0.052743 bs = 0.846 be = 0.952\nThe problem was solved numerically on Ford's Cyber 176 computer using sixteen (16) three-dimensional isoparametric elements. Since there is no angular dependence of the displacement and stress fields, it was necessary to model only a wedge from the cylinder (Fig. 2). The full length of the cylinder (9, = 0.5 in.) was represented with four elements in the axial direction and four in the radial direction. The wedge angle was chosen arbitrarily to be 30 degrees; the angular span was represented by one element.\nThe cylinder was compressed to a stretch ratio of A\u00b0 = 0.785 and then subjected to twist increments up to a total twist of ifro = 0.4 radians/inch. The closed form solution for stresses oPzz, croz andthe normal force No, torque To, static str static Green Lagrange strain components Ezz, Ebz are given in the Appendix. A comparison of the finite element solution and the exact solution is given in Figures 3-6; the two results are practically indistinguishable except for the results for the normal stress component a\u00b0zz in which case the finite element solution is off in the worst case by less than two percent.\nWe now suppose that one end of the stretched and twisted cylinder remains fixed while to the other end are applied small amplitude extensional vibrations of amplitude, E and torsional vibrations of amplitude a. The superposed torque T* and normal force N * may be written in matrix form in terms of e, a as follows:\nwhere closed form expressions for k*N.,, k*NT' Ic4TN' kh are given in the Appendix. A comparison of the results for the normal stiffness kNN and torsional stiffness k TT is presented in Figs. 7 and 8 respectively; the difference between the exact solution and the finite element solution is indistinguishable.\nThe static response calculations required 27 load increment steps and used 945 CP seconds of computer time. The harmonic analysis used 48 CP seconds for each frequency for a total of 192 CP seconds.", + "87\ndistance for final deformation state X 0 = 0.785,C =", + "88\nII. BUTYL RUBBER BODY MOUNT \u2014 In this example we consider the axial vibrations of a pre-loaded automotive body mount made of a carbon-black filled butyl rubber (Fig. 9). This example demonstrates the applicability of the code to filled elastomers which exhibit some dependence on dynamic strain amplitude. Inertia effects are included. No closed-form solutions exist for this problem. Therefore, we will compare finite element computations with available test data for both the static force-deflection response and the low frequency steady-state axial vibrations of the mount.\nThe static material properties are as follows: C 10 = 0.8669 x 10-2 MPa Co, = 0.2555 C\u201e -= 0.1329 x 10-2 C\u201e = 2.1474 x 10-2 C,0 = 5.107 x 10-7\nThe steady-state dynamic viscoelastic material parameters gs(w), &(s)) defined in Eq. (19) were determined from uniaxial test data and the results are plotted in Fig. 10.\nThe problem was solved numerically using 104 20-node isoparametric brick elements. Since the mount is cyclically symmetric, it was convenient to model a sector from the mount beginning half way between two consecutive holes and terminating at the center of one of the holes (Fig. 11).\nThe static response calculations required 27 load increment steps and used 7,938 CP seconds of computing effort on the Cyber 176. The harmonic analysis used 1,104 CP seconds.\nThe computed static force-deflection response is plotted in Fig. 12 along with corresponding test results. Good agreement between analysis and test is observed. The test data were taken from four tests; the tests were repeated to eliminate the possibility of experimental error.\nThe dynamic stiffness was calculated from finite element results. Both experimental and finite element results for stiffness are plotted against frequency in Fig. 13. Excellent correlation between analysis and testing was obtained for the loss" + ] + }, + { + "image_filename": "designv11_7_0002762_1077546312458820-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002762_1077546312458820-Figure1-1.png", + "caption": "Figure 1. Lumped mass representation of a rotor system.", + "texts": [ + " Jun (2004) derived unbalance influence coefficients analytically, using TMM for the Timoshenko beam element. But the influence of bow is not considered. The objective of the present study is to derive analytically the influence coefficients for a flexible rotor system having both mass unbalance and bow using TMM, and balance the rotor at its first bending critical speed in a single trial run and using a single balancing plane. Consider an \u2018n\u2019 station lumped mass and \u2018n 1\u2019 field massless beam system as shown in Figure 1. The ith at UNIV ARIZONA LIBRARY on June 21, 2014jvc.sagepub.comDownloaded from lumped mass is denoted as the ith station, and the massless beam lying between ith and (i\u00fe 1)th station is denoted as the ith field. The state of the field and station elements are characterized by linear and angular displacements, shear forces and bending moments which are termed as state variables. Given the state at one station, the state of a neighboring station is obtained by multiplying with transfer matrices which depend on the properties of the intervening field and station", + " A relationship is established between a set of unknowns of the state variables on the two ends of the system by repetitive multiplications of the intervening transfer matrices, marching from one end of the system to the other. The influence coefficients are extracted after applying suitable boundary conditions to the specified boundary state variables. In the case of a rotor bearing system having mass unbalance and bow, the forces due to mass unbalance and bow are modeled as shear forces acting on the specified stations. As shown in Figure 1, the properties at station, mi, Jpi and Jdi represent the mass, polar and transverse mass moment of inertia of the ith lumped mass. The variables of interest at station i are displacement R, slope , moment M and shear force V which are defined with respect to the inertial frame of reference X, Y, Z. The superscripts r and l denote right and left\u2013hand side of the station. ki and ci represents the support stiffness and damping coefficients. If ei is the eccentricity of the lumped mass from the geometrical axis, the mass unbalance in each of the station is defined as miei and makes an angle i in y-z rotating coordinates fixed on the rotor", + "t\u00fe i\u00de \u00f02\u00de The station transfer-matrix [Tsi] relating variables on the left-and right-hand sides of station i is given by the following equation, in addition to unbalance in Jun (2004), bow effect is added in the present study. Rr i ri Mr i Vr i 8>>>>>>>< >>>>>>>: 9>>>>>>>= >>>>>>>; \u00bc 1 0 0 0 0 1 0 0 0 \u00f0Jpi Jdi\u00de! 2 1 0 mi! 2 jci! 0 0 1 2 66666664 3 77777775 Rl i li Ml i Vl i 8>>>>>>>< >>>>>>>: 9>>>>>>>= >>>>>>>; \u00fe 0 0 0 miei! 2ej \u00f0!t\u00fe i\u00de \u00fe fbie j \u00f0!t\u00fe i\u00de 8>>>>>>>< >>>>>>>: 9>>>>>>>= >>>>>>>; ; at UNIV ARIZONA LIBRARY on June 21, 2014jvc.sagepub.comDownloaded from This can be written as Q\u00f0 \u00deri\u00bc Tsi\u00bd Q\u00f0 \u00de l i\u00fefgi \u00f03\u00de The column matrix {}i indicates the unbalance and bow vector. Considering ith field element shown in Figure 1, Ei, Ii, and Li are the Young\u2019s modulus, area moment of inertia and length of the ith field. The field transfermatrix [Tfi] relating variables on the left- and righthand sides of ith field (beam) is given by Rl i\u00fe1 li\u00fe1 Ml i\u00fe1 Vl i\u00fe1 8>>>>< >>>>: 9>>>>= >>>>; \u00bc 1 Li L2 i =2EiIi L 3 i =6EiIi 0 1 Li=EiIi L2 i =2EiIi 0 0 1 Li 0 0 0 1 2 66664 3 77775 Rr i ri Mr i Vr i 8>>>>< >>>>: 9>>>>= >>>>; This is written as Q\u00f0 \u00deli\u00fe1\u00bc Tfi Q\u00f0 \u00deri \u00f04\u00de Combining equation (4) with equation (3), the overall transfer matrix for a section Ti\u00bd (field\u00fe station) is given by Q\u00f0 \u00deli\u00fe1\u00bc Tfi Tsi\u00bd Q\u00f0 \u00de l i\u00fe Tfi fgi\u00bc Ti\u00bd Q\u00f0 \u00de l i\u00fe Tfi fgi \u00f05\u00de By successive matrix multiplication from left-hand side of station one to the right \u2013hand side of station n, the overall system transfer system equation is given by Q\u00f0 \u00dern\u00bc Tn\u00bd Ti\u00bd Ti 1\u00bd Ti 2\u00bd \u00bdT1 Q\u00f0 \u00de l 1\u00fe Ti\u00bd Ti 1\u00bd Ti 2\u00bd \u00bdT1 fgi\u00fe ; Q\u00f0 \u00de r n\u00bc T\u00bd T Q\u00f0 \u00del1\u00fe \u00f06\u00de The eigen values and eigen vectors are obtained from the overall transfer" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002138_j.triboint.2010.04.001-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002138_j.triboint.2010.04.001-Figure3-1.png", + "caption": "Fig. 3. Reference systems in the journal bearing.", + "texts": [ + " Therefore, assuming a phenomenological description of the shaft cooling by the ambient (through conduction along the shaft axis and convection to the ambient from the surface of the shaft outside of the bushing), a thermal model is obtained by imposing an energy balance on the shaft, taking also into account (in addition to convection into the ambient) heat transfer from the lubricant film:Z Gs k @T f @~n dl \u00bc hsC kf RaL \u00f0T s T a\u00de\u00fe AsC kf RaL @T s @t , \u00f021\u00de with the corresponding characteristic thermal time: tcs \u00bc AsC kf RaL : \u00f022\u00de Newton\u2019s second law of motion predicts the movement of the gravity center of the shaft: M~a \u00bc ~W 0\u00fe ~F , \u00f023\u00de where M denotes the mass of the shaft, ~a the acceleration of its center, ~W 0 the applied external load, and ~F the fluid reaction force. Usually, two reference systems are employed in the dynamical stability analysis (see Fig. 3): a mobile coordinates system, (r,t), where the r axis lays in the line OcOa , and a fixed coordinates system, (X,Y), that it is related to the previous one through the displacement angle f. For computational purposes, one of them can be more adequate than the other. For example, force ~F is expressed in the (r,t) system in the form: ~F \u00bc Fr Ft \" # \u00bc Z O1 p cosy siny Ra dydz, \u00f024\u00de that it is simpler than the corresponding expression in the (X,Y) system. Law (23) is modified by introducing nondimensional values", + " A further comparison with classical results (concerning the nature of solutions in the unstable region) is presented in Section 4.2.3. Finally, the influence of thermal effects on the system stability is considered in Section 4.2.4. Dynamical stability analysis of the journal bearing can be made directly in cases where an analytical pressure, p, and the cavitation region are known (see Fre\u0302ne et al. [10] or Dowson [33]). Taking into account that the shaft can change its position, eccentricity and minimum thickness angle become time func- tions. Shaft position is defined by vector OcOa ! (see Fig. 3), that in polar coordinates it is given by the shaft displacement angle, f, and relative bush-shaft eccentricity, e\u00bc Ce. Under the hypotheses of an uniform temperature of the lubricant, a dimensional Reynolds equation can be written in the form: 1 R2 a @ @y h3 m @p @y \u00fe @ @z h3 m @p @z \u00bc 6 \u00f0o 2 _f\u00de @h @y \u00fe2 _ecosy , \u00f054\u00de that corresponds to take the origin of angles, y, on the line OcOa at each time instant. Therefore, the equation is valid in the mobile coordinate system (r,t). The thickness of the fluid film in (54) is h\u00bc C\u00f01\u00feecosy\u00de, and _f and _e denote time derivatives of OcOa " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003651_s11012-013-9833-5-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003651_s11012-013-9833-5-Figure3-1.png", + "caption": "Fig. 3 The underconstrained 7R mechanism. Cylinders represent revolute joints and the basis vectors of global coordinate system are colored red (Color figure online)", + "texts": [ + " This point is also the only singular point of V(I4bar) as a complex variety so that we have V(I4bar) \u2229R 6 = { (1,0,1,0,1,0) } = ( V(I4bar) ) . So we may say that the original representation is underconstrained but of course the mechanism itself is characterized by IR4bar = \u3008c1 \u2212 1, c2 \u2212 1, c3 \u2212 1, s1, s2, s3\u3009. 5.2 Underconstrained 7R mechanism In this example we investigate a spatial single loop 7R mechanism. The mechanism consists of 6 rigid bodies connected to each other with revolute joints. The lengths and rotation axes are chosen as in Fig. 3. To each body we associate a certain point which is the origin of the body (or local) coordinate system and its Euler parameters which give the orientation of the body. Geometric constraints imposed by kinematic pairs relate the coordinates of adjacent bodies. This approach starts from the individual bodies instead of formulating loop closure constraints, as it is commonly done in the \u2018relative coordinate\u2019 formulations using joint angles. In this way the problems of selecting independent loops in multi-loop mechanisms are avoided. If desired the loop equations can be recovered, as shown below. The origin of body coordinates of the straight rods are fixed to their midpoints. For bodies B4, B5 and B6 the origins are the points O4,O5 and O6 as shown in Fig. 3. The constraint equations for this 7R mechanism are then p1 = ( e1,R(a)e3) = 0 p2 = ( e2,R(a)e3) = 0 p3 = ( R(a)e1,R(b)e3) = 0 p4 = ( R(a)e2,R(b)e3) = 0 p5 = ( R(b)e1,R(c)e3) = 0 p6 = ( R(b)e2,R(c)e3) = 0 p7 = ( R(c)e1,R(d)e3) = 0 p8 = ( R(c)e2,R(d)e3) = 0 p9 = ( R(d)e2,R(e)e3) = 0 p10 = ( R(d)e3,R(e)e3) = 0 p11 = ( R(e)e2,R(f )e3) = 0 p12 = ( R(e)e3,R(f )e3) = 0 p13 = ( R(f )e2, e1) = 0 p14 = ( R(f )e3, e1) = 0 p15...17 = ra \u2212 1 2 R(a)e1 = 0 (9) p18...20 = ra + 1 2 R(a)e1 \u2212 rb + 1 2 R(b)e1 = 0 p21", + " Hence from system (9) we get the following ideal which contains only Euler parameters. I 0 7R = \u3008q1, . . . , q23\u3009 = \u3008p1, . . . , p14,p36, . . . , p41\u3009 + I LC 7R \u2282 Q[a, b, c, d, e, f ]. (10) We thus have a constraint map q = (q1, . . . , q23) : R 24 \u2192R 23 which suggests that dimension of the configuration space is dim(V(I 0 7R)) = 1. To analyze the situation more closely we use the decompositions (7). In order to choose right components for the simplified revolute joint constraints we use the condition that the configuration shown in Fig. 3 must be included in the resulting variety. To describe these conditions conveniently let us introduce some notation. Let I denote the identity matrix. Let us define the following ideals and corresponding rotation matrices: m0(a) = \u3008a0 \u2212 1, a1, a2, a3\u3009 \u2190\u2192 M0 = I, m1(a) = \u2329 a0 \u2212 1/ \u221a 2, a1, a2 + 1/ \u221a 2, a3 \u232a \u2190\u2192 M1 = \u239b \u239d 0 0 \u22121 0 1 0 1 0 0 \u239e \u23a0 , m2(a) = \u3008a0, a1, a2 \u2212 1, a3\u3009 \u2190\u2192 M2 = \u239b \u239d \u22121 0 0 0 1 0 0 0 \u22121 \u239e \u23a0 . In the initial configuration we have R(a) = R(b) = R(c) = R(d) = M0, R(e) = M1, R(f ) = M2" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003560_978-1-4613-4560-2_2-Figure8.71-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003560_978-1-4613-4560-2_2-Figure8.71-1.png", + "caption": "Fig. 8.71. After collision with excited impurity atoms, the energy of electrons is increased by quanta released by the atoms.", + "texts": [ + " A simple way of deriving the distribution of energies among the electrons in the metal is presented here. Suppose that, in the lattice of the metal, there are impurity atoms which can exist either in their ground states with energy zero or in excited states with energy B. Electrons which collide with these impurity atoms can ex change quanta of energy B. Let the initial energy of an electron be E, and, after collision with the impurity atom in its excited state, let the electron energy be raised to E + B (Fig. 8.71). Then, the rate rE-+E+s of the E -+ E + e electronic transitions is pro- portional to the product of three probabilities: (1) PE , the probability of finding the electron before collision in the ene,rgy state E; (2) times P\" the probability of the impurity atom's being in the excited state of energy e; and (3) times the probability that a state of electron energy E + e is vacant in the metal. This third probability is I - PE+F' where PE+, is the probability that the E + e acceptor-energy state is occupied" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003052_10402004.2012.727531-Figure8-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003052_10402004.2012.727531-Figure8-1.png", + "caption": "Fig. 8\u2014Elastomer in contact with the surface cavity (color figure available online).", + "texts": [ + " It was assumed that the seal was moved radially onto the shaft and completely flattened by the shaft as shown in Fig. 7a. The initial displacement[ uint s ] was inserted into Eq. [4] to obtain the corresponding external nodal force needed. It was found that at some area the nodal force was negative. Because the negative contact force does not exist physically, the negative contact force was gradually relaxed to zero as shown in Fig. 7b. The final geometry of the elastomer in contact with the triangular surface cavity is shown in Fig. 8. Details of the algorithm for the contact analysis are shown in Fig. 9. This algorithm is similar to the linear FE model employed by Shen (13) for mixed elastohydrodynamic lubrication (EHL) analyses. The difference was that instead of using the Hertz contact law to deal with the contact, this study assumed that the shaft surface was rigid. Figure 10a shows the 2D axial distribution of the sealing force for the contact between the elastomer and a smooth shaft. This sealing force distribution was similar to the results in Salant and Flaherty (9) and Jia, et al" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003280_1.55923-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003280_1.55923-Figure2-1.png", + "caption": "Fig. 2 Wing angles and stroke-plane angles.", + "texts": [ + " The wings are considered to be thin, flat plates with three degrees of freedom relative to the stroke plane. The stroke plane defines the mean motion of the wing and is defined relative to the longitudinal axis of the body. The three degrees of freedom for the wing are the flapping (sweep) angle ( ), the pitch angle relative to the stroke plane ( ), and the deviation (elevation) angle ( ). The coordinate frames and reference vectors are presented in Fig. 1. The wing angles and stroke-plane angle are presented in Fig. 2. D ow nl oa de d by M cG ill U ni ve rs ity o n N ov em be r 12 , 2 01 2 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /1 .5 59 23 The wings are considered to be holonomically constrained to the central body. The 12 generalized coordinates describing the position of the system qj are q j X Y Z R R R L L L (1) The associated quasi velocities of the system uj are u j u v w p q r pRW qRW rRW pLW qLW rLW (2) The multibody equations of motion can be placed into the following form: M _uj Faero Fg P 3 i 1 _ vi;red ci;red Maero Mg P 3 i 1 Ii " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001868_0278364910365093-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001868_0278364910365093-Figure3-1.png", + "caption": "Fig. 3. A Dubins CC trajectory and associated control line. The control switches from the left rotation center when the right rotation center reaches the line at signed distance H r from the control line.", + "texts": [ + " In these trajectories, all translation segments are parallel to the control line, or there exists a pair of sequential rotation centers that describe a line perpendicular to the control line. 4. Constant-angular-velocity trajectories. If k1 k2 0, then Theorem 1 immediately implies that must be either maximized or minimized over the trajectory, and constant. The Dubins CLC trajectories shown in Figure 1 are examples of tangent trajectories, and the CCC trajectory is a generic trajectory. Tacking trajectories do not occur for the Dubins problem, and the only constant-angular-velocity trajectory is an arc of a circle with no control switches. Figure 3 gives an example of a trajectory that maximizes the Hamiltonian at each time, for some choice of constants. It turns out that the value of the Hamiltonian, which depends on the value of the constants, the maximizing control, and the state x y is the same no matter which reference point is picked. Any control that is not a pure translation has a rotation center, a point that does not move during the rigid-body transform. Therefore, choosing the rotation center as the reference point for computing the Hamiltonian is often very convenient, since x y of this reference point is zero. In this case, it turns out that the value of the Hamiltonian is simply the signed distance of the rotation center from the control line, multiplied by the angular velocity of the body. We can use this observation to describe the trajectory in Figure 3 fairly simply. A Dubins car has two rotation controls, and two rotation centers: one to the right, and one to the left. The value of the Hamiltonian is some constant, H . At a distance of H l from the control line, the left rotation center at UNIV OF MONTANA on April 5, 2015ijr.sagepub.comDownloaded from may be \u201cactive\u201d, and at a distance H r the right rotation center may be active. In configuration 1, the left rotation center is further from the control line, so the value of H computed if we apply the left rotation center is greater this is the maximizing control, and the corresponding value of the Hamiltonian will remain constant over the trajectory. As the body spins about the left rotation center, the right rotation center moves. At any instance, we can compute the Hamiltonian for the right rotation center, and for a while it is less than the Hamiltonian over the trajectory, so the left rotation center remains active. Eventually, the right rotation center reaches a line at distance H r from the control line (configuration 2 in Figure 3). At this time, both controls maximize the Hamiltonian, since both rotation centers are on their associated lines, but whichever control is applied, at the next instance, only the right rotation center will be maximizing. We therefore say that at this control switch that the control associated with the right center is sustainable. For the remaining section of the trajectory shown, the right rotation center remains maximizing. We present an algorithm that takes the set of controls as input, and outputs all possible path structures, described as sequences of controls. This reduces the problem of finding the optimal trajectory between a particular start and goal to the problem of considering each possible path structure, finding the best path of each structure, and then the best path among all structures. We show that the number of generic trajectory structures is polynomial in the number of control inputs. Along the way, there are many details to consider, but the basic idea is that shown in Figure 3: trajectories essentially roll on rotation centers, each of which activates on its own line a particular distance from the control line. If there are translations, there may also be switches to translations at particular angles. We can see that the value of the Hamiltonian in some way characterizes the trajectory: it gives the distances from the line at which rotation centers switch, and the angle at which switches to translations occur. There are also some degenerate cases, for which switching configurations occur at more than a finite set of times during the trajectory", + " The trajectories may include the left and right turns, which are vertices of the control space, but also may include straight lines, which are not vertices. The fact that these straight lines appear in optimal trajectories may be deduced by chattering the controls that are vertices. We now turn to non-chattering trajectories. These trajectories have piecewise-constant controls, and in this section we show that at every point it is possible to write equations to determine which control precedes the switch, and which follows the switch. For example, in Figure 3, in configuration 2, rotations about either of points L or R gives the same value of the Hamiltonian both controls are maximizing. However, regardless of which control is followed, at the next instance only one control will continue to satisfy the maximum principle. Given a (y ) value at a point where multiple controls maximize the Hamiltonian, under what circumstances is it possible to determine the \u2018next\u2019 control? We define a sustainable extremal control at time t and configuration q to be a control such that there exists a strictly positive constant such that applying the control on [t t generates an extremal trajectory with the same constants", + " Analysis of rotation\u2013rotation switches is simplified by considering the rotation center associated with each control. In the frame of the body, the rotation center xi yi corresponding to control ui is xi yi i (51) yi xi i (52) Consider a switch from control ui to control u j , with i j . Let xi yi be the coordinates of the rotation center i with respect to the control line. From Corollary 1, the Hamiltonian corresponding to control i at this configuration is H yi i (53) Geometrically, as we can see in Figure 3 in configuration 2, the switch corresponds to a situation where each rotation center lies on its own line at a distance H from the control line. Since the distance between the rotation centers is fixed by their associated controls, the problem is to fit a line segment in such a way that the endpoints contact two parallel lines. There are only two solutions to this geometric problem, each corresponding to a direction of the switch this is in fact the main idea behind the proof of Theorem 2. The main result in this section is that we show how to identify the correct solution for the configuration, given a value for H , and a directed switch between a pair of controls" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002732_elan.201100399-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002732_elan.201100399-Figure1-1.png", + "caption": "Fig. 1. Measuring setup. 1. Buffer reservoir, 2. HPLC pump, 3. Injector, 4. Thin-layer enzyme reactor, 5. Sample in, 6. Amperometric cell, 7. Amperometric detector, 8. Recorder.", + "texts": [ + " After mixing the milk and the reagent health status of the udder quarter could be determined based on colour (pH) and consistence of the milk. Milk samples/ udder quarters were classified as negative, 1, (healthy) 2, 3 scores (subclinical mastitis) or clinical (visually ill). After scoring milk samples were taken aseptically from some negative quarters after removing a few milk squirts and disinfecting the teat ends. Also, subclinical and clinical quarters were sampled in the same way. A stopped-flow injection analyser (SFIA, Figure 1), consisting of a buffer reservoir, a HPLC pump (ESA, USA), an injection valve (Rheodyne Inc., Cotati, CA, USA), an enzyme reactor and a thin-layer amperometric cell (Mo. 5040, ESA, USA) with glassy carbon measuring electrode (1 3 mm, 55-0184 ESA, USA) connected to an electrochemical detector (Coulochem II., ESA, USA) with recorder were the basic instrumentation of our research. The polarization potential was ensured and fixed S P E C IA L IS S U E 108 www.electroanalysis.wiley-vch.de 2012 Wiley-VCH Verlag GmbH & Co" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003869_s00419-012-0608-6-Figure6-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003869_s00419-012-0608-6-Figure6-1.png", + "caption": "Fig. 6 The mode shapes corresponding to frequency \u03c925 (auxiliary model)", + "texts": [], + "surrounding_texts": [ + "As mentioned earlier, in the geometrical model of the gear, the geometry of the teeth is omitted. It allows us to reduce the system\u2019s FE model size. The simplified geometrical model of the system consists of five sectors (see Fig. 1) that have the cyclic symmetry feature. Each of these segments is meshed by using standard procedures of the ANSYS software. The 3-D solid mesh is elaborated and as mentioned earlier, the ten-node tetrahedral element (solid92) with three degrees of freedom in each node is used to realize each sector. During the mesh generation process, it is assumed that the maximum length of each element\u2019s side needs to be no more than 2.7 [mm]. The developed FE model is displayed in Fig. 2, and it consists of 19,620 elements and 36,188 nodes, respectively. The particular sectors are glued as a whole at the geometrical model preparing the stage by using standard procedure of the ANSYS program. The analysed gear is mounted in the roller bearings. Such bearings typically have slight load capacity under loads perpendicular to the primary supported direction. The gear shaft neck surfaces on which the bearings are assembled are denoted \u201cbearing\u201d (see Fig. 3a). The gear mates with the other devices by the splines. The splines is simplified down to a regular cylinder of the diameter assumed as equal to the splines pitch diameter. The surface denoted \u201cjoint\u201d (see Fig. 3a) is located on the pitch diameter of the splines. Parameters of the analysed system are shown in Table 1a\u2013b. The calculation results for natural flexural oscillations taking into account angular speed of the gear are shown in the paper. In the case of circular discs and annular plates, for each solution where nodal lines are nodal diameters, one obtains two identical arrangements of straight nodal lines, rotated by an angle of \u03b1 = \u03c0/(2n) one to another, where n is the number of nodal diameters. In accordance with the circular and annular plate vibration theory [5,6,12], the particular natural frequencies of vibration are denoted as \u03c9mn , where m refers to the number of nodal circles and n is the mentioned number of nodal diameters. As the shape of the gear model is fairy elaborate, the flexural modes of the system are subject to deformation (as compared to the system without any holes) to such extent that establishing which particular node it refers to becomes rather difficult. This problem is even worse if the angular speed of the gear is varying. The problem of influence of the angular speed on the flexural gear models deformation is analysed. For the purpose of identification of these modes, an algorithm of tagging oscillation modes, which determines the correspondence between vibration of the circular disc versus disc with holes, is used. For this purpose, an auxiliary model of annular plate in the form shown in Fig. 3b is used. The geometrical dimensions of the auxiliary model were taken from the gear geometry (shown in Fig. 1). They are as follows: addendum circle diameter dz , rim mounting diameter dp, root circle diameter dw2, and thickness h p and hz (see Table 1). Dynamic analysis is performed for the auxiliary model cases rotating at predetermined angular speed, where diameter of though holes d01 (see Fig. 3b) varies as seen in Table 2. Findings are compared to each other both quantitatively and qualitatively. This method makes it possible to investigate deformations of nodal lines associated with nodal diameters and circles due to through holes and then determine correspondence between oscillation modes of solid circular disc and a plate with holes. In the final step, solutions found for the auxiliary model are compared with the solution for the system whose FEM model is shown in Fig. 2 (the principal model). As for the principal model case, the 3-D solid mesh and the ten-node tetrahedral element (solid92) are used to discretize the auxiliary models. For all models subject to analysis, the boundary conditions were applied to the nodes. For each model, 1 d f associated with node radial displacement was subtracted from the nodes found on the surface identified as a bearing (see Fig. 3a,b). Furthermore, 1 d f associated with the displacement of nodes along the centreline of each model was subtracted from the nodes found on the surface, identified as a joint (see Fig. 3a,b). For the models obtained in this way, calculations were kept conducted as long as the natural frequency \u03c918 was determined. The calculations were performed assuming that the systems rotate as angular speed of \u03b8 , within the range of 0\u20131047 [ rad/s]. During the computing process, the angular speed values were gradually increased by 80[ rad/s], which made fourteen variants of the results (the natural frequencies and corresponding natural modes), which were subject to further interpretation. The rotation effect was taken into account by determining stress distribution due to rotation, for each model during the computational step associated with static analysis (the so called pre-stress effect). This stress distribution was then included in the computation step associated with modal analysis. The results of the numerical calculations related to the procedure of identifying deformed natural modes of flexural vibration of the gear under consideration are shown below. The results displayed here relate to the determination of the correspondence between the natural frequencies \u03c916 and \u03c925 at high angular speed (\u03b8 = 1047 [ rad/s]) as well as to the correspondence between oscillation modes and the natural frequency \u03c931 at lower angular speeds (\u03b8 = 80 [ rad/s]). The results as shown in Figs. 4, 5, 6, 7, 8, 9 allow for tracking deformations of nodal lines associated with nodal circles and diameters, due to varying diameter of the through holes. With respect to the natural frequency \u03c925, there is marked difference in shapes of natural modes. When one compares the results between each other, one can notice that in order to identify correctly deformed natural modes of the flexural oscillations in the gear under consideration at lower angular speeds, larger number of auxiliary models is required to be included during calculations, as compared to the higher angular speeds. It comes from the fact that additional stresses through the centrifugal effects appear. This effect causes the gear flexural stiffness to be an apparent function of rotational speed (stiffness grows for higher speed). In the next part, results of the numerical calculations associated with the extent of the influence of the angular speed to deformation of mode shapes of oscillations. For each discussed case, both mode solutions related to nodal diameters are shown. These analysed results are sorted by the order of their occurrence. For the frequencies \u03c923 and \u03c918, the results were obtained at angular speeds of \u03b8 = 0 and \u03b8 =1,047 [ rad/s] respectively. For the other cases, results were obtained at angular speeds \u03b8 of, 0, 320, 720, and 1,047 [ rad/s], respectively. Natural frequencies for these modes are included in Table 3. To determine this mode (see Figs. 10, 11), the procedure of tagging natural oscillation modes was required. Nodal lines associated with the circle and diameter are deformed. Minor influence of the angular speed to deformation of the nodal lines is noticeable. The task of determining modes in this case was not too difficult (see Figs. 12); no procedure of tagging natural oscillation modes was required. The slight impact of the gear angular velocity on the distortion of the nodal lines is observed. For these modes (see Figs. 13, 14), procedure of tagging natural oscillation modes was required. It is noticeable that angular speed affects markedly deformation of the nodal lines. Once the angular speed of 720 [ rad/s] is exceeded, the oscillation mode takes different shape. Major deformation of mode shape attributable to the shaft vibrations is evident at this speed. Moreover, additional problem associated with some similarity of the mode being tagged to the mode associated with frequency of \u03c931, emerged during mode identification. Establishing the correspondence between these modes was a complex task (see Figs. 15, 16) due to the shape of oscillation modes similarity to the case discussed earlier. The angular speed affects deformation of nodal lines markedly. Major shape mode variations emerge at \u03b8 = 400 [ rad/s]. The identification process in this mode was not easy (see Figs. 17, 18) . One can notice that angular speed affects the deformation of nodal lines. Major variation in mode shape emerges at \u03b8 = 720 [ rad/s]. Moreover, additional annular shaft vibration emerges at the highest considered angular speed. Finding correct correspondence between the modes in this case was fairly easy (see Figs. 19). High repeatability in deformations of nodal lines on circular plate at various angular speeds is noticeable. As a consequence of the conducted analysis (see Table 3), the Campbell diagram was plotted for the gear under consideration. This is a convenient method of displaying the relationship between gear natural frequencies and transmission system excitations [4]. Excited frequencies are plotted on a vertical axis, and the gear speed of rotation is plotted on the horizontal axis (see Fig. 20). Natural frequencies achieved from numerical analysis are plotted as near-horizontal curves. The forced frequency due to the meshing is determined by the following relation (as in Ref. [4]) f = n0 \u00b7 z 60 (4) where n0 [rpm] is the rotational speed and z is the number of teeth in the gear. For this system, the gear teeth number is z = 59. Vibration resonance phenomenon occurs when forcing frequency (4) matches as to its value with some natural oscillation frequency of the gear. The points where the near-horizontal \u03c9mn curves intersect the straight line (4) indicate the speeds at which the gear resonance will be excited (see Fig. 20). For instance, the rated excitation speed for the natural frequency of \u03c923 is 764 [rpm]. It may be inferred from both the Campbell diagram and Table 3 that the rotating movement makes flexural stiffness of the gear under consideration to increase. Moreover, at speed of 3,820 [rpm], one can notice major surge associated with the mentioned earlier changing of the shape of the natural mode frequency in the case of the frequency of \u03c931. The growth of the gear transversal stiffness observed during gyrate of the gear comes from the appearance of the additional stresses in the toothed gear through the centrifugal effects. The higher rotational speed generates higher centrifugal forces, higher stress level, thereby causing the transversal stiffness of the system to increase. Moreover, the growth of the gear flexural stiffness through the gyrate effect causes reduction of the needed numerical calculations connected with identifying the proper distorted mode shapes." + ] + }, + { + "image_filename": "designv11_7_0001511_204103-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001511_204103-Figure2-1.png", + "caption": "Figure 2. The inertial rotator. The spheres are constrained to move along the circumference of centre P and radius R.", + "texts": [ + " In this case, \u3008W\u03031\u3009 = \u03b53\u03b2(\u03b2 \u2212 1) (\u2212\u03b22 + 3\u03b2 \u2212 1 ) 6(1 + \u03b2)2 A\u03032 + O(\u03b54). (10) Then, in dimensional form, the net translational velocity is \u3008W \u3009 = Repa\u03c9\u03b52\u03b2(\u03b2 \u2212 1) (\u2212\u03b22 + 3\u03b2 \u2212 1 ) 6(1 + \u03b2)2 (A/a)2 + O(Rep\u03b5 3, Re2 p). (11) Note that \u3008W \u3009 tends to zero as L \u2192 \u221e, reflecting the fact that the net translational velocity is due to the interaction between the spheres. The smaller sphere advances in front (\u3008W \u3009 > 0) for 1 < \u03b2 < (3 + \u221a 5)/2, and the larger sphere advances in front (\u3008W \u3009 < 0) for \u03b2 > (3 + \u221a 5)/2. Consider the swimmer shown in figure 2, which is a twosphere version of the rotator devised by Dreyfus et al [15]. As was the case in the previous example, the spheres have radii a and b, which are different but of comparable magnitude, that is, \u03b2 \u2261 b/a = O(1). Again, \u03b2 = 1 is required to break the spatial symmetry and yield net motion. The spheres are constrained to move along the circumference of centre P (which is held fixed) and radius R, which is much larger than a, R\u0302 \u2261 R/a 1. The angle between the spheres, 2\u03b8(t), varies periodically with radian frequency \u03c9 in a prescribed manner" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003305_1.4026080-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003305_1.4026080-Figure3-1.png", + "caption": "Fig. 3 Sectional schematic view of the test apparatus: support to test the thrust bearing", + "texts": [ + " The experimental device can be described as having three essential components: \u2022 the driving system, composed of a 15 kW electrical motor and a precision spindle \u2022 the loading system \u2022 a support to test the thrust bearing The precision spindle is driven by an electrical motor providing enough power to reach 10,000 rpm, using a flat belt for transmission. The thrust bearing is loaded by a pneumatic jack monitored with a high-precision air regulator. This allows for a load varying between 50 N and 8,000 N to be applied. The schematic of the test cell is shown in Fig. 3. The alignment of the runner with the bearing centers is obtained by means of setting the position of the guiding shaft with two plates, which hold patellas. The gap of concentricity is less than 0.1 mm. A spherical hydrostatic thrust bearing was placed upstream of the thrust bearing to keep this alignment regardless of the applied load. It also isolates the tested thrust bearing from external friction. An independent hydraulic system supplies this spherical hydrostatic thrust bearing at a pressure of 1" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002586_j.bios.2010.04.014-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002586_j.bios.2010.04.014-Figure1-1.png", + "caption": "Fig. 1. Miniature bioreactor construction kit. (A) Detailed views of the single elements and gaskets used for the miniature bioreactor assembly. The transparent bottom element is equipped with two sensor spots for measuring pH-value and O2-concentration. (B) Exploded view of an exemplary miniature bioreactor assembled from the construction kit. The shown bioreactor contains a (a) gas supply channel, (b) access channel for media exchange, (c) ion conductive membrane pressed between two neighboring bioreactors and according gaskets (d), (e) channel for interconnection of neighboring bioreactors, (f) gas nozzle and (g) media port. Luer-lock plugs are used f olum c ctrod ( is use", + "texts": [ + " In the following sections the corresponding experimental results are shown and discussed (Sections 4 and 5). Bioele 2 s 2 n g ( T n a f t T c f u t A e t ( B o t t o l 2 i f t c a c t l o e 2 t s a o w a d t t e i c 2 t c A. Kloke et al. / Biosensors and . Concept of the novel miniature bioreactor construction ystem .1. Construction of a miniature bioreactor The novel modular miniature bioreactor is constructed by alterate stacking of individual polycarbonate elements and silicone askets, as shown in Fig. 1(A) and (B). Their central cavities 15 mm \u00d7 15 mm in cross-section) form a central reaction chamber. he volume of the central chamber can individually be varied by the umber of assembled elements. Typically the volume amounts to few millilitre. Bore holes in the stacked elements form channels or aeration and media exchange. These channels are connected o the reaction chamber via nozzles and a media exchange port. hese functional elements are integrated into silicone gaskets and an be used to vary the reactor\u2019s properties such as oxygen transer by choosing between different gaskets", + " A transparent botom element allows for the use of optical sensor spot technology Wolfbeis, 2004) to measure pH-value or oxygen concentration. ubbles generated at the gas nozzles support mixing and define the xygen transfer rate. The media exchange port facilitates access to he reaction chamber for addition or complete exchange of reacion media. If desired, sterile filters can be used to seal off all the penings against microbial contamination. A septum closure at the id facilitates sterile probe sampling. .2. Construction of interconnected bioreactor systems Horizontal bore holes in part \u201cConnector\u201d (see Fig. 1(A)) are ntended for interconnection with neighboring reactors, and allow or the construction of larger bioreactor systems. This interconnecion can for instance be used for the construction of small-scale hemical synthesizers (Ashmead et al., 1994; Bard, 1996; Snyder et l., 2005). In this case each individual miniature bioreactor would ontain one specific physical, chemical or biochemical unit operaion required during a multistage synthesis process. A compact construction of such reactor systems or the paralelized operation of single bioreactors is facilitated by the design f the novel miniature bioreactor because all the connections are ither placed on the lid or bottom of the reactor. .3. Extended setup for electrochemical testing Fig. 1(C) shows an assembly variation for an electrochemical esting cell consisting of two bioreactor columns and two flanking upports, which each contain one reference electrode. Having seprate anode and cathode compartments, this assembly enables the peration of the individual electrodes in separate reaction media ithout cross-contamination effects. Separate reference electrodes re used to measure the anode and cathode potentials indepenently, and to circumvent any influence of the ionic resistance of he membrane on the measured potentials", + " KG (9P01/1 with tubes 032-41-ST, M\u00fcllheim, Germany) and used to set the oxygen partial pressure of inlet gasses. Mass transfer coefficients for oxygen (kLa) were determined at different oxygen flow rates from 0 ml min\u22121 to 16 ml min\u22121 by the dynamic oxygen method (Linek et al., 1989). Hereto the reaction chamber was purged with nitrogen until an oxygen saturation of less than 0.1% was reached. Subsequently the reactor was aerated with pure oxygen. Gas flow rates were set utilizing a gas proportioner. The experiments were performed in a single miniature bioreactor (as shown in Fig. 1(B)) filled with 7 ml of phosphate buffered saline (PBS tabs pH = 7.4, Invitrogen GmbH, Karlsruhe, Germany). Finally, kLa values were extracted by fitting the increase in oxygen saturation to Eq. (1): dC dt = kLa(Ceq \u2212 C) (1) Here C stands for the dissolved oxygen saturation (in %) inside the reactor measured at time t, and Ceq is the corresponding equilibrium value (100% oxygen saturation during our experiments). Similar to the determination of the mass transfer coefficient of oxygen the permeability of the setup towards oxygen was investigated", + " This system is able to set constant galvanostatic loads using timulus generators (STG2008, Multichannel Systems, Reutlingen, ermany) and to simultaneously record electrode potentials with Keithley 2700 data acquisition system (Keithley, Gemering, Gerany). To record data for galvanostatic load curves electrode otentials were measured against the reference electrodes at stepisely increased galvanostatic loads between cathode and the ounter electrode. This galvanostatic load was increased by 5 A very hour and the last value recorded before the load increment erved for load curve construction. .6. Characterization of electron transfer in Shewanella neidensis The miniature bioreactor was assembled as shown in Fig. 1(C). cubic graphite felt (1.64 cm\u22123) was used as electrode, electrically cients for oxygen (kLa) in dependence of the applied oxygen flow rate. Data was recorded for a single miniature bioreactor compartment filled with 7 ml PBS. Error bars correspond to the standard deviations of fitted kLa values obtained by the dynamic oxygen method. connected in the same way as described for the enzymatic cathodes. A platinum mesh in the cathode compartment was used as counter electrode. Nafion\u00ae membranes (Nafion-117, Quintech, G\u00f6ppingen, Germany) were used to separate the single compartments", + " Load curve experiments were in general conducted in the same way as for the enzymatic cathodes (see Section 3.5) with the exception that the load current was increased in steps of 5 A once the electrode potential stabilized to values within a limit of 4 mV h\u22121. Load curves were constructed accordingly. 4. Characterization of the miniature bioreactor 4.1. Oxygen transfer Two different nozzle configurations are compared in Fig. 2 by their mass transfer coefficients for oxygen determined at different volume flow rates. For the configuration \u201cNozzle +\u201d (Fig. 1(A), nozzle cross-section: \u223c200 m \u00d7 350 m) generally higher oxygen transfer rates are observed as for configuration \u201cNozzle 0\u201d (Fig. 1(A), nozzle cross-section: \u223c900 m \u00d7 600 m): at an oxygen flow of 15.5 ml min\u22121 a kLa value of 4.3 \u00d7 10\u22123 s\u22121 was obtained for \u201cNozzle +\u201d, and only 2.1 \u00d7 10\u22124 s\u22121 for \u201cNozzle 0\u201d. The better performance of \u201cNozzle +\u201d is mainly due to the smaller outlet cross-section generating smaller bubbles, resulting in a higher interfacial area and consequently in a faster oxygen transfer (Linek et al., 1989). For bubble column reactors the mass transfer coefficient for oxygen is usually described by a simple power function of the form kLa (u)\u223cub in dependence of the volume flow rate u (Doig et al" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003869_s00419-012-0608-6-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003869_s00419-012-0608-6-Figure4-1.png", + "caption": "Fig. 4 The mode shapes corresponding to frequency \u03c916 (auxiliary model)", + "texts": [], + "surrounding_texts": [ + "As mentioned earlier, in the geometrical model of the gear, the geometry of the teeth is omitted. It allows us to reduce the system\u2019s FE model size. The simplified geometrical model of the system consists of five sectors (see Fig. 1) that have the cyclic symmetry feature. Each of these segments is meshed by using standard procedures of the ANSYS software. The 3-D solid mesh is elaborated and as mentioned earlier, the ten-node tetrahedral element (solid92) with three degrees of freedom in each node is used to realize each sector. During the mesh generation process, it is assumed that the maximum length of each element\u2019s side needs to be no more than 2.7 [mm]. The developed FE model is displayed in Fig. 2, and it consists of 19,620 elements and 36,188 nodes, respectively. The particular sectors are glued as a whole at the geometrical model preparing the stage by using standard procedure of the ANSYS program. The analysed gear is mounted in the roller bearings. Such bearings typically have slight load capacity under loads perpendicular to the primary supported direction. The gear shaft neck surfaces on which the bearings are assembled are denoted \u201cbearing\u201d (see Fig. 3a). The gear mates with the other devices by the splines. The splines is simplified down to a regular cylinder of the diameter assumed as equal to the splines pitch diameter. The surface denoted \u201cjoint\u201d (see Fig. 3a) is located on the pitch diameter of the splines. Parameters of the analysed system are shown in Table 1a\u2013b. The calculation results for natural flexural oscillations taking into account angular speed of the gear are shown in the paper. In the case of circular discs and annular plates, for each solution where nodal lines are nodal diameters, one obtains two identical arrangements of straight nodal lines, rotated by an angle of \u03b1 = \u03c0/(2n) one to another, where n is the number of nodal diameters. In accordance with the circular and annular plate vibration theory [5,6,12], the particular natural frequencies of vibration are denoted as \u03c9mn , where m refers to the number of nodal circles and n is the mentioned number of nodal diameters. As the shape of the gear model is fairy elaborate, the flexural modes of the system are subject to deformation (as compared to the system without any holes) to such extent that establishing which particular node it refers to becomes rather difficult. This problem is even worse if the angular speed of the gear is varying. The problem of influence of the angular speed on the flexural gear models deformation is analysed. For the purpose of identification of these modes, an algorithm of tagging oscillation modes, which determines the correspondence between vibration of the circular disc versus disc with holes, is used. For this purpose, an auxiliary model of annular plate in the form shown in Fig. 3b is used. The geometrical dimensions of the auxiliary model were taken from the gear geometry (shown in Fig. 1). They are as follows: addendum circle diameter dz , rim mounting diameter dp, root circle diameter dw2, and thickness h p and hz (see Table 1). Dynamic analysis is performed for the auxiliary model cases rotating at predetermined angular speed, where diameter of though holes d01 (see Fig. 3b) varies as seen in Table 2. Findings are compared to each other both quantitatively and qualitatively. This method makes it possible to investigate deformations of nodal lines associated with nodal diameters and circles due to through holes and then determine correspondence between oscillation modes of solid circular disc and a plate with holes. In the final step, solutions found for the auxiliary model are compared with the solution for the system whose FEM model is shown in Fig. 2 (the principal model). As for the principal model case, the 3-D solid mesh and the ten-node tetrahedral element (solid92) are used to discretize the auxiliary models. For all models subject to analysis, the boundary conditions were applied to the nodes. For each model, 1 d f associated with node radial displacement was subtracted from the nodes found on the surface identified as a bearing (see Fig. 3a,b). Furthermore, 1 d f associated with the displacement of nodes along the centreline of each model was subtracted from the nodes found on the surface, identified as a joint (see Fig. 3a,b). For the models obtained in this way, calculations were kept conducted as long as the natural frequency \u03c918 was determined. The calculations were performed assuming that the systems rotate as angular speed of \u03b8 , within the range of 0\u20131047 [ rad/s]. During the computing process, the angular speed values were gradually increased by 80[ rad/s], which made fourteen variants of the results (the natural frequencies and corresponding natural modes), which were subject to further interpretation. The rotation effect was taken into account by determining stress distribution due to rotation, for each model during the computational step associated with static analysis (the so called pre-stress effect). This stress distribution was then included in the computation step associated with modal analysis. The results of the numerical calculations related to the procedure of identifying deformed natural modes of flexural vibration of the gear under consideration are shown below. The results displayed here relate to the determination of the correspondence between the natural frequencies \u03c916 and \u03c925 at high angular speed (\u03b8 = 1047 [ rad/s]) as well as to the correspondence between oscillation modes and the natural frequency \u03c931 at lower angular speeds (\u03b8 = 80 [ rad/s]). The results as shown in Figs. 4, 5, 6, 7, 8, 9 allow for tracking deformations of nodal lines associated with nodal circles and diameters, due to varying diameter of the through holes. With respect to the natural frequency \u03c925, there is marked difference in shapes of natural modes. When one compares the results between each other, one can notice that in order to identify correctly deformed natural modes of the flexural oscillations in the gear under consideration at lower angular speeds, larger number of auxiliary models is required to be included during calculations, as compared to the higher angular speeds. It comes from the fact that additional stresses through the centrifugal effects appear. This effect causes the gear flexural stiffness to be an apparent function of rotational speed (stiffness grows for higher speed). In the next part, results of the numerical calculations associated with the extent of the influence of the angular speed to deformation of mode shapes of oscillations. For each discussed case, both mode solutions related to nodal diameters are shown. These analysed results are sorted by the order of their occurrence. For the frequencies \u03c923 and \u03c918, the results were obtained at angular speeds of \u03b8 = 0 and \u03b8 =1,047 [ rad/s] respectively. For the other cases, results were obtained at angular speeds \u03b8 of, 0, 320, 720, and 1,047 [ rad/s], respectively. Natural frequencies for these modes are included in Table 3. To determine this mode (see Figs. 10, 11), the procedure of tagging natural oscillation modes was required. Nodal lines associated with the circle and diameter are deformed. Minor influence of the angular speed to deformation of the nodal lines is noticeable. The task of determining modes in this case was not too difficult (see Figs. 12); no procedure of tagging natural oscillation modes was required. The slight impact of the gear angular velocity on the distortion of the nodal lines is observed. For these modes (see Figs. 13, 14), procedure of tagging natural oscillation modes was required. It is noticeable that angular speed affects markedly deformation of the nodal lines. Once the angular speed of 720 [ rad/s] is exceeded, the oscillation mode takes different shape. Major deformation of mode shape attributable to the shaft vibrations is evident at this speed. Moreover, additional problem associated with some similarity of the mode being tagged to the mode associated with frequency of \u03c931, emerged during mode identification. Establishing the correspondence between these modes was a complex task (see Figs. 15, 16) due to the shape of oscillation modes similarity to the case discussed earlier. The angular speed affects deformation of nodal lines markedly. Major shape mode variations emerge at \u03b8 = 400 [ rad/s]. The identification process in this mode was not easy (see Figs. 17, 18) . One can notice that angular speed affects the deformation of nodal lines. Major variation in mode shape emerges at \u03b8 = 720 [ rad/s]. Moreover, additional annular shaft vibration emerges at the highest considered angular speed. Finding correct correspondence between the modes in this case was fairly easy (see Figs. 19). High repeatability in deformations of nodal lines on circular plate at various angular speeds is noticeable. As a consequence of the conducted analysis (see Table 3), the Campbell diagram was plotted for the gear under consideration. This is a convenient method of displaying the relationship between gear natural frequencies and transmission system excitations [4]. Excited frequencies are plotted on a vertical axis, and the gear speed of rotation is plotted on the horizontal axis (see Fig. 20). Natural frequencies achieved from numerical analysis are plotted as near-horizontal curves. The forced frequency due to the meshing is determined by the following relation (as in Ref. [4]) f = n0 \u00b7 z 60 (4) where n0 [rpm] is the rotational speed and z is the number of teeth in the gear. For this system, the gear teeth number is z = 59. Vibration resonance phenomenon occurs when forcing frequency (4) matches as to its value with some natural oscillation frequency of the gear. The points where the near-horizontal \u03c9mn curves intersect the straight line (4) indicate the speeds at which the gear resonance will be excited (see Fig. 20). For instance, the rated excitation speed for the natural frequency of \u03c923 is 764 [rpm]. It may be inferred from both the Campbell diagram and Table 3 that the rotating movement makes flexural stiffness of the gear under consideration to increase. Moreover, at speed of 3,820 [rpm], one can notice major surge associated with the mentioned earlier changing of the shape of the natural mode frequency in the case of the frequency of \u03c931. The growth of the gear transversal stiffness observed during gyrate of the gear comes from the appearance of the additional stresses in the toothed gear through the centrifugal effects. The higher rotational speed generates higher centrifugal forces, higher stress level, thereby causing the transversal stiffness of the system to increase. Moreover, the growth of the gear flexural stiffness through the gyrate effect causes reduction of the needed numerical calculations connected with identifying the proper distorted mode shapes." + ] + }, + { + "image_filename": "designv11_7_0003352_1.4004304-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003352_1.4004304-Figure1-1.png", + "caption": "Fig. 1 The model of a deformable sphere in contact with a rigid flat under combined normal and tangential loading", + "texts": [ + " The main purpose of the present analysis is to fill a gap in elastic-plastic contact mechanics by offering a missing dimensionless model for the evolution of friction and tangential stiffness in presliding. This will be done by using FE numerical simulation based on the concept of Ref. [12], which assumes full stick contact condition and relaxes the simplifying assumptions of Ref. [2]. The contact problem between an elastic-plastic hemisphere and a rigid flat, subjected to combined normal and tangential loading under stick contact condition, as described in Ref. [12] is shown schematically in Fig. 1. A normal preload P is applied to a hemisphere of radius R, followed by a tangential loading Q. The thick and thin dashed lines show the contours of the sphere before and after the application of the load P, respectively. The solid line shows the final contour of the sphere after adding the tangential load, Q. The normal loading produces an initial interference, x0, and an initial circular contact area of a diameter d0. The final interference and final diameter of the contact area resulting from the additional tangential loading are x, and d, respectively", + " Since the problem is symmetric with respect to the xz-plane, it is sufficient to consider only one half of the hemisphere\u2019s volume 1Corresponding author. Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received January 13, 2011; final manuscript received April 26, 2011; published online July 12, 2011. Assoc. Editor: Robert Jackson. Journal of Tribology JULY 2011, Vol. 133 / 034502-1Copyright VC 2011 by ASME Downloaded From: http://tribology.asmedigitalcollection.asme.org/ on 07/29/2013 Terms of Use: http://asme.org/terms (see Fig. 1). The boundary conditions consist of displacement constrain in the x, y, and z directions at the bottom of the hemisphere (xy-plane) and in the y-direction at the plane of symmetry (xzplane). The surface of the sphere is free elsewhere except for full stick at the contact interface (see, e.g., Ref. [12]). Full stick contact condition between an elastic-plastic sphere and a rigid flat simulates highly adhesive contact. The validity of the full stick contact condition was verified experimentally in Ref" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000299_bf02844114-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000299_bf02844114-Figure1-1.png", + "caption": "Figure 1 Pitch angle", + "texts": [ + " An aluminum rod was set in the cooling wax to serve as an attachment point between the model and the drive system creating the stroke motion. Two hand positions were tested in this experiment, one with 10\u00b0 between each finger and one with 0\u00b0 (fingers flat against each other). A second model for the 10\u00b0 configuration was built and tested in order to assess error due to construction irregularities. For this study, \u2018pitch\u2019 was defined as the angle formed between the plane of the hand and the direction of forward progress of the swimmer. A pitching motion is caused by actuation of the wrist along the axis of the forearm, as shown in Fig. 1. \u2018Roll\u2019 was defined as the angle formed between a swimmer\u2019s forearm and vertical, as shown in Fig. 2. Rolling motion is created by a rotation of the forearm about the elbow. A two-axis motor drove the model hands in a rolling and pitching motion. The two-axis motor was then fixed to a railmounted carriage, which pulled the assembly through the water in the opposite direction to that of a swimmer\u2019s progress. The longitudinal motion of the carriage combined with the transverse pitching and rolling motion of the two-axis motor were designed to produce a stroke pattern similar to the pull-down phase of freestyle swimming as determined by Sato & Hino (2002)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000762_j.jsv.2007.04.016-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000762_j.jsv.2007.04.016-Figure1-1.png", + "caption": "Fig. 1. A rotor-bearing system subjected to random axial forces at both ends.", + "texts": [ + " Next the set of discretized system equations is partially uncoupled by the modal analysis procedure suitable for a gyroscopic system. Then the stochastic averaging method is adopted to obtain Ito\u2019s equations for the response amplitudes of the system. Finally the first- and second-moment stability criteria are utilized to determine the stability boundaries of the system. Consider a typical flexible rotor-bearing system that consists of a rigid disk of mass M, a flexible shaft of length L and a pair of ball bearings and is subjected to a pair of axial forces P(t) at both ends, as shown in Fig. 1. In this figure, (X, Y, Z) is an inertial coordinate system with the X-axis being coincident with the centerline of the undeformed rotor. If the axial motion of the rotor can be neglected, the displacements of a ARTICLE IN PRESS T.H. Young et al. / Journal of Sound and Vibration 305 (2007) 467\u2013480 469 typical cross-section of the rotor are described by the translations V and W in the Y- and Z-directions and the rotations B and G about the Y- and Z-axis, respectively. In this work, the flexible shaft is assumed as a uniform Timoshenko beam with non-rotating viscous damping coefficient c, and the equations of motion of the shaft are discretized by the finite element method" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002938_j.apm.2013.06.024-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002938_j.apm.2013.06.024-Figure1-1.png", + "caption": "Fig. 1. Physical cross-section geometry of a longitudinal rough-surface short journal bearing at the mid-plane z \u00bc 0.", + "texts": [ + " [3], the influences of longitudinal roughness patterns on the Hopf bifurcation characteristics are investigated in the present paper. Bearing performances (including the linear stability regions, Hopf bifurcation regions, sub-critical and supercritical limit cycles) are presented and discussed in comparison with rough bearings of the isotropic structures by Lin [18] and the transverse structures by Lin [19]. The physical cross-section geometry of a longitudinal rough-surface short journal bearing at the mid-plane z \u00bc 0 is described in Fig. 1. The length of the bearing is L, and the inner journal with radius rj rotates within the outer bearing housing with an angular velocity X. Assumed that the incompressible Newtonian fluid flow in the film region is laminar and isothermal, and the thin-film lubrication theory is applicable in the present study. According to the derivation of Cameron [4] and Hamrock [5], the dynamic modified Reynolds equation for the local film pressure pL of a short bearing is expressed as: @ @ z H3 L @ pL @ z \u00bc 6l X 2 db d t @HL @h \u00fe 12l @HL @ t ; \u00f01\u00de where l is the lubricant viscosity, b is the attitude angle, h is the circumferential coordinate, and t denotes the time" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000898_978-0-387-28732-4_4-Figure4-16-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000898_978-0-387-28732-4_4-Figure4-16-1.png", + "caption": "Figure 4-16. The BION. The bionic Neurons are one-channel stimulators which are injected near the motor points by a hypodermic needle. By courtesy of Advanced Bionics, Inc. (Sylmar, CA, USA).", + "texts": [ + " Now they have to be integrated into implantable systems to prove their applicability in neural prostheses. A combination of the polyimide technology with silicone rubber sheets to \u2018Hybrid Cuff Electrodes\u2019 finally led to larger diameter cuffs of high flexibility with the opportunity to integrate electronic circuitry (Fig. 4-15), e.g., multiplexers to reduce the number of cables [216]. A completely different approach has been developed with the \u2018bionic neurons\u2019, the so called BIONs [74]. These single channel stimulators were developed with integrated radio receiver (Fig. 4-16). Up to 255 of them can be combined to distributed neural systems and controlled via a single external coil. They have to be injected near the motor points by a hypodermic needle. First clinical trials run in Europe. Current applications include the prevention of shoulder subluxation in patients after a stroke, and bladder management for incontinence patients. In a slight variation of the cuff type of interfaces there are circum\u2013neural electrodes that vary the nerve geometry to penetrate the epineurium without any damage to the perineurium" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001774_j.matdes.2009.08.024-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001774_j.matdes.2009.08.024-Figure1-1.png", + "caption": "Fig. 1. Two non identical sized rollers in contact (M 2\u201300).", + "texts": [ + " The second stage is the analysis stage where the IH fatigue life theory is applied on the numerical simulation results to estimate the hollow rollers fatigue life. Two main models have been studied. The first one is when the two rollers have the same size (Model 1) and the second model when they have different sizes (Model 2). The two rollers have been assumed to run dry, with no lubricant. In each model, two cases were studied; when both rollers in contact are hollow with the same percentage of hollowness and when only one is hollow while the other roller is solid. Fig. 1 shows an example of Model 2 when both rollers are solid. The optimum hollowness percentage is the percentage of hollowness with the longest fatigue life under certain conditions. To study the optimum percentage of hollowness, different hollowness percentages between 20% and 80% have been tested. Moreover, in order to study the effect of endurance limit on the fatigue life, investigations have been made for five different steels, CVD 52100, carburized steel, VIMVAR M50, M50NiL and inductionhardened steel" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003758_j.camwa.2011.11.031-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003758_j.camwa.2011.11.031-Figure1-1.png", + "caption": "Fig. 1. United gas-lubricated bearing system.", + "texts": [ + " Accordingly, Section 3 develops a hybrid method combining the finite difference method (FDM) and the differential transformation method (DTM) to obtain the required solutions. The solutions are then compared with those obtained using the SOR&FDM (Successive Over Relation and finite difference method) method. Section 4 presents the simulation results obtained using the proposed hybrid method for the vibrations of the rotor center for various rotor masses. The united gas-lubricated bearing model is designed and shown in Fig. 1 and incorporates the following design assumptions: (1) Gas lubricating films are very nearly isothermal because the ability of the bearing materials to conduct away heat is greater than the heat generating capacity of the air-film. Thus, the flow is assumed isothermal. (2) As gas viscosity is somewhat insensitive to changes in pressure, and the temperature is virtually constant, we may assume the gas viscosity to be constant. (3) The mass flow inside and outside of the gas bearing element is equal to the mass flow into the orifice" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000603_s0003-2697(76)80051-6-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000603_s0003-2697(76)80051-6-Figure3-1.png", + "caption": "FIG. 3. Proportionality ofa-glucosidase in dried cells to activity measured in cell extracts. A strain of yeast constitutive for maltose production (MAL6 c) was grown overnight to mid- or late-log phase in Van Wijks medium containing either glycerol, glucose, lactate, galactose, or maltose. A portion of the culture grown on glucose was centrifuged, washed twice with sterile water, and resuspended in Van Wijks medium containing maltose (derepressed culture). One sample was taken of each overnight culture, and samples were taken of the derepressed culture at hourly intervals. Fifty-microliter portions of each sample were applied to filters, and 0.5-ml portions were used to prepare extracts (of final volume approximately 0.4 ml) as described under Materials and Methods. The filters and extracts were assayed for ct-glucosidase activity as described. Overnight cultures; (~7), glycerol: (g), glucose; (11), lactate; (A), galactose; (\u00a9), maltose. Derepressed culture (0).", + "texts": [ + " It does not require any special equipment, uses very small samples (20-100 /zl), and is much easier to carry out than any of the methods referred to above, because it does not involve any washing or centrifuging of the cells. MATERIALS AND METHODS Many different haploid and diploid strains ofSaccharomyces cerevisiae and S. carlsbergensis and hybrids between them have been used in these experiments. Reproducible results have been obtained with all strains tested but the relative efficiencies of permeabilization of the different strains have not been checked. The constitutive strain used for the experiment of Fig. 3 was derived from a strain ofS. carlsbergensis obtained from R. Needleman. In this strain o~-glucosidase production is repressed by glucose but not affected by maltose. The yeast were grown in either YP 1 Abbreviat ions: D M S O , dimethyl sulfoxide; P N P G , p-ni trophenyl-~-D-glucoside. 94 All rights of reproduction in any form reserved broth (1% yeast extract, 2% peptone, 2% carbon source) or the semidefined medium of Van Wijk (5) which contains no peptone and a low concentration of yeast extract", + " 1A, enzyme activity is plotted against incubation time at each cell concentration; in Fig. 1B, enzyme activity is plotted against cell concentration at each incubation time. As shown in the figure, enzyme activity is proportional to both incubation time and number of cells per filter. In the experiment shown in Fig. 2, different volumes (20-100/~1) of the same cell suspension diluted 1:2 were applied to filters; as shown, the enzyme activity is proportional to the sample volume over the range tested. The experiment summarized in Fig. 3 was done to determine if the a-glucosidase activity in dried cells was proportional to the activity in extracts of the same cells over a wide range of culture conditions. To achieve the widest possible range of culture conditions, a constitutive strain of yeast was used because it produces easily assayable amounts of a-glucosidase on media containing many different carbon sources. The constitutive strain was grown in medium containing either glucose, maltose, glycerol, lactate, or galactose and also was derepressed by transfer from glucose to maltose. Dried cell samples and extracts were prepared from each culture either after growth overnight on the various carbon sources or at 1-hr intervals during derepression. Each dried sample and an equivalent portion of each extract were assayed for a-glucosidase activity; the results of the two assays are plotted against each other in Fig. 3. As shown in the figure, the two assays are proportional to each other over approximately a 12-fold range in enzyme activity per milliliter of culture; this corresponds to about a six-fold range in enzyme activity per cell. The results shown in Figs. 1-3 indicate that o~-glucosidase can be assayed quantitatively in small samples (20-100/.tl) of unwashed cells permeabilized by drying on filters at room temperature, o~-Glucosidase measured in these dried cells is proportional to cell number (Fig. IB), sample volume (Fig. 2), assay incubation time (Fig. 1A), and enzyme activity per cell as measured in extracts (Fig. 3). Preliminary results with other assays suggest that many other yeast enzymes are stable to the drying procedure and can also be assayed quantitatively in dried cells. The permeabilization procedure described in this paper is extremely easy to carry out because it avoids the centrifuging, filtering, or washing of cell samples. The small amounts of medium transferred along with the cells do not appear to interfere with the assay of t~-glucosidase under the conditions tested. If the medium must be removed because it contains substances that interfere with this or any other assay, the dried filters can be washed together in batch" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000731_jmes_jour_1978_020_048_02-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000731_jmes_jour_1978_020_048_02-Figure4-1.png", + "caption": "Fig. 4. Squeeze-film bearing", + "texts": [ + " Experimental observations were also made of the axial pressure distribution for the case of the pressure transducer situated at the base of the'clearance circle. It was found that the pressure was a maximum in the central area of the bearing land, falling to a value equal to the supply pressure at the groove and to a value approaching atmospheric at the end. The most significant features of the pressure recordings are the double peak for case C and the consistent indication of large subatmospheric pressures during about half the pressure cycle for cases C and D. Indeed, this subatmospheric pressure is sometimes so low as to be 3.1 Dynamical equations Fig. 4 shows a ball-bearing squeeze-ring surrounded by its oil-film under the action of a steady load, P, due to the dead weight of the rotor that it supports. Vibration arises from a centrifugal force, P,, due to unbalance. The amplitude of any orbital motion will depend on P, P,, P, and P,. The latter two forces, P, and P,, are those arising hydrodynamically from the squeeze film, the effect of supply pressure being negligible under normal circumstances. The equations governing the motion of the bearing are then ) (1) -P, + P cos y + P, cos ( 0 2 - y) = me(& - $&) - ~ , - ~ s i n y + ~ , s i n ( w t - y ~ ) = m c ( ~ y l + 2 k " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001403_gt2009-59226-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001403_gt2009-59226-Figure3-1.png", + "caption": "Fig. 3 Prototype shrouds", + "texts": [ + " Lubrication oil is supplied to the gear meshing and the bearings, and the inner spline of the input gear shaft. The air with oil mist inflow comes from the upper area of the gearbox through the peripheral area of the input shaft. There are discharges from a scavenger pick-up and from the backward of the output gear. A shroud was set to cover the lower half of the output gear. In the experiment, the difference in temperature between the oil supply and the oil discharge was measured with three types of prototype shrouds, as shown in Fig. 3. Shroud #1 covers almost the lower half of the output gear. Shroud #2 is the same shape as shroud #1 with the out-of-mesh side cut. Shroud #3 is the opposite shape with the into-mesh side of shroud #1 cut. The power loss induced by fluid dynamics was derived from the loss evaluated by the difference between the oil supply temperature and the discharge temperature, in which the frictional loss on the gear mesh and the bearings was eliminated. As a result, the loss of shroud #2 increased by 13% compared with shroud #1" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002601_1.3534836-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002601_1.3534836-Figure4-1.png", + "caption": "Fig. 4. Poisson\u2019s explanation for the special case of two equal forces.", + "texts": [ + " 4, April 2011 Downloaded 30 Dec 2012 to 152.3.102.242. Redistribution subject to AAPT li some dimensionless function g.43 Because R and P g x must both have dimensions of force and P has dimensions of force, it follows that =1, and hence R= Pg x . Poisson had now reduced the problem to explaining why g is in accordance with the parallelogram law. To create another instance of two equal forces acting in different directions, let P1 be the resultant of two forces, each of magnitude Q, subtending angle 2z see Fig. 4 . Hence P=Qg z . Because R= Pg x , it follows that R=Qg z g x . By the composition law\u2019s rotational symmetry, these two forces rotated through the same angle have P2 as their resultant see Fig. 4 . The resultant of the four Q forces is the resultant of P1 and P2, with magnitude R. The two inner Q forces in Fig. 4 create another instance of the same problem: Their resultant bisects the angle 2 x\u2212z between them, and therefore it points in the same direction as the resultant of P1 and P2 and has magnitude Qg x\u2212z . Likewise, the resultant of the two outer Q forces is in the same direction, with magnitude Qg x+z . Poisson then invoked the principle that if two forces point in the same direction, their resultant\u2019s magnitude is the arithmetic sum of their magnitudes. Therefore, as the magnitude of the four Q forces\u2019 resultant, R equals the sum of Qg x \u2212z and Qg x+z ", + " If equal and opposite forces are rotated by a half-circle around an axis perpendicular to their common line of action, then by rotational symmetry, the resultant is rotated by the same amount. But because the two forces have merely swapped places, the resultant must be unchanged because the resultant depends only on the forces\u2019 magnitudes and directions. The 384Marc Lange cense or copyright; see http://ajp.aapt.org/authors/copyright_permission only resultant unchanged under such rotation is a zero resultant. From Eq. 7 for R=0 when x= /2 remember that the angle subtended by the two forces is 2x, see Fig. 4 , it follows that a must be an odd integer. But if a=3, for example, then cos ax=0 for x= /6, and so by Eq. 7 , R=0. This zero resultant for forces subtending an angle 2x= /3 is disallowed by Poisson\u2019s premise that if two forces have zero resultant, then they must be equal and opposite. Again, although Poisson presented this premise as an independent assumption, it follows from premises to which he had already appealed. If forces A and B have zero resultant, then the resultant of A, B, and some third force is the third force", + " 34, pp. v, 214\u2013220; P. Barlow, \u201cMechanics,\u201d Encyclopaedia Metropolitana Griffin, London, 1848 , Vol. 3, pp. 10\u201311; B. Price, A Treatise on Infinitesimal Calculus, Vol. 3: A Treatise of Analytical Mechanics, 2nd ed. Clarendon Press, Oxford, 1868 , pp. 19\u201321; W. E.Johnson, Ref. 19; W. H.Macaulay, Ref. 19; F. R. Moulton, Ref. 19, p. 403. 388 Am. J. Phys., Vol. 79, No. 4, April 2011 Downloaded 30 Dec 2012 to 152.3.102.242. Redistribution subject to AAPT li 41For example, J. R. Young, Ref. 40, p. 250 for Fig. 4 , p. 20 Fig. 5 , p. 21 Fig. 6 . 42Strictly speaking, Poisson is entitled to conclude only that the resultant lies along the bisector of the larger angle or along the bisector of the smaller angle between P1 and P2. To explain why it lies along the smaller angle\u2019s bisector, Poisson could have appealed to two further premises: That the resultant of two equal forces depends continuously on their angle and that the resultant of two forces in the same direction points in that direction, too, and thus bisects the smaller angle measuring zero radians between them" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001424_0094-114x(75)90076-2-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001424_0094-114x(75)90076-2-Figure4-1.png", + "caption": "Figure 4.", + "texts": [ + " This surely makes the solution more sophisticated, but the necessity to determine all of the relative motion parameters does not arise in all problems of kinematic analysis. If the determination of all of the relative motion parameters is necessary, the use of the procedure described enables one to realize it in several stages, using within any of them less equations than with other procedures. The procedure in question is applied by the author together with Grossman to the determination of how axis misalignment in the Oldham coupling affects the precision of the motion transmission. Figure 4 shows a skeleton of the Oldham coupling. Half-couplings 1 and 3 are connected to the frame with the turning pairs P~o and P3h. Cross 2 is connected to link 1 with the sliding pair P2,. Links 2 and 3 are connected to each other with the kinematic pair P23, which is a combination of a spherical surface and a plane. kinematic pair P23. Use the equation of tangency of the P23 pair elements to correlate the motions of the disconnected parts of the mechanism. Introduce the coordinate systems St, $2, $3, So and $4 rigidly connected to links 1, 2, 3 and to the frame" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000583_j.cma.2008.11.014-Figure18-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000583_j.cma.2008.11.014-Figure18-1.png", + "caption": "Fig. 18. Geometry, load condition and mate", + "texts": [ + " From this figure, one can deduce that the wrinkling model maintains the convergence rate of O(h2) as the size of element is reduce by 1/2 the error is reduced by the factor of 1/4. The last example demonstrates the capability of the proposed model to investigate the evolution of wrinkles in a flat square isotropic membrane and the comparison of the results with the ent. nt at point M during mesh refinement. experiments mentioned in [40]. An extension to the orthotropic case is straightforward. This square membrane is pulled at its four corners by two diagonal pairs of equal and opposite forces (T1 and T2 in Fig. 18). For comparison purpose, all geometrical, material and load parameters given in Fig. 18 comply with those specified in [40]. All edges are reinforced with cable elements just to prevent convergence problem due to unidentified boundary conditions. To prevent rigid body motions, the center point of this membrane is fixed and the out of plane displacement (z-direction) of all edges is restrained. This membrane is discretized by 900 bilinear quadrilateral membrane elements with three translational dof per node and analyzed by a nonlinear static analysis. In this example, the loading process is subdivided into three stages. In the first stage, the square flat membrane is prestressed as specified in Fig. 18 to create initial stiffness within the flat membrane. In the second phase, a pair of symmetric loads T1 = T2 = 5 N are applied at all corners. Then, in the third stage T2 is maintained constant at 5 N while T1 is increased up to 20 N with the final load ratio of T1/T2 = 4. The last two load stages are carried out as a follow-on to the first stage according to those defined in [40]. In Fig. 19, wrinkle trajectories are plotted with different load ratios (T1/T2). As depicted from Fig. 19a, the wrinkle trajectories are symmetric and concentrated around all corners of the membrane if the load ratio is unity" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001403_gt2009-59226-Figure19-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001403_gt2009-59226-Figure19-1.png", + "caption": "Fig. 19 Experimental and simulation results with shroud U-shape drain, 180\u02da position, 30\u02da size, with back plate", + "texts": [], + "surrounding_texts": [ + "The calculation model is shown in Fig. 12. The revolutions of the gears were set to the same as the experiment. The bearings were modeled to cylindrical shape that filled the space between the rollers of the bearing. On the axial surface of the cylinder, the revolution of a bearing holder was assigned. The flow rate of the oil supply for the bearings was modeled to constant leakage from the surface of the cylinder that had the simplified shape of the bearing rollers. Figure 13 shows the calculation cells of the unshrouded gears. In these calculation cells, in order to simulate the oil supply in the into-mesh direction of the gears, the size of the cells around the meshing part was made small until the flow in the minimum space between the gears could be calculated. The bottom surface of cell block #4 was set on a constant pressure boundary and other surfaces of the block were set on a non-slip wall. In the calculation case with the shrouds, the velocity out of the shrouds is low and influence of the casing wall is nearly isolated. Therefore, with regard to the simulation with the nloaded From: http://proceedings.asmedigitalcollection.asme.org/pdfaccess.ashx shrouds, to reduce calculation time, cell block #4 was omitted and the outer surfaces of blocks #1, #2, #3 were set on constant pressure boundaries except for wall boundaries on the back of the gears. Other calculation conditions were set the same as Table 2. The CPU times with single CPU in 10 rotation of the input gear were 8.9 days in unshrouded case and 5.2 days in shrouded case." + ] + }, + { + "image_filename": "designv11_7_0000069_841057-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000069_841057-Figure3-1.png", + "caption": "Fig. 3 - Liapunov stability results using standard method for data set 2", + "texts": [ + " Thfs quartic equation was solved repeatedly for different values of V to generate a curve in the V fi - plane thai: represents the boundary of The region in which V, < 0. The final step in determining the region of stability, or domain of attraction, is that of fitting the largest possible V, = constant curve inside the tf. < 0 region. The V, - 0 curve, the associated V, - constant curve, and the stability boundary obtained by digitally simulating Eqs. (5) and (6) are shown in Fig. 1 for Data Set 1 and in Fig. 3 for Data Set 2. Next, the modified kinetic energy function, V?s will be used for the nonlinear problem. STnce B,?>0 and B?1>0 for Data Sets 1 and 2, the funcTlon \\L of^q. (16) can be written as I. V2 = 2B. V 2B, al 12 J \"\"21 which is a positive definite function. equation for V2 can be written as , (B\u201eV.. + B,\u201e8- + B^V. The v2 = - 12 ii y '12\"z 16\\y 5 B17Vynz + B18Vyflz + B19az' B^ 0; \u00f018\u00de o/ ox x \u00bc 1: \u00f019\u00de In addition, from Eq. (14) can be seen that the following condition is required: o/ ox < 0 \u00f020\u00de to have a positive control signal, and finally in order to keep the state variable within its limits we also need lim x" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003868_2014-01-1085-Figure7-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003868_2014-01-1085-Figure7-1.png", + "caption": "Figure 7. Bending of quarter circular arch", + "texts": [ + " Analytical solutions of the deflection of thin curved beams under simple loading have been developed at the beginning of the 20th century [19]. It is used to check the accuracy of the proposed curved beam finite element model. In addition, a comparison with straight beam finite elements previously used to model piston rings is made. The structural problem used to make the comparison between analytical, curved, and straight beam solutions is the bending of a circular ring in its plane of curvature. Figure 7 illustrates this problem: The ring forms a quarter of a circle of radius R and is submitted to a radial load at its tip Fr. Its base located at \u03b8=0 is clamped. Under the action of the radial force the arch is bent outwards. For deformations that are small compared to the ring radius, the radial displacement of the neutral axis, y, can be expressed as [19]: (28) E and I are the ring Young's modulus and area moment of inertia. The ring is meshed with the curved beam element presented here and a straight beam element found in the literature [11]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001411_iccas.2008.4694526-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001411_iccas.2008.4694526-Figure4-1.png", + "caption": "Fig. 4 Preprogrammed gait forces (red vectors) used to achieve desired force vectors (blue vectors).", + "texts": [ + " However, this being infeasible, instead we must carefully choose only a few preprogrammed gaits that the vehicle navigation control system can draw from [5]. Therefore, the control system uses combinations of this limited set of gaits to generate the infinite number of fin force vectors needed to perform six degree-of-freedom (6-DOF) maneuvers. The results from Figs. 2~3 identify trends in force output which help determine the preprogrammed gaits. Four gaits have been chosen, including a maximum forward thrust gait (Kf), a maximum reverse thrust gait (Kr), and maximum upward and downward thrust gaits (Ku and Kd, respectively) (Fig. 4). Any desired force vector (Kc) for each fin can be achieved through weighted combinations of preprogrammed gaits [5], and then maps of these combinations to forces through the equation, ( )durfc KKKKfK ,,,= . (5) Note that all gaits are chosen to be entirely uncoupled allowing each gait to be independently optimized and studied to improve the overall controller. Extensive experimental testing has been carried out to determine optimum gaits for generating maximum forward and reverse thrust, and maximum positive and negative lift [6]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000243_20070903-3-fr-2921.00020-Figure6-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000243_20070903-3-fr-2921.00020-Figure6-1.png", + "caption": "Fig. 6. Deterministic navigation, including nominal trajectories (grey) and real path (black).", + "texts": [ + " Therefore the waypoints of a total number of 11 admissible routes are defined in advance, resulting in an overall course length of 250 m. With the current robot position and various destinations given by a high level controller, flexible routing is performed by the path planner. Based on the waypoints of the selected routes a continuous-curvature trajectory is generated and associated with a maximum velocity profile. The generated trajectories are followed by a combination of feedforward and feedback control whereas no lateral obstacle avoidance is performed in this application. Figure 6 shows the resulting paths. The nominal trajectories are labelled in grey and the real path piloted by the fork lift in black. According to the maximum velocity profile, the speed of the vehicle is adjusted by a velocity controller. Within the admissible velocity, speed is decreased/increased dynamically in dependence of the closeness to obstacles. At any time, motion and maximum velocity of the robot is predefined resulting in a deterministic behaviour of the robotic fork lift truck. A motion picture of this exemplary application including the experimental results can be found online at our website (see references)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003742_s0263574711000397-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003742_s0263574711000397-Figure1-1.png", + "caption": "Fig. 1. Passivity-based dynamic bipedal walking model with flat feet and compliant ankle joints. The biped is powered by hip torque and ankle actuation. The thigh and the shank are connected at the knee joint, while the foot is mounted on the ankle with a torsional spring. Similar to Wisse et al.,12 a kinematic coupling has been used in the model to keep the body midway between the two legs. The knee joints and ankle joints are modeled as passive joints that are constrained by torsional springs.", + "texts": [ + " Section 4 gives the simulation results. http://journals.cambridge.org Downloaded: 15 Dec 2014 IP address: 138.251.14.35 In Section 5, we discuss the effects of ankle stiffness on gait selection and compliant leg behavior. We conclude in Section 6. To obtain further understanding of real human walking, we propose a passivity-based bipedal walking model that is more close to human beings than other passivity-based dynamic walking models. We add flat feet and compliant ankle joints to the model. As shown in Fig. 1, the two-dimensional model consists of two rigid legs interconnected individually through a hinge with a rigid upper body (mass added stick) connected at the hip. Each leg includes thigh, shank, and foot. The thigh and the shank are connected at the knee joint, while the foot is mounted on the ankle with a torsional spring. A point mass at hip represents the pelvis. The mass of each leg and foot is simplified as point mass added on the Center of Mass (CoM) of the shank, the thigh, and the foot, respectively", + " Thus, similar to other related studies,12, 15, 16 we allow it if the foot travels below the floor not very seriously. We suppose that the x-axis is along the ground while the y-axis is vertical to the ground upward. The configuration of the walker is defined by the coordinates of the point mass on hip joint and several angles, which include the swing angles between vertical axis and each thigh and shank, the angle between vertical axis and the upper body, and the foot angles between horizontal axis and each foot (see Fig. 1 for details), which can be arranged in a generalized vector q = (xh, yh, \u03b81, \u03b82, \u03b83, \u03b82s, \u03b81f , \u03b82f )T. The positive directions of all the angles are counterclockwise. Note that the dimension of the generalized vector in different phases may be different. When the knee joint of the swing leg is locked, the freedom of the shank is reduced and the angle \u03b82s is not included in the generalized coordinates. Consequently, the dimensions of mass matrix and generalized active force are also reduced in some phases", + " Since the mass of the model is distributed as point masses, the angles in x and the moments of inertia in M could be taken off for simplification. Denote F as the active external force vector in rectangular coordinates. The constraint function is marked as \u03be (q), which is used to maintain foot contact with ground and detect impacts. Note that \u03be (q) in different walking phases may be different since the contact conditions change. For example, the constraint function \u03be (q) in the single-support phase (the full foot of the stance leg keeps contact with ground, as shown in Fig. 1) can be written as following: \u03be (q) = \u23a1 \u23a2\u23a2\u23a2\u23a2\u23a3 \u03b83 \u2212 1 2 (\u03b81 + \u03b82) xh + l sin \u03b81 \u2212 xankle yh \u2212 l cos \u03b81 \u2212 lf h sin \u03b81f yh \u2212 l cos \u03b81 + lf t sin \u03b81f \u23a4 \u23a5\u23a5\u23a5\u23a5\u23a6 , (5) where xankle is the x-coordinate of the ankle of leg 1, l is leg length as shown in Fig. 1, and lf h and lf t are the distances from heel to ankle and from ankle to toe, respectively. Each component of \u03be (q) should keep zero to satisfy the contact condition. The contact of stance foot is modeled by one ground reaction force (GRF) along the floor and two GRFs perpendicular to the ground act on the two endpoints of the foot, respectively. If one of the forces perpendicular to the ground decreases below zero, the corresponding endpoint of the stance foot will lose contact with ground and the stance foot will rotate around the other endpoint" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001468_j.optlastec.2009.02.005-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001468_j.optlastec.2009.02.005-Figure2-1.png", + "caption": "Fig. 2. Assembly configuration.", + "texts": [ + " The distance between laser impact and arc impact is 5 mm. The moving of welding head is carried out with a numerically controlled 6 axes robot KUKA KR 600. Table 1 Thermal properties of 2024 T3 (MATWEB). Specific heat capacity 0.875 Jg 1 1C 1 Thermal conductivity 193 Wm 1 K 1 Melting point 502\u2013638 1C Solidus 502 1C Liquidus 638 1C Table 2 Welding conditions for the laser process. The welding conditions are summarized in Table 3. The transfer metal mode is the pulsed mode and the welding configuration is a \u2018\u2018T\u2019\u2019 (Fig. 2). The camera used was a FLIR ThermaCAM S40 imaging system. It has a 240 320 pixels focal-plane-array uncooled microbolometer detector, with a sensitive range of 7.5\u201313mm. Imaging and storage was made at a frequency rate of 50 Hz. A 100 mm close-up lens was used, which allowed a spatial resolution of 100mm. The infrared thermography system recorded IR image of the face of the piece not directly illuminated by the sources (the back face). The viewed plate is coated with a graphite coating whose emissivity was measured" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000495_robot.2007.363615-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000495_robot.2007.363615-Figure2-1.png", + "caption": "Fig. 2. Navigation Function around 2 obstacles.", + "texts": [], + "surrounding_texts": [ + "A. 2D Sphere World In this section we will formally show that the function \u03d5, constructed in the previous section is indeed a navigation function. Let the workspace W with obstacles O = \u22c3 i Oi, where i = 1, . . . ,M , with M the number of obstacles. Furthermore, define the free space, as the space remains after removing all the obstacles from the workspace F , W \u2212O Let \u01eb > 0, define Bi(\u01eb) , {q | 0 < \u03b2i < \u01eb}. We have partition the free space into following five subsets: 1) The destination point: Fd , {q | \u03b3d(q) = 0} 2) The free space boundary: \u2202F , \u03b2\u22121(0) 3) The set \u201cnear the obstacles\u201d: F0(\u01eb) , \u22c3 i Bi(\u01eb)\\Fd 4) The set \u201cnear the workspace boundary\u201d: F1(\u01eb) , B(\u01eb)\\ (Fd \u22c3F0(\u01eb)) 5) The set \u201caway from the obstacles\u201d: F2(\u01eb) , F\\ (Fd \u22c3 \u2202F \u22c3F0(\u01eb) \u22c3F1(\u01eb) \u22c3F2(\u01eb)) The following technical lemma, which gives formulas for the Hessian of a rational function at a critical point, will be very useful in the sequel of the proof. Lemma 1: Let \u03bd, \u03b4 be at least twice differentiable, and define \u03c1 , \u03bd \u03b4 . At a critical point c of \u03c1, [11] \u22072\u03c1 |c= 1 \u03b42 [ \u03b4\u22072\u03bd \u2212 \u03bd\u22072\u03b4 ] Firstly, we will show that the goal configuration qd is a non-degenerate local minimum of the navigation function. Proposition 1: If the workspace is valid, the destination point, qd, is a non-degenerate local minimum of \u03d5. Proof: The gradient of function \u03d5 of (1) is \u2207\u03d5(qd) = 1 (\u03b3d + \u03b2) 2 [(\u03b3d + \u03b2)\u2207\u03b3d \u2212 \u03b3d\u2207(\u03b3d + \u03b2)] |qd = 0 (5) since, both \u03b3d and \u2207\u03b3d vanish at qd. The Hessian of \u03d5 at qd, using Lemma 1, will be \u22072\u03d5 = 1 (\u03b3d + \u03b2) 2 [ (\u03b3d + \u03b2)\u22072\u03b3d \u2212 \u03b3d\u22072(\u03b3d + \u03b2) ] |qd (6) Since, \u03b3d vanish at qd and it holds that \u22072\u03b3d = 2I , we have that \u22072\u03d5 = 2\u03b2\u22121I which implies that qd is a non-degenerate local minimum of \u03d5. We can assume by using coordinate transformation, that the obstacle is located (the center of obstacle) at qi = ( 0 , yi ), yi > 0. We define a new coordinate system, using polar coordinates, as depicted in Fig. 1, with r measuring the distance from the obstacle\u2019s center, and with \u03d1 measuring the angle associated with the point. The coordinate transformation is given by x = r sin \u03d1 y = yi + r cos \u03d1 (7) Function \u03b3d becomes \u03b3d = y2 i + r2 + 2ryi cos \u03d1 (8) While function \u03b2 becomes \u03b2i = h(r \u2212 \u03c1i) h(r \u2212 \u03c1i) + h(\u01ebi + \u03c1i \u2212 r) (9) The gradient of \u03b3d is computed as \u2207\u03b3d = [ 2r + 2yi cos \u03d1 \u22122yir sin \u03d1 ]T (10) and the Hessian of \u03b3d can be computed as \u22072\u03b3d = [ 2 \u22122yi sin\u03d1 \u22122yi sin\u03d1 \u22122yir cos \u03d1 ] (11) Furthermore, the gradient and the Hessian of \u03b2i are respectively: \u2207\u03b2i = [ \u2202\u03b2i \u2202r 0 ]T (12) \u22072\u03b2i = [ \u22022\u03b2i \u2202r2 0 0 0 ] (13) In order to compute the derivatives of \u03b2i w.r.t r, it is convinient to introduce the following parameters: h1 = h(r \u2212 \u03c1i) , h2 = h(\u01ebi + \u03c1i \u2212 r) (14) By (9), we have that \u03b2i = h1 h1+h2 , and therefore, we can compute its derivatives: \u2202\u03b2i \u2202r = \u03b2r = \u03b2i(1\u2212\u03b2i) [ \u01ebi (r \u2212 \u03c1i)2 + \u01ebi (\u03c1i + \u01ebi \u2212 r)2 ] (15) \u22022\u03b2i \u2202r2 = \u03b2i(1 \u2212 \u03b2i)(1 \u2212 2\u03b2i) [ \u01ebi (r\u2212\u03c1i)2 + \u01ebi (\u03c1i+\u01ebi\u2212r)2 ]2 + 2\u03b2i(1 \u2212 \u03b2i) [ \u01ebi (\u03c1i + \u01ebi \u2212 r)3 \u2212 \u01ebi (r \u2212 \u03c1i)3 ] = \u03b2rr (16) Lemma 2: For every \u03c1i > 0 there exists a positive \u01ebi s.t. the distance of all critical points associated with ith obstacle is greater then three quarters of the boundary zone, i.e. q \u2208 C\u03d5i \u21d2 r < \u03c1i + 3/4\u01ebi, where C\u03d5i is the set of all critical points associated with obstacle i. Proof: Obviously, due to the fact that the gradient of \u03b3d points to the target, and the gradient of \u03b2i is radial, the critical point will always be at \u03d1 = 0. So,in a critical point, from (5), the following equation holds: \u03b2i\u2207\u03b3d = \u03b3d\u2207\u03b2i (17) By taking norms of the two sides, and using (8), (10), and (12), we have that 2\u03b2i(r + yi) = (r + yi) 2\u03b2r , \u03d1 = 0 So at a critical point we have that, \u03b2r \u03b2i = 2 r+yi . But 2 r+yi < 1 \u03c1i , as r > \u03c1i, and yi > \u03c1i. It suffice to show that \u03b2r \u03b2i > 1 \u03c1i , for r < \u03c1i + 3/4\u01ebi. \u03b2r \u03b2i = (1 \u2212 \u03b2i) [ \u01ebi (r\u2212\u03c1i)2 + \u01ebi (\u03c1i+\u01ebi\u2212r)2 ] It holds,by direct computation, that (1 \u2212 \u03b2i) \u2265 0.065 for r \u2264 \u03c1i + 3/4\u01ebi, so \u03b2r \u03b2i \u2265 0.065 \u01ebi (r\u2212\u03c1i)2 \u2265 0.11 \u01ebi Thus, by choosing \u01ebi < 0.11\u03c1i, all critical points are on the quarter of the boundary zone. Lemma 3: For \u01ebi > 0 \u21d2 \u03b2i > (r \u2212 \u03c1i)/\u01ebi, r > \u03c1i + \u01ebi/2. Proof: Let w = r \u2212 \u03c1i \u03b2i > w/\u01ebi \u21d4 e\u2212\u01ebi/w e\u2212\u01ebi/w+e\u2212\u01ebi/(\u01ebi\u2212w) > w/\u01ebi \u21d4 e\u2212\u01ebi/w > we\u2212\u01ebi/w/\u01ebi + we\u2212\u01ebi/(\u01ebi\u2212w)/\u01ebi \u21d4 e\u2212\u01ebi/w(1 \u2212 w/\u01ebi) > we\u2212\u01ebi/(\u01ebi\u2212w)/\u01ebi \u21d4 e(\u2212\u01ebi/w)+(\u01ebi/(\u01ebi\u2212w)) > w/(\u01ebi \u2212 w) We set as p = \u01ebi/(\u01ebi \u2212 w) and q = \u01ebi/w and we have that \u03b2i > (r \u2212 \u03c1i)/\u01ebi \u21d4 ep\u2212q > p/q \u21d4 ep/p > eq/q Since w > \u01eb/2 we have that \u01ebi \u2212 w < \u01eb/2 < w so p > q. We check the monotonicity of f(v) = ev/v. We have that f \u2032(v) = ev/v \u2212 ev/v2 = ev(1/v \u2212 1/v2). For v > 1, we have that f \u2032(v) > 0 and therefore p > q \u21d4 ep/p > eq/q. v > 1 \u21d4 q > 1 \u21d4 \u01ebi/w > 1 \u21d4 w < \u01ebi \u21d4 r \u2212 pi < \u01ebi, which is always true. Lemma 4: For a, b > 0, and a \u2212 b > 0, a > 3+ \u221a 5 2 b \u21d2 (b \u2212 a) ( 1 a2 + 1 b2 )2 + 2 ( 1 b3 \u2212 1 a3 ) < 0. Proof: We have that (b \u2212 a) ( 1 a2 + 1 b2 )2 + 2 ( 1 b3 \u2212 1 a3 ) = (b\u2212a)(a2+b2)2 a4b4 + 2(a3\u2212b3) a3b3 = (b\u2212a)(a2+b2)2+2ab(a3\u2212b3) a4b4 Let now take the numerator N : N = (b \u2212 a)(a2 + b2)2 + 2ab(a \u2212 b)(a2 + ab + b2) = (b \u2212 a)[a4 + b4 + 2a2b2 \u2212 2ab(a2 + ab + b2)] = (b \u2212 a)[a4 + b4 \u2212 2a3b \u2212 2ab3] Let A = a4 + b4 \u2212 2a3b \u2212 2ab3, then we have that: A = (a \u2212 b)4 + 2a3b + 2ab3 \u2212 6a2b2 = (a \u2212 b)4 + 2ab(a2 \u2212 3ab + b2) Therefore, it holds that N = (b \u2212 a)A < 0, since a > 3+ \u221a 5 2 b and according to the other predefined conditions, and consequently, the proof is completed. Proposition 2: For every \u01ebi < 0.11\u03c1i, and r > \u03c1i +3/4\u01ebi \u21d2 \u03b2rr < 0. Proof: From (16) it suffices to show: L(r) = (1 \u2212 2\u03b2i)\u01ebi [ 1 (r\u2212\u03c1i)2 + 1 (\u03c1i+\u01ebi\u2212r)2 ]2 + 2 [ 1 (\u03c1i+\u01ebi\u2212r)3 \u2212 1 (r\u2212\u03c1i)3 ] < 0 since 0 < \u03b2i < 1, for r \u2208 (\u03c1i, \u03c1i + \u01ebi). We have that \u03b2i > (r \u2212 \u03c1i)/\u01ebi according to Lemma 3, therefore, (1 \u2212 2\u03b2i) \u2264 (2\u03c1i + \u01ebi \u2212 2r)/\u01ebi,\u2200r > \u03c1i + 3\u01ebi/4. Thus, we have that: L(r) \u2264 (2\u03c1i + \u01ebi \u2212 2r) [ 1 (r\u2212\u03c1i)2 + 1 (\u03c1i+\u01ebi\u2212r)2 ]2 + 2 [ 1 (\u03c1i+\u01ebi\u2212r)3 \u2212 1 (r\u2212\u03c1i)3 ] Assuming that r\u2212\u03c1i = a and \u03c1i+\u01ebi\u2212r = b, and according to Lemma 4, based on the conditions a\u2212b = 2r\u22122\u03c1i\u2212\u01ebi > 0, and a > 3+ \u221a 5 2 b, it holds that L(r) < 0 The last condition is proved as follows: a > 3+ \u221a 5 2 b \u21d2 2a > (3 + \u221a 5)b \u21d2 r \u2212 \u03c1i > 3+ \u221a 5 5+ \u221a 5 \u01ebi which is true since r \u2212 \u03c1i > 3/4 > 3+ \u221a 5 5+ \u221a 5 \u01ebi. Finally, with the next proposition it is shown that the navigation function \u03d5 is a Morse function (it is ensured that the critical points are saddles). Proposition 3: For \u01ebi < 0.11\u03c1i, all the critical points of \u03d5 are non-degenerate. Proof: According to (6), we can take the numerator, and by using (11), and (13), we have that: ( \u03b2i\u22072\u03b3d \u2212 \u03b3d\u22072\u03b2i ) |C\u03d5 = \u03b2i|C\u03d5 [ 2 0 0 \u22122yir ] \u2212 \u03b3d|C\u03d5 [ \u03b2rr 0 0 0 ] = [ 2\u03b2i|C\u03d5 \u2212 \u03b3d|C\u03d5 \u03b2rr 0 0 \u22122\u03b2i|C\u03d5 yir ] It is a diagonal matrix. Since we are at a critical point, and since \u01ebi < 0.11\u03c1i the critical point lies on the outer quarter of the boundary zone, according to Lemma 2. Since the critical point lies on the outer quarter of the boundary zone, according to Proposition 2. Since \u03b3d > 0, and \u03b2i > 0, we conclude that 2\u03b2i|C\u03d5 \u2212 \u03b3d|C\u03d5 \u03b2rr > 0 Moreover, since \u03b2i > 0, yi > 0, r > 0 we conclude that \u22122\u03b2i|C\u03d5 \u00b7 yi \u00b7 r < 0 Thus, the Hessian of \u03c6 at the critical point is a diagonal matrix, with one positive and one negative element. The eigenvalues of this matrix are therefore positive and negative. Therefore, the critical point is not a local minima, but a saddle point." + ] + }, + { + "image_filename": "designv11_7_0003516_physreve.85.036304-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003516_physreve.85.036304-Figure1-1.png", + "caption": "FIG. 1. IB representation of the swimming sheet.", + "texts": [ + " Given a distribution of network volume fraction, the method uses the generalized minimal residual method (GMRES) with a box-type multigrid scheme preconditioner to solve collectively the momentum and incompressibility equations (4), (5), and (7) to get un, us , and p. Then \u03b8n is updated by solving the transport equation (2) using a high-resolution unsplit Godunov scheme as described in Ref. [18]. All simulations were done in the laboratory frame. To capture the coupled fluid-structure interactions between the swimmer and the surrounding fluid mixture, we develop an extension of the classical immersed boundary method [14]. Because of the existence of two velocity fields, we represent the sheet by two immersed boundaries, denoted n and s as illustrated in Fig. 1. Each of the immersed boundaries is composed of an array of discrete Lagrangian points connected by linear springs and communicates with only one of the fluids in the mixture. That is, forces from n are spread only to fluid n, and values of un are interpolated to points of n to update their positions. Similarly, s interacts with fluid s. Each immersed boundary point on each of n or s is connected with its neighboring points by weak springs in order to simulate an extensible sheet. The up and down motions of the immersed boundary points are driven by linking them to moving \u201ctether\u201d points through stiff springs with zero rest length" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003663_1.3653072-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003663_1.3653072-Figure1-1.png", + "caption": "Fig. 1 Schematic of rotor-bearing system", + "texts": [ + " The results are plotted in dimensionless form and indicate regions which deserve considerably more experimental verification. While the authors feel that the analyses are adequate for the prediction of half-frequency-whirl threshold in plain-cylindrical journal bearings, there is virtually no analysis available for other bearing geometries. Some of the theoretical methods presented in this paper lend themselves readily to stability analysis of other than plain-cylindrical journal bearings. Dynamics Consider a symmetrical rotor-bearing system as schematically shown in Fig. 1(a). Assume that the rotor is rigid and that the bearings are perfectly aligned. The rotor axis is inclined at an angle /30, such that, at static equilibrium, the reaction of each bearing is (FA)o = (FB)o = F = mg cos /30 (1) Assume that the axial displacement of the rotor is negligible \u2022Nomenclature1 c = mean radial clearance of }xA, etc. = i-component of bearing A m = half-rotor mass bearing reaction per unit axial P = p/pa dimensionless gas-film c = dimensionless clearance pa- length, etc. pressure rameter, Table 1 g = gravitational constant P< = initial distribution of P C + = dimensionless clearance parameter, Table 1 H = h/C V = gas-film pressure h = lubricant-film thickness Pa = ambient pressure D I = lateral moment of inertia of R = radius of journal = journal diameter rotor t = time e = eccentricity or length of line of centers JP = polar moment of inertia of rotor x, y = translational displacements of rotor F = half lateral load, bearing L = journal length x, y, z = Cartesian coordinates reaction I = rotor span CContinued on next page) J o u r n a l of Basic Eng ineer ing J U N E 1 9 6 4 / 3 2 1 Copyright \u00a9 1964 by ASME Downloaded From: http://fluidsengineering.asmedigitalcollection.asme.org/pdfaccess.ashx?url=/data/journals/jfega4/27254/ on 06/06/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use SCHEMATIC OF ROTOR - BEARING SYSTEM SCHEMATIC OF A JOURNAL BEARING = I + e COS 0 < = Ce and that its angular speed is maintained constant; then the rotor has a total of four degrees of freedom, which correspond to the transnational displacements (x,y) and the rotational displacements (4>Xi y), as shown in Fig. 1(6). For the trauslational degrees of freedom, dynamical equilibrium requires FXA + FXB = 2 m\u00a3, FyA + F\u201eB = 2M(Y + g cos /?0), and for the rotational degrees of freedom, (2) (3) I (FxA ~FXB) \u2014 (FuA \u2014 FVB) p L / 2 J \u2014 L/2 (fxA + fxBVdz' = I\u201e - J\u201e0>X, ( 4 ) 'L /2 t r L / 2 - - ( L A + fynVdz' = 7 0 , + JPU4>\u00ab z J -L/2 (5) If the bearing length is small in comparison with the rotor span, then the second terms in both equations (4) and (5) can be omitted, and any instantaneous misalignment maj' be neglected when considering bearing reactions" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002222_9783527627646-Figure11.7-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002222_9783527627646-Figure11.7-1.png", + "caption": "Figure 11.7 Elution curve and parameters for the evaluation of N.", + "texts": [ + " However, in this text, the term HETP (height equivalent to the theoretical plate) is not used in order to avoid confusion with the HETP of packed columns for distillation and absorption. The shape of the elution curve for a pulse injection can be approximated by the Gaussian error curve for NW100, which is almost the case for column chromatography [2]. The value of N can be calculated from the elution volume VR (m3) and the peak width W (m3), which is obtained by extending tangents from the sides of the elution curve to the baseline and is equal to four times the standard deviation sv (m 3)\u00bc (VR 2/N)1/2, as shown in Figure 11.7. Hs \u00bc Z N \u00bc Z VR sv 2 \u00bc Z 16\u00f0VR=W\u00de2 \u00f011:19\u00de With a larger N, the width of the elution curve becomes narrower at a given VR, and a better resolution will be attained. The dependence of the value of N on the 11.6 Separation by Chromatography | 177 characteristics of packing material and operating conditions is not clear with the stage model, because the value of N is obtained empirically. The dependence ofHs on these parameters can be obtained by the following rate model. 11.6.2.3 Rate Model This treatment is based on the two differential material balance equations on a fixed-bed and packed particles" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000964_j.mechmat.2008.09.004-Figure6-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000964_j.mechmat.2008.09.004-Figure6-1.png", + "caption": "Fig. 6. Tangent planes and their traces.", + "texts": [ + "17)) nor von Mises yield surface. One of the key points of the synthetic theory is that the position of the tangent plane in S5 can be determined by means of its trace in S3. As seen from Eq. (3.9), the quantity h0 can take values from the following range:ffiffiffi 2 p sS 6 h0 <1: Therefore, the traces of the tangent planes, given by Eq. (3.21), fill up the whole space beyond the sphere (3.23) in S3. In other words, any plane located beyond the sphere (3.23) is the trace of some plane tangential to the yield surface in S5. Fig. 6 illustrates the case1 when the tangent planes in S5, marked by 0, 1 and 2, with different normal vectors ~N0, ~N1 and ~N2, have their traces with identically oriented normal vectors ~m in S3. As is seen from Fig. 6 and Eq. (3.9), the angle k, gives the possibility to distinguish identically oriented planes in S3 as the traces of different planes in S5. Two planes in S3 with the same orientation, i.e. for fixed values ~a and ~b, but with different values of angle k are parallel to each other, but have different values of distance h0. Furthermore, Eq. (3.9) gives H0 = h0 for k = 0; therefore, the plane tangential to the yield surface in S5 is at the same time tangential to the yield surface in S3, sphere (3.23), (the plane is marked by 0 in Fig. 6). In general, any plane in S3 is the trace of an infinite set of planes from S5, of which one is tangent to the yield surface in S5. Those planes which are not tangential to the yield surface in S5 are not taken into account. The main suggestion (Sanders, 1954) is that the stress deviator vector shifts planes tangential to the yield surface on its endpoint during loading. The movements of the planes located at the endpoint of vector~S are translational, i.e. without a change of their orientation" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003823_icosc.2013.6750965-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003823_icosc.2013.6750965-Figure2-1.png", + "caption": "Figure 2. The inertial, body and vehicle frames of reference.", + "texts": [ + " MATHEMATICAL MODEL OF THE QUADROTOR To test the proposed hybrid intelligent control system, a simulation environment is developed. A mathematical model contain the equation of motion are resumed in this section. We will follow the derivation given in [8] when they used a simple derivation of the famous equation of Coriolis. For quadrotors there are several coordinate systems that are of interest. In this section we will use the following coordinate frames: the inertial frame, the vehicle frame, and the body frame as shown in Figure 2. In this section we provide the expressions for the kinematics and the dynamics of a rigid body. While the expressions derived in this section are general to any rigid body, we will use notation and coordinate frames that are typical in the aeronautics literature. The state variables of the quadrotor are the following twelve quantities : x = the inertial position of the quadrotor along xi in Ri , y = the inertial position of the quadrotor along yi in Ri , h = the altitude of the aircraft measured along -zi in Ri , u = the body frame velocity measured along xv in Rv , 978-1-4799-0275-0/13/$31" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003281_1.4006277-Figure12-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003281_1.4006277-Figure12-1.png", + "caption": "Fig. 12 Parabolic velocity profiles at h 5 hs for u 5 du dy 5 0 and fluid distribution downstream the film rupture", + "texts": [ + " Nevertheless, this kind of analytical approach cannot give any information on surface tension effects on exit meniscus abscissa, or the liquid distribution on each surface a priori. In Fig. 4, for instance, the analytical value of the exit meniscus abscissa corresponds to the asymptotic value obtained at high capillary numbers (when surface tension effects are not predominant). However, by using two phase flow results, the assumption that at the rupture abscissa xs, the fluid is dragged out of the contact following each surface (see Fig. 12) can be made. Indeed, as shown previously, even if a recirculation area is found when capillary Journal of Tribology OCTOBER 2012, Vol. 134 / 041503-7 Downloaded From: http://tribology.asmedigitalcollection.asme.org/pdfaccess.ashx?url=/data/journals/jotre9/926076/ on 04/27/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use effects are predominant (see Sec. 4), this area is a stagnant zone and does not affect the fluid distribution at the exit. The liquid distribution can then be calculated with the mass flow conservation (see Appendix), as: D \u00bc d1 d1 \u00fe d2 \u00bc 1 2 \u00fe SRR 1\u00fe ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 SRR 2 2 s ", + "org/about-asme/terms-of-use um \u00bc u1\u00feu2 2 \u00f0m s 1\u00de \u00bc entrainment velocity U\u00f0m s 1\u00de \u00bc reference velocity v\u00f0m s 1\u00de \u00bc fluid velocity along y-axis x\u00f0m\u00de \u00bc spatial coordinate along the direction of flow xe\u00f0m\u00de \u00bc inlet abscissa xs\u00f0m\u00de \u00bc outlet rupture abscissa y\u00f0m\u00de \u00bc spatial coordinate across film thickness z\u00f0m\u00de \u00bc spatial coordinate along the cylinder thickness c\u00f0m3 s kg 1\u00de \u00bc mobility d1\u00f0m\u00de \u00bc film thickness on bottom moving surface d2\u00f0m\u00de \u00bc film thickness on top moving surface Dt\u00f0s\u00de \u00bc numerical time step Dx\u00f0m\u00de \u00bc numerical space step in the x-direction Dy\u00f0m\u00de \u00bc numerical space step in the y-direction e\u00f0m\u00de \u00bc interfacial thickness g\u00f0Pa s\u00de \u00bc general fluid viscosity gi\u00f0Pa s\u00de \u00bc viscosity of phase i g0\u00f0Pa s\u00de \u00bc reference viscosity hs\u00f0rad\u00de \u00bc static contact angle q\u00f0kg m 3\u00de \u00bc general fluid density qair\u00f0kg m 3\u00de \u00bc air density qi\u00f0kg m 3\u00de \u00bc density of phase i q0\u00f0kg m 3\u00de \u00bc reference density r\u00f0N m 1\u00de \u00bc surface tension / \u00bc phase field variable v\u00f0m s kg 1\u00de \u00bc mobility parameter x2\u00f0rad s 1\u00de \u00bc angular velocity of solid Xi An analytical model is built based on classical lubrication assumptions: \u2013 the film thickness is very thin compared to other contact dimensions \u2013 the lubricant is Newtonian \u2013 the fluid flow is laminar \u2013 the lubricant boundary surfaces are parallel or at a small angle with respect to each other \u2013 there is no slip between the fluid and the solid boundaries \u2013 inertial and body forces are neglected \u2013 viscosity and density are constant across the film thickness The Reynolds equation is then written on the following form for an isoviscous fluid [22]: dp dx \u00bc 6g0\u00f0u1 \u00fe u2\u00de\u00f0h h \u00de h3 (A1) with p the fluid pressure, h \u00bc h0 \u00fe x2 2R the film thickness, h the film thickness where dp dx \u00bc 0, g0 the fluid viscosity, and u1 and u2 respectively the lower and upper surface velocities. As an analytical reference value, the classical Hopkins-Prandtl condition [23] is used concerning the exit condition: it is assumed that the rupture abscissa (x \u00bc xs and h \u00bc hs) is located where u \u00bc du dy \u00bc 0, i.e. the zero-reverse flow condition (see Fig. 12). Velocities are defined as functions of the mean velocity um and the Slide-to-Roll Ratio SRR, as u1 \u00bc um 1\u00fe SRR 2 and u2 \u00bc um 1 SRR 2 . The system to solve can thus be written for h \u00bc hs, from [22], as: us \u00bc 1 2g0 dp dx s y2 yhs \u00fe umSRR hs y\u00fe um 1\u00fe SRR 2 \u00bc 0 (A2a) @us @y \u00bc 1 2g0 dp dx s 2y hs\u00f0 \u00de \u00fe umSRR hs \u00bc 0 (A2b) By expressing y as a function of dp dx s in Eq. (A2b) and by replacing in Eq. (A2a), two values for dp dx s can be found, linked to two values of y. One is valid concerning our model, the other not. Indeed, the y-value for which u \u00bc du dy \u00bc 0, y, has obviously to be lower than hs (see Fig. 12). Under the assumption that 2 SRR 2, both y-values are studied. For the first value, one finds that 0 yj\u00f01\u00de hs 1 for 2 SRR 2 and for the second, yj\u00f02\u00de hs 0 for 2 SRR < 0 and yj\u00f02\u00de hs 1 for 0 < SRR 2. Consequently, the correct solution used for the following calculations will be: dp dx s \u00bc 4g0um 1\u00fe ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 SRR 2 2 s ! h2 s (A3a) and y \u00bc hs 2 1\u00fe SRR 2 1\u00fe ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 SRR 2 2 s ", + " (A1)) for h \u00bc hs, the value of the rupture film thickness as a function of h can then be obtained: hs h \u00bc 3 2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 SRR 2 2 s (A4) This ratio hs h is thus only a function of the Slide-to-Roll Ratio and gives the information of the size of the contact exit area, by changing only the kinematic conditions. Now, by assuming that at the fluid rupture location hs\u00f0 \u00de, the fluid over or under the y-value is dragged out of the contact by the upper or lower surface respectively, it is possible to find the liquid distribution on each surface, only as a function of the Slideto-Roll Ratio. As shown Fig. 12, and by assuming that the velocity profiles downstream the film rupture, are unidirectional, one can define the flow rate as: Q \u00bc Q1 \u00fe Q2 \u00bc u1d1 \u00fe u2d2 (A5) with Q the total flow rate, Q1 \u00bc u1d1 and Q2 \u00bc u2d2 the flow rates under and over the y-value respectively, and d1 and d2 the liquid thicknesses on the lower and upper surfaces. By integrating the velocity (Eq. (A2a)), from 0 to y for Q1 and from y to h for Q2, one finds: Qj1 2 \u00bc umh 2 16 SRR K SRR2 \u00fe 12 1\u00fe ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 SRR 2 2 s0 @ 1 A 0 @ 1 A 0 @ 1 A (A6) with K \u00bc 16 1\u00fe 1\u00fe SRR2 8 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 SRR 2 2 q Verifications are then performed with the mass flow conservation to ensure results validity" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000224_icar.2005.1507391-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000224_icar.2005.1507391-Figure1-1.png", + "caption": "Fig. 1 Kinematical Scheme of the Mobile Robot", + "texts": [ + " Experimental results are reported in Section IV to demonstrate the performance of the whole system. Conclusions are given in Section V. I 580-7803-9177-2/05/$20.00/\u00a92005 IEEE 1183 2 In this paper, we take a two-wheeled mobile robot as an object. The wheel rotation is limited to one axis, and the navigation is determined by the speed change in either side of the robot. Therefore, this kind of robot has nonholonomic constraints which should be considered during path planning. The kinematical scheme of a mobile robot can be depicted as Fig. 1, where V is the velocity of robot centroid, VL is the velocity of the left wheel, VR is the velocity of the right wheel, r is the radius of wheel, L is the distance between two wheels, x and y are the position of the mobile robot, and \u03b8 is the orientation of the robot. According to the motion principle of rigid body kinematics, the motion of a mobile robot can be presented as following (1) and (2), where \u03c9L and \u03c9R are angular velocities of left wheel and right wheel respectively, \u03c9 is the angular velocity of centroid" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002690_978-90-481-9689-0_41-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002690_978-90-481-9689-0_41-Figure3-1.png", + "caption": "Fig. 3 3D model and experimental setup of the cable-driven parallel robot IPAnema with eight cables.", + "texts": [ + " Miermeister and A. Pott The reference value for the d-axis is set to zero, since a motor current along the d-axis has no influence on the motor torque. As with the velocity, the current is controlled by a proportional integral controller with an amplification of kdq,i , a time constant kTdq,i , and the control deviation idq,i = idq,ref,i \u2212 idq,eff,i yielding the supply voltage udq,i = [ kd,i ( id,i ) + k\u22121 Td,i \u222b id,i dt kq,i ( iq,i ) + k\u22121 Tq,i \u222b iq,i dt ] . (14) The cable-driven parallel robot IPAnema (Fig. 3) provides a six degrees-of-freedom end-effector with seven or eight cables and focuses on industrial applications in the field of material handling. The winches are equipped with the permanent magnet synchronous motors IndraDyn S by Bosch-Rexroth, which contain multi-turn absolute encoders. The control system is based on an industrial PC with the real-time extension RTX and an adopted NC-controller by ISG (Stuttgart, Germany). The robot can be programmed by G-Code (DIN 66025) similar to machine tools" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002392_j.matdes.2012.02.002-Figure16-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002392_j.matdes.2012.02.002-Figure16-1.png", + "caption": "Fig. 16. The photo of the whole multi-sheet cylinder sandwich structure after SPF process.", + "texts": [ + " The action of pressure is to ensure no welded position to form smoothly. The internal structure of Inconel718 superalloy multisheet cylinder sandwich structure is complex. In order to ensure the structure to form successfully, the slow rate of loading pressure, the higher final forming pressure and the long dwell time should be selected. The relationship curve between the pressure and time is shown in Fig. 15. The photo of the multi-sheet cylinder sandwich structure after superplastic forming is shown in Fig. 16. It can be seen in Fig. 16 that multi-sheet cylinder sandwich structure after SPF has high symmetry of internal structure, the full formed outer wall, no dents and other defects. This result is indicating that the selection of the parameters of SPF process is correct. The forming experiment result shows that LBW/SPF technology is suitable for manufacturing multi-sheet cylinder sandwich structure of Inconel718 superalloy. Microstructures in the weld fusion are shown in Fig. 17a and b. From Fig. 17. It is noted the dendritics occurred in the weld fusion" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003499_s11771-013-1495-x-Figure14-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003499_s11771-013-1495-x-Figure14-1.png", + "caption": "Fig. 14 Edge contact caused by pinion", + "texts": [ + " (2013) 20: 354\u2013362 360 contact pair is also decided by P P b1 T P C P C R (15) To reduce the consuming time of ABAQUS, a FEM model was created with five teeth (see Fig.8), to compute the contact stresses of teeth in contact, the amount of mesh should be confirmed to be large enough to calculate the contact stress exactly. In the field outputs of ABAQUS, we can know the contact stresses from the outputs of CPRESS. Figure 12 shows the cloud picture of the contact stress in a moment (the loaded torque on gear is 10.24 kN\u00b7m, the same below). When the teeth come into or quit meshing, the edge contact happens, as shown in Fig. 13 and Fig. 14. In Fig. 15, the curve of contact stresses in the whole meshing process is given, and the maximal contact stress is 894.3 MPa (see Fig. 12), excluding edge contact, which happens in the boundary of double-tooth meshing region. Fig. 12 Cloud picture of maximal contact stress Fig. 13 Edge contact caused by gear J. Cent. South Univ. (2013) 20: 354\u2013362 361 Basing on the results in Table 3, we think the contact stress of every meshing point is approximate, because their induced curvatures are almost identical" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003351_j.engfracmech.2012.12.001-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003351_j.engfracmech.2012.12.001-Figure3-1.png", + "caption": "Fig. 3. The 3D mesh of the 920 mm rail wheel.", + "texts": [], + "surrounding_texts": [ + "In this analysis, the material was assumed to be a high carbon steel wheel AAR grade B. For the initial verification study, the material properties are assumed to be equivalent to Microalloyed AAR Class B wheel steel and are extracted from [42]. The room temperature yield strength of the material is set at 800 MPa, Young\u2019s modulus at 206 GPa, Possions ratio at 0.286 and the density at 7870 kg/m3. The material thermal properties used are specific heat \u2013 490 J/kg C, coefficient of thermal expansion \u2013 14 10 5, thermal conductivity \u2013 47.5 W/m C and free convection heat transfer coefficient \u2013 25 10 6 W/ C m2. For the non-linear analysis, the effect of temperature on the stress strain characteristics is considered. The variations of the yield strength and the elastic\u2013plastic property with temperature have been shown in Fig. 5. The coefficient of thermal expansion, thermal conductivity and specific heat also varied with temperature and the functional form of these variations were given in [42]. The software NE/NASTRAN [36] used for the non-linear finite element modelling allows those parameters to be varied with temperature." + ] + }, + { + "image_filename": "designv11_7_0003965_tmech.2014.2316007-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003965_tmech.2014.2316007-Figure3-1.png", + "caption": "Fig. 3. Two-mass model of a biped robot.", + "texts": [ + " This concept is similar to that of the GCIPM, where the trajectory of the body of a biped robot is computed based on the dynamics of the two particles: one for the main body and the other for the swing leg/foot. Typically, expressing the segmented 2-D dynamics of an inverted pendulum, as is usually done in the inverted pendulum mode, is done with respect to the fixed coordinates on the ground [1], [2]. However, in order to make a biped robot turn, the 3-D dynamics need to be considered. The momentum equation for a biped robot model consisting of two rigid bodies shown in Fig. 3 can be written as \u2211 i MO,i = H\u0307O (13) where MO,i is the moment about point O due to the external force or the torque applied at particle i, and HO is the angular momentum about point O. This is defined as HO \u0394= \u2211 i ri \u00d7 (mivi) (14) where mi is the mass of particle i that composes the rigid body, ri is the position vector from point O to the position of the particle, and vi = r\u0307i . This momentum equation can be written as p \u00d7 M p\u0308 + q \u00d7 mq\u0308 + H\u0307O = p \u00d7 Mg + q \u00d7 mg + \u03c4 f (15a) or Mp \u00d7 (p\u0308 \u2212 g) + mq \u00d7 (q\u0308 \u2212 g) + H\u0307O = \u03c4 f (15b) where p and q are the vectors from point O to the center of the main body of the robot and the swing foot, M and m denote the mass of the main body and the swing foot/leg, respectively, HO and \u03c4 f denote the angular momentum of the main body about its center of gravity, point O, and the torque generated at the foot by the friction on the ground, and g denotes the gravitational acceleration" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003257_1.3617043-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003257_1.3617043-Figure1-1.png", + "caption": "Fig. 1 Journal coordinate system", + "texts": [ + " The entire time history of the motion of each part of the system subsequent to arbitrary initial conditions was obtained and examined for stability, frequency response, steady-state characteristics, and sensitivity to unbalance. The detailed treatment of both the lubrication equation and the system dynamics is presented in the following since it can be of interest for related studies. Dynamics Shaft Dynamics The shaft is assumed to be a rigid body and its motion identified with the motion of the geometrical axis. The kinematic parameters involved are shown in Fig. 1. A reference stationary coordinate system is selected so that the x-y plane contains the shaft mass center. The thrust bearings restraining the axial motion of the shaft, are assumed to exist but are not considered in the system. In the present system the unbalance is considered as an external load caused by a point mass (m2) attached to the surface of the shaft in the cross-sectional plane containing the center of mass, and two equal masses (mi) attached to the surface of the shaft each at a distance p\u201e from the aforementioned plane and located symmetrically with respect to the mass center" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003267_j.phpro.2012.10.063-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003267_j.phpro.2012.10.063-Figure5-1.png", + "caption": "Fig. 5. Tensile strength as a function of polar angle and strut diameter, according to [9]", + "texts": [ + " At a higher surface to volume ratio (as in case of small diameters), these notches have a greater influence on the material properties of the whole strut and worsen its behavior [9]. Furthermore, a strong dependency of the Young\u2019s modulus and the polar angle can be recognized. This anisotropic material behavior of additive manufactured parts can also be found in literature, as for example in [7] and [8]. As it can be seen, the values are strongly decreasing for big polar angles. This is due to the bad manufacturability of horizontal struts, which leads to strong geometrical defects. The analogue results for the tensile strength can be seen in Fig. 5. As in case of the Young\u2019s modulus, an influence of the struts diameter as well as the polar angle can clearly be recognized. Furthermore, the worse mechanical properties for bigger polar angles due to the manufacturability can be recognized [9]. The trend of the mechanical properties in dependency of the struts\u2019 diameters leads to the conclusion, that the surface roughness has a strong influence on the mechanical properties of the struts. Therefore, it is necessary to enhance this parameter as much as possible to reach satisfying values" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000742_09544054jem913-Figure11-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000742_09544054jem913-Figure11-1.png", + "caption": "Fig. 11 The part with inside holes, a cone-shaped structure, and a through-hole from left to right: (a) part diagram; (b) (i), (ii) denote section A and B of part, respectively; (c) before machining; (d) after machining", + "texts": [ + "comDownloaded from When scanning of the middle portion of the subzone begins, the front of the middle portion is the portion formed at a relatively high temperature, which will slow down the speed of heat transfer; therefore, the input energy of the middle portion must be reduced greatly. When scanning of the end portion of the subzone begins, the temperature of the front of the end portion is high, but the back of the end portion is the unmelted powder portion at a rather low temperature; therefore the rate of thermal transfer is rapid. Consequently, the required energy of the end portion is slightly greater than that of the middle portion. As a summary, the modified scanning method of filling lines in EBSM is shown in Fig. 10. The part that is shown in Fig. 11(a) includes inside holes of various diameters, a cone-shaped structure with a 20\u030a angle, and a through-hole from left to right. As the part mainly consists of a circle, the split method is used to divide the multi-outline sections into two separate subzones, as shown in Fig. 11(b). The parameters of the melting step are as follows: accelerating voltage, 50kV; beam diameter, 0.3mm; degree of vacuum, 5 \u00b7 10 2 Pa; electron beam current, 2.5\u20133.0mA; the focusing current, 400mA; interspace of the scanning points, 0.15mm; time acting on every point, 3\u20135ms; interspace of the filling lines, 0.15mm; layer thickness, 0.5mm; forming materials, 316L stainless steel powder. The processing time is demonstrated as follows. The height of this part is 45mm and it consists of 90 layers. The total number of layers was 93, of which the initial three layers were cut down by removing the basic plate. The average manufacturing time of each layer is about 120 s. The time of spreading the powder is 20 s. The general time is about 4h. After manufacturing and cooling for 20min, the part is taken out from the vacuum chamber. Because the temperature is not cold enough to take the part out, an oxidation mark is visible on the surface as shown in Fig. 11(c). Figure 11(d) is a photograph of the part after machining. By using the high precision of a Z-axis lift system and the quantificational powder feeder according to the degree of compaction, the error in the Z-axis direction can be neglected. Owing to the heat-affected zone, the outside diameter is greater than the original value (\u00fe0.3mm) and the inside diameter is smaller than the original value ( 0.2mm). These divergences appear more obvious with increasing height. The reason is that the field temperature is increasing continuously and the heat-affected zone is broadened too" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001093_09544062jmes923-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001093_09544062jmes923-Figure1-1.png", + "caption": "Fig. 1 Schematic of the undeformed rotating shaft and coordinates X \u2013Y \u2013Z", + "texts": [ + " The equations of motion are derived with the large deformation assumption and then are transformed to the complex form. The non-linearity is due the extension of shaft centre-line (stretching non-linearity). The frequency\u2013response curves are plotted for the first two modes. It is shown that these resonance curves are of the hardening type. The effects of eccentricity and damping coefficient are investigated on the steady-state response of the rotating shaft. To verify the perturbation results, a numerical method is used, and a good agreement is shown. Figure 1 shows the schematic of a rotating shaft. Frame X \u2013Y \u2013Z is an inertial coordinate system.The axes x\u2013y\u2013z are local coordinates, which are the principal axes of the shaft cross-section. The axes are attached to the centre-line of the deformed shaft (Fig. 2) at position x. Displacements of a particle in arbitrary location x along X , Y , and Z axes are u(x, t), v(x, t), and w(x, t), respectively. The following assumptions are employed: (a) the shaft has uniform circular cross-section, and it spins about longitudinal axis X with a constant speed ; (b) the shaft is slender and shear deformation is neglected. Rotary inertia and gyroscopic effects are considered; (c) rotating shaft is simply supported; (d) supports O and O\u2019 of the shaft are fixed along the X -axis (Fig. 1); (e) the only dissipating mechanism in the system is the external viscous damping; and (f) amplitude is large, and stretching non-linearity due to extension of shaft centre-line is considered [1, 5]. The relation between the original frame X \u2013Y \u2013Z and the deformed frame x\u2013y\u2013z is described by three successive Euler angles \u03c8(x, t), \u03b8(x, t), and \u03b2(x, t) as shown in Fig. 3. First, the X \u2013Y \u2013Z system is rotated by an angle \u03c8 about the Z-axis to an intermediate coordinate system X1\u2013Y1\u2013Z . Then, the X1\u2013Y1\u2013Z system Proc" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003756_j.triboint.2014.09.023-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003756_j.triboint.2014.09.023-Figure1-1.png", + "caption": "Fig. 1. FE-models (top) and bearing design (bottom) of different bearing types.", + "texts": [ + " The basic approach for calculating the change in the load-carrying capacity due to elastic deformations and the calculation of the elasticity factors can be assumed from [16]. However, the elastic deformations of a bearing differ, depending on the structural design of the bearing shell and the adjoining housing. Yet, with adequate accuracy, the large number of possibilities can be reduced to a small number of basic types. Three possible basic types of bearing/housing designs are illustrated in Fig. 1. In Tribo-X the different, pressure-related elastic deformations of the three basic types are accounted for with so-called elasticity matrices, which are derived from FEM calculations (Finite Element Method) and are explained in detail in [6]. Moreover, to derive new elasticity factors from the numerical calculations, the following simplifications had to be made: no dependence of the viscosity and density on temperature and pressure no lubricant feed pressure, calculation with complete filling of the bearing neglect of the shaft deformation use of ideally smooth surfaces", + " The elastic properties of the materials are described in the analytical model with a reduced Young\u2019s modulus E\u2019. Since the shaft generally has a considerably greater Young\u2019s modulus than the bearing shell, it is assumed to be rigid. The Young\u2019s modulus of the bearing shell depends on the design of the bearing, which usually consists of a steel back and one or several sliding layers. In addition, the Young\u2019s modulus of the bearing housing needs to be taken into consideration, where the design of the housing can vary, see Fig. 1. However, when determining the reduced Young\u2019s modulus, it is not necessary to consider the entire housing in the calculation. Analyses of different model limits by means of the finite element method have shown that it suffices to limit the bearing environment to the double bearing radius (see Fig. 1). The following equation in combination with Fig. 1 can be used to determine the reduced Young\u2019s modulus for the new approach: 1 E' \u00bc \u03a3 n i \u00bc 1 hi htotal 1 Ei\u00f01 \u03bd2i \u00de \u00f010\u00de Calculations for the three bearing types in Fig. 1 were conducted for the B/D ratios\u00bc{0.25; 0.5; 0.75; 1.0} and Sommerfeld numbers So\u00bc{0.5; 1; 5; 10; 50} to determine the elasticity factors KE. The differences in the elasticity factors between the bearing types are mainly due to the varying elastic deformations. For illustration purposes, the different film thicknesses across the bearing width in the range of the minimum oil film thickness are illustrated in Fig. 2 with B/D\u00bc0.5 and So\u00bc10 as an example for one bearing size. The minimum oil film thickness hmin of the journal bearing is required for calculating the elasticity factor", + " In addition, it becomes apparent with bearing type A that the elasticity factors for a constant Sommerfeld number increase with rising B/D ratio. The lower limit is an elasticity factor of KE\u00bc1, with which the elastic deformation does not affect the minimum oil film thickness. The curves in Fig. 3 illustrate that elastic deformations can be ignored with Sommerfeld numbers of Soo1. The curve parameters a1 to a4 required for calculating the elasticity factor KE according to Eq. (11) are listed in Table 1 for bearing type A. As illustrated in Fig. 1, bearing type B contains a circumferential groove in the centre of the housing because of the oil supply and/or light-weight design. As shown in Fig. 2, greater necking occurs at the edges of the bearing as a negative consequence of the increased elasticity in the centre of the bearing. Due to the same proportions in all FE-models the B/D ratio has a major influence on the deformation of the bearing. Hence, at small B/D ratios the elastic deformation of bearing type B is similar to the deformation of bearing type A", + " In so doing, the elastic deformation of the bearing shell in the form of elasticity matrices and \u2013 in contrast to the analytical calculation \u2013 the surface roughness in the form of flow factors and solid contact pressure curves were taken into consideration [5]. As illustrated in Fig. 7 using bearing 2 as an example, the elasticity matrices were derived from FE models of real bearing and housing for the comparison with the bearing type A. In contrast, the elasticity matrices for bearing types B and C were calculated using idealised housing geometries as illustrated in Fig. 1. The flow factors and solid contact pressure curves were determined based on 3D surface measurements of real plain bearing surfaces as in [5]. Deviating from the analytical calculations, the pressure dependence of the viscosity and density, the oil supply through a pocket as well as the occurrence of cavitation were additionally considered in the numerical calculations, to obtain the best possible reference for comparison. More details about the calculation model and the used input parameters are provided in [5,24]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000395_0094-114x(80)90004-x-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000395_0094-114x(80)90004-x-Figure2-1.png", + "caption": "Figure 2. Element oriented system co-ordinates.", + "texts": [ + " This implies that three system coordinates are defined at each intermediate node within a link in the directions matching with the element oriented element co-ordinate system attached to that link. For nodes connecting the end points of several links, three system co-ordinates for each of the links are defined as in case of the intermediate nodes and thus the total number of the system co-ordinates for each of such nodes is equal to three times (for planar mechanisms) the number of the links attached to that node. Examples for this kind of system co-ordinates are shown in Fig. 2. After completing the assembly of the element matrices in eqn (13) by code-system [I], the correponding system matrices are formed and the equation of motion for the whole system is rewritten in n numbers (say) of the system co-ordinates as follows: M f l + 2Cd(J + 2C~(J + ( K ~ + to2K~)U = P (14) where hi c = Z ;toM ./=1 hi C e = /=t [C/2 cos (j - 1)tot + Q2 sin jto~'] hi K ~ = ~ [K i' cos (j - 1)toz + K 2 sin jtor] (15) j=l hi K V = ~ /=1 [K~ 3 cos (j - 1)tor + K~ sin jtor] hi i=1 [Pj' cos (j - 1)to~\" + pj2 sin jtor] and U = n \u00d7 1 unknown displacement vectors in the system co-ordinates" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003534_978-1-4419-6022-1-Figure7.13-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003534_978-1-4419-6022-1-Figure7.13-1.png", + "caption": "Fig. 7.13 Working principle of laser", + "texts": [ + " This is a very important feature in many biosensor applications using fluorescent dyes, where each fluorescent dye must be excited with different color. A laser diode is a special type of LED that generates laser, which is a coherent beam of light that is extremely monochromatic. Figure 7.12 in the previous page shows the extremely monochromatic character of laser in comparison with LED. Let us begin our study with laser first. Laser is an acronym for light amplification by stimulated emission of radiation. Figure 7.13 shows a basic apparatus for generating laser. Two mirrors are sandwiching a small column, called gain medium. In a HeNe laser, the earliest yet still very popular type of lasers, the gain medium is helium-neon gas. When a DC voltage is applied into this gain medium, photons are generated at a very specific wavelength. For HeNe laser, l \u00bc 633 nm (red color). These photons will bounce back and forth between two mirrors, thus amplifying the light intensity. The right mirror is made partially transparent, and some of this amplified, monochromatic light can escape from the system" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000037_811309-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000037_811309-Figure2-1.png", + "caption": "Fig. 2 \u2014 Finite element idealization of the 30\u00b0 wedge sector used in the analysis of a pre-loaded cylinder subjected to small superposed torsional and axial vibrations.", + "texts": [ + " (19) were determined from experimental test data for uni-axial storage and loss modulus and the results were fitted to the following: gc(w) Acw be' gs (w) = Asw-bs The fitted parameters are as follows: As = 0.192940 Ac = 0.052743 bs = 0.846 be = 0.952 The problem was solved numerically on Ford's Cyber 176 computer using sixteen (16) three-dimensional isoparametric elements. Since there is no angular dependence of the displacement and stress fields, it was necessary to model only a wedge from the cylinder (Fig. 2). The full length of the cylinder (9, = 0.5 in.) was represented with four elements in the axial direction and four in the radial direction. The wedge angle was chosen arbitrarily to be 30 degrees; the angular span was represented by one element. The cylinder was compressed to a stretch ratio of A\u00b0 = 0.785 and then subjected to twist increments up to a total twist of ifro = 0.4 radians/inch. The closed form solution for stresses oPzz, croz andthe normal force No, torque To, static str static Green Lagrange strain components Ezz, Ebz are given in the Appendix" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001621_j.actaastro.2009.10.037-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001621_j.actaastro.2009.10.037-Figure1-1.png", + "caption": "Fig. 1. Geometry of the proposed tethered satellite system.", + "texts": [ + " The formulation of both the control laws to account for tether failure is also described. For a detailed assessment of the performance of the proposed attitude control strategies, numerical simulations are shown in Section 4. In Section 5, we present the main conclusions obtained from this study. The investigation is initiated by formulating the equations of motion of the proposed TSS moving in a circular orbit. The proposed system model assumes a downward deployment of a small auxiliary mass from the satellite through a two-tether system (Fig. 1). Two identical tethers are attached to the satellite at two distinct points symmetrically offset from its mass center and below the satellite\u2019s principal z-axis. The other ends of the two tethers are connected to an auxiliary mass. The auxiliary mass (m2) is assumed to be much smaller than the main satellite mass (M) and is hence treated as a particle. The main purpose of the study proposed in this paper is to access the dynamics of the tethered system when the tether attachments points are used as control actuators" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003201_j.mechmachtheory.2013.04.003-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003201_j.mechmachtheory.2013.04.003-Figure4-1.png", + "caption": "Fig. 4. Incremental rotation minimization.", + "texts": [ + " The interesting features of preservation of the length, dying-out of motion and eventual aligning of the curve along the perturbation is discernible in the simulations and accompanying animation files. In the previous section, we presented a metric that expresses minimization of velocities of the trailing end for a given input velocity of a leading end. In this section, we present two additional possible metrics. In Section 5, we compare these metrics. Consider a straight rigid segment AP and the leading end P is moved to pointQ. Wewish to obtain themotion of the trailing end A such that the straight rigid segment rotates the least. In Fig. 4, point A is schematically shown to move to B and hence the rotation angle is given by \u2220BQR where line QR is parallel to AP. We now pose a minimization problem: Minimize xB ;yB : \u2220BQR\u00f0 \u00dej j Subject to : BQj j \u00bc L Data : L; Step Length PQ It may be noted that minimization of the rotation is in the same spirit as the L2 velocity minimization discussed in the previous section. Since a general rigid body motion can be considered to be a combination of translation and rotation, a solution of the above problem in combination with the tractrix approach may result in more natural rigid-body motions" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002943_j.jbiomech.2012.08.038-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002943_j.jbiomech.2012.08.038-Figure1-1.png", + "caption": "Fig. 1. The two representations used of the human body. (a) Mechanical model: simple model: linearized inverted pendulum, i.e. the CoM travels at a constant height h.", + "texts": [ + " (2010) for biped robot walking situations to human balance recovery tasks. The resulting balance recovery model will be used to predict the step lengths for different experimental data sets from the literature by employing simple models of human body and inputting the step timings. In this study, the balance recovery is considered only in the sagittal plane using a mechanical model of the human body placed in closed loop with a controller. This mechanical model is an inverted-pendulum-plus-foot model representing the support limb (see Fig. 1a). The trailing limb is not explicitly modeled and its influence on the system dynamics is neglected. The length of the pendulum is constant for each step but can change from one step to another. The resulting trajectories of the Center of Mass (CoM) are thus circles of possibly different diameters (see Fig. 5) and can experience only instantaneous double support phases. The feedback loop is based on a Model Predictive Control (MPC) approach (Fig. 2), using an internal model which can be different and simpler than the real mechanical model", + " The adequate control actions are then selected by minimizing this cost function, given the current state of the system. The controller implemented in this study is largely based on the Linear MPC (LMPC) recently proposed by Herdt et al. (2010). The internal model used here is a classical Linear Inverted Pendulum (LIP) model (Kajita and Tani, 1991), consisting of two massless feet and legs, the whole body mass being concentrated at its CoM. The height of the CoM is considered constant and the contact forces below the feet are reduced to a single force acting at the Center of Pressure (CoP) (Fig. 1b). The resulting dynamic equation can be written then as \u20acxcom \u00bc g h \u00f0xcom xcop\u00de, \u00f01\u00de where g is the norm of gravity force, h is the height of CoM, and xcom and xcop are respectively the coordinates of the CoM and CoP along the X axis (see Fig. 1b). The timing of the foot contacts (take-off and landing) is fixed in advance. It consists of: inv a reaction time, Treac , between the onset of the perturbation and the beginning of the reaction (activation of the controller), an additional delay, the step preparation time Tprep , considered before the initiation of the first step, the durations of the further steps (delay between contralateral feet landings) defined by the values of Tstep. Future actions are predicted over a time horizon of duration Thorizon \u00bc 1 s, over which the constraints on the CoP with respect to the positions of the feet on the ground are checked every Tsampling \u00bc 25 ms", + " In order to compare our prediction model with experimental data, we need experimental situations which: (1) involve single and multiple steps recovery strategies; (2) involve relatively simple perturbations in order to avoid complex perception models at this stage; (3) provide sufficient details about the perturbation, the delays and the resulting recovery steps. We used data from two studies that comply with these requirements. They focus on tether-release conditions, a common experimental protocol in which the subjects are inclined to a stationary forward leaning position thanks to a tether and a safety harness (c.f. Fig. 1) and released in this unstable posture. These studies the study from Hsiao-Wecksler and Robinovitch (2007) reports the maximum inclination angles for single-step recovery given a specific step length. Young subjects were inclined forward and asked to recover balance after release by taking a single step, no larger than a given target length. The maximum lean angle for four target lengths, averaged across subjects, were used as inputs to our model. The predicted step lengths are compared to the target lengths" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000715_3.61139-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000715_3.61139-Figure2-1.png", + "caption": "Fig. 2 Rotating rotor blade coordinate system.", + "texts": [ + " For air resonance and ground resonance, in hover and on the ground, respectively, vertical translation and yaw rotation of the body are insignificant. In this analysis, therefore, only longitudinal translation X, lateral translation 7, body roll $x, and body pitch $y are included. The landing gear provides stiffness and damping restraining X,Y,$x,$y motion depending on the landing gear geometry. The rotor blades are attached to the hub and rotate at constant angular velocity !}. The azimuth angle of the kin blade is ^=fl/ + (2ir/b]\\(k- 1). The blade axis system and built-in angular offsets for the kin blade are illustrated in Fig. 2. A simplified schematic of the rotor blade model is shown in Fig. 3 with all deformations and built-in angular offsets equal to zero. Details of the pitch-control systems are to be discussed. The pitch angle of the rotor blade may be changed by various types of control systems. In order to model several representative types of pitch-control systems, four model configurations were selected, schematically shown in Fig. 4. Case I, for which there is no control system, is the simplest. D ow nl oa de d by R E N SS E L A E R P O L Y T E C H N IC I N ST IT U T E o n M ar ch 5 , 2 01 5 | h ttp :// ar c" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003288_1.4025234-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003288_1.4025234-Figure3-1.png", + "caption": "Fig. 3 The connection of a face tooth", + "texts": [ + " With the mass and rigidity of a central tie rod counted in, an equivalent mass diameter and stiffness diameter can be defined as follows: dmi \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4mi=\u00f0pqLi\u00de p (9) dki \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi E\u00f0D4 i d4 i \u00de 4 q (10) 2.2.2 Impellers and Contact Stiffness Analysis. The heavy gas turbine has many stages of compressor and turbine impellers, and the impellers are connected with each other via a face tooth located in the top part of the impellers as shown in Fig. 3. In the model, the impeller is simplified as two nodes, and an elastic axis is set between the two nodes. Considering the mass of the blade installing on the impeller and the contact effect on the meshing area of the face tooth, the dm and dk of the impeller can be defined: 122505-2 / Vol. 135, DECEMBER 2013 Transactions of the ASME Downloaded From: http://gasturbinespower.asmedigitalcollection.asme.org/ on 05/06/2015 Terms of Use: http://asme.org/terms dmi \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4mi=\u00f0pqLi\u00de \u00fe 4m0i=\u00f0pq0Li\u00de q (11) dki \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi kE\u00f0D4 i d4 i \u00de 4 q (12) 2" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002287_iros.2012.6385948-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002287_iros.2012.6385948-Figure1-1.png", + "caption": "Fig. 1. System decomposition: Under-actuated postural system and upperlimbs impedance subsystems", + "texts": [ + " Conversely, motor activity related to the task adapts to constraints related to postural balance. The optimization of the overall performance implies a particular organization of the motor response with the aim to effectively coordinate the APAs and the focal activity [2]. One might be tempted to translate these principles observed in humans to control whole-body movement coordination of humanoid robots under external perturbations. From a mechanical point of view, they can be seen as parallel coupled sub-systems (see Fig. 1). The upper-limbs can be considered as adjustable mechanical impedances connected to an under-actuated mechanical platform sustentated on the ground by unilateral joints in a dynamic equilibrium through the lower-limbs motions. Motions of these subsystems induce mutual perturbations [3] and their behavior is affected by the interaction dynamics. The control issue of these interacting sub-systems having coupled dynamics and decoupled constraints and objectives can be addressed using a distributed model predictive control (DMPC) technique [4]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003499_s11771-013-1495-x-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003499_s11771-013-1495-x-Figure1-1.png", + "caption": "Fig. 1 Point contact of general profiles", + "texts": [ + " When the friction between the tooth flanks is out of consideration, only normal contact force exists; when considering the point contact, the elliptic contact zone is only a fraction of tooth flank (without regarding to edge contact), and their principal relative radii of curvature are rather small. Therefore, the theories of contact mechanics is applicable to studying the contact stresses and deformations of face gear loaded. 2.1.1 Hertz theory on normal contact of elastic solids for general profiles A normal force P is applied between the profile 1 and profile 2 (see Fig. 1). Before deformation, the separation between the corresponding points S1 and S2 is h. During the compression, distant points M1 and M2 move towards point O, parallel to z axis, by displacements \u03b41 and \u03b42. The profiles would overlap with the assumption of non-deformation, just like the dotted lines in Fig. 1. Due to the pressure, the profiles are displaced by amounts u1 and u2 relative to the distant points M1 and M2. The corresponding points S1 and S2 should satisfy the displacement compatibility conditions, which is determined as follows: Inside the contact zone: Or, outside the contact zone: 1 2u u h (2) The equations of profiles can be outspreaded by Maclaurin Series. When the radii of curvature of the profiles are large enough, higher order terms are neglected: 2 2 1 1 1 1 1 1 1 1z A x C x y B y 2 2 2 2 2 2 2 2 2 2( )z A x C x y B y (3) When a proper coordinate system is adopted, C1 and C2 come to zero, and A1, B1, A2 and B2 are relative to the principal radii of curvature" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000812_mobhoc.2007.4428594-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000812_mobhoc.2007.4428594-Figure1-1.png", + "caption": "Fig. 1. Heterogeneous WSN.", + "texts": [ + " INTRODUCTION In this paper we address topology control in heterogeneous WSNs consisting of two types of wireless devices: resource-constrained wireless sensor nodes deployed randomly in large numbers and a much smaller number of resource-rich supernodes, placed at known locations. The supernodes have two transceivers, one to connect to the wireless sensor network (WSN), and another to connect to the supernode network. The supernode network provides better QoS and is used to quickly forward sensor data packets to the user. With this setting, data gathering in heterogeneous WSNs has two steps: first, sensor nodes transmit and relay measurements on multihop paths towards a supernode (see Figure 1). Once a data packet encounters a supernode, it is forwarded using fast supernode-to-supernode communication toward the user application. Additionally, supernodes could process sensor data before forwarding. 1-4244-1455-5/07/$25.00 c\u00a92007 IEEE A study by Intel [9] shows that using a heterogeneous architecture results in improved network performance, such as lower data gathering delays and a longer network lifetime. Hardware components of the heterogeneous WSNs are now commercially available [4]", + " However, these algorithms are centralized. Our work differs from the work in [15] by considering a heterogeneous WSN architecture. In this paper, we propose a centralized algorithm - GATCk - that minimizes the maximum transmission range, and a distributed and localized algorithm - DATCk - that is feasible for practical deployment of large scale WSNs. We consider a heterogeneous WSN consisting of two types of wireless devices: resource-constrained wireless sensor nodes and resource-rich supernodes, as illustrated in Figure 1. Sensor nodes have low cost, limited battery power, short transmission range, low data rate, and a low duty cycle. The main tasks performed by a sensor node are sensing, data processing, and data transmission/relaying. Supernodes have two radio transceivers, one for communication with sensor nodes and the other which is used to communicate with other supernodes. Supernodes are more expensive, have more power reserves, higher data rates, and better processing and storage capabilities than sensor nodes" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003117_1.3616998-Figure9-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003117_1.3616998-Figure9-1.png", + "caption": "Fig. 9 Stat ionary specimens assembly", + "texts": [ + " The pressure of the gas in the cylinder presses the head of the piston rod against the restraining block (3). When the force between the two specimens exceeds the force of the gas in the pneumatic cylinder on the piston, the head of the piston rod moves back from the restraining block, and the ram and piston rod move together and fur ther compress the gas. T h e forward motion of the ram is stopped by an auxiliary hydraulic system in the broaching machine. A more detailed view of the assembly holding the stat ionary specimen is shown in Fig. 9. The head of the piston rod is labeled (1) and the restraining block (2). Three screws (3) serve as a coarse adjus tment for the alignment of the two specimens. The stat ionary specimen is the ' /Vin-dia hardened steel rod labeled (4). Oil is placed on the surface of this specimen. The impact block (5) is initially lapped flat with the specimen (4), bu t then is made to project, ahead of it by the inserted shim (6). The thickness of the shim controls the minimum film thickness attained in an experiment" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003350_1.j051530-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003350_1.j051530-Figure3-1.png", + "caption": "Fig. 3 Three states of the membrane element.", + "texts": [ + " Material Modification for Wrinkling Analysis of Before the PVP for the 2-D bimodular problem is established, it is worthwhile to clarify the relationship between the bimodular problem and wrinkling of membranes. A membrane is a very thin elastic sheet that has extremely low bending stiffness and no compressive resistance.Amembranewillwrinklewhen a compressive or shear load is applied. In the past years, various wrinkling models and many computational methods for wrinkling analysis have been developed. The representative material modification models can be found in [21\u2013 24].According to these studies, the three states of themembrane canbe illustrated as shown in Fig. 3, and the three wrinkling criteria are summarized in Table 1. Inspired by the idea of material modification, the authors attempt to use the bilinear constitutive model to simulate the wrinkling of membranes. Specifically, the compressive resistance of material is removedby setting the compressivemodulus as zero,which is a special case of the bimodular problem. For the convenience of description, the element a12 in the elasticity matrix D can be denoted as R, i.e., v =E R. WhenE and v are taken as infinitesimals, R and R2 are both extremely small" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001825_icma.2009.5246308-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001825_icma.2009.5246308-Figure2-1.png", + "caption": "Fig. 2 The structure ofthe proposed microrobot", + "texts": [ + " Then the diving/surfacing experiments were realized by the characteristic of electrolysing water around the IPMC surface. And the last is our conclusions. 978-1-4244-2693-5/09/$25.00 \u00a92009 IEEE 3330 C. Mechanism and the Model ofthe rotating Motions The rotating example in counter clockwise is shown in Fig.5. From c to d, the drivers push the body to rotate. In the other time, the drivers are pushed up by supporters to prepare for the next stroke [14]. (I) (2) A. The Structure ofA Proposed Biomimetic Microrobot The structure of a proposed bimimetic microrobot is shown in Fig.2, which is a centrosymmetric structure and 8 legs are symmetrically distributed around its symmetry center. It is 33mm in length, 56mm in width and 9mm in height. It has 8 pieces of IPMC actuators, from A to H. A, B, C and D are called the drivers, and their bending directions are shown in Fig.3. The other 4 pieces of actuators are supporters. The actuators are all Ilmm in length, 3mm in width and O.2mm in thickness. On one side of the robot, the distances between two drivers or between a driver and a supporter are all of 10mm" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002340_j.triboint.2011.10.017-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002340_j.triboint.2011.10.017-Figure3-1.png", + "caption": "Fig. 3. Thrust pad showing center of pressure.", + "texts": [ + " Pi\u00fe1,j Ri,jH 3 i,j DR2mi,j \u00fe Ri\u00fe1,jH 3 i\u00fe1,j mi\u00fe1,jDR2 \" # \u00fePi 1,j Ri,jH 3 i,j DR2mi,j \u00fe Ri 1,jH 3 i 1,j mi 1,jDR2 \" # \u00fePi,j\u00fe1 H3 i,j Ri,jmi,jb 2Dy 2 \u00fe H3 i,j\u00fe1 Ri,jmi,j\u00fe1b 2Dy 2 2 4 3 5 \u00fePi,j 1 H3 i,j Ri,jmi,jb 2Dy 2 \u00fe H3 i,j 1 Ri,jmi,j 1b 2Dy 2 2 4 3 5 \u00fePi,j 2 Ri,j DR2 H3 i,j mi,j Ri\u00fe1,j mi\u00fe1,j H3 i\u00fe1,j DR2 Ri 1,j mi 1,j H3 i 1,j DR2 \" 2 H3 i,j Ri,jmi,jb 2Dy 2 H3 i,j\u00fe1 Ri,jmi,j\u00fe1b 2Dy 2 H3 i,j 1 Ri,jmi,j 1b 2Dy 2 3 5 \u00bc 6Ri,j Dy \u00bdHi:j\u00fe1 Hi,j 1 \u00fe12Ri,jbV \u00f013\u00de The calculation procedure uses these pressures along with numerical methods for integration to obtain the load capacity, radial and angular location of center of pressure. Fig. 3 shows the location of the center of pressure on the thrust pad. This yields the non-dimensional pressure at each node. Solution of the energy equation is also set up in finite differences. The propagation method is used to solve the equation in view of its first order. The initial temperature at the leading edge is specified so that successive values of the downstream temperature are marched out in the flow direction. In this procedure, taking hot oil carry over effect into consideration the temperature distribution is obtained in a single sweep" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003499_s11771-013-1495-x-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003499_s11771-013-1495-x-Figure5-1.png", + "caption": "Fig. 5 Contact stress of meshing point 6", + "texts": [], + "surrounding_texts": [ + "J. Cent. South Univ. (2013) 20: 354\u2013362\n357\n2.1.4 Calculation procedures of maximal Hertz contact stresses.\n1) Follow the rules on the sign of principal curvatures, and take \u03c111, \u03c112, \u03c121 and \u03c122 in Table 2 into Eq. (5), then the values of A and B are obtained.\n2) Use the numerical method to solve the value of e in the first formula of Eq. (9).\n3) When the torque T (1 600 N\u00b7m) is determined, through Eq. (11), the values of normal contact force P on every meshing point can be gotten.\n4) Bring the values of e and P into Eq. (10) and solve the values of a and b. The maximal contact stress is obtained in the third formula of Eq. (10).\nFollowing the procedures above, the results can be obtained, as listed in Table 3.\nTable 3 shows that, the semi-major axis at meshing point 1 reaches 49.14 mm, while the face width is 88 mm, so the contact zone exceeds the gear surface. In this situation, it mismatches the conditions of elastic half-space theory, and the value of contact stress is smaller. The edge contact exists, and there is a stress concentration.\nIn order to validate the results of analytical method above, and determine the mesh amounts of FEM model for an exact value of contact stress, a single tooth FEM model was created under the same torque, namely T=1600 N\u00b7m. In the meshing coordinate system without assembly errors, the models of face gear and pinion are built. Finite element analyses were introduced in detail in Ref. [6], so we can give the same boundary condition as Ref. [6]. But the values of contact stresses could not be determined exactly, before a proper mesh size is given. With the contrast between the results of these two methods, different mesh amounts are continuously attempted, and the balance achieves. At last, the proper mesh size is found, and the results become more reliable.\nAs shown in Fig. 4, after installation, the face gear and pinion both take the right meshing position. In Table 2 and Fig. 3, there are eleven positions to calculate. The first meshing point is point 6; as for other points, we need to rotate the right rotation angle at Table 2 around their axes.\nIn the step module of ABAQUS, with the contact stress of history output and field output, and we can get the relative results. The output of CPRESS is the contact stress that we need, because there is no friction in the model [14]. Figures 5\u20136 are the cloud pictures of meshing point 6 and meshing point 1, respectively, and it states that the edge contact happens at meshing point 1. The results of two methods are described, and compared in detail as listed in Table 4.\nFor the meshing points close to the addendum, their semi-major axes are longer, while their contact stresses are less. The meshing points 1 and 2 are close to the addendum, so the results are slightly unreliable. As shown in Fig. 6 and Table 4, the edge contact appears at meshing point 1. Due to the existence of edge contact,", + "J. Cent. South Univ. (2013) 20: 354\u2013362 358\nthe analytical method fails, and the error in contrast is vast. The stress concentration happens in ABAQUS at point 1. At every meshing point except points 1 and 2, the errors of contact stresses are all below 10%, and the contact forces of two methods have identical value. It is proved that the two methods of contact stress calculation are verified by each other.\nTaking the face-gear parameters into account as shown in Table 1, we can build the FEM models with multi-tooth in ABAQUS [15], which is used to the loaded meshing simulation. The contact stresses are calculated in the FEM models with five teeth, and the middle tooth have refined mesh, whose size should come up to one of single tooth FEM model mentioned above. To research the transmission error and maximal load distribution factor, the model with seven teeth is necessary, because the contact ratio of face gear is greater than two. The finite element analysis models are shown in Figs.7\u20138. The FEM on face-gear are proposed in Refs. [6\u20137], in which all degrees of freedom of the gear are fixed, and the torque on the pinion about its rotation axis is applied. We would like to take this method as the loaded analysis, not a loaded meshing simulation. To achieve this, we give an angular displacement on the coupling point of pinion, which is about the rotation axis, so the gear can rotate with the pinion by the contact ratio; the torque is applied on the coupling point of gear, and the degree of freedom about its rotation axis should be released, as shown in Fig. 7.", + "J. Cent. South Univ. (2013) 20: 354\u2013362\n359\nWhen the contact ratio is larger than two, it means that there are three teeth in contact at the same time. In this situation, a seven teeth model is required, because five teeth are not enough to research transmission errors and load distribution factor. 3.2.1 Outputs for transmission errors of face-gear drive\nDuring the loaded meshing simulation, the loaded transmission error is computed at every rotation position. The angular displacements of the pinion and gear are\nrecorded at any moment of simulation. Then, the loaded transmission error is defined by\n1 1 2\n2\nz\nz\n (13)\nwhere \u0394\u03b51 and \u0394\u03b52 are the angular displacements of the pinion and gear, respectively, z1 and z2 represent the tooth number, and \u0394\u03b5 is the loaded transmission error.\nIn the history outputs of ABAQUS, the angular displacements of the coupling points of gear and pinion are recorded at every moment. Through Eq. (13), the loaded transmission error is obtained (see Fig. 9). The conclusion shows that, under different torques, the transmission errors are presented in different levels. The amplitude increases with the loaded torque, while the transmission is steadier.\n3.2.2 Outputs for load distribution factor of face-gear drive\nIf the contact ratio is larger than two, there are two or three pairs of teeth in meshing. Under a torque, the total contact force is constant, which is decided by Eq. (11). The ABAQUS can export contact force of every contact pair, recorded in the history of outputs as CNORMF (see Fig. 10). Assuming that the contact force of contact pair 2 is P2, while P1 and P3 represent the contact forces of contact pair 1 and 3, respectively, we can obtain the load distribution factor of the contact pair 2 by\n2 p\n1 2 3( )\nF C\nF F F (14)\nAt last, computed with Eq. (14), the load distribution factor of the contact pair 2 is shown in Fig. 11, and its maximum value is gotten in the posted process of ABAQUS. Obviously, the contact force of a" + ] + }, + { + "image_filename": "designv11_7_0002222_9783527627646-Figure7.7-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002222_9783527627646-Figure7.7-1.png", + "caption": "Figure 7.7 Typical impeller types: (a) a six-flat blade turbine; (b) a two-flat blade paddle; (c) a three-blade marine propeller. See the text for details of the abbreviations.", + "texts": [ + "1 General Stirred (agitated) tanks, which are widely used as bioreactors (especially as fermentors), are vertical cylindrical vessels equipped with a mechanical stirrer (agitator) or stirrers that rotate around the axis of the tank. The objectives of liquid mixing in stirred tanks are to: (i) make the liquid concentration as uniform as possible; (ii) suspend the particles or cells in the liquid; (iii) disperse the liquid droplets in another immiscible liquid, as in the case of a liquid\u2013liquid extractor; (iv) disperse gas as bubbles in a liquid in the case of aerated (gassed) stirred tanks; and (v) transfer heat from or to a liquid in the tank, through the tank wall, or to the wall of coiled tube installed in the tank. Figure 7.7 shows three commonly used types of impeller or stirrer. The six flatblade turbine, often called the Rushton turbine (Figure 7.7a), is widely used. The standard dimensions of this type of stirrer relative to the tank size are as follows: d=D \u00bc 1=3 D \u00bc HL d \u00bc Hi L=d \u00bc 1=4 b=d \u00bc 1=5 where D is the tank diameter, HL is the total liquid depth, d is the impeller diameter, Hi is the distance of the impeller from the tank bottom, and L and b are the length and width of the impeller blade, respectively. When this type of impeller is used, typically four vertical baffle plates, each onetenth of the tank diameter in width and the total liquid depth in length, are fixed perpendicular to the tank wall so as to prevent any circular flow of liquid and the formation of a concave vortex at the free liquid surface", + " When liquid mixing with this type of impeller is accompanied by aeration (gassing), the gas is supplied at the tank bottom through a single nozzle or via a circular sparging ring (which is a perforated circular tube). Gas from the sparger should rise within the radius of the impeller, so that it can be dispersed by the rotating impeller into bubbles that are usually several millimeters in diameter. The 112 | 7 Bioreactors dispersion of gas into bubbles is in fact due to the high liquid shear rates produced by the rotating impeller. Naturally, the patterns of liquid movements will vary with the type of impeller used. When marine propeller-type impellers (which often have two or three blades; see Figure 7.7c) are used, the liquid in the central part moves upwards along the tank axis and then downwards along the tank wall. Hence, this type of impeller is categorized as an axial flow impeller. This type of stirrer is suitable for suspending particles in a liquid, or for mixing highly viscous liquids. Figure 7.7b shows a flat-blade paddle with two blades. If the flat blades are pitched, then the liquid flow pattern becomes intermediate between axial and radial flows. Many other types of impeller are used in stirred tanks, but these are not described at this point. Details of heat transfer in stirred tanks are provided in Sections 5.4.3 and 12.3. 7.4.2 Power Requirements of Stirred Tanks The power required to operate a stirred tank is mostly the mechanical power required to rotate the stirrer. Naturally, the stirring power varies with the stirrer type", + " Live steam is often used to sterilize the inside surfaces of the fermentor, pipings, fittings, and valves. Instrumentation for measuring and controlling the temperature, pressure, flow rates, and fluid compositions, including oxygen partial pressure, is necessary for fermentor operation. (Details of these are available in specialty books or catalogues.) 12.2 Stirrer Power Requirements for Non-Newtonian Liquids Some fermentation broths are highly viscous, and many are non-Newtonian liquids, that follow Equation 2.6. For liquids with viscosities up to approximately 50 Pa s, impellers (see Figure 7.7a\u2013c) can be used, but for more viscous liquids special types of impeller, such as the helical ribbon-type and anchor-type, are often used. When estimating the stirrer power requirements for non-Newtonian liquids, correlations of the Power number versus the Reynolds number (Re; see Figure 7.8) for Newtonian liquids are very useful. In fact, Figure 7.8 for Newtonian liquids can be used at least for the laminar range, if appropriate values of the apparent viscosity ma are used in calculating the Reynolds number" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003308_1.1656477-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003308_1.1656477-Figure1-1.png", + "caption": "FIG. 1. Sessile drop of width wand height h.", + "texts": [ + " INTRODUCTION The shape of a drop of liquid sitting on an inert plaque is determined by a balance between gravity, which tends to flatten the drop, and surface tension, which tends to form a spherical drop. Bashforth and Adams l (hereafter referred to as BA) equated the pressure due to gravity to the pressure due to surface tension and obtained a nonlinear differential equation, of which thev obtained numerical solutions. The essen tial features' of their treatment are as follows: taking the origin of coordinates at the top of the drop, with z measured into the drop, the shape is given by a function, z(x), Fig. 1. The size of the drop is characterized by a length parameter b, the radius of curvature of the drop profile at the origin. The shape is characterized by a parameter (3=pgb2/y, where p is the density difference between the liquid drop and the surrounding fluid, g the gravitational constant, and 'Y the surface tension of the interface between the liquid and the surrounding fluid. A parametric solution is obtained in two func tions, x(cp)/b and z(cp)/b, where cp is the angle between the negative z axis and the normal to the profile at the position z(x)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003350_1.j051530-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003350_1.j051530-Figure5-1.png", + "caption": "Fig. 5 Bar with bimoduli in tension and compression.", + "texts": [ + " D ow nl oa de d by D re xe l U ni v L ib ra ri es o n M ar ch 1 7, 2 01 3 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /1 .J 05 15 30 Numerical examples are presented in this section. Examples 1 and 2 are used to demonstrate the validity of the proposed method for nonlinear dynamic analysis of bimodular structures, whereas example 3 is an application of the proposed method to thewrinklingregion analysis of membranes. A. Example 1: Free Vibration of the Bimodular Bar Consider the free vibration of a bimodular bar as illustrated in Fig. 5. The bar is of elongation u0 under the concentrated forceP. At time t 0, if P is released, the bar will vibrate periodically. The analytical solution of this problem can be found in the work of Ambartsumyan [1]. With the vibration period remarked as T, the Fig. 12 Von Mises stress contours at different times. D ow nl oa de d by D re xe l U ni v L ib ra ri es o n M ar ch 1 7, 2 01 3 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /1 .J 05 15 30 initial conditions and analytical solution within t 2 0; T=2 are given by u x; 0 u0 l0 x P E A0 x _u x; 0 0 (41) u x; t 8>< >: u0 l0 x; 0 t t0 l0 x a1 u0 l0 l0 a1t ; t0 t t1 l0 a1 x a2 u0a1 l0a2 x; t1 t T 2 l0 a1 l0 a2 (42) in which a1 E s ; a2 E s (43) The variables l0 and A0 are the original length and section area of the bar, respectively; x is the position of arbitrary cross section; and is the density of the material", + " Next, the validity of the proposed method will be investigated by using a narrow and long plane-stress 2-D finite element model to simulate the longitudinal vibration of the bimodular bar. A narrow and long 2-D region is analyzed and its finite element model is illustrated in Fig. 6. The length-to-width ratio is 50:1, so that the analytical solution of the bar will be a good approximate solution for the 2-D problem. The parameters for numerical analysis are E 2:0 106 Pa, E 1:0 106 Pa, v 0:3, v 0:15, 1:0 103 kg=m3, l0 1:0 m, and P 1:0 103 Pa. Time step t 1 10 5 s is adopted. Figure 7 gives the analytical solution of free vibration of point A (see Fig. 5) and the numerical result obtained by the 2-Dfinite elementmodel. It can be seen that the two curves accord very well, which demonstrates the validity of the proposed method. Furthermore, the tensile modulus has been kept as E 2:0 106 Pa and the problems have been computed with a different modular ratioE =E . The results are presented in Fig. 8, in which the differences of periods and amplitudes can be observed obviously. B. Example 2: Dynamic Response of the Bimodular Foundation A bimodular foundation is analyzed to show the difference between the bimodular problem and the classical elastic problem" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000150_tro.2006.875489-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000150_tro.2006.875489-Figure1-1.png", + "caption": "Fig. 1. ith robot joint.", + "texts": [ + " In this study, we present the development of an adaptive JTF controller that takes uncalibrated joint-torque signals and then identifies the sensor calibration parameters as well as all joint parameters, including rotor inertia, the link twist angles, and joint-friction parameters. We show that asymptotic stability of the proposed adaptive controller can be ensured if an upperbound on the estimated sensor gain is respected. Subsequently, the parameter adaptation law is modified according to the projection parameter adaptation to meet a boundedness condition. Fig. 1 depicts the ith motor axis and joint axis of a robot with n revolute joints where each joint is driven by a geared motor with gear ratio ni. Assume that the motor shaft is cut right at its junction to the link. Then, writing torque balances once on the link system and then on the rotor system lead to two sets of differential equations as described in [14], [16], [18], and [19] for modeling and control of manipulators with elastic joints. On the other hand, the JTF-based control of manipulators require only the rotor dynamics, if the overall deformation of the joints are negligible [9]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003952_j.compstruc.2011.11.006-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003952_j.compstruc.2011.11.006-Figure1-1.png", + "caption": "Fig. 1. (a) Principal space and a set of the base tensors i, s, t. (b) Geometrical relations between two sets of the bases s, t and x2, x3 in p plane.", + "texts": [ + " Denote the three principal axes of the stress by n1, n2, n3. Three eigenvalue bases are defined by ai \u00bc ni ni \u00f0i \u00bc 1;2;3;no sum over i\u00de: \u00f06\u00de Three coordinate axes are associated with ai (i = 1,2,3) respectively to establish the so called principal space. Then, coaxial tensors can conveniently be characterized by vectors in this principal space. Geometrically, i is along the axis which subtends equal angles with the three coordinate axes, s and t are in the deviatoric plane or p plane and mutually orthogonal, as shown in Fig. 1(a). Solving the characteristic equation of the normalized stress derivator s, ones obtain its three principal values in terms of the Lode angle. Then we can express s in the spectral form s \u00bc ffiffiffi 2 3 r sin h\u00fe 2p 3 a1 \u00fe ffiffiffi 2 3 r sin ha2 \u00fe ffiffiffi 2 3 r sin h 2p 3 a3 \u00f07a\u00de Inserting (7a) into (3), t is also expressed in the spectral form t \u00bc ffiffiffi 2 3 r cos h\u00fe 2p 3 a1 \u00fe ffiffiffi 2 3 r cos ha2 \u00fe ffiffiffi 2 3 r cos h 2p 3 a3 \u00f07b\u00de Comparing (7b) with (7a), one easily obtains (7b) by the substitution of h + p/2 for h in (7a)", + " When the base tensors are employed in the return mapping algorithm, it is disadvantageous to some degree since the Lode angle changes with stress update. Consider two deviatoric tensors x2 and x3 which are coaxial with s and t, and have the fixed Lode angle of 0 and p/2 respectively. Upon the substitution of 0 and p/2 for h in (7a) respectively, the two tensors can be written as x2 \u00bc ffiffiffi 2 p 2 \u00f0a1 a3\u00de; x3 \u00bc 1ffiffiffi 6 p \u00f0 a1 \u00fe 2a2 a3\u00de \u00f08\u00de Obviously, the two defined tensors depend only on the principal axes. Denote x1 = i, as shown in Fig. 1(a). After a simple operation, one has trx2 1 \u00bc trx2 2 \u00bc trx2 3 \u00bc 1; trx1x2 \u00bc trx2x3 \u00bc trx3x1 \u00bc 0 \u00f09\u00de It follows that x1, x2 and x3 are mutually orthogonal unit tensors. They serve as a new set of the base tensors, with which we work in the sequel. Since x2 and x3 are deviatoric tensors, they can be expressed as linear combination of s and t. Using (7) and (8), one obtains tr(sx2) = tr(tx3) = cosh, tr(sx3) = tr(tx2) = sinh. Therefore, the relations between two sets of the base tensors are x2 \u00bc s cos h t sin h; x3 \u00bc s sin h\u00fe t cos h \u00f010\u00de Denote the projection axes of the coordinate axes a2 and a3 onto p plane by (a2)p and (a3)p respectively. Using (8), (10) and the definition of p plane, it can be shown that the vector axis associated with x3 coincides with (a3)p and the vector axis associated with x2 is perpendicular to it in p plane. Moreover, the angle between s and x2 is the Lode angle, which is measured anti-clockwise from the positive x2-axis, as depicted in Fig. 1(b). Eq. (10) clearly shows that the transformation between x2, x3 and s, t follows the transformation rule of vectors, in other words, x2 and x3 are obtained from s and t by clockwise rotation by an angle h about the axis i, as depicted in Fig. 1(b). With this expression, we can evaluate x2 and x3 directly from the normalized stress devi- ator s, instead of the principal axes. This is advantageous in the return mapping algorithm since the explicit computation of the principal axes will be avoided. Using (10) to express s in terms of x2 and x3, and recalling that the decomposition of the stress r = pi + qs, one can express the stress referred to this new set of the base tensors r \u00bc X3 I\u00bc1 r\u0302IxI \u00f011a\u00de where r\u03021 \u00bc p; r\u03022 \u00bc q cos h; r\u03023 \u00bc q sin h \u00f011b\u00de Those three coefficients constitute a new set of the invariants of the stress, which geometrically indicate the projection of the stress onto the axes xI (I = 1,2,3) respectively" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001091_j.jmatprotec.2007.04.122-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001091_j.jmatprotec.2007.04.122-Figure2-1.png", + "caption": "Fig. 2 \u2013 Nd:YAG pulsed laser treatment setup.", + "texts": [ + ", 2005a,b; Gordani and azavi, 2006), the laser treatment could produce the crack-free n g t e c h n o l o g y 1 9 5 ( 2 0 0 8 ) 154\u2013159 156 j o u r n a l o f m a t e r i a l s p r o c e s s i tion was 600 mJ, 10 HZ and 200 s, respectively. The distance between each track was kept constant with an overlapping of 50% from the previous track. Laser scan rate was controlled between 15 and 40 mm/min and the melted area was protected with a continuous flow of argon gas to avoid oxidation. Nd:YAG pulsed laser treatment setup is shown in Fig. 2. 2.2. Microstructure and microhardness analysis The microstructure was studied in cross-section samples by means of scanning electron microscopy (SEM) using energy dispersion analysis X-ray (EDAX). For microscopic observations, the samples were etched in Keller\u2019s etchant (2 ml HF + 3 ml HCl + 5 ml HNO3 + 90 ml H2O). X-ray diffraction analysis was carried out to identify the compounds at the surface of the work piece. After laser surface remelting, microhardness tests were carried out across the work piece cross-sections at a load of 100 gf" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000171_tie.2005.862293-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000171_tie.2005.862293-Figure1-1.png", + "caption": "Fig. 1. (a) Estimated and actual rotor flux linkage vectors, \u03c8\u0302 R and \u03c8 R , respectively. (b) Current test signal vector and its d- and q-components in the rotor flux reference frame.", + "texts": [ + "00 \u00a9 2006 IEEE signal, which is subsequently controlled to zero by adjusting the test signal to coincide the direction of the rotor flux [11]. This paper reviews the observer principle and describes a sensorless controller based on it. The observer is shown to be insensitive to motor parameter errors. Experimental results confirm the finding. In the following, \u03b81 and \u03b8\u03021 are the actual and estimated directions of the rotor flux, respectively, expressed in the stationary reference frame, and \u03b5 = \u03b8\u03021 \u2212 \u03b81 denotes the error angle between the estimated and actual directions, as depicted in Fig. 1(a). This error should be zero in rotor flux oriented vector control. Since \u03b5 is not explicitly known, an error signal F\u03b5 that depends on \u03b5 is introduced, ideally with the following properties: F\u03b5 = 0 for \u03b5 = 0; F\u03b5 > 0 for \u03b5 < 0; and F\u03b5 < 0 for \u03b5 > 0. If such a signal F\u03b5 is forced to zero by a controller, then the error angle \u03b5 is also zero and \u03b8\u03021 = \u03b81. The signal F\u03b5 is the output of the observer. The observer is based on superimposing an alternating current (ac) test signal, written as i\u03b5cd(t) = \u221a 2I\u03b5cd cos(\u03c9ct) (1) on the d-component irefd0 of the stator current in the controller\u2019s reference frame, the d-axis of which is attached to the estimated rotor flux direction. Thus the test signal is at angle \u03b8\u03021 relative to the stationary reference frame. Signals in the controller\u2019s reference frame are marked by superscript \u201c\u03b5.\u201d The spatial angle of the ac test signal is \u03b5 in the rotor flux reference frame, where the test signal appears as a vector, defined as ic(t) = i\u03b5cd(t) cos \u03b5+ ji\u03b5cd(t) sin \u03b5 (2) as indicated in Fig. 1(b). In the vicinity of perfect orientation, where \u03b5 \u2248 0, the sign of the error angle determines whether the q-component of ic(t) is in phase or in the opposite phase with the test signal i\u03b5cd(t). Consequently, the phase of the torque oscillation is also determined by the sign of the error angle. The torque oscillation creates an oscillation in the speed and, further, in the back EMF. Consequently, the phases of these oscillations are also determined by the sign of the error angle. The complex signal flow diagram of the system is given in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001482_tmag.2009.2015052-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001482_tmag.2009.2015052-Figure1-1.png", + "caption": "Fig. 1. Material geometry data. (a) Shows the direct approach. (b) Shows the new method with a region where the relative permeability is altered. The dark stripe represents the region , here .", + "texts": [ + " (6) In short: any imaginable irregularity can be simulated. If it is possible to express the irregularity as a function , or an implicit function from which can be extracted, then it can also be simulated. The method described above was implemented in a two-dimensional finite-element program, and was used to simulate a few cases of nonuniform air gaps for a salient pole hydropower generator. The data of the generator is summarized in Table I. Electromagnetic forces are calculated from Maxwell\u2019s stress tensor in the stationary part of the air gap. In Fig. 1, two scenarios, one being the new method, are shown. The top figure shows the normal direct approach and the lower figure shows the same geometry where the material properties, i.e., the relative permeability, has been altered in the dark stripe in the air gap. A time dependent simulation using a time stepping method was used with a full description of the damper bars and, where applicable, parallel connections for the stator winding which is known to reduce the UMP [12], [13]. The method utilizes a sliding mesh where half the air gap rotates with the rotor" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001776_j.tws.2009.10.010-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001776_j.tws.2009.10.010-Figure1-1.png", + "caption": "Fig. 1. The paraboloidal shell and coordinate system.", + "texts": [ + " It appears that there is no literature that pertains to the vibration of paraboloidal shells that include shear deformation and rotary inertia. The paraboloidal coordinate system (f, c) employed by Tzou et al. [4,5] is used here as well as the Lame\u0301 parameters that are defined in [4]. The Lame\u0301 parameters can be derived using methods of vector analysis and are equivalent to determining the scale factors for the corresponding paraboloidal coordinate system (see [1,2]). 2. Governing equations The paraboloidal shell and coordinate system are shown in Fig. 1 and is essentially that given by Tzou et al. [4]. The equation ll rights reserved. anan). defining the parabola in terms of coordinates r and z is z\u00bc c 1 r a 2 \u00f01\u00de where c is the height at the center of the shell and a is the radius at the base of the shell. The meridional radius of curvature Rf corresponding to the shell coordinate f is Rj \u00bc b=cos3j \u00f02\u00de while the circumferential radius of curvature is Rc corresponding to the circumferential coordinate is Rc \u00bc b=cosj \u00f03\u00de where b=a2/2c and the focal length for the parabola is f=b/2", + " There are sufficient results available to establish the accuracy of the current analysis. The results given in [7] did not include the cases for circumferential wave number n=0 or n=1. Nondimensional variables were assumed and r, G and shell height c were assigned unit values while 0.3 was assumed for Poisson\u2019s ratio n. All other parameters can be computed in terms of the assumed variables. It follows that the nondimensional frequency O is computed as O \u00bc oc ffiffiffiffiffiffiffiffiffi r=G p \u00f034\u00de The finite element mesh is determined using Fig. 1, where f defines an angle between a line drawn perpendicular to the shell and the z axis. The angle f is divided into an even number of spaces to obtain a mesh in angular measure. It follows that tanj\u00bc a=b \u00f035\u00de where b is given by b=a2/2c. The results of a convergence and accuracy study are given in Table 1. Free vibration frequencies are given in [3] and Table 1 shows the agreement with the elasticity solution of [3] and the thin shell results of [7]. The analysis based upon [7] does not include shear deformation or rotary inertia" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001596_0094-114x(73)90020-7-Figure9-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001596_0094-114x(73)90020-7-Figure9-1.png", + "caption": "Figure 9. Mechanism of a special pump.", + "texts": [ + " If it is necessary to consider power losses in kinematic pairs, the preceding dynamic analysis yields the necessary reaction force values. The developed general subprogram computes the coefficients of the members of equation (8) and uses the Runge-Kut ta method or, alternatively, the Hamming method for numerical solution of this equation. Let us apply the procedure described above to the following two problems. E x a m p l e 1. The mechanism of a special pump, the kinematic scheme of which is shown in Fig. 9, is created by the frame 1, driving link 2, binary group 4, 8, ternary group 3, 5, 7, 6 and binary groups 9, 10 and 11, 12. A customer, interested in kinematic analysis, gives the dimensions of all members and the motion of the driving links. The programmer describes the kinematic schema by vector polygons shown in Figs. 9(a)-(e). The structure of the whole program will then be as follows: (1) Input geometric and kinematic data. (Kinematic data describes the motion of the driving links.) (2) Call subprogram \"binary group\" which is created in our case by members 4 and 8, Fig. 9(a). The solution gives ~02, \u00a2~ and corresponding angular velocities and accelerations.~ *All programs and subprograms are written in the S L A N G language what is a variant of A L G O L designed for the computer M INS K 22. The name of the whole program is K I D Y A N (Kinematic and Dynamic Analysis). :~Indices of kinematic quantit ies correspond here with the indices of vector ~olygons and not with numbers of links in the main kinematic scheme. (3) Assign values q~2, ~b,, if: to the vector 16. (4) Call procedure \"ternary group\" that is created by members 3, 5, 7, 6, Figs. 9(b) and 9(c). The solution gives ~7, (\u00a28 = q~,_,, (p9 = ~,_, and q~,, and their first and second time derivatives. (5) Assign ~o,,= q~l,, q~s=~lz+~0, ~b~,= ~b~s= ~b~,, ~ l , = ( ~ s = ~ , . (6) Call subprogram \"binary group\"--members I1, 12, Fig. 9(d). The solution yields (7) Solve binary group 9, 10, Fig. 9(e). The solution gives 1,9, 12o and their time derivatives. (8) If link 2 is not in an end position, angle ~t is increased by the step A~o~ and the program returns to step 2. During the dynamic analysis the sequence of investigated groups are reversed. We start with the binary groups 9, I0 and I 1, 12 and compute the reaction forces in the kinematic pairs occuring in these groups. Then we solve the ternary group 3, 5, 7, 6 treating reactions in joints J and K as external forces loading member 6" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000706_j.triboint.2007.12.003-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000706_j.triboint.2007.12.003-Figure2-1.png", + "caption": "Fig. 2. Schematic diagrams of analyzed bearings: (a) fixed p", + "texts": [ + " Then, a numerical analysis is executed to solve isothermal Reynolds equation for the laminar flow, taking into account the inlet pressure and the pad\u2013pivot friction. The pad\u2013pivot friction is used to calculate the tilt angle of the pad and the inlet pressure of the pad is used as a boundary pressure at the pad entrance. This study explains the influences of pad\u2013pivot friction on the bearing characteristics by utilizing the proposed model and the numerical analysis. In this study, two types of bearings are analyzed, such as the fixed pad journal bearing and the tilting pad journal bearing. Analyzed bearings are depicted in Fig. 2, where Fig. 2(a) shows a schematic figure of the fixed pad journal bearing and Fig. 2(b) shows a schematic figure of the tilting pad journal bearing. The fixed pad journal bearing is made into four partial bearings and the tilting pad journal bearing consists of four tilting pads. Additionally, the coordinates, load direction and pad number for the numerical analysis are indicated in Fig. 2. The specifications of the bearings and lubricant which are used in this study are listed in Table 1. For the fixed pad journal bearing, the equivalent tilt angle is zero and the preload is 0.3. In this study, it is assumed that the dynamic friction coefficient has the constant and same value as the static friction coefficient m. The model of the pad\u2013pivot friction is depicted in Fig. 3. The friction force is the product of the normal force by the friction coefficient between pad and pivot. The normal force indicates the force that is exerted on the pad by the lubricant film" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001138_ac60323a003-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001138_ac60323a003-Figure5-1.png", + "caption": "Figure 5. H-type mercury-pool controlled-potential electrolysis cell", + "texts": [ + " Four types of controlled-potential electrolysis cells were examined. The first, shown in Figure 3, is a mercury-pool cell that has a virtually uniform potential and current distribution because of the large, conforming counterelectrode separator ( 4 , 41). Cells similar to this have been used by Karp and Meites (62) and by Moinet and Peltier ( 6 3 , The second, shown in Figure 4, is the cell routinely used at this Laboratory for controlled-potential coulometric determinations (64). The third cell, shown in Figure 5 , is an unsymmetrical modification that is similar to widely-used designs based on the polarographic H-cell. The three mercury-pool cells have nominally identical working-electrode areas (10 cm2) and solution volumes (6 ml). The platinum-working-electrode cell, shown in Figure 6, is the one used here for routine analytical work (65). Except for minor edge effects, this cell is characterized by a uniform potential and current distribution (41). The planar area of the gauze electrode is 69 cmz and the cell is operated with 25 ml of solution" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000312_s11071-005-9016-6-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000312_s11071-005-9016-6-Figure3-1.png", + "caption": "Figure 3. Linear spring and damper.", + "texts": [ + " , Mi nm act on the rigid body i, then we will have vectors of generalised forces that can be expressed as Qi R = Fi 1 + Fi 2 + \u00b7 \u00b7 \u00b7 + Fi n f = k f\u2211 j=1 Fi j (16) Qi \u03b8 = GiT [ Mi 1 + Mi 2 + \u00b7 \u00b7 \u00b7 + Mi nm ] \u2212 [( Ai \u02dc\u0304u i 1G\u0304i )T Fi 1 + ( Ai \u02dc\u0304u i 2G\u0304i )T Fi 2 + \u00b7 \u00b7 \u00b7 + ( Ai \u02dc\u0304u i n f G\u0304i )T Fi n f ] = GiT km\u2211 j=1 Mi j \u2212 k f\u2211 j=1 [( Ai \u02dc\u0304u i j G\u0304 i )T Fi j ] (17) where Qi R and Qi \u03b8 are the vectors of generalised forces associated with the generalised translational and rotational coordinates respectively. Consider two bodies i and j connected by a spring-damper element at points Pi and P j respectively as shown in Figure 3. Let ks be the spring constant, c be the damping coefficient, and l0 be the undeformed length of the spring. The magnitude of the-spring-damper force along a line that connects points Pi and P j can be written as Fs = ks(l \u2212 l0) + cl\u0307 (18) where l is the current spring length. If ri j P is the position vector of point Pi with respect to point P j which is defined by ri j P = ri P \u2212 r j P = Ri + Ai u\u0304i P \u2212 R j \u2212 A j u\u0304 j P (19) The torsional spring-damper that is often used in the wagon suspension system can be represented schematically by the diagram as shown in Figure 4" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003013_s11340-012-9600-x-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003013_s11340-012-9600-x-Figure2-1.png", + "caption": "Fig. 2 Schematic diagram of the piston assembly", + "texts": [ + " This is the first time that the secondary motion of the piston has been fully captured for all the modes and that the frequency of each mode has been determined. These results are important because they will enable better understanding of the nature of the secondary motion of the piston and the influence of each mode on the piston slap. Hardware Implementation Construction of Measurement System An experimental rig was designed and fabricated as shown in Fig. 1, and a 126 cc four-stroke motorcycle engine block is used in this study. The geometric and physical properties of the piston assembly are shown in Fig. 2 and Table 1. The piston assembly does not allow firing, and the crankshaft of the piston assembly was driven by an AC motor (MarelliMotori MAA80 MB4) controlled by a variable frequency controller (Emerson Commander SK). Piston Motion Measurement A measurement system consisting of three laser displacement sensors (Keyence LK-G152) is located at the front of the piston assembly, and the three laser spots are aimed at three different locations on piston crown. In order to capture the different piston secondary motion, two laser spots, L1 and L2, are directed toward the surface of a 24-mm-long flat slot located on the right side of the piston head surface to capture the piston rotational motion, while the other laser spot, L3, is directed toward the 45\u00b0 slope profile located on the left side of the piston head surface, which has a slope height h1 of 2 mm, to capture the piston lateral motion" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003801_1350650112470059-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003801_1350650112470059-Figure2-1.png", + "caption": "Figure 2. 3D representation and MAAG diagram of profile modifications.", + "texts": [ + " The efficiency is deduced from the input and lost energies over one mesh period and is expressed as \u00bc 1 f 1 u\u00f0 \u00de Z1 1 cos b \" \u00f09\u00de with , a loss factor Considering symmetric linear tooth profile modifications, two parameters are required to define their geometry, namely (i) the amplitude at tooth tip/ root characterised by the dimensionless parameter P \u00bc C= m and (ii) the extent of modification along at RMIT UNIVERSITY on July 20, 2015pij.sagepub.comDownloaded from the tooth profile measured as a dimensionless distance \" on the base plane (cf. Figure 2). Because the contact line geometry and the profile modifications for internal gears are similar to that for external gears, the expressions of J1, J2 and J3for internal gear are the same as those given in Velex and Ville20 for external gear. The corresponding loss factors for unmodified and modified gears are given in Appendix 2. at RMIT UNIVERSITY on July 20, 2015pij.sagepub.comDownloaded from Comparison with some classic formulas and influence of gear profile modifications on power losses in internal and external gears As shown in Velex and Ville,20 the results delivered by equation (9) compare well with the classic formulas of Buckingham,17 Niemann and Winter19 for unmodified external gears with deviations of about 10% for helical gears and 20% for spur gears" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003606_b978-0-12-417049-0.00011-0-Figure11.16-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003606_b978-0-12-417049-0.00011-0-Figure11.16-1.png", + "caption": "Figure 11.16 (A) Direction of motion when the robot obstacle distance d is smaller than the proper (desired) distance dp. (B) Motion alongside the obstacle \u00f0d5 dp\u00de. (C) Direction of motion when d. dp.", + "texts": [ + " The polar histogram of the obstacle configuration of Figure 11.14 has the form of Figure 11.15B, and its counterclockwise pseudoprobability polar histogram (from A to C) on the H-k plane has the form of Figure 11.15A. The peaks A, B, and C in Figure 11.15A result from the obstacle clusters A, B, and C in the histogram grid. To determine the safe directions of motion, a threshold T in POD is used. If POD. T, then we have unsafe (prohibited) direction of motion. If POD, T, we can select the most suitable direction in this sector. Figure 11.16A C depicts three possible cases of robot motion alongside an obstacle. When the robot is too close to the obstacle, the steering angle \u03c8steer points away from the obstacle. If the robot is away from the obstacle, \u03c8steer points toward the obstacle. Finally, when the robot is at the proper distance from the obstacle, the robot moves alongside it. As discussed in Section 11.2, mobile robot path planning is distinguished in local and global path planning. In the first, which is performed while the robot is moving, the robot can find a new path according to the changes of the environment (obstacles, stairs, etc" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002156_robot.2009.5152525-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002156_robot.2009.5152525-Figure2-1.png", + "caption": "Fig. 2. Experimental Setup: 1 DOF Planar Ball-throwing Robot", + "texts": [ + " We show that the condition of contact between the robot finger and ball transits from one underactuated contact model, named a \u2018finger-link contact model\u2019, to another underactuated contact model, named a \u2018fingertip contact model\u2019, during the motion. This paper presents preliminary results of numerical simulation and experiments on the capability of controlling the three kinematic variables independently. A numerical algorithm to acquire joint torque commands is developed by applying a simulated annealing (SA) method. The validity of the contact models is confirmed by experiments. Experimental results indicate that the independent control on the three kinematic variables is feasible. 978-1-4244-2789-5/09/$25.00 \u00a92009 IEEE 1655 Figure 2 shows the experimental system developed for this study. To simplify the problem, throwing motion in the horizontal plane is considered. The planar manipulator has a single DOF swing-arm mechanism driven by a DC motor. A plastic disk (hereafter called a ball). is used instead of a 3-dimensional ball. The friction between the ball and the link is assumed high enough so that the ball rolls on the link surface without slip because of anti-skid rubber attached on the link. To eliminate the friction between the ball and the floor an air table is used" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001956_oceanssyd.2010.5603565-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001956_oceanssyd.2010.5603565-Figure2-1.png", + "caption": "Fig. 2 (a) Surge, sway, and yaw motions are generated by the four horizontal thrusters (#1-#4) and (b) heave and pitch motions are by the two vertical thrusters (#5 and #6). The yaw motion can be produced by both pairs (#1, #2) and (#3, #4).", + "texts": [ + " In Section IV, a series of simulations are carried out and the results are discussed. Finally, our AUV simulator that can run hardwarein-the-loop simulation is briefly introduced in Section V. II. THRUSTER CONFIGURATION MATRIX The target hovering AUV of this study (Fig. 1) has six thrusters to deal with its 5-DOF motions, i.e., surge, sway, heave, pitch, and yaw. The roll motion does not be actively controlled; instead, the vertical distance between the center of mass and the center of buoyancy automatically stabilizes the roll motion. Fig. 2 shows the arrangement of thrusters and the motions to be generated by the thrusters. Four thrusters are placed horizontally for surge, sway, and yaw motions (one starboard (#1), one port (#2), one forward (#3), and one aft (#4)) and two are placed vertically for heave and pitch motions (one forward (#5) and one aft (#6)). In what follows, we investigate the thruster configuration matrix of the target AUV, which maps the thrusts exerted by the thrusters on the resultant forces and moments applied to the AUV" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000066_978-3-540-49823-0_3-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000066_978-3-540-49823-0_3-Figure2-1.png", + "caption": "Fig. 2. Minimum gap between three tangential sensing ranges", + "texts": [ + " In this section, we investigate the case where R < 2r and provide a configuration using a minimum number of sensors, thus minimizing the overlap between their sensing ranges, while achieving full sensing coverage. Theorem 4 proves that the deployment of the sensors according to the configuration in Fig. 3 is optimal in terms of minimum overlap between the sensing ranges of adjacent sensors. Theorem 4 (Optimal sensor deployment for sensing 1-coverage). The sensor deployment strategy according to the configuration in Fig. 3 is optimal. Proof. Consider the configuration given in Fig. 2. The equilateral triangle, \u0394d, in the gap area has a side length equal to d. In order to cover all the gap area, we need to cover \u0394d. To do so, both of the sensors s2 and s3 should be moved horizontally and in opposite directions until they intersect at the center of gravity, g, of the triangle \u0394d. This action will not be able to cover the whole gap as the triangle \u0394d is not fully covered. To cover the rest of \u0394d, the sensor s1 should move vertically and bottom-up until its sensing range hits the intersection point of both sensing ranges of s2 and s3, i.e., the center of gravity, g. In fact, the farthest point from any of the locations of the sensors s1, s2, and s3, is the point g. Hence, covering the entire gap area require covering its center of gravity, g. Therefore, the configuration given in Fig. 2, where any pair of sensing ranges of adjacent sensors have a constant overlap and any adjacent three sensing ranges intersect at only one point, is optimal. Theorem 5, which follows from theorem 4, states a condition that implies network connectivity provided that sensing coverage is guaranteed. Theorem 5 (Condition for connectivity given sensing 1-coverage). A homogeneous kCWSN with k = 1 is guaranteed to be connected if the sensing and transmission ranges of the sensors, r and R, respectively, satisfy R \u2265 \u221a 3r. Proof. Consider the configuration given in Fig. 2. The maximum distance between any pair of tangential sensors is 2r. To cover the entire gap area of the tangential three sensing ranges of the sensors s1, s2, and s3, the distance separating s2 and s3 should be equal to 2r \u2212 d. We have D = rcos(\u03b1) = \u221a 3 2 r, where \u03b1 = \u03c0 6 , and d = 2r \u2212 2D = r(2 \u2212 \u221a 3). Hence, the distance between any pair of adjacent sensors, given by 2r \u2212 d, is equal to \u221a 3r. Thus, if a field is sensing 1-covered, then the network is guaranteed to be connected if R \u2265 \u221a 3r holds" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002376_j.fusengdes.2011.01.018-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002376_j.fusengdes.2011.01.018-Figure3-1.png", + "caption": "Fig. 3. Base of Stewart: (i) bearing h", + "texts": [ + " The coordinate Xg 0 Yg 0 Zg 0 is defined as the global frame, and all local coordinates are related to the global frame: Xg 1 Yg 1 Zg 1 moves along the gear track and Xg 2 Yg 2 Zg 2 along the ball screw; Xg 3 Yg 3 Zg 3 rotates around the Zg 2 axis; Xg 4 Yg 4 Zg 4 is the basement coordinate of the Stewart and rotates around the Xg 3 axis; Xg 5 Yg 5 Zg 5 is fixed in the centre of the end-effector as the tool frame. The analytical stiffness model of the basic element evaluated in this paper is based on MSA. In order to illustrate the application of the MSA on the multi-beam structure, the stiffness modeling of bearing house and U-joint in the base side of Stewart platform in the robot is taken into account (Fig. 3). For simplification, the bearing house, U-joint and the base are described by the frame structure in Fig. 4. For applying the MSA method we firstly define the elements of structure and their nodes. Each element of structure is defined by a number enclosed with a circle, and its two nodes by two numbers. A local coordinate is given for each element. ouse, t i t o F n i In Fig. 4(iii), Ob 0A is the base frame of Stewart platform, Ou 1Ou 6 he frame of U-joint, and ABOu 1 the frame of bearing house includng the U-joint shaft" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000582_j.jsv.2007.02.019-Figure8-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000582_j.jsv.2007.02.019-Figure8-1.png", + "caption": "Fig. 8. Diagram showing the disc subsystem (left) in contact with the pin subsystem (right).", + "texts": [ + " [3], where it was shown that the stability criterion becomes dependent on the sliding speed when the coefficient of friction is no longer assumed to be constant. Continuation of this experimental study is under way to allow this extended theory to be tested. The authors thank Bosch Braking Systems for financial support, Professor K. L. Johnson and Dr. Derek Smith for valuable discussions and the team of technicians from Mechanics Laboratory of the Cambridge University Engineering Department for their skilful work. A diagram showing the disc sybsystem (left) in contact with the pin subsystem (right) is given in Fig. 8. ARTICLE IN PRESS P. Duffour, J. Woodhouse / Journal of Sound and Vibration 304 (2007) 186\u2013200200 [1] K.L. Johnson, Tribology research: from model experiment to industrial problem, in: G. Damaz, A.A. Lubrecht, D. Dowson, M. Priest (Eds.), Tribology Series Proceedings of the 27th Leeds-Lyon Symposium on Tribology INSA, vol. 39, Elsevier Science Dynamic friction, Lyon, 2001. [2] P. Duffour, J. Woodhouse, Instability of systems with a sliding point contact. Part 1: basic modelling, Journal of Sound and Vibration 271 (2004) 365\u2013390" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000205_tmag.2006.879138-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000205_tmag.2006.879138-Figure1-1.png", + "caption": "Fig. 1. Lamination of steel under uniaxial magnetization.", + "texts": [ + " The classical eddy-current loss can be calculated provided assumptions, such as linearity between local B and H within the lamination and sinusoidal nature of quantities, are made. However, a better accuracy in the estimation of the classical eddy-current losses requires the consideration of nonlinearity in soft magnetic materials. A lamination of steel (width ; thickness ) of conductivity and absolute permeability is magnetized Digital Object Identifier 10.1109/TMAG.2006.879138 under sinusoidal excitation at a frequency and a peak value of flux density Bp (see Fig. 1). The flux density has one only component in the direction, which is assumed constant in the direction . From Maxwell\u2019s electric field equation [7], it is derived that and (the displacement-current is neglected at low ). By introducing the constitutive relation of the material into Maxwell\u2019s equation as derived from Ampere\u2019s Law [8], the flux density and the electric field across the lamination are defined by (1) and (2). The peak value of flux density is set equal to Bp in the surface of the lamination and its variation in the center of the lamination equal to zero (1) (2) (3) After solving the differential equations [9] to determine and , Poynting\u2019s vector is calculated and integrated along the boundary of the eddy-current space [10]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003923_jr9640005101-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003923_jr9640005101-Figure2-1.png", + "caption": "FIG. 2.", + "texts": [ + " Many of the present results were analysed by Sato\u2019s methods but the results were unsatisfactory. Figs. 1 and 2 give the data for the initial and final stages of this reaction, respectively. Fig. 1 shows that the value of the intercept a t t = 0 is not accurately defined, and much depends upon the certainty of the first point. The best value for K appeared to be 14.4 sec.-l equiv.-2 g.2. Use of the second method did not yield a straight line at large times, although the first and last points shown in Fig. 2 refer to 75 and 87% reaction, respectively. The slope of the straight line through the last three points gave a value of 115 sec.-l equiv.-2 g.z for K\u2019. By use of this value, the best agreement with the experimental conversion-time curve was obtained with K = l l . O , , a value in poor agreement with that from the first method. For these reasons a different approach was adopted in which for given values of K and K\u2019, the times corresponding to the experimental values of x were calculated from eqn" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003762_robio.2012.6491146-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003762_robio.2012.6491146-Figure4-1.png", + "caption": "Fig. 4. Front view of biped robot", + "texts": [ + " Table II shows the Fr and SR of the PDW of our biped robot at max speed and those of the active walking of the conventional biped robots [3], [4], [5], [6] (Fr and SR of Meta at the most energyefficient walking shown in [5]). From this table, we see that the PDW of our biped robot is much faster than the active walking of the conventional biped robots. Moreover, the PDW of our biped robot is much more energy-efficient than the active walking of the conventional biped robots. We can thus expect that our biped robot achieves more high-speed and energy-efficient active walking than the conventional biped robots by mimicking this PDW on level ground. Fig. 4 shows a front view of our biped robot. This robot has mechanical parameters as shown in Table I. To measure each joint angle and leg\u2019s angular velocity, this robot has rotary encoders and a gyroscope. This robot also has motors and timing belts for active walking on level ground. Fig. 5 shows the foot of our biped robot. This foot has a spring, joint damping and a rotary inerter at the ankle. Moreover, it has a toe-switch and heel-switch to detect contact conditions of the robot. Fig. 6 shows the rotary inerter at the ankle" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003655_etfa.2011.6059226-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003655_etfa.2011.6059226-Figure5-1.png", + "caption": "Figure 5. Synchronous tracking \u2013 relative poses (left) and asynchronous tracking \u2013 absolute poses (right).", + "texts": [ + " One advantage of the synchronous programming is the providing of a direct visual feedback of the trajectories to the worker. We propose an additional asynchronous tracking method to program single poses and trajectories without moving the robot synchronously. With the help of pointing gestures one can program absolute poses in the working space without moving the robot. This allows the individual definition of a variety of poses in a short time. Subsequently, the poses can be connected to program flow. Figure 5 demonstrates the principles of synchronous and asynchronous tracking for a linear path with the objective of circumventing an obstacle. Both methods, the synchronous and the asynchronous tracking, can also be considered as offline programming methods. While synchronous tracking is conceivable with the help of a CAD supported simulation system, asynchronous tracking can be carried out in a copy of the target robot cell. A prerequisite for the transfer of offline-programmed poses is still a precise workcell calibration" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003616_j.1460-2695.2012.01686.x-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003616_j.1460-2695.2012.01686.x-Figure3-1.png", + "caption": "Fig. 3 (a) Schematic illustrating the surface displacement \u03b4 resulting from ratchetting and (b) an experimental specimen displaying surface displacement after a ratchetting experiment (experimental results are obtained from the disk on disk tests with p0 = 1800 MPa, at the University of Sheffield, UK).", + "texts": [ + "19 Following the passage of the load, stress and strain components are different than zero based on the elastic stress cycle. However, the geometrical constraints require these stresses and strains are zero after the passage of the load.11 Consequently, a proportional relaxation procedure is implemented to relax the appropriate residual stress and strain components to zero. This procedure has been found to return comparable stress\u2013strain values to those obtained from a FE model.12 After the residual stresses and strains are determined, the surface displacement (Fig. 3a) or surface flow (Fig. 3b) can be determined by integrating the accumulated ratchetting strain as \u03b4 = \u222b \u221e 0 (\u03b3xz)r dz, (6) where \u03b4 is the cumulative surface displacements and (\u03b3xz)r is the ratchetting strain at a given depth. The (\u03b3xz)r increases with repeated loading cycles. In order to predict fatigue life under rolling contact loading, a multiaxial fatigue model must be implemented. Many different fatigue parameters have been proposed to determine the critical plane, including the normal stress range, shear stress range, maximum normal stress, maximum shear stress, normal strain range, normal plastic strain range, shear strain range and maximum normal strain" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002513_piee.1971.0124-Figure7-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002513_piee.1971.0124-Figure7-1.png", + "caption": "Fig. 7", + "texts": [ + "4 This showed that the effect of the fringing flux from both ends was approximately equal to that in 1-2 times the slot width of untransposed conductor considered to lie within the slot length. winding was considered, at 20 positions, and the flux variation with time for each circulating-current path was obtained. The fundamental component predominated, the third harmonic being only 20% of it. Voltage phasors have been drawn for the instant when phase-A current is a maximum and the machine is on fullload short circuit. Phasor values of the voltage in circuit 1 (see Fig. 1) of a bar in the top layer in two positions are shown in Fig. 7. The difference between the two, apart from the 4 Motional mutual inductance of rotor with circulating-current paths A motional mutual inductance expresses a relationship between a direct current in one circuit and a voltage appearing in a second circuit which is in motion relative to the first. The mutual inductance must also express the correct generation of voltage phasorially, and is a complex quantity with reference to rotor position. In combining the rotor and stator components of the endfield, the correct phasor combination must be obtained" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000084_s00170-005-0312-6-Figure19-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000084_s00170-005-0312-6-Figure19-1.png", + "caption": "Fig. 19 Illustration of collision-free zone at the second stage Fig. 20 Illustration of clearance value and tilting angle of cutter", + "texts": [ + " The included angles between the collision points at the 3 zones and the \u2013YL2 axis of the second detecting coordinate system can be calculated: \u00f0\u03b8cn\u00deA \u00bc \u03b2cn \u03b1cn , in which: cn \u00bc Ycn Yrn X cn X rn Ycn > Y rn X cn X rn \u00fe Ycn > Y rn X cn < X rn 2 Ycn < Y rn X cn < X rn \u00bc Tan 1 jX cn X rnj jYcn Y rnj cn \u00bc Sin 1 Rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u00f0Ycn Yrn\u00de2 \u00fe \u00f0Xcn Xrn\u00de2 q 8>>< >>: (11) In this equation, Xcn, Ycn represents the position of a certain collision point n within COL A, cutter\u2019s center (Xrn, Yrn) is the original point of the second detecting coordinate, and R, is the radius of cutter. Hence, taking each of the collision zones as the unit, the maximum and minimum included angle between \u2013YL2 axis and tangential line of each collision zone can be calculated, they are (\u03b8A)max, (\u03b8A)min, (\u03b8B)max, (\u03b8B)min, (\u03b8C)max, and (\u03b8C)min. After order arrangement, mixing and eliminating the extreme values that cause collision zones, the collisionfree angle range can be found out. From Fig. 19, it is found that the collision-free zone is between (\u03b8A)min and (\u03b8C)max, as well as (\u03b8B)max and (\u03b8C)min. Thus, any angles within these collision-free ranges can also become the yaw angle of the cutter. The description in the previous sections shows the determination of collision-free tilting angle and yaw angle range of cutter respectively. Within these ranges, no collision will be caused between cutter and surface. Within the collision-free angle range at the first stage cutter collision detection, the tilting angle range must have the minimum cross-angle with axis YL1 as shown in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000136_app.23597-Figure8-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000136_app.23597-Figure8-1.png", + "caption": "Figure 8 Model of the section morphology of PMP hollow fiber. The section is composed of outer surface and three layers: a loose lamella layer, lamella layer, and a spherical crystal layer.", + "texts": [ + " In addition to the already-mentioned observed difference between the outer and inner surfaces of the original and annealed hollow fibers, additional contrasts in morphology along the radius of the fiber cross section also were defined (see Fig. 7). From the inside to the outside of the hollow fibers, there were three kinds of macromolecular coagulation; the interlayers especially showed a regular piled structure, which indicated the presence of more perfect lamellae. We named these layers (see Fig. 8), going from the inside boundary to outer side of the section, the loose lamella layer, the lamella layer, and the spherical crystal layer. The thicknesses of these layers, shown in Figure 7, were approximately 9, 30, and 6 m, respectively, evaluated from the cross section of the resulting hollow fiber. The morphology of this hollow-fiber cross section depended on variations in the cooling speed and the stress field along the fiber section. This three- layer model can be used to explain qualitatively the macromorphology of PMP hollow fibers formed in the spinning and take-up processes" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003867_j.powtec.2012.11.027-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003867_j.powtec.2012.11.027-Figure3-1.png", + "caption": "Fig. 3. Dependence of the normalized velocity field V\u03b7, at normalized times \u03c4=0.3 and \u03c4=0.49, on the normalized spatial coordinates (\u03be,\u03b7) and two-dimensional contours of the same normalized velocity field.", + "texts": [ + " (46) and (47) become: \u2202 \u2202\u03c4 NV\u03be \u00fe 1 \u03be \u2202 \u2202\u03be \u03beNV2 \u03be \u00fe \u2202 \u2202\u03b7 NV\u03beV\u03b7 \u00bc \u2212N\u22121 \u2202N \u2202\u03be \u00f050\u00de \u2202 \u2202\u03c4 NV\u03b7 \u00fe 1 \u03be \u2202 \u2202\u03be \u03beNV\u03beV\u03b7 \u00fe \u2202 \u2202\u03b7 NV2 \u03b7 \u00bc \u2212N\u22121 \u2202N \u2202\u03b7 \u00f051\u00de \u2202N \u2202\u03c4 \u00fe 1 \u03be \u2202 \u2202\u03be \u03beNV\u03be \u00fe \u2202 \u2202\u03b7 NV\u03b7 \u00bc 0 \u00f052\u00de For the numerical integration we shall impose the initial conditions V\u03be 0; \u03be; \u03b7\u00f0 \u00de \u00bc 0;V\u03b7 0; \u03be;\u03b7\u00f0 \u00de \u00bc 0;N 0; \u03be;\u03b7\u00f0 \u00de \u00bc 1=5;1\u2264\u03be\u22642;0\u2264\u03b7\u22641 \u00f053a e\u00de as well as the boundary conditions V\u03be \u03c4;1;\u03b7\u00f0 \u00de \u00bc V\u03be \u03c4;2;\u03b7\u00f0 \u00de \u00bc 0; V\u03b7 \u03c4;1;\u03b7\u00f0 \u00de \u00bc V\u03b7 \u03c4;2;\u03b7\u00f0 \u00de \u00bc 0 V\u03be \u03c4; \u03be;0\u00f0 \u00de \u00bc V\u03be \u03c4; \u03be;1\u00f0 \u00de \u00bc 0; V\u03b7 \u03c4; \u03be;0\u00f0 \u00de \u00bc V\u03b7 \u03c4; \u03be;1\u00f0 \u00de \u00bc 0 N \u03c4;1;\u03b7\u00f0 \u00de \u00bc N \u03c4;2;\u03b7\u00f0 \u00de \u00bc 1=5 N \u03c4; \u03be;0\u00f0 \u00de \u00bc 1 10 exp \u2212 \u03c4\u22121=5 1=5 2 exp \u2212 \u03be\u22123=2 1=5 2 \" # N \u03c4; \u03be;1\u00f0 \u00de \u00bc 1=5 \u00f054a g\u00de The equations system (50)\u2013(52) with the initial conditions (53 a-e) and the boundary ones (54 a-g) was numerically resolved by using the finite differences [36]. We present in Figs. 1\u20133 the numerical solutions for the normalized density field N(\u03be,\u03b7) \u2014 Fig. 1 for the normalized velocity field V\u03be(\u03be,\u03b7)\u2014 Fig. 2 and for the normalized velocity field V\u03b7(\u03be,\u03b7) \u2014 Fig. 3 at the normalized time sequence \u03c4=0.3 and \u03c4=0.49, both three-dimensional and two-dimensional (Figs. 1\u20133) solutions, through contour curves. By analyzing these numerical solutions, it can be concluded: i) the normalized density field is of soliton-type for \u03c4=0.3 or solitonpackage-type for \u03c4=0.49 [37] (Fig. 1); ii) the normalized velocity field V\u03be is symmetric with respect to the symmetry axis of the spatio-temporal Gaussian (Fig. 2); iii) shock waves and vortices are induced at the structure periphery for the normalized velocity field V\u03b7 (Fig. 3). In Figs. 4 and5wepresent the normalized forcefield for the F\u03be component (three-dimensional dependence and two-dimensional contour Fig. 4) and the normalized force field for the F\u03b7 component (threedimensional dependence and two-dimensional contour Fig. 5). It results that the simultaneous presence of soliton \u2014 anti-solitons (Fig. 4) and solitons packages (Fig. 5) from the force fields, equivalent with the vortex generation in fluid [33\u201335], specifies the transition from a differentiable flow (along the same stream line) to a nondifferentiable flow (the jump from one stream line to another)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000385_s00170-006-0604-5-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000385_s00170-006-0604-5-Figure4-1.png", + "caption": "Fig. 4a\u2013c 5-(RRpR)(RR) parallel manipulator (1\u20139)", + "texts": [ + " Similar to the 5-RRR(RR) manipulator, five $r2 and the common $r1 are six linear independent screws. So, the selection of base actuators is feasible. 3.3 Manipulator 5-(RRpR)(RR) A kind of revolute joint in a prismatic form (Rp) shown in Fig. 3 is adopted to build some novel parallel manipulators in this study. The relative motion of the kinematic pair is that a slider moves on an arc-track. It is equivalent to a revolute joint, since the slider rotates around the axis S. The manipulator 1\u20139, 5-(RRpR)(RR), is taken as the example, as shown in Fig. 4. Different to the 5-(RRR)(RR) manipulator, the second kinematic pair adjacent to the base platform is an Rp pair. The constraint screws and input selection analysis for this manipulator are omitted as they are similar to that of manipulator 5-(RRR)(RR). On the basis of the constraint synthesis and input selection methods, this paper proposed 18 fully symmetrical 5-DoF 3R2T (three rotational, two translational) parallel manipulators with better actuating modes (11 manipulators are identified from nearly seventy currently existing ones and another seven are novel ones)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000175_j.chaos.2006.05.068-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000175_j.chaos.2006.05.068-Figure2-1.png", + "caption": "Fig. 2. Cross section of a porous squeeze film journal bearing.", + "texts": [ + " The dynamic trajectories of the rotor and bearing center, power spectra, Poincare\u0301 maps, bifurcation diagrams and the maximum Lyapunov exponent are applied to analyze the rotor-bearing system. Fig. 1 shows a flexible rotor supported horizontally by two identical and aligned porous squeeze couple stress fluid film journal bearings with non-linear springs. Om is the center of rotor gravity, O1 is the geometric center of the bearing, O2 is the geometric center of the rotor, O3 is the geometric center of the journal. Fig. 2 shows the cross section of the fluid film journal bearing where (X,Y) is the fixed coordinate and (e,u) is the rotated coordinate, e being the offset of the journal center and u being the attitude angle of the X-coordinate. From the equilibrium of force, the forces applied to the journal center O3 are F 364 C.-W. Chang-Jian, C.-K. Chen / Chaos, Solitons and Fractals 35 (2008) 358\u2013375 F x \u00bc fe cos u\u00fe fu sin u \u00bc Kp\u00f0X 2 X 3\u00de=2 \u00f01\u00de F y \u00bc fe sin u fu cos u \u00bc Kp\u00f0Y 2 Y 3\u00de=2 \u00f02\u00de where fe and fu are the resulting damping forces in the radial and tangential directions" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000419_1.2735636-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000419_1.2735636-Figure1-1.png", + "caption": "Fig. 1 The general 5R serial robot", + "texts": [ + " Therefore, the idea of the new approach in this paper provided the theory basis for a simple new method for kinematic analysis of complex multiloop mechanisms especially parallel manipulators . Preliminaries Inverse Kinematic Analysis of General 5R Serial Robot. The inverse kinematics problem of the general 5R robot has been discussed in Ref. 15 . It has been recognized that the solution to this problem is unique, and the unique solution has been obtained based on linear transformation theory in Ref. 16 . The configuration of the general 5R serial robot is shown in Fig. 1. The computing steps and algorithm for the inverse kinematics problem of the general 5R robot can be stated as follows: Step 1. Given the structural parameters, position p and orientation z6 ,x6 of the end effector, convert the 5R serial robot problem to the 5R single-loop mechanism problem; Step 2. Establish loop vector equations, and derive a set of triangular equations; and Step 3. Let x=tan c5 /2 , y=tan c1 /2 , transform the triangular equations mentioned above into polynomial equations. Multiplying the polynomial equations by y, x, and xy, respectively, we obtain the following linear equation system D 16 16 X = 0 1 where X = x3y3 ,x3y2 ,x2y3 ,x3y ,x2y2 ,xy3 ,x3 ,x2y ,xy2 ,y3 ,x2 ,xy , y2 ,x ,y ,1 T, and D 16 16 is a coefficient matrix, and its every element is the only function of structural parameters", + " Now the new derivation of coefficient matrix D 16 16 is resented in detail as below. The configuration of the general 5R serial robot is shown in ig. 1, where xi ,zi i=1\u20136 are all unit vectors, ai, li, and twist ngle i,i+1 are known structural parameters, and p ,z7 ,x7 is the iven position and orientation of end effector. Connecting the first and the fifth pairs by common perpendicuar line a7x7 of their joint axes z1 and z5, we can convert the eneral 5R robot to its corresponding 5R single-loop mechanism, s shown in Fig. 1. Obviously, the auxiliary structural parameters lc1, lc5, d1, d5, and a7x7 can be readily determined, where l5 lc5 is the mutual perpendicular distance or offset between sucessive links a4x4 and a7x7, and lc1 is the offset of a7x7 and a1x1, d1 and d5 represent the right-hand-rotation angle from x0 to x7 bout z1, and the angle from x5 to x7 about z5, respectively. Given the position and orientation of the end effector, p ,z6 ,x6 , and structural parameters, the auxiliary structural paameters can be obtained as follows x5 = \u2212 z6 x6 z5 = cos 56z6 \u2212 sin 56x6 51 = cos\u22121 z5 \u00b7 z1 x7 = cos 51 z5 z1 A1 he rotary variables of the first and the fifth pairs can be specified s c1 = 1 \u2212 d1 c5 = 5 + d5 A2 here d1 = cos\u22121 x0 \u00b7 x7 d5 = cos\u22121 x5 \u00b7 x7 he position of the end effector, p, can be written as p = lc1z1 \u2212 a7x7 + lc5z5 + a5x5 + l6z6 A3 he scalar products of x7 ,z1 ,z5 with both sides of Eq" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003643_robio.2011.6181649-Figure8-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003643_robio.2011.6181649-Figure8-1.png", + "caption": "Fig. 8. The inverse problems for the motion determination.", + "texts": [ + " The error distance of the free fall at the hitting point is about 70 [mm] close to the edge of the racket. This implies that the racket may not be able to hit the ball. The motion determination is performed by solving the following two inverse problems: (3-1) Suppose that the position \ud835\udc91\u2032 \ud835\udc4f just after the re- bound on the racket and the desired point \ud835\udc91\ud835\udc4f\ud835\udc51 = [\ud835\udc5d\ud835\udc4f\ud835\udc65\ud835\udc51, \ud835\udc5d\ud835\udc4f\ud835\udc66\ud835\udc51, 0] T on the table are given. Then, find the velocities (\ud835\udc97\u2032 \ud835\udc4f,\ud835\udf4e \u2032 \ud835\udc4f) just after the rebound on the racket with the equation of (4) (See Fig. 8 (a)). (3-2) Suppose that the velocities (\ud835\udc97\ud835\udc4f,\ud835\udf4e\ud835\udc4f) and (\ud835\udc97\u2032 \ud835\udc4f,\ud835\udf4e \u2032 \ud835\udc4f) just before and after the rebound on the racket are given. Then, find the angles (\ud835\udefd, \ud835\udefc) and the velocity of the racket \ud835\udc7d\ud835\udc45 with the equations of (2), (4), (5) and (6) (See Fig. 8 (b)). It is difficult to solve these problems directly because of the followings: (i) The calculation time has to be finished early to secure enough time for the control. (ii) The racket velocity is limited as \u2225\ud835\udc7d\ud835\udc45\u2225 \u2264 1 [m/s] due to the joint velocity limitation. (iii) The aerodynamics of (4) is the nonlinear differential equation and there are the redundancy of the elevation angle of \ud835\udc97\u2032 \ud835\udc4f and the rotational velocity \ud835\udf4e\u2032 \ud835\udc4f. (iv) The rebound of the racket of (2), (4), (5) and (6) consists of the complex simultaneous nonlinear equations" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001269_1.3197178-Figure11-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001269_1.3197178-Figure11-1.png", + "caption": "Fig. 11 Cuboid of uniform plastic strain", + "texts": [ + " Nomenclature Cn cuboid of size 2 x ,2 y ,2 z and center point x ,y ,z Dkij A ,Cn influence function of the ij strain component of cuboid Cn on the component k of the residual displacements at the surface point A ur k A residual displacement of a surface point A in the k-direction ue k A elastic displacement of a surface point A in the k-direction u k M displacements created by a unit force applied along the k-axis at the origin of the surface, and calculated at the subsurface point M ki rigid body displacement along the k-direction for body i p ij Cn plastic strain component kij A ,Cn ij strain component created in the cuboid Cn by a unit force along the k-axis applied at the surface point A p plastic volume Appendix: Normal Displacements Let us consider a virtual state corresponding to the application of a unit force along the x-axis applied on the elementary surface area centered at point A see Fig. 11 5 . The displacements generated are expressed by Boussinesq see Ref. 1 . MARCH 2010, Vol. 77 / 021014-5 6 Terms of Use: http://www.asme.org/about-asme/terms-of-use T m b i C s t T i 0 Downloaded Fr U x = P 4 \u00b7 \u00b7 G \u00b7 x \u00b7 z R3 \u2212 1 \u2212 2 \u00b7 \u00b7 x R \u00b7 R + z U y = P 4 \u00b7 \u00b7 G \u00b7 y \u00b7 z R3 \u2212 1 \u2212 2 \u00b7 \u00b7 y R \u00b7 R + z U z = P 4 \u00b7 \u00b7 G \u00b7 z2 R3 + 2 \u00b7 1 \u2212 R A1 he reciprocal theorem is used to express the surface displaceents as a function of contact forces and plastic strains within the ody under the assumption that the plastic volume is incompressble, i" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002603_02533839.2010.9671680-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002603_02533839.2010.9671680-Figure5-1.png", + "caption": "Fig. 5 Relation between revolution speed and tool wear", + "texts": [ + " 3 The curve of the tool life equation D ow nl oa de d by [ \"Q ue en 's U ni ve rs ity L ib ra ri es , K in gs to n\" ] at 0 9: 50 2 8 D ec em be r 20 14 \u2234logV + nlogT = logC (3) \u2234logV = -nlogT + logC (4) In general, tool wear is discriminated from flank wear, crater wear, and depth of notch wear (DOCN), as shown in Fig. 4. Typical flank wear takes place due to friction between rank face and wear land. The flank wear area is parallel with the cutting face and extends to the tool edge gradually when milling. Therefore the cutting force and interface temperature increase in the wake of the wear process. They cause the tool to be damaged rapidly, as shown in Fig. 5. The process of flank wear can be described in three steps: primary wear area, uniform wear area, and expediting wear area. And the main causal factor of the expediting wear area is temperature variation. On the other hand, tool crater wear is observed at the rake face, caused by contact friction from moving chips. The tool surface melts due to the elevated contact stress and temperature at tool/chip interfaces. Then the chips induce crater wear. The shapes of the craters often resemble the curly chip shapes" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002900_icma.2013.6617997-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002900_icma.2013.6617997-Figure1-1.png", + "caption": "Fig. 1 Component of harmonic reducer", + "texts": [ + " dg Diameter of flexspline\u2019s reference circle. I. INTRODUCTION Harmonic drive system is widely used in many automation equipment such as radar, moment controlled gyroscope, industrial robot joint because of its large transmission ratio, high precision, small backlash, stable transmission and small volume and weight [1]. Harmonic drive system often works as a reducer, it consists of three components which are an elliptical wave generator(WG), a non-rigid flexspline(FS) and a rigid circular spline(CS), as shown in Fig. 1 [2]. Circular spline has an inner teeth and flexspline outer teeth. Periodic elastic deformation of the flexspline by the wave generator causes a relative rotation in the opposite rotation direction of the wave generator in the circular spline. The harmonic reducer\u2019s main failure forms are fatigue fracture of roots and wear of tooth surface. However, the complicated load conditions of robots may have a tremendous impact on the harmonic reducer and even increase the possibility of its failures. So the deformation and stress calculation and analysis of short flexspline with different loads are of great significance" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000742_09544054jem913-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000742_09544054jem913-Figure2-1.png", + "caption": "Fig. 2 Five types of scanning mode: (a) unidirectional raster scanning; (b) multi-directional raster scanning; (c) spiral scanning; (d)contour offset scanning; (e) zigzag scanning", + "texts": [ + " *Corresponding author: Center for Laser Rapid Forming, Department of Mechanical Engineering, Tsinghua University, Tsinghua Yuan, Beijing 100084, People\u2019s Republic of China. email: hbqi@mail.tsinghua.edu.cn JEM913 IMechE 2007 Proc. IMechE Vol. 221 Part B: J. Engineering Manufacture at Universidad de Valencia on July 20, 2015pib.sagepub.comDownloaded from The possible scanning modes of filling lines have five typical types including unidirectional raster scanning, multi-directional raster scanning, spiral scanning, offset contour scanning, and zigzag scanning [5, 6]. They are shown in Fig. 2. In unidirectional raster scanning, the electron beam scans along one direction, and the electron beam returns to the starting point of the next filling line. The algorithm of unidirectional raster scanning is simple, and the scanning speed can be fast. However, unidirectional raster scanning has two problems. One is that the microstructure will be anisotropic owing to the single-direction scanning, and the other is the retracing time of the vacancy path. In order to decrease the irregular shrinkage and wrap, multi-directional raster scanning is adopted" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002523_j.elecom.2011.12.005-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002523_j.elecom.2011.12.005-Figure1-1.png", + "caption": "Fig. 1. Schematic diagram showing the vinyl-CDtrodes fabrication procedure. A, the layout of the electrodes is transferred to the vinyl adhesives using a cutting plotter. B, the undesired portions is peeled off the release liner. C, an application tape is placed on the vinyl surface. D, the vinyl adhesive is transferred to the gold surface. E, the application tape is removed, leaving the vinyl adhesive attached to the gold surface.", + "texts": [ + " Cyclic and square wave voltammograms were recorded with an Autolab PGSTAT20 Electrochemical Analyzer (Eco Chemie BV, Utrecht, Netherlands). The working electrode, saturated calomel reference electrode (Model ZE11311, Aldrich, St. Louis, MO), and platinum wire counter electrode were inserted into a 20 ml cell through holes in a Teflon cover. The diameters of the circular structures cut on the vinyl adhesives were measured from images digitalized using a Sony CCD camera (DXC-390P) using a graphics editing program. 2.2. Electrode fabrication Fig. 1 schematically illustrates the electrode fabrication procedure. The layout of the electrodes was drawn using the CorelDraw 11.0 software package (Corel, Ottawa, Canada). The patterns were transferred to the vinyl adhesives (3M ScotchcalMR D3000, 0.09-mmthick) using a cutting plotter (Model GX-24, Roland DG Corporation, Hamamatsu, Japan) with nominal resolution of 100 \u03bcm (Fig. 1A). The undesired portions were peeled off the release liner using a needle, leaving only the portion that contains the electrode layout as a negative mask (Fig. 1B). Next, an application tape was placed on the vinyl surface to hold the structure in place while transferring to the substrate surface (Fig. 1C). The gold electrodes were constructed using recordable compact disks (CDs) as the gold source. For this purpose, the CDs (Mitsui MAM-M Standard Gold CD-R, Mitsui & CO., Tokyo, Japan) were treated with concentrated nitric acid to remove the polymeric film that protects its metallic layer [1]. The CDs were then cut in small pieces with approximately 0.8 cm in width and 5 cm in length, using a paper guillotine. The vinyl adhesive containing the electrode layout was transferred to the gold surface using the application tape (Fig. 1D). The application tape was removed, leaving the vinyl adhesive attached to the gold surface, thus defining the disk format of the electrode and leaving the opposite edge to clamp a crocodile clip (Fig. 1E). An insulator ink was used for covering parts of the gold layer around the electrode edge avoiding the contact with the solutions. The cutting plotter utilized in this work was able to make welldefined circular structures down to 447\u00b112 \u03bcm (n=3) in diameter and square shape structures (microchannels) down to 107\u00b113 \u03bcm (n=3) in width. Depending on the quality of the cutting plotter, better resolutions can be obtained. Bartholomeusz et al. [10], for example, utilized a cutting plotter that was able to produce square shape structures down to 18 \u03bcm in width" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000312_s11071-005-9016-6-Figure9-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000312_s11071-005-9016-6-Figure9-1.png", + "caption": "Figure 9. Main dimensions of the wheel and the rail profile.", + "texts": [ + " The 27 constraint equations also implied that the size of the sub-Jacobian matrix Cq was 27 \u00d7 28 and size of the sub-Jacobian matrix Cs was 27 \u00d7 8. Hence, the total dimension of the augmented matrix of the mass matrices and sub-Jacobian matrices in Equation (25) was 63 \u00d7 63. For the constant speed simulation a velocity constraint in the longitudinal direction was added, which increased the dimension of the augmented matrix to 64 \u00d7 64 and reduced the unrestrained degrees of freedom to eight. The wheel and the rail profile used in the simulation are shown in Figure 9. AS 60 kg/m plain carbon rail and LW2 wheel profile in new condition are considered. Both profiles are taken from Queensland Rail (QR) data. The method of formulation of the wheel rail contact demands the derivatives of the spline representation of the wheel and the rail profile up to the third order. Therefore, fifth order splines were selected using the wheel and the rail profile generated from the measured data points by using Spline2 V6.0 software developed by Delft University of Technology [23]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003270_amr.199-200.1984-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003270_amr.199-200.1984-Figure1-1.png", + "caption": "Figure 1. The staircase effect and lamination weakness problems caused by conventional flat-layer rapid prototyping.", + "texts": [ + " The parts currently produced by FDM systems are reasonably strong plastic components that are well suited to basic functional testing and can easily be sanded and painted to reproduce the aesthetics of the production product thus also making them useful for consumer testing. Though each RP technology has advantages and disadvantages over the others, one of the weaknesses common to all current flat-layer RP technologies is a relatively poor surface finishes caused by the \u2018staircase\u2019 effect on curved surfaces and a lamination weaknesses in a direction perpendicular to the layer direction (Fig. 1). If smooth surfaces are required for the component, the staircase effect can require sometimes substantial post-processing of the part (sanding and polishing) in order to produce smooth surfaces. All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications, www.ttp.net. (ID: 152.14.136.77, NCSU North Carolina State University, Raleigh, USA-03/05/15,19:03:23) This paper looks at the application of curved-layer FDM [3] (Fig 2) for producing plastic components with integral conductive tracks that allow for the elimination of wiring or printed circuit boards from products" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002900_icma.2013.6617997-Figure7-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002900_icma.2013.6617997-Figure7-1.png", + "caption": "Fig. 7 Radial distribution of flexspline cylinder deflection without load", + "texts": [ + " And the deflection of flexspline cylinder at the major axis of wave generator is larger than at the minor axis and at the middle axis between the major axis and the minor axis of wave generator. With load, the axial distribution change of cylinder deflection at the major axis of wave generator is shown in Fig. 6. On the whole, the deflection \u0394Cf of cylinder decreases with the increase of load T. The average increment is less than 1% of the deflection without load. The order of magnitude of the increment is so little that it could be ignored. And then we analysed the deflection of three cross sections to study the radial distribution of flexspline cylinder deflection. As Fig. 7, we could find that the three figures of flexspline cylinder deflection without load are all like cruciate flowers, the maximum deflection point is at the major axis of wave generator and the minimum deflection point is at the point 45\u00b0 away from minor axis of wave generator. The front cross section deflection is larger than other two sections, and the maximum is 0.2773mm. The rear cross section deflection is less, and the minimum is 0.1607mm. With Load, the deflection distribution of flexspline at gear cross section rotates clockwise about 45\u00b0, in the same direction of tangential component of meshing force, as shown in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003869_s00419-012-0608-6-Figure11-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003869_s00419-012-0608-6-Figure11-1.png", + "caption": "Fig. 11 The mode shapes corresponding to frequency \u03c921 (the second mode)", + "texts": [], + "surrounding_texts": [ + "As mentioned earlier, in the geometrical model of the gear, the geometry of the teeth is omitted. It allows us to reduce the system\u2019s FE model size. The simplified geometrical model of the system consists of five sectors (see Fig. 1) that have the cyclic symmetry feature. Each of these segments is meshed by using standard procedures of the ANSYS software. The 3-D solid mesh is elaborated and as mentioned earlier, the ten-node tetrahedral element (solid92) with three degrees of freedom in each node is used to realize each sector. During the mesh generation process, it is assumed that the maximum length of each element\u2019s side needs to be no more than 2.7 [mm]. The developed FE model is displayed in Fig. 2, and it consists of 19,620 elements and 36,188 nodes, respectively. The particular sectors are glued as a whole at the geometrical model preparing the stage by using standard procedure of the ANSYS program. The analysed gear is mounted in the roller bearings. Such bearings typically have slight load capacity under loads perpendicular to the primary supported direction. The gear shaft neck surfaces on which the bearings are assembled are denoted \u201cbearing\u201d (see Fig. 3a). The gear mates with the other devices by the splines. The splines is simplified down to a regular cylinder of the diameter assumed as equal to the splines pitch diameter. The surface denoted \u201cjoint\u201d (see Fig. 3a) is located on the pitch diameter of the splines. Parameters of the analysed system are shown in Table 1a\u2013b. The calculation results for natural flexural oscillations taking into account angular speed of the gear are shown in the paper. In the case of circular discs and annular plates, for each solution where nodal lines are nodal diameters, one obtains two identical arrangements of straight nodal lines, rotated by an angle of \u03b1 = \u03c0/(2n) one to another, where n is the number of nodal diameters. In accordance with the circular and annular plate vibration theory [5,6,12], the particular natural frequencies of vibration are denoted as \u03c9mn , where m refers to the number of nodal circles and n is the mentioned number of nodal diameters. As the shape of the gear model is fairy elaborate, the flexural modes of the system are subject to deformation (as compared to the system without any holes) to such extent that establishing which particular node it refers to becomes rather difficult. This problem is even worse if the angular speed of the gear is varying. The problem of influence of the angular speed on the flexural gear models deformation is analysed. For the purpose of identification of these modes, an algorithm of tagging oscillation modes, which determines the correspondence between vibration of the circular disc versus disc with holes, is used. For this purpose, an auxiliary model of annular plate in the form shown in Fig. 3b is used. The geometrical dimensions of the auxiliary model were taken from the gear geometry (shown in Fig. 1). They are as follows: addendum circle diameter dz , rim mounting diameter dp, root circle diameter dw2, and thickness h p and hz (see Table 1). Dynamic analysis is performed for the auxiliary model cases rotating at predetermined angular speed, where diameter of though holes d01 (see Fig. 3b) varies as seen in Table 2. Findings are compared to each other both quantitatively and qualitatively. This method makes it possible to investigate deformations of nodal lines associated with nodal diameters and circles due to through holes and then determine correspondence between oscillation modes of solid circular disc and a plate with holes. In the final step, solutions found for the auxiliary model are compared with the solution for the system whose FEM model is shown in Fig. 2 (the principal model). As for the principal model case, the 3-D solid mesh and the ten-node tetrahedral element (solid92) are used to discretize the auxiliary models. For all models subject to analysis, the boundary conditions were applied to the nodes. For each model, 1 d f associated with node radial displacement was subtracted from the nodes found on the surface identified as a bearing (see Fig. 3a,b). Furthermore, 1 d f associated with the displacement of nodes along the centreline of each model was subtracted from the nodes found on the surface, identified as a joint (see Fig. 3a,b). For the models obtained in this way, calculations were kept conducted as long as the natural frequency \u03c918 was determined. The calculations were performed assuming that the systems rotate as angular speed of \u03b8 , within the range of 0\u20131047 [ rad/s]. During the computing process, the angular speed values were gradually increased by 80[ rad/s], which made fourteen variants of the results (the natural frequencies and corresponding natural modes), which were subject to further interpretation. The rotation effect was taken into account by determining stress distribution due to rotation, for each model during the computational step associated with static analysis (the so called pre-stress effect). This stress distribution was then included in the computation step associated with modal analysis. The results of the numerical calculations related to the procedure of identifying deformed natural modes of flexural vibration of the gear under consideration are shown below. The results displayed here relate to the determination of the correspondence between the natural frequencies \u03c916 and \u03c925 at high angular speed (\u03b8 = 1047 [ rad/s]) as well as to the correspondence between oscillation modes and the natural frequency \u03c931 at lower angular speeds (\u03b8 = 80 [ rad/s]). The results as shown in Figs. 4, 5, 6, 7, 8, 9 allow for tracking deformations of nodal lines associated with nodal circles and diameters, due to varying diameter of the through holes. With respect to the natural frequency \u03c925, there is marked difference in shapes of natural modes. When one compares the results between each other, one can notice that in order to identify correctly deformed natural modes of the flexural oscillations in the gear under consideration at lower angular speeds, larger number of auxiliary models is required to be included during calculations, as compared to the higher angular speeds. It comes from the fact that additional stresses through the centrifugal effects appear. This effect causes the gear flexural stiffness to be an apparent function of rotational speed (stiffness grows for higher speed). In the next part, results of the numerical calculations associated with the extent of the influence of the angular speed to deformation of mode shapes of oscillations. For each discussed case, both mode solutions related to nodal diameters are shown. These analysed results are sorted by the order of their occurrence. For the frequencies \u03c923 and \u03c918, the results were obtained at angular speeds of \u03b8 = 0 and \u03b8 =1,047 [ rad/s] respectively. For the other cases, results were obtained at angular speeds \u03b8 of, 0, 320, 720, and 1,047 [ rad/s], respectively. Natural frequencies for these modes are included in Table 3. To determine this mode (see Figs. 10, 11), the procedure of tagging natural oscillation modes was required. Nodal lines associated with the circle and diameter are deformed. Minor influence of the angular speed to deformation of the nodal lines is noticeable. The task of determining modes in this case was not too difficult (see Figs. 12); no procedure of tagging natural oscillation modes was required. The slight impact of the gear angular velocity on the distortion of the nodal lines is observed. For these modes (see Figs. 13, 14), procedure of tagging natural oscillation modes was required. It is noticeable that angular speed affects markedly deformation of the nodal lines. Once the angular speed of 720 [ rad/s] is exceeded, the oscillation mode takes different shape. Major deformation of mode shape attributable to the shaft vibrations is evident at this speed. Moreover, additional problem associated with some similarity of the mode being tagged to the mode associated with frequency of \u03c931, emerged during mode identification. Establishing the correspondence between these modes was a complex task (see Figs. 15, 16) due to the shape of oscillation modes similarity to the case discussed earlier. The angular speed affects deformation of nodal lines markedly. Major shape mode variations emerge at \u03b8 = 400 [ rad/s]. The identification process in this mode was not easy (see Figs. 17, 18) . One can notice that angular speed affects the deformation of nodal lines. Major variation in mode shape emerges at \u03b8 = 720 [ rad/s]. Moreover, additional annular shaft vibration emerges at the highest considered angular speed. Finding correct correspondence between the modes in this case was fairly easy (see Figs. 19). High repeatability in deformations of nodal lines on circular plate at various angular speeds is noticeable. As a consequence of the conducted analysis (see Table 3), the Campbell diagram was plotted for the gear under consideration. This is a convenient method of displaying the relationship between gear natural frequencies and transmission system excitations [4]. Excited frequencies are plotted on a vertical axis, and the gear speed of rotation is plotted on the horizontal axis (see Fig. 20). Natural frequencies achieved from numerical analysis are plotted as near-horizontal curves. The forced frequency due to the meshing is determined by the following relation (as in Ref. [4]) f = n0 \u00b7 z 60 (4) where n0 [rpm] is the rotational speed and z is the number of teeth in the gear. For this system, the gear teeth number is z = 59. Vibration resonance phenomenon occurs when forcing frequency (4) matches as to its value with some natural oscillation frequency of the gear. The points where the near-horizontal \u03c9mn curves intersect the straight line (4) indicate the speeds at which the gear resonance will be excited (see Fig. 20). For instance, the rated excitation speed for the natural frequency of \u03c923 is 764 [rpm]. It may be inferred from both the Campbell diagram and Table 3 that the rotating movement makes flexural stiffness of the gear under consideration to increase. Moreover, at speed of 3,820 [rpm], one can notice major surge associated with the mentioned earlier changing of the shape of the natural mode frequency in the case of the frequency of \u03c931. The growth of the gear transversal stiffness observed during gyrate of the gear comes from the appearance of the additional stresses in the toothed gear through the centrifugal effects. The higher rotational speed generates higher centrifugal forces, higher stress level, thereby causing the transversal stiffness of the system to increase. Moreover, the growth of the gear flexural stiffness through the gyrate effect causes reduction of the needed numerical calculations connected with identifying the proper distorted mode shapes." + ] + }, + { + "image_filename": "designv11_7_0000515_iros.2007.4399292-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000515_iros.2007.4399292-Figure1-1.png", + "caption": "Fig. 1. Coordinate systems of UVMS", + "texts": [ + " In section II, kinematic modeling of UVMS is conducted. Position and orientation of the end-effector are expressed by vehicle\u2019s pose and joint variable. And then velocity relation between the end-effector and vehicle/joint variables is modeled. In section III, the redundancy resolution scheme for minimizing restoring moments is presented. Before that, background of redundancy resolution problem is given. And in section IV, simulation results for demonstrating performance of proposed algorithm are provided. Fig. 1 shows coordinate systems of underwater vehicle with n-link manipulator. \u03a30, \u03a3V and \u03a3E represent the inertial frame, vehicle body-fixed frame and end-effector frame, respectively. Position and orientation of the vehicle relative to the inertial frame can be represented by homogeneous 1-4244-0912-8/07/$25.00 \u00a92007 IEEE. 3522 transformation matrix. 0pV = [ 0rV 0 \u2126V ] ; 0T V = [ 0RV (0\u2126V ) 0rV 01\u00d73 1 ] , (1) where 0pV \u2208 R 6 is the position and orientation vector and 0RV \u2208 SO(3) is the rotation matrix of \u03a3V with respect to \u03a30" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003404_isma.2013.6547379-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003404_isma.2013.6547379-Figure1-1.png", + "caption": "Figure 1. Quadrotor propellers and movements", + "texts": [ + " This paper provides a simulation platform of a quadrotor equipped with different sensors, which can be used to investigate different algorithms and controllers for indoor applications before implementing those algorithms on the physical systems, which reduces the risk during algorithms validation on the physical system and speed up the development cycle. Quadrotor modeling and control is discussed in the next section. Section three demonstrates the integrated simulation platform. Finally, the concluded remark is summarized in section four. The Quadrotor main idea was to have a helicopter that can handle larger capacity and can maneuver in areas that were difficult to reach. Generally it consists of four propellers (front, rear, right and left), as shown in Figure 1 [10]. By changing the control command to these motors \u03a9i, their speed will vary and the quadrotor direction is updated, accordingly the quadrotor can navigate in different directions. For instance, the quadrotor can move in the vertical Z direction by varying the speed of all propellers at the same time and by the same amount as shown in Figure 2. To command the quadrotor to move in the X direction, the speed of the front and rear propellers should be changed by the same amount and in opposite directions as shown in Figure 3" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001193_mra.2008.921547-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001193_mra.2008.921547-Figure2-1.png", + "caption": "Figure 2. Multifunctional gripper with sensor devices. Blocks of the game can be gripped in two different configurations. The arbor is used to push single blocks out of the Jenga tower.", + "texts": [ + " Finally, the underlying control architecture and the user application for playing Jenga are outlined. The robot used for all experiments in this context is a St\u20acaubli RX60 industrial manipulator. Its original controller has been replaced as described in [9], and only the original power electronics has been retained. Depending on the experiment or application, the control system consists of several PC nodes, and, here, we use four PCs. With the high-level hybrid controller, we achieve a control rate of 2 kHz, whereas the lowlevel joint controller runs at rate of up to 20 kHz. Figure 2 illustrates the developed gripper, which is mounted to the end effector of the manipulator. The gripper is equipped with a 6- D force/torque sensor, a 6-D acceleration sensor, and a laser triangulation distance sensor. The acceleration sensor can be used for the application of a 6-D sensor data fusion approach programmers implement guarded and guided motion commands with respect to any reference coordinate system? IEEE Robotics & Automation Magazine80 SEPTEMBER 2008 to compute forces and torques established by environmental contacts [10], [27]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001154_auv.2008.5290529-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001154_auv.2008.5290529-Figure4-1.png", + "caption": "Fig. 4. Geometric configuration of a bearing-only sensor and acoustic source at time instance k", + "texts": [ + " Electronics The electronics are divided into two subsystems: digital communication (Ethernet interface) and analog conditioning (1) (2) (3) Zi = h(x, qi, 'l/Ji) + Vi IT h(x, qi, 'l/Ji) = ')'(x,qi, 'l/Ji) - 2\" signal has been identified,the beamforming algorithm extracts bearing information, which is then fed through a generalized extended Kalman filter [19] that is discussed in Section III-A. The output of the filter is made available to other processes for tracking and control. A. Generalized extended Kalman filter The location of the acoustic source can be estimated from a series of bearing measurements using a generalized extended Kalman filter. In this section, we briefly define the estimation problem and present the generalized filter. As depicted in Figure 4, the position of the acoustic source is denoted x and the position of sensor i is denoted qi. The heading angle of sensor i, as might be measured by a magnetic compass, is denoted 'l/Ji. The vectors eN and eE are the north and east basis vectors, respectively, Each sensor obtains a bearing measurement to the source, denoted Zi and defined by As the sensor obtains discrete-time measurements, we further assume that each sample vi[k] is independent. Of particular interest is that the covariance of the measurement noise O\"i is dependent on the state of the sensor and the acoustic source. For a uniform linear acoustic array it is shown in [20] that where ')'(x,qi, 'l/Ji) is the relative angle of the sensor with respect to the source, as shown in Figure 4. The bearing angle measured by the sensor is zero when the acoustic source is broadside to the sensor, thus the term -\"i in (2). In the sequel we suppress the dependence of hand')' on states x, qi, and 'l/Ji' The sensor noise Vi is zero mean Gaussian, and data acquisition (DAQ). Each subsystem is implemented on a custom printed circuit board, The two subsystems communicate with each other via a 6Mhz SPI bus and two dedicated handshaking lines. The primary function of the digital communication board is to establish and maintain an Ethernet connection to the host (AUV) and act as a bridge between the host and the DAQ board", + " Thus we first address the motion control problem by assuming that all vehicles can share data. In Section IV-B, we propose a method for addressing the practical realities of underwater communication in which vehicles share data infrequently. By inspecting the gradients that make up the information term U, defined in (5), we see that the parameters affecting the information are the relative distance between source and sensor Ti = Ilx - qill, the relative angle of the sensor with respect to the source \"Ii, and the absolute bearing to the source (3i (see Figure 4 and the Appendix). A standard approach to this class of problems is to apply a gradient descent algorithm to actively control these parameters so that a suitable cost function is minimized, such as in [21]. Following [2] and [4], we implement a gradient-based control system to locally minimize the cost function considering the joint probability distribution of measurements taken from different sensors. Using the maximum likelihood approach one obtains equations analogous to (5) that account for shared measurements and predictions", + " Assume that at time k the states qi[k] and \\bilk] are known. The state at time k + 1 is updated according to the following kinematics (IS) (14) Taking the time derivative of the first equation and substituting from (9) with the assumption of stationary source so that j; = 0, we obtain iJi = l (Vicos \\bi sin (3i - Vicos ,Bi sin \\bi) Ti Rearranging terms and approximating the time derivative as in (10) we express Vi as V; _ (3i Ti \u2022 - cos \\bisin (3i - cos (3i sin \\bi ,BiTi sin \"/i where we used the relation, see Figure 4 \"/i = (3i - \\bi (10) (3ilk + 1] = (3ilk] + ,Bilk] \"/ilk+ 1] = \"/i[k] + ii[k] where Inputs ,Bi and ii are generated through gradient-descent laws to minimize (8) (16) (17) (l8b) y[k] = (x[klk] q[k] \\b[k]) T ;~ = (0 T (eN sin (3 - eE cos (3) 1) T Taking the time derivative of (IS) and substituting from (10) we express Wi as B. Local Observer Note that U incorporates information from all sensors at each time step, not just from those sensors that communicate during that time step. Since communication only occurs inter mittently, in general sensor i does not have all the necessary information to compute Uj for j i=- i", + " Using (5) and the following equalities from matrix calculus odetA d A [A-I {)A]~--= Iet tr -aT aT OA-I = _A-lOAA-I aT aT we can derive expressions for the partial derivatives in (II) {)U 1 f)(Ji ( TIT ) ~=-2~ \\1xhi\\1xhi+~\\1x(Ji\\1x(Ji V\"/i (Ji V\"/i a, 1 (O\\7~(Ji T O\\7xUi)+ 2 2 -~-.-\\1x(Ji + \\1x(Ji-~-.(Ji v,,/. v\"/. {)U = l (0\\1~hi \\7 h. \\1T h. {)\\1Xhi) 0(3\u00b7 (J' 0(3\u00b7 ,x. + x \u2022 ~(3.t t-:\u00ab 't 'l. 1I 1. 1 (0\\7~~ T O\\7x~) + 2(J1 ~ \\1x(Ji + \\7x (Ji O(3i Expressions for derivatives appearing in (12) are given in the Appendix. The next step is to express Vi and Wi in terms of the geometry and the control inputs ,Bi and ii. Consider the kinematic relations, see Figure 4 and Yij and Yj equal, respectively, the function Y in (17) evaluated at the local estimates xdklk], iiij, (f;ij, and at the ,:ommunicated quantities xj [kIk], qj, 'l/Ji: Control parameters Vij and Wij are estimated using the relationships (14) and (16). The observer updates the local position and yaw angle estimates of sensor j using gij [k + 1] = iiij [k] + T'Vij [k] (eN cos (f;ij [k] + eE sin (f;ij [k]) (f;ij[k+ 1] = (f;ij[k] +TWij[k] where iiij and (f;ij are, respectively, the estimate of the position and the estimate of the yaw angle of sensor j maintained by sensor i for all j -I- i, The fused information matrix 0' is computed using the estimated sensor positions iiij", + " Each sensor uses its local fused state estimate Xi computed through (6). Field trials were conducted at Claytor Lake, a 4,500 acre hydroelectric impoundment of the New River near Dublin, VA. Two Virginia Tech 475 AUVs were equipped with towed array sensors to measure the relative bearing to an acoustic source located on a support craft. The vehicles were able to communi cate with one another using a WHOI micromodem. The goal of the experiments was to demonstrate that with only intermittent communication the two vehicles could control their geometry, as defined in Figure 4, to minimize the cost function (8). Intuition along with inspection of (3) and (6) suggest that at steady-state, both vehicles should circle the estimated location of the acoustic source so that their sensors are broadside to the acoustic source (relative bearing \"Yi is 7r /2), and so that both vehicles are separated by 7r/2 around the circle (difference in absolute bearings /3i is 7r /2). The sensor parameters used for the experiments, derived for our array configuration, are K, = 0.0054, ao = 0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002609_icra.2011.5979602-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002609_icra.2011.5979602-Figure5-1.png", + "caption": "Fig. 5. Coordination system and rotational center", + "texts": [ + " 4, the soles of the feet are always fully touching the ground): (a) sequential side-slipping motion (b) simultaneous nonparallel shuffling motion (c) simultaneous parallel shuffling motion In this paper, we target the simultaneous parallel shuffling motion depicted in Fig. 4-(c), which requires the same motion for both legs. The load distributions are easy to control in this method. To realize this motion, shuffle turn must be realized repeatedly and precisely. Therefore, we apply a proportionalintegral (PI) control scheme and its efficiencies are a priori investigated by experiments using a humanoid robot. The coordination system of the feet \u03a3B is illustrated in Fig. 5-(a),(b). The origin position of the coordination system \u03a3B is arranged in the middle between the rotational center points. The positions of the rotational center of the right and left sole in the initial state are described as After the shuffle turn by qr is conducted, the positions of the rotational centers in \u03a3B can be written as: re = Rrs (3) le = Rls (4) R = [ cos qr sin qr \u2212 sin qr cos qr ] (5) The coordination system \u03a3H , which is shown in Fig.5-(c), is settled on the center of the hip joint of the robot. The joint angles of legs on \u03a3H are calculated from re and le by solving the inverse kinematics problem. The error value between the current angle and the target angle is feedbacked by the PI feedback algorithm. The control scheme is given by: qe(t) = qr(t) \u2212 qc(t) (6) qr(t+1) = q\u0302r(t+1) + Kpqe(t) + Ki \u222b qe(t)dt (7) where q\u0302r(t+1) is the target angle at t+1, qc(t) is the rotated angle at t, qe(t) is the angular error at t, qr(t + 1) is the modified target angle at t + 1, and Kp(= 0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001917_2009-01-2868-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001917_2009-01-2868-Figure5-1.png", + "caption": "Figure 5: Variator Force Balance", + "texts": [ + " Figure 4 explains this approach using a simplified model of the driveline with the variator represented by two discs and a single roller and the driveline and flywheel represented by two inertias. Applying a reaction force F to the roller causes a reaction torque (Ta and Tb) at the variator discs and consequently an acceleration of the two inertias (driveline side inertia A and flywheel side inertia B). This may change the speed of the driveline and/or flywheel inertia resulting in a change of variator ratio. The application of a castor angle to the roller carriages (Figure 5) enables the rollers to \u2018steer\u2019 to a new angle of inclination (ratio). This happens automatically \u2013 only the variator disc speeds and reaction force are defined externally. In the Torotrak design, reaction force is applied hydraulically to individual roller carriage pistons. FORMULA 1 MECHANICAL HYBRID SYSTEM The specification for the Flybrid Systems\u2019 Formula 1 Kinetic Energy Recovery System (KERS) is provided in Table 1 : Power 60kW Energy Transfer 400kJ per lap System Weight 25kg Flywheel weight 5kg CVT weight 5kg Flywheel Diameter 200mm Flywheel Length 100mm Efficiency > 70% round trip SAE Int" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001447_05698197508982750-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001447_05698197508982750-Figure5-1.png", + "caption": "Fig. 5-A cylinder and a plane", + "texts": [ + " Now one assumes a Gaussian asperity height distribution, the number of asperities between the height z and z + dz will be \\ 1 {A4(z)dz = {A)- exp [-(a- d)2/2u2][dz [16] u& then the total macroscopic load and friction will be where I,V, and F, are defined in [15] and can be expressed as functions of z . In [18] (h,/2) (aP,/ax) is the part of macroscopic hydrodynamic friction which can be calculated by using [I21 in the macroscopic scale and it must be added to the sum of microscopic asperity friction. EXAMPLE I-A ROTATING ROUGH CYLINDER AND A PLANE The problem studied in this section is a rougn cylinder rotating against a rigid, smooth plane as shown in Fig. 5. This configuration was used in many previous lubrication researches (13). The solution is represented by plotting Hersey's number vU/W against the coefficient of friction f = F/W, while other nondimensional parameters are varied in different figures for comparison. The nondimensional parameters used in this calculation are (rf/H), ( E I H ) , (Rid), (d/R,), (h.,/d) and (uld). Among them, calculation showed that with a ten-fold variation of (E/H) and (R/d), the variation of coefficient of friction was less than 5 percent, so that they can be ignored" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003169_0369-5816(65)90020-7-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003169_0369-5816(65)90020-7-Figure2-1.png", + "caption": "Fig. 2. Simplified circumscribed yield surface.", + "texts": [ + "= ~o = X O = 5 p = % = 2 A , mer id i an angle to nozzle in te rsec t ion , mer id ian angle to outer edge of r e in fo rce - ment pad, mer id i an angle to shell hinge c i rc le , dis tance f rom nozzle junct ion to nozzle hinge c i rc le , = nozzle thickening factor , = shell thickening factor , = Tp /Ts , ~ . - dPi, yield s t r e s s in uniaxial tension. 3. ANALYSIS The geometry under cons idera t ion is shown in fig. 1. The ma te r i a l is assumed to be perfect ly plast ic and t ime effects are not considered. The T r e s c a c r i t e r i on of yielding is a ssumed to gove rn the ma te r i a l together with the s implif ied yield surface suggested by Drucker [2] which is shown in fig. 2. With this yield surface, the hoop moment M~b is cons idered insignif icant which is a valid assumpt ion except for reg ions of the shell r e la t ive ly near the axis. The t r a n s v e r s e shear force does not affect the yield surface, but is important in the equi l ibr ium equations. The yield surface of fig. 2 c i r c u m s c r i b e s the co r rec t yield surface. If the d imens ions a re reduced by 3, it will insc r ibe the co r r ec t yield surface. Therefore a good approximate answer is found by using the surface of fig. 2 reduced by ~. The equivalent resu l t is obtained by mult iplying the f inal l imi t load obtained with the c i r c umsc r i be d yield surface by ~. These quest ions are d i s - cussed in detail in ref. [2]. In the following, a lower bound to the l imi t p r e s s u r e is found using the equi l ib r ium equations, the c i r c umsc r i be d yield surface and the lower bound theorem. The lower bound theorem may be stated as follows [8]: \"Any sys tem of forces and moments which sa t i s f ies the equi l ibr ium equations and has no components outside of the yield surface, cons t i - tutes a lower bound to the l imi t load\"" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003197_ias.2011.6074331-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003197_ias.2011.6074331-Figure4-1.png", + "caption": "Fig. 4. d-axis currents in each section at (a) wt =0\u00b0; (b) 40\u00b0,", + "texts": [ + " By the net vector sum in three sections, thus the suspension force is generated in the x positive direction. By these controlled d-axis currents, the 978-1-4244-9500-9/11/$26.00 \u00a9 2011 IEEE suspension force can be successfully generated in the arbitrary radial direction. Figs. 4 (a) and (b) show the d-axis direction and the d-axis currents in the rotor angular position at OJ! = 0\u00b0 and 40\u00b0 (mech.), respectively. In each section, the number of the d axes is either 2 or 3 depending on the rotor angular position. In Fig. 4 (a), there are three d-axes at wt = 0\u00b0. In Fig. 4 (b), there are two d-axes at wt = 40\u00b0. The d-axis rotates according to the rotor rotation so that the direction of suspension force is also varied depending on the rotor angular position. In the next section, it is discussed how the d-axis currents are regulated to generate the suspension force. IV. RADIAL POSITION CONTROL METHOD A. Coordinate transformation in two- and three-axes In order to derive the relationship between the d-axis currents and the suspension force, the axes in the coordinate are defined in this section" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002759_j.triboint.2012.11.012-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002759_j.triboint.2012.11.012-Figure3-1.png", + "caption": "Fig. 3. Schematic diagram of the model for the lubrication between the rough surface of the porous self-lubricating composite and a smooth surface.", + "texts": [ + " Thus, the value of Ei for the selflubricating composite can be easily deduced. According to Eq. (1), the cermet matrix phase modulus can be determined as Es \u00bc 229:4 GPa and the elastic modulus of the silicone oil colloids can be inferred from colloidal properties [15] as El \u00bc 0:8 MPa. Thus, Eq. (2) can be expressed as E\u00f0f 0\u00de \u00bc 1 2 \u00f0Es\u00f01 f 0\u00de\u00feElf 0\u00de\u00fe EsEl 2\u00f0Esf 0\u00feEl\u00f01 f 0\u00de\u00de \u00f02\u00de where f0 is the volume fraction of the solid lubricant phase, which is also called porosity. A novel model that combines roughness and porosity is developed to address the aforementioned issue. Fig. 3 shows the rough surface of the porous self-lubricating composite sliding against a smooth plane. During sliding, the lubricant phase in the composite is squeezed out as a result of the contact stress. This result leads to the formation of an elastohydrodynamic lubricant film that reduces friction and wear. The film also allows the smooth running of machine components and results in a satisfactory component lifespan. A thin film forms between the two moving surfaces. However, when the pressures on the elastohydrodynamically lubricated machine components are too high or if the running speeds are too low, the lubricant film becomes penetrated", + " The lubrication mechanism is governed by the physical properties of the composite as well as by its surface topography. Therefore, the microstructural design is optimized and the composite roughness is reduced so as to prevent the solid contact problem of the machine components. The problem requires the simultaneous solution of all these equations, using the numerical method similar to those described in detail by Hamrock and Dowson and by other researchers [16\u201318]. Assume that the two surfaces shown in Fig. 3 are moving in the x-direction with a relative speed V \u00bc V2 V1. If the fluid with pressure dependent viscosity Z and density r occupies the region between the surfaces, then the lubricant distribution h, due to the relative motion of the surfaces is modeled by the Reynolds equation as follows: div h3r\u00f0p\u00de Z\u00f0p\u00de =p ! \u00bc 6V @\u00f0r\u00f0p\u00deh\u00de @x \u00f03\u00de Note that a boundary condition of pressure p\u00bc0 at the edges of the solution domain as well as a normal cavitational condition on the outlet side must be satisfied when solving this equation" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002979_20130703-3-fr-4038.00130-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002979_20130703-3-fr-4038.00130-Figure1-1.png", + "caption": "Fig. 1. Sequence of estimates and waypoints", + "texts": [ + " To generate by Monte Carlo a 2-dimensional random perturbation vector \u2206i which components are independently generated from a zero mean probability distribution satisfying the preceding conditions. A common choice for each component of \u2206i is to use a Bernoulli \u00b11 distribution with probability of 1/2 for each \u00b11 outcome. (4) Proceeding to the new waypoints. To proceed to next two points u\u2212 i and u+ i . They are intersections of the UAV trajectory projection on 2D plain and the line which goes through the point of the previous estimate x\u0302(i\u22121) in the direction of the vector \u2206i (see Fig. 1). (5) Velocity function evaluations. Obtain two measurements at the points u\u00b1 i of the velocity function y\u00b1i = F (u\u00b1 i ). (6) Computing the values \u03b2\u00b1 i . To measure the dis- tances from the the point of the previous estimate x\u0302(i\u22121) and points u\u2212 i and u+ n and compute such two values \u03b2\u00b1 i that u\u00b1 i = x\u0302(i\u2212 1) + \u03b2\u00b1 i \u2206i. (7) Quasigradient calculation. To calculate the quasigradient: g\u0302 = \u2206i y+ i \u2212 y \u2212 i \u03b2+ i + \u03b2\u2212 i . (8) Updating center estimation. Use the standard stochastic approximation form x\u0302(i) = x\u0302(i\u2212 1) + \u03b1g\u0302 to update the current center estimation" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003305_1.4026080-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003305_1.4026080-Figure2-1.png", + "caption": "Fig. 2 Sectional schematic view of the test apparatus: test rig arrangement", + "texts": [ + " Manuscript received August 19, 2013; final manuscript received November 18, 2013; published online February 5, 2014. Assoc. Editor: Jordan Liu. Journal of Tribology APRIL 2014, Vol. 136 / 021703-1Copyright VC 2014 by ASME Downloaded From: http://tribology.asmedigitalcollection.asme.org/ on 01/28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use configuration has been analyzed more recently by Harika et al. [1] and Bouyer et al. [8]. A drawing of the test rig used for the experiment is shown in Fig. 2. The experimental device can be described as having three essential components: \u2022 the driving system, composed of a 15 kW electrical motor and a precision spindle \u2022 the loading system \u2022 a support to test the thrust bearing The precision spindle is driven by an electrical motor providing enough power to reach 10,000 rpm, using a flat belt for transmission. The thrust bearing is loaded by a pneumatic jack monitored with a high-precision air regulator. This allows for a load varying between 50 N and 8,000 N to be applied" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003761_j.compstruc.2012.08.005-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003761_j.compstruc.2012.08.005-Figure3-1.png", + "caption": "Fig. 3. Symmetric uniform pressure.", + "texts": [ + " Poisson\u2019s ratio: m = 0.3. Shear modulus: G \u00bc E 2\u00f01\u00fem\u00de. Mass density: q = 7850 kg m 3. No warping is considered, therefore the polar inertia I0 coincides with the Saint\u2013Venant torsional modulus J. Two kinds of loads are applied to the structure for computation: A symmetric pressure according to the Z direction. A concentrated load at a specific point of the middle line. 4.1. Symmetric uniform pressure along the Z direction A symmetric uniform force per unit length is applied on the middle line of the beam, see Fig. 3. The only non zero force component is ff, defined as follows: h 2 \u00bd p; p=2 ; f f\u00f0h\u00de \u00bc p h 2 p=2;p=2 ; f f\u00f0h\u00de \u00bc p h 2 p=2;p ; f f\u00f0h\u00de \u00bc p 8>< >: \u00f024\u00de The Fourier expansion of the applied load is reduced to: ff\u00f0h\u00de \u00bc X1 m\u00bc0 \u00f0 1\u00dem\u00fe1 4p \u00f02m\u00fe 1\u00dep cos\u00f02m\u00fe 1\u00deh \u00f025\u00de So according to the notations of (21), one obtains: F1m \u00bc \u00f00;0;0;0;0;0\u00de F2m \u00bc 0;0;0;0; \u00f0 1\u00dem\u00fe1 4p \u00f02m\u00fe1\u00dep ; 0 ( \u00f026\u00de Eq. (22) has the following form: K1m X1m \u00bc 0 K2m X2m \u00bc F2m \u00f027\u00de After resolving these systems of equations, the numerical validation of the element consists in comparing the harmonic response obtained with those obtained by the FEM" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002340_j.triboint.2011.10.017-Figure11-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002340_j.triboint.2011.10.017-Figure11-1.png", + "caption": "Fig. 11. Front view of pad structural deformation.", + "texts": [ + " The result for temperature distribution in the oil film for a conventional pad is shown in Fig. 9. The maximum temperature is at the corner of the trailing edge and the outer radius. The temperature contours near the trailing edge and the inner radius is bent forward, which shows less temperature rise. The temperature variation along the left half of the pad is less when compared to the right half. Fig. 10 below shows the pad indicating the extent of structural-thermal deformation due to pressure and thermal gradient, which amounts to 0.704E-3 mm. Likewise Fig. 11 shows the plane structural deformation of the pad. For the plane-structural analysis deformation of the pad for the given parameters is equal to 0.726e-3 mm. The renewed film thickness is the sum of the original nodal film thickness plus the corresponding nodal deformation of the pad, which tantamounts to 0.836e-3 mm. The non dimensional dynamic stiffness Kn values are got using Eq. (21) corresponding to % ho variation for the 2-1 pair where Kn \u00bc DW 0 DX h3 min BL2Umef f \" # \u00f021\u00de Fig. 12 shows the plot where the values of K* tend to converge asymptotically to one value for variation of % ho" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002099_j.cad.2010.08.007-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002099_j.cad.2010.08.007-Figure2-1.png", + "caption": "Fig. 2. Position relation between \u03c3a and \u03c3d .", + "texts": [ + " By using the classical method of differential geometry, it is easy to obtain the unit normal vector, the two principal curvatures, and the two corresponding principal directions of \u03a3d, as follows: (n)a = ma(\u03b8, \u03c6); k1 = \u2212 1 \u03c1 , k2 = \u2212 sin\u03c6 \u03c1 sin\u03c6 + p ; (g1)a = na (\u03b8, \u03c6) , (g2)a = ga (\u03b8) . (2) The outward direction of (n)a is positive. During the first envelope, the grinding wheel revolves about its own axis and executes the movement together with the cutter frame. In order to investigate the relative motion between the grindingwheel and theworm blank, it is possible to let themoving coordinate system \u03c3d(od; id, jd, kd) be rigidly connected to the tool post. The unit vector, kd, is along the axis of the tool post. Fig. 2 shows the position relationship between the coordinate systems \u03c3a and \u03c3d. The vector equation of \u03a3d and its unit normal vector, as well as its two principal directions can be represented in \u03c3d by coordinate transformation, and the results are as follows. (rd)d = R [id, \u2212 (90\u00b0 \u2212 \u03b2)] (ra)a \u2212 a0id = xdid + ydjd + zdkd, (3) xd = xa \u2212 a0, yd = ya sin\u03b2 + za cos\u03b2, zd = \u2212ya cos\u03b2 + za sin\u03b2; (n)d = R [id, \u2212 (90\u00b0 \u2212 \u03b2)] (n)a = nxid + nyjd + nzkd, (4) nx = sin\u03c6 cos \u03b8, ny = sin\u03b2 sin\u03c6 sin \u03b8 + cos\u03b2 cos\u03c6, nz = \u2212 cos\u03b2 sin\u03c6 sin \u03b8 + sin\u03b2 cos\u03c6; (gm)d = R [id, \u2212 (90\u00b0 \u2212 \u03b2)] (gm)a = gmxid + gmyjd + gmzkd, m = 1, 2; (5) g1x = cos\u03c6 cos \u03b8, g1y = sin\u03b2 cos\u03c6 sin \u03b8 \u2212 cos\u03b2 sin\u03c6, g1z = \u2212 cos\u03b2 cos\u03c6 sin \u03b8 \u2212 sin\u03b2 sin\u03c6; g2x = \u2212 sin \u03b8, g2y = sin\u03b2 cos \u03b8, g2z = \u2212 cos\u03b2 cos \u03b8; where a0 = a \u2212 rf1 \u2212 rd and R [id, \u2212 (90\u00b0 \u2212 \u03b2)] = 1 0 0 0 sin\u03b2 cos\u03b2 0 \u2212 cos\u03b2 sin\u03b2 " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002071_s0091-0279(71)50004-1-Figure13-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002071_s0091-0279(71)50004-1-Figure13-1.png", + "caption": "Figure 13.", + "texts": [ + " This is the anterior contact point. The limb will stay in contact with the ground until the anterior half of the body has passed over this point, thus terminating the stride (Fig. 12). The hindlimb also has a calculable stride of great importance. In motion, the hindlimb is extended to the middle ofthe body and is placed in contact with the ground a split second after the forelimb has been lifted. The hindlimb then stays in contact with the ground to about an equal distance past the normal stance position (Fig. 13). In anteroposterior views of limb placement, normal variations will occur between the two basic shapes of dogs. Long legged, deep chested dogs-mostly the hunting breeds, where endurance necessi tates the conservation of energy- walk by placing one limb in a direct line with the limb of the opposite side (single tracking). This type of movement requires much less energy because the dog's body is stable, with no rolling of weight from side to side. These dogs are capable of running for many miles before showing signs of fatigue" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001768_j.robot.2009.09.014-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001768_j.robot.2009.09.014-Figure5-1.png", + "caption": "Fig. 5. Set of five AvoidObstacle behaviors based on the robot\u2019s scanning IR array. Each behavior is bounded by two IR sensor readings, shown with active distances within the behavior view regions.", + "texts": [ + " These behaviors can be combined in situations where a combination of reactive and deliberative behaviors is required (e.g., reactive waypoint navigation). The following weighted reactive behaviors are used in the system: AvoidObstacle: This behavior allows the robot to reactively navigate around obstacles sensed by the scanning IR range array. The IR sensor array\u2019s 180\u25e6 view angle is divided into five behaviors. Each behavior corresponds to a section of the total view (bounded by two IR sensor readings), and is weighted differently based on its area of focus (center weighted highest, decaying outward). Fig. 5 illustrates the set of five AvoidObstacle behaviors based on the IR array\u2019s FOV. Each behavior is considered active at specific obstacle distances. The further outward from the center, the shorter the active distance threshold. This is accomplished by computing the range (maximum observable distance \u2014 minimum observable distance) and magnitude ((closest obstacle distance \u2014 minimum sensing distance)/range) of the IR sensor readings. The computed range for both AvoidObstacle and AttractObstacle is linearly mapped to [0,1]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000395_0094-114x(80)90004-x-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000395_0094-114x(80)90004-x-Figure1-1.png", + "caption": "Figure 1. Description of a general element E'.", + "texts": [ + " Next the displacements are expressed in Fourier series, the constraints expressed by the compatibility equations are eliminated from the system equation of motion and thus the original differential equation of motion is reduced to a set of algebraic equations. From the solution of these algebraic equations and their back transformation, the steady state deflections and stresses within the links are finally calculated. The sine and cosine of the angles between some fixed reference line and each link of mechanism with the crank rotating at a constant speed may be expressed in the form of Fourier series. For slider crank and crank rocker mechanisms, such expressions may be found in [10-13]. Thus for any element E' of length 1, shown in Fig. 1, the sine and cosine of the angle 0E, can be expressed as follows: h I cos 0E, = ~ [ccj cos (j - l)oJr + csi sin j~oz] (1) /= l hi sin OE, = ~ [sq cos (j - 1)tot + ssj sin jtor] (2) j= l where, hi = total number of sine/cosine terms taken in each series. ~o = constant input speed and ~\" = time. ccj, csj, sc~, ss~ are deterministic Fourier co-efficients for 1 - hi. The following trigonomatical relation is used to find the absolute angular velocity wE, of the element in the form of Fourier series: ~E' = ~ = cos 0~, (sin 0~,)- sin OE' (COS 0~,)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003499_s11771-013-1495-x-Figure8-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003499_s11771-013-1495-x-Figure8-1.png", + "caption": "Fig. 8 Model with five teeth", + "texts": [ + " Assuming that the contact force of contact pair 2 is P2, while P1 and P3 represent the contact forces of contact pair 1 and 3, respectively, we can obtain the load distribution factor of the contact pair 2 by 2 p 1 2 3( ) F C F F F (14) At last, computed with Eq. (14), the load distribution factor of the contact pair 2 is shown in Fig. 11, and its maximum value is gotten in the posted process of ABAQUS. Obviously, the contact force of a J. Cent. South Univ. (2013) 20: 354\u2013362 360 contact pair is also decided by P P b1 T P C P C R (15) To reduce the consuming time of ABAQUS, a FEM model was created with five teeth (see Fig.8), to compute the contact stresses of teeth in contact, the amount of mesh should be confirmed to be large enough to calculate the contact stress exactly. In the field outputs of ABAQUS, we can know the contact stresses from the outputs of CPRESS. Figure 12 shows the cloud picture of the contact stress in a moment (the loaded torque on gear is 10.24 kN\u00b7m, the same below). When the teeth come into or quit meshing, the edge contact happens, as shown in Fig. 13 and Fig. 14. In Fig. 15, the curve of contact stresses in the whole meshing process is given, and the maximal contact stress is 894" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003869_s00419-012-0608-6-Figure13-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003869_s00419-012-0608-6-Figure13-1.png", + "caption": "Fig. 13 The mode shapes corresponding to frequency \u03c916 (the first mode)", + "texts": [], + "surrounding_texts": [ + "As mentioned earlier, in the geometrical model of the gear, the geometry of the teeth is omitted. It allows us to reduce the system\u2019s FE model size. The simplified geometrical model of the system consists of five sectors (see Fig. 1) that have the cyclic symmetry feature. Each of these segments is meshed by using standard procedures of the ANSYS software. The 3-D solid mesh is elaborated and as mentioned earlier, the ten-node tetrahedral element (solid92) with three degrees of freedom in each node is used to realize each sector. During the mesh generation process, it is assumed that the maximum length of each element\u2019s side needs to be no more than 2.7 [mm]. The developed FE model is displayed in Fig. 2, and it consists of 19,620 elements and 36,188 nodes, respectively. The particular sectors are glued as a whole at the geometrical model preparing the stage by using standard procedure of the ANSYS program. The analysed gear is mounted in the roller bearings. Such bearings typically have slight load capacity under loads perpendicular to the primary supported direction. The gear shaft neck surfaces on which the bearings are assembled are denoted \u201cbearing\u201d (see Fig. 3a). The gear mates with the other devices by the splines. The splines is simplified down to a regular cylinder of the diameter assumed as equal to the splines pitch diameter. The surface denoted \u201cjoint\u201d (see Fig. 3a) is located on the pitch diameter of the splines. Parameters of the analysed system are shown in Table 1a\u2013b. The calculation results for natural flexural oscillations taking into account angular speed of the gear are shown in the paper. In the case of circular discs and annular plates, for each solution where nodal lines are nodal diameters, one obtains two identical arrangements of straight nodal lines, rotated by an angle of \u03b1 = \u03c0/(2n) one to another, where n is the number of nodal diameters. In accordance with the circular and annular plate vibration theory [5,6,12], the particular natural frequencies of vibration are denoted as \u03c9mn , where m refers to the number of nodal circles and n is the mentioned number of nodal diameters. As the shape of the gear model is fairy elaborate, the flexural modes of the system are subject to deformation (as compared to the system without any holes) to such extent that establishing which particular node it refers to becomes rather difficult. This problem is even worse if the angular speed of the gear is varying. The problem of influence of the angular speed on the flexural gear models deformation is analysed. For the purpose of identification of these modes, an algorithm of tagging oscillation modes, which determines the correspondence between vibration of the circular disc versus disc with holes, is used. For this purpose, an auxiliary model of annular plate in the form shown in Fig. 3b is used. The geometrical dimensions of the auxiliary model were taken from the gear geometry (shown in Fig. 1). They are as follows: addendum circle diameter dz , rim mounting diameter dp, root circle diameter dw2, and thickness h p and hz (see Table 1). Dynamic analysis is performed for the auxiliary model cases rotating at predetermined angular speed, where diameter of though holes d01 (see Fig. 3b) varies as seen in Table 2. Findings are compared to each other both quantitatively and qualitatively. This method makes it possible to investigate deformations of nodal lines associated with nodal diameters and circles due to through holes and then determine correspondence between oscillation modes of solid circular disc and a plate with holes. In the final step, solutions found for the auxiliary model are compared with the solution for the system whose FEM model is shown in Fig. 2 (the principal model). As for the principal model case, the 3-D solid mesh and the ten-node tetrahedral element (solid92) are used to discretize the auxiliary models. For all models subject to analysis, the boundary conditions were applied to the nodes. For each model, 1 d f associated with node radial displacement was subtracted from the nodes found on the surface identified as a bearing (see Fig. 3a,b). Furthermore, 1 d f associated with the displacement of nodes along the centreline of each model was subtracted from the nodes found on the surface, identified as a joint (see Fig. 3a,b). For the models obtained in this way, calculations were kept conducted as long as the natural frequency \u03c918 was determined. The calculations were performed assuming that the systems rotate as angular speed of \u03b8 , within the range of 0\u20131047 [ rad/s]. During the computing process, the angular speed values were gradually increased by 80[ rad/s], which made fourteen variants of the results (the natural frequencies and corresponding natural modes), which were subject to further interpretation. The rotation effect was taken into account by determining stress distribution due to rotation, for each model during the computational step associated with static analysis (the so called pre-stress effect). This stress distribution was then included in the computation step associated with modal analysis. The results of the numerical calculations related to the procedure of identifying deformed natural modes of flexural vibration of the gear under consideration are shown below. The results displayed here relate to the determination of the correspondence between the natural frequencies \u03c916 and \u03c925 at high angular speed (\u03b8 = 1047 [ rad/s]) as well as to the correspondence between oscillation modes and the natural frequency \u03c931 at lower angular speeds (\u03b8 = 80 [ rad/s]). The results as shown in Figs. 4, 5, 6, 7, 8, 9 allow for tracking deformations of nodal lines associated with nodal circles and diameters, due to varying diameter of the through holes. With respect to the natural frequency \u03c925, there is marked difference in shapes of natural modes. When one compares the results between each other, one can notice that in order to identify correctly deformed natural modes of the flexural oscillations in the gear under consideration at lower angular speeds, larger number of auxiliary models is required to be included during calculations, as compared to the higher angular speeds. It comes from the fact that additional stresses through the centrifugal effects appear. This effect causes the gear flexural stiffness to be an apparent function of rotational speed (stiffness grows for higher speed). In the next part, results of the numerical calculations associated with the extent of the influence of the angular speed to deformation of mode shapes of oscillations. For each discussed case, both mode solutions related to nodal diameters are shown. These analysed results are sorted by the order of their occurrence. For the frequencies \u03c923 and \u03c918, the results were obtained at angular speeds of \u03b8 = 0 and \u03b8 =1,047 [ rad/s] respectively. For the other cases, results were obtained at angular speeds \u03b8 of, 0, 320, 720, and 1,047 [ rad/s], respectively. Natural frequencies for these modes are included in Table 3. To determine this mode (see Figs. 10, 11), the procedure of tagging natural oscillation modes was required. Nodal lines associated with the circle and diameter are deformed. Minor influence of the angular speed to deformation of the nodal lines is noticeable. The task of determining modes in this case was not too difficult (see Figs. 12); no procedure of tagging natural oscillation modes was required. The slight impact of the gear angular velocity on the distortion of the nodal lines is observed. For these modes (see Figs. 13, 14), procedure of tagging natural oscillation modes was required. It is noticeable that angular speed affects markedly deformation of the nodal lines. Once the angular speed of 720 [ rad/s] is exceeded, the oscillation mode takes different shape. Major deformation of mode shape attributable to the shaft vibrations is evident at this speed. Moreover, additional problem associated with some similarity of the mode being tagged to the mode associated with frequency of \u03c931, emerged during mode identification. Establishing the correspondence between these modes was a complex task (see Figs. 15, 16) due to the shape of oscillation modes similarity to the case discussed earlier. The angular speed affects deformation of nodal lines markedly. Major shape mode variations emerge at \u03b8 = 400 [ rad/s]. The identification process in this mode was not easy (see Figs. 17, 18) . One can notice that angular speed affects the deformation of nodal lines. Major variation in mode shape emerges at \u03b8 = 720 [ rad/s]. Moreover, additional annular shaft vibration emerges at the highest considered angular speed. Finding correct correspondence between the modes in this case was fairly easy (see Figs. 19). High repeatability in deformations of nodal lines on circular plate at various angular speeds is noticeable. As a consequence of the conducted analysis (see Table 3), the Campbell diagram was plotted for the gear under consideration. This is a convenient method of displaying the relationship between gear natural frequencies and transmission system excitations [4]. Excited frequencies are plotted on a vertical axis, and the gear speed of rotation is plotted on the horizontal axis (see Fig. 20). Natural frequencies achieved from numerical analysis are plotted as near-horizontal curves. The forced frequency due to the meshing is determined by the following relation (as in Ref. [4]) f = n0 \u00b7 z 60 (4) where n0 [rpm] is the rotational speed and z is the number of teeth in the gear. For this system, the gear teeth number is z = 59. Vibration resonance phenomenon occurs when forcing frequency (4) matches as to its value with some natural oscillation frequency of the gear. The points where the near-horizontal \u03c9mn curves intersect the straight line (4) indicate the speeds at which the gear resonance will be excited (see Fig. 20). For instance, the rated excitation speed for the natural frequency of \u03c923 is 764 [rpm]. It may be inferred from both the Campbell diagram and Table 3 that the rotating movement makes flexural stiffness of the gear under consideration to increase. Moreover, at speed of 3,820 [rpm], one can notice major surge associated with the mentioned earlier changing of the shape of the natural mode frequency in the case of the frequency of \u03c931. The growth of the gear transversal stiffness observed during gyrate of the gear comes from the appearance of the additional stresses in the toothed gear through the centrifugal effects. The higher rotational speed generates higher centrifugal forces, higher stress level, thereby causing the transversal stiffness of the system to increase. Moreover, the growth of the gear flexural stiffness through the gyrate effect causes reduction of the needed numerical calculations connected with identifying the proper distorted mode shapes." + ] + }, + { + "image_filename": "designv11_7_0002889_s11771-013-1751-0-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002889_s11771-013-1751-0-Figure4-1.png", + "caption": "Fig. 4 Finite element models: (a) Disk; (b) Blade; (c) Casing", + "texts": [ + " [19\u221220], there are d b c d b c[ ] ( , , , , , )YE Y (15) d b c d b c[ ] ( , , , , , )YD Y D (16) The reliability index \u03b2 and probability R in Ref. [19] are represented by ; ( )Y Y R D (17) 4.2.1 Finite element models The BTRRC of an aeroengine HPT is shown in Fig. 3(a). Obviously, the analysis of BTRRC may be decomposed into the radial deformation analyses of sub- J. Cent. South Univ. (2013) 20: 2414\u22122422 2418 components (disk, blade and casing). These assembly objects were simplified to establish their finite element models (FEMs), as shown in Fig. 4. In FEMs, the tenon of blade is assumed to be contained in the disk and the pin-holes of disk are ignored. The loads and constraint conditions on disk are axisymmetric. There are much air to cool turbine disk. Different temperatures at different positions (A1, A2, A3, B1, B2 and B3) of disk model are gained according to Refs. [2, 6\u221210, 21\u221222]. Similarly, the FEM of blade is built by ignoring the tenon, the cooling holes and the cooling effect since there is no impact almost on the analysis results of BTRRC" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000312_s11071-005-9016-6-Figure7-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000312_s11071-005-9016-6-Figure7-1.png", + "caption": "Figure 7. Rail head surface.", + "texts": [ + " Wheels are described as a surface obtained by rotating a two-dimensional curve (Equation (34)) that defines the wheel profile through 360 degrees about the wheel axis as shown in Figure 6. x = x0 + r ( sw 2 ) sin sw 1 y = y0 + sw 2 z = z0 \u2212 r ( sw 2 ) cos sw 1 \u23ab\u23aa\u23ac\u23aa\u23ad (34) where sw 1 and sw 2 are the surface parameters of the wheel. In this case the parameter sw 1 represents the rotation about the wheel axis and the parameter sw 2 represents the translation in the lateral direction. Rail is described by translating a two-dimensional curve that defines the rail profile (Equation (35)) in the longitudinal direction as shown in Figure 7 x = x0 + sr 1 y = y0 + sr 2 z = z0 + f ( sr 2 ) \u23ab\u23aa\u23ac\u23aa\u23ad (35) Because of the constraint, the components of the vector of generalised coordinates q and the surface parameters s are not independent and can be written in partitioned form as follows: q = [ qT d qT i ]T (36) s = [ sT d sT i ]T (37) where qd and qi are, respectively, dependent and independent generalised coordinates, and sd and si are, respectively, dependent and independent surface parameters. For a virtual change in the system coordinates, the constraint equation (Equation (27)) transforms as Cq\u03b4q + Cs\u03b4s = 0 (38) Then applying the coordinate partitioning of Equations (36) and (37), we can write Cqd \u03b4qd + Cqi \u03b4qi + Csd \u03b4sd + Csi \u03b4si = 0 (39) In matrix form Equation (39) can be rewritten as [ Cqd Csd ][ \u03b4qd \u03b4sd ] + [ Cqi Csi ][ \u03b4qi \u03b4si ] = 0 (40) Because the total number of dependent generalised coordinates and the number of dependent surface parameters altogether is the same as the number of constraint equations nc, and the constraint equations are assumed to be linearly independent, the matrix [Cqd Csd ] is square of size nc \u00d7 nc and is nonsingular" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001718_cca.2010.5611301-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001718_cca.2010.5611301-Figure1-1.png", + "caption": "Fig. 1. 2R planar manipulator.", + "texts": [ + " The control input and update law in those cases then depend on s, a regressor matrix Y (q, q\u0307, q\u0307r, q\u0308r) and the estimation of unknown/uncertain parameters. The method proposed in this paper does not require such a definition of the error signal. The adaptive input, which compensates for errors, together with the skewsymmetry of the interconnection matrix of the error system directly results in the adaptation law for the uncertain parameters and passivity of the error system. The adaptive tracking control is applied on a fully actuated 2 DOF planar manipulator (2R planar manipulator). The system is shown in figure 1. The manipulator has links with length li, angles \u03b8i, mass mi, the center of the mass is denoted by ri and the moment of inertia Ii with i = 1, 2. The system works in the horizontal plane so gravity influence can be neglected. The Hamiltonian can then be defined by only kinetic energy: H(q, p) = 1 2 p\u22a4M\u22121(q)p (40) with q = (\u03b81, \u03b82) \u22a4 and p = M(q)q\u0307. Define the constants a1 = m1r 2 1 + m2l 2 1 + I1 a2 = m2r 2 2 + I2 b = m2l1r2 The mass matrix becomes M(q) = [ a1 + a2 + 2b cos \u03b82 a2 + b cos \u03b82 a2 + b cos \u03b82 a2 ] (41) This system can be described as a standard PH mechanical system (12) with G a 2\u00d7 2 identity matrix since the system is fully actuated with input signal u = (u1, u2) which are the control torques on the two joints" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001555_iros.2008.4650574-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001555_iros.2008.4650574-Figure5-1.png", + "caption": "Fig. 5. Schematics of a 3-RPS parallel mechanism", + "texts": [ + " The system of screws degenerates if the determinant of the Jacobian J, of which the lines are composed of the coordinates of the screws Rij (j = 1, 2), vanishes. After simplification, this determinant can be written as: ( )\u03b8\u03b8 cos1cos 8 27det +=J . (17) Disregarding \u03b8 = \u03c0, (13) leads us to the only remaining possibility for Type 2 singularities: \u03b8 = \u00b1\u03c0/2. Thus, for any 3-PPS parallel manipulator, the workspace is bounded by the orientation \u03b8 = \u00b1\u03c0/2 of the platform, for any altitude z and angle \u03c6. B. Singularity Loci of 3-RPS Parallel Mechanisms As shown in Fig. 5, for this mechanism, Ri1 and Ri2 are two forces located at point Bi, the first directed along the line AiBi and the second perpendicular to the plane of the legs. The system of screws degenerates if: 0)3cos()3(cosdet 01 2 2 =++= ccc \u03c6\u03c6J , (18) where c0, c1 and c2 depend on angle \u03b8, on the altitude z of the center of the platform and on the radius Rb of the circumcircle of the base, ( )( )3 2 1coscos1 16 27 \u2212+= \u03b8\u03b8zc , ( )( ) ( )( )3)14()1(21 64 27 )4812()13(1 64 27 22 1 \u2212\u2212+\u2212+\u2212\u2212 +++++\u2212\u2212\u2212= bb b RccRcs Rczccccsc \u03b8\u03b8\u03b8\u03b8 \u03b8\u03b8\u03b8\u03b8\u03b8\u03b8 , ( )( ) ( )( ))2()1(41 32 27 4)34(1 32 27 22 0 bb RccRcz zccccczc +\u2212+\u2212 ++\u2212\u2212\u2212+\u2212= \u03b8\u03b8\u03b8 \u03b8\u03b8\u03b8\u03b8\u03b8 " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000716_s11740-008-0136-y-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000716_s11740-008-0136-y-Figure5-1.png", + "caption": "Fig. 5 Correlations in beveloid gear grinding [5, 7]", + "texts": [ + " The complete transformation matrix is built up by multiplying the single matrices in the correct order. 4.2 Simulation realization For the realization of the grinding simulation the definition of the tool as well as of the kinematic relations between workpiece and the tool is crucial. The tool itself represents in its normal section a basic rack. The normal section is the chosen contour for the simulation. It is defined by its dedendum hf, addendum ha, transverse pressure angle at, module mn, tip radius rk and the grinding wheel diameter, Fig. 5, right hand side. The rest of the tool data can be derived of these definitions. Since the tool is needed for a simulation in which the generation condition formulated by Litvin has to be solved [13], the tool is represented by an array of points distributed on the normal section of the tool. For each of these points the simulation checks whether it fulfills the generating condition at a simulation increment or not. To do so, the normals of the points have to be part of the tool representation. Furthermore the simulation needs the complete transformation matrix in order to calculate position and velocity of the tool for a simulation increment. The transformation matrix follows from the kinematical relations shown in Fig. 5, left and middle. The process as shown in Fig. 5, left, is in accordance with the process proposed by Roth [5]. To define the transformation matrix correctly, all necessary translations and rotations have to be described separately. Those include the movements of the machine tool and all translations and rotations necessary for the initial positioning of the tool relative to the workpiece. One important aspect for the correct simulation of beveloid gear grinding is the representation of the changing in-feed over the tooth width. Therefore it is necessary to synchronize the motions in x- and z-direction. Additionally a swivel angle is needed for the simulation of helical beveloid gears. Since the tool is represented by its normal section, this section has to be rotated in a certain way to represent the angular contact zone, as shown in Fig. 5, middle. A translation of the tool in y-direction forms together with the workpiece rotation the generation motion. All these movements, including the tool rotation, have to be variable over the simulation time. Thus the simulation will be able to simulate different modifications. Given these movement requirements in connection with the positioning requirements, the following motions result. Every motion can be represented by a single rotation or translation matrix. Together they form the transformation matrix" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003761_j.compstruc.2012.08.005-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003761_j.compstruc.2012.08.005-Figure2-1.png", + "caption": "Fig. 2. Local coordinate system describing the cross section.", + "texts": [ + " Circular arc beam geometry The geometry of a circular arc beam is defined by a constant radius of curvature R and a constant cross-section S oriented so that the principal axis of inertia Z stays normal to the plane of the beam and the principal axis of inertia Y stays parallel to this plane. The middle line of the beam is described by a curvilinear abscissa s, as shown in Fig. 1. We note G(s) a current point of the middle line. The position of each point M of the cross-section S is described in an orthogonal curvilinear coordinate system by the three numbers (s,g,f) (see Fig. 2). The position vector OM is given by the following expression: OM\u00f0s;g; f\u00de \u00bc OG\u00f0s\u00de \u00fe gY\u00f0s\u00de \u00fe fZ \u00f02\u00de Thus at each point G, the local basis (X,Y,Z) coincides with the Frenet basis (t,n,b) defined along the middle line of the beam. Therefore this basis satisfies the Frenet\u2013Serret formulas (3): @X @s \u00bc 1 R Y and @Y @s \u00bc 1 R X \u00f03\u00de In this curvilinear coordinate system, the explicit expression of the gradient of a vector field is: V \u00bc Vs\u00f0s;g; f\u00deX\u00fe Vg\u00f0s;g; f\u00de Y \u00fe V f\u00f0s;g; f\u00deZ is given by (4). \u00bdrV \u00bc 1 1 g R @Vs @s Vg R @Vs @g @Vs @f 1 1 g R @Vg @s \u00fe Vs R @Vg @g @Vg @f 1 1 g R @Vf @s @Vf @g @Vf @f 0 BBBB@ 1 CCCCA \u00f0X;Y;Z\u00de \u00f04\u00de 2" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001369_rcs.273-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001369_rcs.273-Figure1-1.png", + "caption": "Figure 1. Various coordinate systems and transformations involved in the augmented reality endoscope set-up", + "texts": [ + " Such a system will help the surgeon in better understanding and orientation to the surgical anatomy. The surgeon can select as many landmarks as he/she requires. He/she can define critical spots in the operating area. The colour of the overlaid critical spot changes to red depending on the proximity of an instrument or endoscope to it, and hence functions as an alert system. Simplified and automatic endoscope calibration and registration routines are implemented which suit the surgical set-up and are fast enough to be repeated during the course of surgical procedure, if the need arises. Figure 1 shows an overview of the system we have developed. A dental cast-based dynamic reference base (DRB), D, is attached to the patient\u2019s upper jaw. Segmented CT data of the patient are registered to D, whose position and orientation can be tracked optoelectronically using easyTrack O (EasyTrack 200 and 500; Atracsys, Bottens, Switzerland) (10), which establishes the global coordinates. Another opto-electronic marker shield, E, is attached to the endoscope for its tracking. Now, any point on the patient can be represented in endoscopic image coordinates (xi,yi) according to equation 1: xi yi 1 = P TMC TEM TDE XDi YDi ZDi 1 (1) TDO and TOE can be easily solved" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001774_j.matdes.2009.08.024-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001774_j.matdes.2009.08.024-Figure2-1.png", + "caption": "Fig. 2. Two Identical rollers in contact, both are hollow with 80% hollowness (M 2\u2013 80 ONE).", + "texts": [ + " A certain way is used for naming the models based on being identical sized rollers or not, the percentage of hollowness, and whether one roller is hollow or both rollers are hollow. The name of each model starts with M, which refers to Model. Sometimes the T precedes the letter M to indicate that this model is subjected to a combined normal and tangential loading. As mentioned earlier, identical sized models are called Model 1 (M1), while non identical sized roller models are called Model 2 (M2). Then the name is followed by the percentage of hollowness and the word \u2018\u2018ONE\u201d if only one roller is hollow or the word \u2018\u2018TWO\u201d if both rollers are hollow. Fig. 2. shows a model of two identical sized rollers; both rollers are with percentage of hollowness of 80. So it is called M 1\u201380 Two. In 1985, Ioannides and Harris [12] reported a new model for fatigue life prediction of roller bearings. Their model was a modification of the Lundberg\u2013Palmgren (LP) life theory. The IH model is based on the statistical relationship between the probability of survival, the fatigue life and the stress level above the endurance limit in a certain region of the roller, called the risk volume" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001555_iros.2008.4650574-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001555_iros.2008.4650574-Figure1-1.png", + "caption": "Fig. 1. Examples of 3-DOF 3-[PP]S parallel mechanisms", + "texts": [ + ". INTRODUCTION OR the last few decades, parallel mechanisms are increasingly being used and studied. Even if most works on parallel mechanisms have focused on 6-degrees-offreedom (DOFs) mechanisms (mainly hexapods), recently, more interest has been paid to mechanisms with less than 6 DOFs. The most popular of these mechanisms belong undoubtedly to the group of 3-DOF symmetric parallel mechanisms whose mobile platform is attached to three identical legs via spherical joints (Fig. 1). The legs constrain the centers of the spherical joints to move in three equally spaced vertical planes intersecting at a common line. These mechanisms will be referred to as 3-[PP]S ones1. There is abundant literature on this group of mechanisms, studying their kinematics, singularity analysis and design. For example, a 3-PPS parallel mechanism was proposed in [1] (Fig. 1a), the 3-RPS architecture (Fig. 1b) was analyzed in [2-6], two different 3-PRS designs were studied in [7] (Fig. 1c) and [8] (Fig. 1d), the latter design being best known through the Z3 Head by DS Technologie [9], and finally a 3-RRS robot was investigated in [10]. Of all these publications, only [3] seems to identify the exact nature of the interdependence of the orientation parameters and its geometric significance. To fill this important gap, the second author studied the kinematic geometry of 3-[PP]S parallel mechanisms and showed clearly their motion pattern [11]. Manuscript received January 25, 2008. This work was supported by FQRNT and the French Minist\u00e8re des Affaires \u00e9trang\u00e8res et europ\u00e9ennes", + " 1 It is common to denote parallel mechanisms by using the symbols P, R, and S, which stand respectively for prismatic, revolute and spherical joint. When a joint is actuated, its symbol is underlined. In this paper, we also use [PP] to denote any combination of joints that allows 2-DOF planar motion. In this paper, we use a special orientation representation to obtain simplified relations for the singularity analysis of these mechanisms. This orientation representation was recently applied to the derivation of the closed-form direct kinematics of the mechanisms shown in Fig. 1(a-c)[12]. It was shown that this representation considerably simplify the expressions of the direct kinematics of such mechanisms. Thus, in the next section, we describe briefly this orientation representation and use it in Section 3 to derive the simple interdependence between the orientation angles and the position of the platform of a general 3-[PP]S parallel mechanism. Then, in Section 4, we present the expression of the singularity loci of four 3-[PP]S parallel mechanisms, namely the 3-PPS design (Fig. 1a), the general 3-RPS design (Fig. 1b), and two common 3-PRS designs (Fig. 1c and 1d). We also analyze the size of the singularity-free workspace of these structures, as a function of the design parameters, taking into account all singular configurations. Finally, conclusions are drawn in Section 5. F 978-1-4244-2058-2/08/$25.00 \u00a92008 IEEE. 1952 A novel three-angle orientation representation, later called the Tilt-and-Torsion (T&T) angles, was proposed in [13] in 1999, in conjunction with a new method for computing the orientation workspace of symmetric spatial parallel mechanisms", + " However, in both papers, the obtained expressions are numerous and complicated due to the use of general Euler angles and are basically not exploitable. Reference [21] presents a short singularity analysis of the 3-PRS structure, but gives no expressions characterizing the singular configurations. Finally, reference [22] presents a geometric approach to finding Type 2 singularities of three-legged parallel mechanisms. In this section, we will analyze the Type 2 singularities of four 3-[PP]S parallel mechanisms, namely the 3-PPS design, proposed in [1] (Fig. 1a), the general 3-RPS design (Fig. 1b), and the two 3-PRS designs proposed in [7] and [8] (Fig. 1c and 1d). To realize this analysis, we will study the degeneracy of a 6-dimensional matrix composed of the screws applied on the platform by the legs [20] and will give for the first two mechanisms (the 3-PPS and the 3-RPS) simple analytical expressions characterizing the singularity loci obtained by the use of the T&T angles. We will show for the other two mechanisms that the singularity loci can be represented by a polynomial of high order (of degree 24). Moreover, for each mechanism, the maximal reachable workspace taking into account the singular configuration will be represented as a function of the design parameters", + " Thus, it can be observed that the size of the workspace increases with the altitude of the platform and decrease with the value of Rb. C. Singularity Loci of 3-PRS Parallel Mechanisms As for the previous mechanism, Ri1 and Ri2 are two forces located at point Bi, the first directed along the direction of the leg and the second perpendicular to the plane of the legs. The system of screws degenerates if: 1 2 3 2 1 3 3 1 2 1 1 2 2 3 3 det 0 A A A B B B C = \u0393 \u0393 + \u0393 \u0393 + \u0393 \u0393 + \u0393 + \u0393 + \u0393 + = J , (20) for the mechanism of Fig. 1c, with 8/)()1()1()1()1(9)(1 \u03b8\u03c6\u03b8\u03b8\u03c6\u03c6\u03c6 scz+cc+ccAA \u2212\u2212\u2212== , )3/2(2 \u03c0\u03c6 \u2212= AA , )3/2(3 \u03c0\u03c6 += AA , )34344( )4741 64 9)( 22232 22 1 \u03b8\u03b8\u03b8\u03b8\u03c6\u03b8\u03c6 \u03b8\u03c6\u03b8\u03c6\u03c6\u03c6 ssz+c+szcsc cc+cc(cBB \u2212+ \u2212\u2212\u2212== , )3/2(2 \u03c0\u03c6 \u2212= BB , )3/2(3 \u03c0\u03c6 += BB , )43()1( 32 27 32 3 3 zz+scs+ccC \u03b8\u03c6\u03b8\u03b8\u03b8 \u2212\u2212\u2212= , )(1 \u03c6\u0393\u00b1=\u0393 , where 2222 22)( \u03b8\u03c6\u03b8\u03c6\u03c6 sczsc+zL \u2212\u2212=\u0393 )3/2(2 \u03c0\u03c6 \u2212\u0393\u00b1=\u0393 , )3/2(3 \u03c0\u03c6 +\u0393\u00b1=\u0393 , and, 0 det 332211 213312321321 =\u0394+\u0394+\u0394+ \u0394\u0394+\u0394\u0394+\u0394\u0394+\u0394\u0394\u0394= FFF EEEDJ , (21) for the mechanism of Fig. 1d, with )1( 6 27 +ccD \u03b8\u03b8\u2212= , )2344( )1474( 64 9)( 22 22 1 bR+c++ccc +cc+cccsEE \u2212\u2212 \u2212\u2212== \u03c6\u03b8\u03b8\u03c6 \u03b8\u03c6\u03c6\u03c6\u03c6\u03b8\u03c6 , )3/2(2 \u03c0\u03c6 \u2212= EE , )3/2(3 \u03c0\u03c6 += EE , 2 2 4 2 1 2 2 2 2 9( ) 4 ( 2 1) 4 ( 5 8 2 2 3) 2 ( ) \u03c6 \u03b8 \u03c6 \u03b8 \u03b8 \u03c6 \u03b8 \u03b8 \u03b8 \u03b8 \u03b8 \u03c6= = \u2212 + + \u2212 + + \u2212 \u2212 + \u2212 + b b b b F F s s c c c c c c R c R c R c R , )3/2(2 \u03c0\u03c6 \u2212= FF , )3/2(3 \u03c0\u03c6 += FF , )(1 \u03c6\u0394\u00b1=\u0394 , where 2/122 42 )4/394)3212()38 30)3(16()28316(334()( \u2212+\u2212+\u2212 \u2212+\u2212\u2212=\u0394 bbb b RRcR Rc++L \u03c6 \u03c6\u03c6 )3/2(2 \u03c0\u03c6 \u2212\u0394\u00b1=\u0394 , )3/2(3 \u03c0\u03c6 +\u0394\u00b1=\u0394 . In these expressions, \u0393i and \u0394i are radicals depending on the working mode (solution of the inverse kinematics) of the mechanism and L is the length of the legs", + " Since this procedure requires a huge computation time and is difficult to perform symbolically, we firstly assign random integer values to the coefficients \u03b8, Rb, L, and z. Then, we eliminate the radicals by rearranging terms and squaring the equations three times. Finally, as the system is symmetrical, it is possible to rearrange the obtained polynomial in cos \u03c6 and sin \u03c6 into a polynomial in cos 3\u03c6. Finally, it can be observed that the obtained polynomials are of degree 16 for the mechanism of Fig. 1c, and of degree 24 for the mechanism of Fig. 1d. Fig. 8 shows examples of singularity loci in the workspace of the 3-PRS parallel mechanisms under study. Finally, we analyze the size of the singularity-free workspace represented by the minimum of all maximal reachable angles \u03b8 for any angle \u03c6, without reaching a singularity, as a function of the altitude of the platform and of the design parameters Rb and L (Fig. 9a and 9b). We use an algorithm similar to that used for the 3-RPS parallel mechanism. It can be observed that: - for the mechanism of Fig. 1c, the size of the singularity-free workspace increases with the altitude of the platform; moreover, for L close to 2 and for a high altitude z, the value of angle \u03b8 reaches 90\u00b0. - for the mechanism of Fig. 1d, the size of the singularity-free workspace increases when L increase and Rb decrease; moreover, for Rb close to 1, the value of angle \u03b8 reaches 80\u00b0. We presented in this paper yet another example of the advantages of using Tilt-and-Torsion angles for the analysis of 3-DOF zero-torsion parallel mechanisms. In particular, we proposed relatively simple expressions for the singular configurations of four different zero-torsion mechanisms, namely a 3-PPS design, the general 3-RPS design, and two 3-PRS design" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000904_j.mechmachtheory.2008.08.005-Figure11-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000904_j.mechmachtheory.2008.08.005-Figure11-1.png", + "caption": "Fig. 11. A spatial 5R manipulator.", + "texts": [ + " It indicates that for the equal total link length and the same task, the manipulator with multiple degrees of redundancy can be used to reduce the JVJ and improve its stability during fault tolerant operations. Besides, when one joint fails and is locked, the manipulator with multiple degrees of freedom is still redundant. Hence, its fault tolerant workspace is far greater than that of the manipulator with one redundancy, which is also very beneficial to the post-failure fault tolerant operations. Fig. 11 is a spatial 5R manipulator, whose D\u2013H parameters d1, d2, d3, d4, d5 and dt are 0.1 m, 0.14 m, 0.42 m, 0.16 m, 0.38 m and 0.15 m, respectively. If the operational task is end-effector positioning only, the manipulators has two degrees of redundancy, i.e., n m = 2. The velocity of end-effector _X \u00bc \u00bd0:2p sin\u00f02pt\u00de;0:2p cos\u00f02pt\u00de;0 T m=s, the coefficient K = 7 106, other simulation conditions is the same as above. Fig. 12 is the JVJ of the manipulator when the reduced manipulator continues the desired task in optimal joint velocity and least-norm joint velocity, respectively" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002968_0022-2569(69)90013-5-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002968_0022-2569(69)90013-5-Figure1-1.png", + "caption": "Figure 1. A six-link spatial mechanism.", + "texts": [ + " O,/~nH I;13 TaKHx: mcc'rH3SCHHJbXll npoc'rpaHC'rBCHHbflt MexaHI43M C BpamazembHbtwtH napaMR R3cneayeTcs B Hac'romllell pa6oTe, rnaaHo\u00a2 3acHo 3Toro MeXaHH3Ma Mema/II=l-I]M~ 6apa6aK O[IHCldBaeT 06IlIfe rlpOCTDaHCTBeHHOe J1BHXEeHHe. ['[pP[MeH~I~I MeTO]I MaTpH~, 061.ua~l aHa/IHTH\"ICCKa~I KRHeMaTHKa MexaITH3Ma. o n , calla H TaKHM o6pa30M eo3]~aHo \u00a2peJ~c'rBo .ILrIFI pelIIeHHR pa3ymtuu,lx KHHeMaTHtIeCKHX H ~HaM]a,~eczHx npo6Y[CM. ~BH)KeHHe 6apa6ana H3Cnen~,c'rc~ 6onc\u00a2/(eTa/I~HO. MIXING machines used in many fields incorporate very interesting mechanisms. The kinematic schematic of one of these mechanismst is shown in Fig. 1. The main member is the drum 4, which supports the container with the material to be mixed. The drum moves with a general spatial motion. The driving member is shaft 2. The mechanism itself employs six links and contains only revolutes. The axes 02 t and o 4 t are parallel; the others are always perpendicular to the two adjacent axes. The characteristic dimension is the length a = O304= b ,0~ = O~,O s = (~/313)O 10 ~ . * Docent, Technical University, Prague, Czechoslovakia. t This mechanism is used in \"Turbula\" brand mixing machines manufactured by the Swiss company W", + " This equation indicates that an arbitrary point of the member 4 moves on the same trajectory with respect to the frame, regardless of whether the motion of member 4 is described by the chain (sequence) 1, 2, 3, 4 or 1, 6, 5, 4. Sinceequation(2a) holds for an arbitrary point M, it can be written, after cancelling ?M~: T43 T32 T2 l = \"~45 T56 T61 \u2022 (2b) This equation alone is sufficient for the determination of the desired relations (1). For the individual members coordinate systems Oi(x~, y~, zi), i= 1, 2 , . . . , 6 are introduced according to Fig. 1. For member 4 an additional auxiliary system O',,(x'4, Y'4, z',,) is introduced. The transformation matrices acquire then the form cosrP2t sintP2t 0 0 --sin ep21 COS~21 0 0 0 0 1 0 0 0 0 1 (3a) 1 0 0 0 0 cos qTa2 sin q~32 0 0 - s i n (P32 COS ~032 0 0 0 0 1 (3b) T,3= m c0s~043 0 - s i n e 4 3 0 0 1 0 0 sine43 0 cosq~43 0 0 0 a 1 (3c) I 0 0 0 - 1 0 0 0 - 1 0 0 0 - - w 0 1 0 0 0 0 1 0 0 COS (-Pa5 - sin q~,~ 5 0 0 sin qo.~5 COS (P.~5 a 0 0 0 I (3d) r 6= cosq~56 0 -sin~o56 0 0 I 0 0 sin~o56 0 cosmos6 0 0 0 0 1 (3e) cosq~6t sin~o 6~ 0 0 - s i n ~ o 6t cos~o 6t 0 0 0 0 1 0 0 - a x / 3 0 1 (3f) where: ~02t =rota t ion of member 2 with respect to member 1 about axis 021 = z l =z2, q~32=rotation of member 3 with respect to member 2 about axis oa2=x2~xa, ~o45 =ro ta t ion of member 4 with respect to member 5 about axis 0 4 5 - x ' 4 [ [ x s , q~56 = rotation of member 5 with respect to member 6 about axis o56 =Y5 =Y6, (\u00a261=rotation of member 6 with respect to member 1 about axis 061~-~Z6]]Z1" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001345_j.ijmecsci.2008.10.008-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001345_j.ijmecsci.2008.10.008-Figure2-1.png", + "caption": "Fig. 2. Positions of residual stress measurement.", + "texts": [ + " The residual stress distribution in the subsurface of specimens was measured by X-ray diffraction method. A GE XRD-5 diffractometer with a CrKa radiation tube was used. Residual stresses were computed based on the sin2c technique, which is elaborated by Noyan and Cohen [13]. Residual stresses were measured in circumferential direction (Fig. 1). The measurements were made at the exposed surface and six different depths: 2.54, 5.08, 7.62, 10.16, 12.7, and 25.4mm below the surface. Additionally, the measurements were made at five different positions (Fig. 2) at each depth to investigate the residual stress scatter. To measure the residual stresses at different depths, an electrolytic etcher, saturated NaCl solution, was used to remove a layer. The thickness of the specimen was measured to check the removed depth of a layer after each etching. The repeatability of residual stress measurements was assessed by measuring the same point on the same specimen by loading and unloading the specimen in the X-ray diffractometer to obtain eight residual stress measurements [14]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001814_14644193jmbd266-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001814_14644193jmbd266-Figure2-1.png", + "caption": "Fig. 2 Relaxation length concept schematic", + "texts": [ + " This belongs to the category of \u2018point contact\u2019 transient tyre models [8] and is based on the combination of a steady-state slip-based force function that accepts a transient state as an input. The steady-state force function can be a linear, slip-based model such as that presented in the preceding section, or a non-linear slip-based model such as Pacejka\u2019s magic formula model [10]. The state used as the input is the socalled transient slip quantity [8], which represents the first-order lagging response of the slip at the contact when the macroscopic slip (given by equation (13)) is applied to the wheel. The principle of the relaxation length is depicted in Fig. 2, which shows a wheel and tyre operating in traction. The sliding speed at the contact patch is denoted Vsc, while the wheel rim tangential speed is defined as Vs = \u03c9R \u2212 Vx . From this, the rate of deflection of the spring representing the tyre carcass compliance is defined as \u2202h \u2202t = Vs \u2212 Vsc (17) where h represents the longitudinal deflection of the carcass. The localized slip ratio at the contact patch can be approximated as \u03bat = Vsc Vx (18) If it is assumed that the friction force is generated instantaneously at contact patch level in response to this localized slip ratio, and that the slip ratio is small, the longitudinal tyre force can be calculated using Fx = CFx\u03bat (19) where CFx represents the traction or slip stiffness of the tyre" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003112_2013.40500-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003112_2013.40500-Figure1-1.png", + "caption": "FIG. 1", + "texts": [ + " The graphical integration of the measured normal stresses and the cal culated tangential forces, however, sat isfy equilibrium conditions with good accuracy. FORCES ACTING O N A RIGID W H E E L Driven Wheels The wheel is driven when a moment (M) is imposed upon the wheel in the direction of the mo tion. The wheel will have a tendency to slide relatively to the ground, depend ing on the magnitude of torque ap plied. Shearing forces (T<\u00a3 and C) on the contact surface will oppose motion. From geometry the normal force (N) passes through the center of the wheel. By adding T<\u00a3 to N, R must act at relative to N when soil failure or slip occurs (Fig. 1) . (f> is defined as the friction angle and may take one of two possible values. When the angle of internal friction of the soil is greater than the interface friction of the soil and wheel, <\u00a3 refers to the friction between the wheel and soil. When the angle of internal fric tion is smaller than the interface fric tion angle, (f) refers to the angle of internal friction. In other words, the small value of the friction angle be tween soil and wheel or the friction angle between soil and soil will be as signed to (j> depending upon whether slip or soil failure is most likely to occur" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000464_cdc.2005.1583188-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000464_cdc.2005.1583188-Figure4-1.png", + "caption": "Fig. 4. Optimal (static) state estimation over graphs", + "texts": [ + "3: The linear control law Kd(s) robustly stabilizes the system of relative states for an uncertain RSN Gj if \u2016\u2206jd\u2016 < 1/\u2016S(Md,Kd)\u2016, where Md(s) := [ 0 Pd(s) I Pd(s) ] ; S(Md,Kd) denotes the lower linear fractional transformation of Md(s) and Kd(s), and the norm for a transfer matrix is its maximum singular value across all frequencies (i.e., its H\u221e-norm). Consider now the scenario where a controller has been designed for the minimal system specified by the sensing spanning tree yd(t) = D(Gd)T x(t). Suppose that the measured sensing topology for one of the nodes is y\u0303j(t) = D(Gj)T x(t) + vj(t), where vj is the noise on the corresponding edges. In this section we consider the problem of finding the transformation Tdj that results in the minimum variance estimate for yd(t). We will denote this estimate by y\u0302d(t); see Fig. 4. For this purpose, we assume a zero mean measurement noise with measurement covariance \u03c32 ik for each relative state measurement xik. The covariance matrix for the complete graph is given by the diagonal matrix R: R = Diag ([\u03c32 12 \u03c32 13 . . . \u03c32 (n\u22121)n ]T ). The noise covariance on the graph Gj is denoted by Rj with diagonal entries that coincide, in an orderly way, with the diagonal entries of R for each measured edge of Gj . We first show that the transformation Mdj satisfies the cycle constraints" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001815_004051757104100401-Figure16-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001815_004051757104100401-Figure16-1.png", + "caption": "FIG. 16. Flexibility analysis for a loop.", + "texts": [ + ", the case when the unwinding of the spiral starts, Equation 7-f gives The above equation gives only one positive value for limiting X. Let this value be denoted by Xo, then Equation 74 is valid onlv for values of .1~ greater than Xo given by Equation 76 (where II = 1) and less than 21fRo (where >1 = 0). For values of less than Xo, 11 can, for all practical purposes, be taken as 1. Flexihil ily :lrrdlysis Jnr a Loop If one end of the loop is fixed, an expression for the flexibilitv of the other end can be obtained by using the matrix method described by Hall and Woodhead E7]. Let us consider a loop as shown in Figure 16, in which one end .1 is fixed and the other end B is free. The six actions, three forces, and three moments at B are related to the six displacements at B by 36 flexibility coefficients in the form of a (6 X 6) matrix denoted by f Be. The six actions pi through p6, represented by column matrix pB, are transposed to another arbitrary point Q, where angle BOQ = 0. Let the actions at Q be represented bv column matrix pQ which is given by where, .4~ is a (6 X 6) matrix depending on the geometry of the structure. For the case of the loop shown in Figure 16, the matrix A Q,~ is given by at UNIV OF PITTSBURGH on March 10, 2015trj.sagepub.comDownloaded from 293 The first column of this matrix contains the internal actions at Q caused by unit p, at R; the second column contains the actions at Q caused by unit P2 at li, and so on. Section properties at any particular point are given by the elements of the following rigidity matrix (I:I): where, /l i, Al, and .13 are the effective areas of cross section in the directions of the axes 1, 2, and 3, and 11, 12 and 13 are the moments of inertia around axes 1, 2, and 3, respectively" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003869_s00419-012-0608-6-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003869_s00419-012-0608-6-Figure5-1.png", + "caption": "Fig. 5 The mode shapes corresponding to frequency \u03c925", + "texts": [], + "surrounding_texts": [ + "As mentioned earlier, in the geometrical model of the gear, the geometry of the teeth is omitted. It allows us to reduce the system\u2019s FE model size. The simplified geometrical model of the system consists of five sectors (see Fig. 1) that have the cyclic symmetry feature. Each of these segments is meshed by using standard procedures of the ANSYS software. The 3-D solid mesh is elaborated and as mentioned earlier, the ten-node tetrahedral element (solid92) with three degrees of freedom in each node is used to realize each sector. During the mesh generation process, it is assumed that the maximum length of each element\u2019s side needs to be no more than 2.7 [mm]. The developed FE model is displayed in Fig. 2, and it consists of 19,620 elements and 36,188 nodes, respectively. The particular sectors are glued as a whole at the geometrical model preparing the stage by using standard procedure of the ANSYS program. The analysed gear is mounted in the roller bearings. Such bearings typically have slight load capacity under loads perpendicular to the primary supported direction. The gear shaft neck surfaces on which the bearings are assembled are denoted \u201cbearing\u201d (see Fig. 3a). The gear mates with the other devices by the splines. The splines is simplified down to a regular cylinder of the diameter assumed as equal to the splines pitch diameter. The surface denoted \u201cjoint\u201d (see Fig. 3a) is located on the pitch diameter of the splines. Parameters of the analysed system are shown in Table 1a\u2013b. The calculation results for natural flexural oscillations taking into account angular speed of the gear are shown in the paper. In the case of circular discs and annular plates, for each solution where nodal lines are nodal diameters, one obtains two identical arrangements of straight nodal lines, rotated by an angle of \u03b1 = \u03c0/(2n) one to another, where n is the number of nodal diameters. In accordance with the circular and annular plate vibration theory [5,6,12], the particular natural frequencies of vibration are denoted as \u03c9mn , where m refers to the number of nodal circles and n is the mentioned number of nodal diameters. As the shape of the gear model is fairy elaborate, the flexural modes of the system are subject to deformation (as compared to the system without any holes) to such extent that establishing which particular node it refers to becomes rather difficult. This problem is even worse if the angular speed of the gear is varying. The problem of influence of the angular speed on the flexural gear models deformation is analysed. For the purpose of identification of these modes, an algorithm of tagging oscillation modes, which determines the correspondence between vibration of the circular disc versus disc with holes, is used. For this purpose, an auxiliary model of annular plate in the form shown in Fig. 3b is used. The geometrical dimensions of the auxiliary model were taken from the gear geometry (shown in Fig. 1). They are as follows: addendum circle diameter dz , rim mounting diameter dp, root circle diameter dw2, and thickness h p and hz (see Table 1). Dynamic analysis is performed for the auxiliary model cases rotating at predetermined angular speed, where diameter of though holes d01 (see Fig. 3b) varies as seen in Table 2. Findings are compared to each other both quantitatively and qualitatively. This method makes it possible to investigate deformations of nodal lines associated with nodal diameters and circles due to through holes and then determine correspondence between oscillation modes of solid circular disc and a plate with holes. In the final step, solutions found for the auxiliary model are compared with the solution for the system whose FEM model is shown in Fig. 2 (the principal model). As for the principal model case, the 3-D solid mesh and the ten-node tetrahedral element (solid92) are used to discretize the auxiliary models. For all models subject to analysis, the boundary conditions were applied to the nodes. For each model, 1 d f associated with node radial displacement was subtracted from the nodes found on the surface identified as a bearing (see Fig. 3a,b). Furthermore, 1 d f associated with the displacement of nodes along the centreline of each model was subtracted from the nodes found on the surface, identified as a joint (see Fig. 3a,b). For the models obtained in this way, calculations were kept conducted as long as the natural frequency \u03c918 was determined. The calculations were performed assuming that the systems rotate as angular speed of \u03b8 , within the range of 0\u20131047 [ rad/s]. During the computing process, the angular speed values were gradually increased by 80[ rad/s], which made fourteen variants of the results (the natural frequencies and corresponding natural modes), which were subject to further interpretation. The rotation effect was taken into account by determining stress distribution due to rotation, for each model during the computational step associated with static analysis (the so called pre-stress effect). This stress distribution was then included in the computation step associated with modal analysis. The results of the numerical calculations related to the procedure of identifying deformed natural modes of flexural vibration of the gear under consideration are shown below. The results displayed here relate to the determination of the correspondence between the natural frequencies \u03c916 and \u03c925 at high angular speed (\u03b8 = 1047 [ rad/s]) as well as to the correspondence between oscillation modes and the natural frequency \u03c931 at lower angular speeds (\u03b8 = 80 [ rad/s]). The results as shown in Figs. 4, 5, 6, 7, 8, 9 allow for tracking deformations of nodal lines associated with nodal circles and diameters, due to varying diameter of the through holes. With respect to the natural frequency \u03c925, there is marked difference in shapes of natural modes. When one compares the results between each other, one can notice that in order to identify correctly deformed natural modes of the flexural oscillations in the gear under consideration at lower angular speeds, larger number of auxiliary models is required to be included during calculations, as compared to the higher angular speeds. It comes from the fact that additional stresses through the centrifugal effects appear. This effect causes the gear flexural stiffness to be an apparent function of rotational speed (stiffness grows for higher speed). In the next part, results of the numerical calculations associated with the extent of the influence of the angular speed to deformation of mode shapes of oscillations. For each discussed case, both mode solutions related to nodal diameters are shown. These analysed results are sorted by the order of their occurrence. For the frequencies \u03c923 and \u03c918, the results were obtained at angular speeds of \u03b8 = 0 and \u03b8 =1,047 [ rad/s] respectively. For the other cases, results were obtained at angular speeds \u03b8 of, 0, 320, 720, and 1,047 [ rad/s], respectively. Natural frequencies for these modes are included in Table 3. To determine this mode (see Figs. 10, 11), the procedure of tagging natural oscillation modes was required. Nodal lines associated with the circle and diameter are deformed. Minor influence of the angular speed to deformation of the nodal lines is noticeable. The task of determining modes in this case was not too difficult (see Figs. 12); no procedure of tagging natural oscillation modes was required. The slight impact of the gear angular velocity on the distortion of the nodal lines is observed. For these modes (see Figs. 13, 14), procedure of tagging natural oscillation modes was required. It is noticeable that angular speed affects markedly deformation of the nodal lines. Once the angular speed of 720 [ rad/s] is exceeded, the oscillation mode takes different shape. Major deformation of mode shape attributable to the shaft vibrations is evident at this speed. Moreover, additional problem associated with some similarity of the mode being tagged to the mode associated with frequency of \u03c931, emerged during mode identification. Establishing the correspondence between these modes was a complex task (see Figs. 15, 16) due to the shape of oscillation modes similarity to the case discussed earlier. The angular speed affects deformation of nodal lines markedly. Major shape mode variations emerge at \u03b8 = 400 [ rad/s]. The identification process in this mode was not easy (see Figs. 17, 18) . One can notice that angular speed affects the deformation of nodal lines. Major variation in mode shape emerges at \u03b8 = 720 [ rad/s]. Moreover, additional annular shaft vibration emerges at the highest considered angular speed. Finding correct correspondence between the modes in this case was fairly easy (see Figs. 19). High repeatability in deformations of nodal lines on circular plate at various angular speeds is noticeable. As a consequence of the conducted analysis (see Table 3), the Campbell diagram was plotted for the gear under consideration. This is a convenient method of displaying the relationship between gear natural frequencies and transmission system excitations [4]. Excited frequencies are plotted on a vertical axis, and the gear speed of rotation is plotted on the horizontal axis (see Fig. 20). Natural frequencies achieved from numerical analysis are plotted as near-horizontal curves. The forced frequency due to the meshing is determined by the following relation (as in Ref. [4]) f = n0 \u00b7 z 60 (4) where n0 [rpm] is the rotational speed and z is the number of teeth in the gear. For this system, the gear teeth number is z = 59. Vibration resonance phenomenon occurs when forcing frequency (4) matches as to its value with some natural oscillation frequency of the gear. The points where the near-horizontal \u03c9mn curves intersect the straight line (4) indicate the speeds at which the gear resonance will be excited (see Fig. 20). For instance, the rated excitation speed for the natural frequency of \u03c923 is 764 [rpm]. It may be inferred from both the Campbell diagram and Table 3 that the rotating movement makes flexural stiffness of the gear under consideration to increase. Moreover, at speed of 3,820 [rpm], one can notice major surge associated with the mentioned earlier changing of the shape of the natural mode frequency in the case of the frequency of \u03c931. The growth of the gear transversal stiffness observed during gyrate of the gear comes from the appearance of the additional stresses in the toothed gear through the centrifugal effects. The higher rotational speed generates higher centrifugal forces, higher stress level, thereby causing the transversal stiffness of the system to increase. Moreover, the growth of the gear flexural stiffness through the gyrate effect causes reduction of the needed numerical calculations connected with identifying the proper distorted mode shapes." + ] + }, + { + "image_filename": "designv11_7_0000222_icar.2005.1507412-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000222_icar.2005.1507412-Figure5-1.png", + "caption": "Fig. 5. Examples of different positions of revolute joint axis connecting leg A2 to the moving platform", + "texts": [ + " 3 and the following figures we have denoted by eA the elements belonging to the leg A1 (eA eA1), by eB the elements of the leg A2 (eB eA2), by eC the elements of A3 (eC eA3) and by eD the elements of A4 (eD eA4). To obey to conditions (5)-(13), the axes of revolute joints connecting legs A1 and A3 to the moving platform must be superposed and the reference point H must be situated on this common axis, as we can see in the examples presented in Figs. 3-4. The axis of revolute joint connecting the leg A2 to the moving platform could be: (i) superposed with the axis of the last revolute joint of leg A4, as in Fig. 3 and Fig. 5-a, (ii) superposed with the axis of the last revolute joints of the legs A1 and A3, as in Fig. 5-b or (iii) not superposed with the axis of another joint, as in Fig. 5-c. These different positions do not involve structural modifications of the basic solution of PMs with decoupled Sch\u00f6nflies motions. In all cases, four revolute joints are adjacent to the mobile platform and the mechanisms are fully-parallel. The other 623 basic structural solutions of PMs with decoupled Sch\u00f6nflies motions without idle mobilities and elementary legs can be obtained by analogy with the solutions presented in Figs. 3-4 by using various types of legs presented in Tables 1-3 and Figs. 1-2. The legs are coupled with the mobile platform by using any solution presented in Fig. 5. Derived structural solutions of PMs with decoupled Sch\u00f6nflies motions can be obtained from the basic solutions by: regrouping in a common element the last elements of legs (i) A1 and A2 (Fig. 6-a), (ii) A2 and A3 (Fig. 6-b), (iii) A2 and A4 (Fig. 6-c), (iv) eliminating the last revolute joint of leg A1 and integrating in a common element the last elements of legs A1 and A3 (Fig. 6-d), (v) eliminating the last revolute joint of leg A1 and regrouping in a common element the last elements of legs A1 and A3 and in another common element the last elements of legs A2 and A4 (Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001687_1.3464553-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001687_1.3464553-Figure2-1.png", + "caption": "FIG. 2. Color Diagram of mounted pillar and force-sensing cantilever. The black arrows indicate the relative motion of the pillar and cantilever. The blue and green arrows indicate the direction of positive forces exerted on the cantilever. This convention is used in the force plots.", + "texts": [ + " Understanding how fibril shape affects the adhesive properties will help in the creation of fibrillar adhesives with customized properties. To characterize the adhesive properties, we determine the set of shear and normal force pairs for which stable attachment is possible. We use a flat-tipped piezoresistive cantilever capable of simultaneously measuring forces along two orthogonal axes to measure the forces at the adhesive interface. The dual-axis cantilever utilized is described in Refs. 8 and 9 and is depicted in Fig. 2. This sensor is a microfabricated silicon cantilever with implanted piezoresistive regions that form strain sensors that change resistance when the cantilever is deflected. It is similar to an atomic force microscope cantilever but instead of a sharp tip, this sensor has a 20 40 m2 platform for the pillar to adhere to and its unique geometry enables simultaneous detection of normal and shear forces applied at the tip. The change in resistance is sensed by a Wheatstone bridge signal conditioning circuit and converted to a voltage", + " To calibrate the sensor, we measure the displacement sensitivity of the cantilever and signal conditioning circuit directly, and then estimate the cantilever\u2019s stiffness using a combination of resonant frequency measurement, finite-element modeling, and interaction measurements with a reference cantilever.10 The cantilever has a normal spring constant of 0.7 N/m and a shear spring constant of 3.9 N/m. The adhesive pillar and cantilever are placed in a custom system that allows for alignment of the pillar and cantilever, motion control, and force data collection. Figure 2 shows the relative orientations of the cantilever and pillar, the convention for forces on the cantilever, and the directions of pillar motion during the test. The cantilever approaches the tip, makes contact, and applies compressive stress to the interface. In these tests, we apply compressive forces of 1\u20135 N. After the compression phase, the cantilever is a Electronic mail: dsoto@stanford.edu. 0003-6951/2010/97 5 /053701/3/$30.00 \u00a9 2010 American Institute of Physics97, 053701-1 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 129.105.215.146 On: Fri, 19 Dec 2014 00:53:34 withdrawn from the pillar along a straight line at an angle to the cantilever surface Fig. 2 . The angle varies from 0\u00b0 to 90\u00b0 to provide loads varying between primarily shear and primarily normal. For high shear loads, the pillar is deflected and the side of the pillar contacts the substrate. We find the forces present at the moment of failure by analyzing the force trace data Fig. 3 . The stresses at the interface increase until the interface breaks, at which point the measured forces either decrease rapidly or level off. Failure can be either a vertical detachment from the surface or a slipping failure while the pillar is still in contact" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002079_3.59009-Figure9-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002079_3.59009-Figure9-1.png", + "caption": "Fig. 9 Modified Nyquist plots for existing power actuator.", + "texts": [ + " This change gives about 15 db Ref -10 'ii -20 -30 Ranqe of F-4 Short Period Mode Frequency \u2014\u2014\u2014\u2014IT Range of Flutter Mode Frequency with 370-Gallon'Tanks I 100.01.0 10.0 \u2022Frequency- Hz Note: Plot is of High Pass Filter, Power Actuator, and Compensation Only decrease of relative open loop gain at the flutter frequency of 8.3 Hz. An increase in the open loop electrical gain by 15 db (a factor of 5.625) to ^=11.25 will compensate for this loss of mechanical gain and give the same open loop gain as for the improved power actuator case. The Nyquist plots of Fig. 9 indicate a stable system for an open loop gain of 25.0 and a structural damping coefficient of g = 0.04 for all velocities through 800 KEAS. Figure 10 shows an enlarged Nyquist plot for the velocity of 700 KEAS. The phase margin for this design is 27\u00b0 for g = 0.04, but only 9\u00b0 for g = 0.02. The system is unstable for g = 0.0. The stability boundaries, shown in Fig. 11, indicate that the open loop gain could be reduced to 11.25 for a structural damping coefficient of g = 0.02 at a velocity of 700 KEAS without losing control of flutter" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003247_tmag.1970.1066780-Figure6-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003247_tmag.1970.1066780-Figure6-1.png", + "caption": "Fig. 6. Dc mot.or; two-dimensional gridsgstem. Distribution of magnetic field at, no-load and a t rated rotor-current, calclllated with difference method.", + "texts": [ + " As an oxydmagnet was used in the device, the relationship H = f ( B ) could be a,pproximated by a straight line and the calculation could be done with constant magnetization M . The difference between measured and calculated values of the induction in the air. gap were less than 5 percent. From Figs. 4 and -5 the difference between a usual and a screened loudspeaker system for television sets can be seen. The magnetic field of a dc motor with permanent magnet excitation is in a two-dimensional sectional plane. Fig. 6 shows a pa'rt of the gridsystem used. This consists of two parts, one for the stator and one for the rotor. These two gridsystems are overlapped in the air gap. In the stator a 288 IEEE ON JUNE 1970 grid of polar elements is applied, rn the rotor rectarlgular [31 F. C. Trutt., E. A. Erdelyi, and 11. E. Hopkins, \u201dR.epresentation and polar finite element\u2019s have to be used to fit the grid- puter use,\u201d IEEE Trans. Power Apparatus and Systems, V O ~ . of the magnetisation characteristic of de machines for comPAS-87, pp. 665-669, March 1968 system to the rotor\u2018 The difference method gives the [4] (7. F. T, Widger, \u2018 0 for \u03b8 = 0 and Si(0) = 0. 2. Si(\u03b8) is twice continuously differentiable, and the derivative si(\u03b8) = dSi (\u03b8) d\u03b8 is strictly increasing in \u03b8 for |\u03b8 | < \u03b3i with some \u03b3i and saturated for |\u03b8 | \u2265 \u03b3i , i.e. Si(\u03b8) = \u00b1si for \u03b8 \u2265 +\u03b3i and \u03b8 \u2264 \u2212\u03b3i , respectively. 3. There is constant ci > 0 such that Si(\u03b8) \u2265 cisi 2(\u03b8) (6) for \u03b8 = 0. Some examples of the saturation function can be found in refs. [16] and [21]. Substituting (4) into (2) and using (3), we obtain the closedloop equation as follows: Mv\u0307 + C(v)v + D(v)v + KpJT (\u03b7)s(e) + Kvv + Z(\u03b7) \u03b8 = 0, (7) where \u03b8 = \u03b8 \u2212 \u03b8\u0302 " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002210_9781782420545.178-Figure6.4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002210_9781782420545.178-Figure6.4-1.png", + "caption": "Fig. 6.4 Cyclic voltammogram for a reversible process, 0 + 2 \u0302 R. Initially only O present in solution.", + "texts": [ + " However, as the potential approaches Fe\u00b0 the R present near the electrode starts to be reoxidised back to O (in order for the surface concentrations to be those required by the Nernst equation) and a reverse current flows. With the changing electrode potential the surface concentration of R eventually reaches zero. Using similar arguments as were used for the forward sweep, it can shown that the current on the reverse sweep will also exhibit a peaked response, though of course of opposite sign. A typical cyclic voltammogram is shown in Fig. 6.4. It may also be noted that the charge associated with the anodic process is low compared to the forward reduction process. This is because throughout most of the experiment, there is a concentration difference driving R away from the electrode; most of the product, R, therefore diffuses into the bulk solution and cannot be reoxidised on the timescale of a cyclic voltammetric experiment. Sec. 6.1] Reversible reactions 183 In order to determine mathematically the exact form of the cyclic voltammogram it is again necessary to solve Fick's 2nd Law for 0 and R, Equations (6", + "0 W,Uo RT (E-Et) -I = nFD\\ (dec W/ _\u201e For a sweep rate of v 0 < t < X t > X E = Ei-vt E = El- 2v\\ + i/f where /s^ is the initial potential and X the time at which the sweep is reversed. The solution is quite difficult because of the time dependent potential term, but is can be shown that for planar diffusion [1, 2, 3] inF\\112 j p = -0.4463 \u00ab F \u2014 I c S \u00a3 V V / 2 (6.4) This is called the Randles-Sevttik equation, and at 25\u00b0C this reduces to the form L = -(2.69 X 10s) w ^ c o ^ W 2 (6.5) where 7p, the peak current density (measured as shown in Fig. 6.4) is in A cm-\"2, D is in cm2 s~\\ v is in V s\"1, and CQ is in mol cm - 3 . Thus we see that the peak current density is proportional to the concentration of electroactive species and to the square roots of the sweep rate and diffusion coefficient. Fig. 6.5 shows a set of typical cyclic voltammograms obtained for a reversible system over a range of sweep rates. 184 Potential sweep techniques and cyclic voltammetry [Ch. 6 Having obtained such results, a test of the reversibility of the system is to check whether a plot of/p as a function of y^2 is both linear and passes through the origin (or alternatively whether Ip/i'1^2 is a constant). If this is found to be true then there are further diagnostic tests to be applied, all of which should be satisfied by a reversible system. A complete list of these tests is given in Table 6.1, whilst the symbols used are defined in Fig. 6.4. The direct graphical determi nation of the reverse peak height, /\u00a3, can sometimes be difficult. In these cases one should use the indirect method of Nicholson [4]. When applying these tests of reversibility it is very important that results obtained over a wide range of sweep rates (preferably at least two orders of magnitude) are analysed, or false conclusions may be reached. A failure to satisfy one or more of the conditions in Table 6.1 implies that the electron transfer is not reversible on the timescale of the experiment, and that the process is more complicated than had been assumed" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000084_s00170-005-0312-6-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000084_s00170-005-0312-6-Figure1-1.png", + "caption": "Fig. 1 Step length of a tool path", + "texts": [ + " In the CAD/CAM realm, within the acceptable deviation range, the calculation can usually be simplified by two parametrical values, called parametrical surfaces, which are represented by Bezier surface, BSpline surface, NURBS surface, and Bicubic surface. If R (u,v) is used to represent the parametrical surface, then the cutting path of the surface is a curve processing in u or v direction, which is carried out by the increments of u or v. During curve cutting, the u and v increments are determined by the cutter step length and tool path interval. Within the acceptable deviation range, the interval between the current cutter contact point and the next cutter contact point is called step length s, as shown in Fig. 1. s \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4e 2r e\u00f0 \u00de p (1) where e is the acceptable deviation (or called chord deviation) assigned by the user, s is the step length, and r is the radius of curvature on the surface. The distance between the two mutually accompanying tool paths is called tool path interval (L), which is determined by the acceptable cusp height h, radius of curvature \u03c1 and radius of cutter R, as shown in Fig. 2. L\u00bc \u03c1j j ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi f4\u00f0 \u03c1j j R\u00de2\u00f0 \u03c1j j h\u00de2 \u00bd\u03c12 2R\u03c1\u00fe \u00f0 \u03c1j j h\u00de2 2g q \u00f0 \u03c1j j R\u00de\u00f0 \u03c1j j h\u00de (2) In this equation, the upper and lower symbols represent convex and concave surfaces, respectively" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002278_icelmach.2012.6349905-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002278_icelmach.2012.6349905-Figure4-1.png", + "caption": "Fig. 4. Analytical model of the 3M-PC PM motor.", + "texts": [ + " When the negative d-axis pulse current is applied to the 4-pole armature winding, the variable magnetized magnets are demagnetized (Fig. 3(c)). Conversely, the rotor of the 4- pole-RM mode changes to the 8-pole-PM mode. When connections of the armature winding switch from 4 to 8 poles, an 8-pole magnetic field is generated in the rotor because of the pulse current. The variable magnetized magnets are magnetized to the 8-pole mode. A finite-element-method (FEM) magnetic field analysis is performed to clarify the basic pole-changing characteristics and to verify the feasibility of a 3M-PC PM motor. Fig. 4 shows the analytical 3M-PC PM motor model. PMs are arranged in a V-shape and embedded in the rotor core. Table I shows the motor specifications of the analytical model, while Fig. 5 shows the winding connections for the pole changing of the stator. Fig. 6 shows the magnetic property in the PMs for magnetization. We verified the pole changing of the rotor by using magnetic field analysis. Fig. 7 shows the distributions of the magnetic flux density in the motor for varying pole configurations. When all the PMs are magnetized with the same polarity, the magnetic flux forms an 8-pole distribution, as shown in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002278_icelmach.2012.6349905-Figure12-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002278_icelmach.2012.6349905-Figure12-1.png", + "caption": "Fig. 12. Distribution of magnetic flux density and magnetic flux during magnetization of 3M-PC PM motor.", + "texts": [ + " Therefore, the magnetizing current is the d-axis current in the new pole after pole changing. Fig. 10 shows the magnetization vector in the PM before and after magnetization by magnetizing current. The magnetization vector shows that the polarity in the PM reverses. Fig. 11 shows the magnetization characteristics of the PM when the rotor changes from 8 to 4 poles and vice versa. For a change from 8 to 4 poles, the magnetization in the PMs varies from 100% to \u221280% because of a magnetizing current of 4 pu. As a result, the PMs show reverse polarity. Fig. 12(a) shows the distribution of the magnetic flux density when a 4-pole magnetic field magnetizes the PMs. For a change from 4 to 8 poles, the magnetization of the PMs varies from \u2212100% to 80% because of a magnetizing current of 6 pu and the PMs show reverse polarity. Fig. 12(b) shows the distribution of the magnetic flux density when an 8-pole magnetic field magnetizes the PMs. Fig. 12(c) shows the distribution of the magnetic flux density when a 4-pole magnetic field demagnetizes the PMs. These results indicate that the PMs in the rotor core can be magnetized to reverse their polarity. Therefore, the proposed motor can change the number of poles by magnetizing the PMs in the rotor. In this section, we discuss the different torque modes. The torque components of the motor vary with the number of poles in the rotor. The torque analysis is performed using FEM as a function of the current phase to determine the torque components" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002513_piee.1971.0124-Figure8-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002513_piee.1971.0124-Figure8-1.png", + "caption": "Fig. 8", + "texts": [ + " The end- 692 Voltage components in circulating-current paths at full-load-current short circuit a Circuit 1 of a top bar at one end of a phaseband (slot 193, see Fig. 12) b Circuit 1 of a top bar at the other end of a phaseband (slot 198, see Fig. 12) 1 Component arising from other coils in the stator 2 Component arising from the same coil 3 Component arising from slot fringing 4 Component arising from rotor phase, is caused by the relative position of the bottom layer, the conductor in the top layer of slot 193 being over the centre of the phaseband. Fig. 8a shows the voltages due to the rotor and stator currents in circuit 1 of the top-layer bars over a phaseband. The rotor-induced voltage changes smoothly with bar position, but the stator component has a little irregularity in angle, especially in the centre. This again may largely be attributed to the effect of the bottom-layer change of phase at this point. Fig. 8b shows the voltages in all four circuits arising from the rotor and stator currents. The 180\u00b0 shift in phase from circuits 1 and 2 to those of circuits 3 and 4 arises from the arbitrary choice of current directions in the circulating-current paths. The flux from the rotor passing through the bar is almost of uniform phase; that of the stator lags by about 20\u00b0 towards the top of the bars. Fig. 8c shows the phasors for voltage in the bars in the bottom layer corresponding to Fig. 8a for the top layer. Here, the effect of the rotor is approximately halved, and that of the stator conductors is 20% less. Overall, the effects of the rotor and the stator are both significant, and are virtually in phase under short-circuit conditions. The application of the above methods to other salient-pole machines would be straightforward. If the stator and rotor cores did not end on the same plane, as occurred in machine B, it might be thought that the use of image conductors to represent the end of the stator core would be unjustifiable" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001917_2009-01-2868-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001917_2009-01-2868-Figure1-1.png", + "caption": "Figure 1: Schematic of Flywheel Hybrid System", + "texts": [ + "(1) where :- E = Kinetic Energy I = Moment of Inertia of the rotating mass = Angular Velocity Rather than employ a solid flywheel, a carbon filament wrapped composite flywheel can be utilized whose moment of inertia is defined in Equation 2 : I = \u00bd m (r1\u00b2 - r2\u00b2)\u2026\u2026..(2) where :- m = mass of the flywheel r1 = outer radius of the flywheel r2 = inner radius of the flywheel The flywheel is connected to the vehicle by a Continuously Variable Transmission (CVT) and control of energy storage or recovery is managed by an electro hydraulic control system. A clutch allows disengagement of the device when not in use and during flywheel start. Figure 1 describes the system schematically :- As the quantity of energy storage in the flywheel is dependant upon the mass / inertia and the speed of the flywheel, either a large, low speed flywheel or a small, high speed flywheel can be used. With the squared velocity term in Equation 1, increasing the speed of the flywheel becomes far more beneficial from weight and package perspectives than increasing the mass. Energy increases with the square of speed, linearly with inertia. Hence the flywheel based mechanical hybrid system developed for motorsport and automotive applications by Flybrid Systems LLP uses a light weight composite flywheel rotating at high speed" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002448_s0263574710000433-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002448_s0263574710000433-Figure4-1.png", + "caption": "Fig. 4. Pictures of the experiment.", + "texts": [ + "251 Assuming that there are three points in the workspace, i.e., points A, B, and C, which are collinear and point B is located between A and C. And \u03b4eA and \u03b4eC are the compensation values of points A and C, which are already known according to the measured output errors. Then, the compensation value of point B should be \u03b4eB = \u03b4eA + |AB| |AC| (\u03b4eC \u2212 \u03b4eA). This is the basic idea of the linear interpolation. The experiment of kinematic calibration was carried out and the pictures of the experiment are shown in Fig. 4. The experimental results are shown in Figs. 5\u201313. In Fig. 5, the error of \u03b4y in RM 4 is convergent after two iterations and reduced from \u00b10.021 mm to \u00b10.003 mm. In Figs. 6 and 7, the errors of \u03b4y and \u03b4z in RM 8 are convergent within two iterations and reduced from \u00b10.45 mm and \u00b10.34 mm to \u00b10.12 mm and \u00b10.17 mm. After linear compensation, the errors of \u03b4y and \u03b4z in RM 8 are reduced to \u00b10.07 mm and \u00b10.06 mm, respectively, as shown in Figs. 8 and 9. The final results in RM 8 are shown in Figs. 10 and 11" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003801_1350650112470059-Figure9-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003801_1350650112470059-Figure9-1.png", + "caption": "Figure 9. Influence of profile modifications (P and ) on planetary gear set efficiency.", + "texts": [ + "comDownloaded from power losses7 for a sun-gear torque ranging from 250 to 1000 Nm are compared with the analytical results using an average friction coefficient of 0.055. Here again, in spite of some deviations, the two sets of results agree well. Finally, the influence of planet tooth tip relief on planetary gear efficiency has been investigated. A broad range of relief is considered with dimensionless tip relief amplitudes P varying from 0 to 2.5 and dimensionless extents of profile modification between 0 and 25%. The friction coefficient is kept constant and set to 0.055. The results in Figure 9 clearly show the significant impact of tip relief on planetary gear train efficiency; by modifying the planet tooth profiles, efficiency increases by 0.25 points. In order to stress on the power loss reduction induced by profile modifications, the corresponding gain for a sun-gear torque of 500 Nm and sun-gear speed of 4000 r/min is illustrated in Figure 10 in which power loss reductions as large as 30% can be observed. An analytical formulation for the calculation of tooth friction losses in internal gears is presented which makes it possible to account for tooth profile modifications" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001856_14763140903414391-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001856_14763140903414391-Figure1-1.png", + "caption": "Figure 1. The effect of shank to thigh ratio on body position at the catch. These diagrams illustrate that when a vertical shank angle is adopted, a lower shank to thigh ratio should result in a more extended knee angle. For example; High STR: Shank Length \u00bc 0.55m, Thigh Length \u00bc 0.55m, Horizontal Displacement between feet and seat \u00bc 0.40m, Knee Angle at Catch \u00bc 47.78. Low STR: Shank Length \u00bc 0.52m, Thigh Length \u00bc 0.55m, Horizontal Displacement between feet and seat \u00bc 0.43m, Knee Angle at Catch \u00bc 51.58. (Height of Seat above feet \u00bc 0.18m). A vertical shank angle at the catch has been reported in the literature to be desired by coaches (Nolte, 2001).", + "texts": [ + " While anthropometric variables have been shown to correlate with overall performance the effect of anthropometric differences on the coordination and timing of the rowing stroke, as well as joint power production, have not previously been quantified. A vertical angle of the shank segment at the catch has been advocated in the coaching literature (Nolte, 2001) and therefore the shank thigh ratio may be an important factor affecting the rower\u2019s position. If a vertical shank position was adopted at the catch, then those rowers displaying a low shank to thigh ratio (STR) may suffer a shorter horizontal drive length because the seat of the rower at the catch would be positioned further from the feet than those with a high (or more equal) STR (Figure 1). Any subsequent changes in the rowing position that result from these anthropometric discrepancies may bring about changes in the sequencing, coordination and power production of the joints at or around the catch, which in turn may have a significant effect upon the performance of the rowing stroke. The aim of the study is to measure the timing and magnitude of joint power production during the drive phase of the rowing stroke, and to investigate the effect of differences in STR. We hypothesise that there will be differences between high and low STR rowers in drive length, segment and joint angles, and consequently joint coordination and power production", + "9 2 ^ 0 .9 2 H IG H S T R 1 3 .4 4 ^ 2 .4 1 2 7 .3 8 ^ 3 .5 8 1 8 .3 5 ^ 2 .0 4 2 2 .1 7 ^ 7 .5 8 2 0 .0 3 ^ 5 .2 2 2 2 .6 2 ^ 2 .4 2 4 0 .2 4 ^ 2 .4 7 * S ig n ifi ca n t d if fe re n ce b et w ee n lo w S T R a n d h ig h S T R g ro u p s (P # 0 .0 5 ). N o p o w er a b so rp ti o n o cc u rr ed a t th e h ip jo in t in a n y su b je ct s. It was initially hypothesised that the low STR rowers, when compared to the high STR group, would display differences in their rowing position at the catch (Figure 1). It was anticipated that a longer thigh length would require the seat to be further from the feet at the catch. If this were the case, rowers with a proportionally longer thigh segment (low STR) would have to gain length at or around the catch in order to maintain the same point of force application and length of drive phase compared to those with a high STR. The lumbar angle was comparable for both groups at the catch, as were the ranges of lower limb joint motion, segment angles and drive length, irrespective of STR" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003461_016009-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003461_016009-Figure1-1.png", + "caption": "Figure 1. \u2018Compact\u2019 arc deposition system inside a 1.6-cell RF superconducting electron injector.", + "texts": [ + " It is expected that the photocathodes prepared in such an optimized way will be further examined in terms of resonant quality and QE in a TESLA-like electron injector. Vacuum arc devices used in the early stage of National Centre for Nuclear Research (NCBJ) photocathode group activity 0031-8949/14/014071+05$33.00 1 \u00a9 2014 The Royal Swedish Academy of Sciences Printed in the UK included the following filters of micro-droplets: diaphragms in a \u2018compact\u2019 arc deposition system introduced directly into a 1.6-cell niobium cavity (figure 1) and a 60\u25e6 knee-type magnetic filter (figure 2). The former was used to coat a 3.5 mm diameter, thin-film lead photocathode directly on the rear wall of a RF cavity. The deposition device was contained in a grounded stainless steel capsule mounted inside the cavity. The top part of the capsule was terminated with a niobium mask placed at a short distance (<1 mm) from the back wall. The position and size of a circular opening in the mask determined the position and size of the photocathode to be deposited" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002821_9781119970422-Figure6.5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002821_9781119970422-Figure6.5-1.png", + "caption": "Figure 6.5 Communication with the sink can be guaranteed whenever a vehicle stops to collect data from nodes. (a) Synchronized movement after the 4th visited point. (b) Synchronized movement at the end of the mission. (c) Velocities.", + "texts": [ + " Adding a simple linear constraint may reduce or extend the computational complexity by magnitudes, without restricting any quality of the solution In the proposed example (Figure 6.4), we minimized the sum of velocities by solving min ui,k ,vi,k { nv\u2211 i=1 nt\u2211 k=1 k ( (vxik) + ( vyik )) } subject to the constraints resulting from (6.1)\u2013(6.5). The number of visited breakpoints per vehicle is at most nt \u2212 1, such that the user is formulate a problem similar to the capacitated CVRP by fixing nt \u2264 nb. Furthermore, in a subsequent computation after solving the MILP, the time intervals [tk, tk+1] can be shortened or stretched according to desired maximal or minimal velocities (Figure 6.5(c)). Due to the NP-hard characteristics of the underlying TSP, the time to compute the guaranteed global optimum explodes with the increasing number of breakpoints and timesteps. For a problem with three mobile entities, the solution of the corresponding MILP3 (342 variables, 1656 constraints) for a setting with 10 points on a grid of seven timesteps took approximately 5.5 s. For a problem with three mobile entities, the computation for a setting with 21 points on a grid of 10 timesteps (816 variables, 8244 constraints) took approximately 16 500 s" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001557_j.triboint.2008.01.009-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001557_j.triboint.2008.01.009-Figure2-1.png", + "caption": "Fig. 2. Driving and driven disks of the twin-disk test machine (mm): (a) Test piece (outside diameter contact surface with rounded shape and no dents). (b) Test piece with dents.", + "texts": [ + " The ballon-rod RCF tester more closely simulates a bearing structurally, and because sliding that is generated at the contact surface between the ball and rod is only differential slip, it becomes easier to understand the direction of sliding in the contact area. Fig. 1 shows a schematic of the twin-disk machine. The driving disk (with higher peripheral speed) was directly connected to a motor. The driven disk (lower peripheral speed) rotated at a reduced speed to create sliding using gears. Two types of disk were used as test pieces for the testing carried out (Fig. 2). Both types were made in bearing steel (JIS SUJ2), which had been heat treated (through-hardened and tempered) to produce a surface hardness of 60\u201364 HRC. Following heat treatment, one type of disk was ground to produce a crowned radius on the outer circumference and a surface roughness (Ra) of 0.09 mm (Fig. 2(a)). The other type was ground to produce a straight profile and a surface roughness (Ra) of 0.05 mm (Fig. 2(b)). After grinding, eight evenly spaced dents were introduced axially in to the center of the outer circumference of the disks with a straight profile and surface roughness (Ra) of 0.05 mm (Fig. 2(b)). The dents were formed with a diameter of 150 mm and a depth of approximately 10 mm using a Rockwell C indenter. Table 1 lists the three different sets of test conditions used for the twin-disk tests conducted. Each test was carried out using one disk test piece of each type (Fig. 2). All of the tests were conducted using the same maximum contact pressure of Pmax \u00bc 3.2GPa and ISO-VG68 dripfeed lubrication conditions. The first set of test conditions involved using the disk test pieces with no indents (Fig. 2(a)) as the driving disk and the disk test piece with indents (Fig. 2(b)) as the driven disk. The speed of the driving disk was maintained at a constant speed (500min 1), while the speed of the driven disk was adjusted to given a slip ratio of 5%. The second set of test conditions used were the same as the first, but the configuration of the disk test pieces was reversed, i.e. the ARTICLE IN PRESS Table 1 Twin-disk test conditions Contact pressure Pmax (GPa) Rotating speed of driving member (min 1) Slip ratio (%) Lubrication oil Test piece in driving member Test piece in driven member I 3.2 500 5 Drip-feed lubrication of VG68 oil Fig. 2(a) Fig. 2(b) II Fig. 2(b) Fig. 2(a) III 0 Fig. 2(a) Fig. 2(b) T. Ueda, N. Mitamura / Tribology International 41 (2008) 965\u2013974 967 one with no indents was used as the driven disk and the one without indents as the driving disk. The third set of test conditions was the same as the first, but the speed of the driven disk equaled the speed of the driving disk, i.e. zero slip. Fig. 3 shows a schematic of the ball-on-rod RCF tester. The ball-on-rod RCF test is a rolling element test that is similar in structure to the actual bearings. It is composed of two outer rings with a tapered bore, a 12" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003495_iet-cta.2013.0074-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003495_iet-cta.2013.0074-Figure1-1.png", + "caption": "Fig. 1 State trajectories of four agents xi, i = 1, . . . , 4, (left figure) and synchronous errors xi \u2212 x1, i = 2, 3, 4 (right figure)", + "texts": [ + " The block diagonalisation of A is T \u22121AT = [ 0.2 1 0 \u22121 0.2 0 0 0 \u22121 ] , T = [\u22121 0 0 1 1 1 2 1 0 ] (43) The self-dynamics of agent has one negative eigenvalue and a pair open right half-plane complex eigenvalues. Since the local output is the state, the internal model controller (7) is adopted with A1 = [ 0.2 1 \u22121 0.2 ] , T1 = [\u22121 0 1 1 2 1 ] , G = [ 0.0818 2.1720 ] K = [ 26.1804 1.7444 27.4942 ] where K and G are obtained by running the synthesis algorithm with \u03b5 = 20. The simulation result is shown in Fig. 1 with the initial states of agent and controller produced randomly in the IET Control Theory Appl., 2013, Vol. 7, Iss. 17, pp. 2110\u20132116 2115 doi: 10.1049/iet-cta.2013.0074 \u00a9 The Institution of Engineering and Technology 2013 range of (\u22120.5, 0.5). It can be seen that after some transition time 12 trajectories of four agents asymptotically converge into three trajectories to demonstrate synchronisation, under the proposed internal model controller (7), although the synchronisation state is divergent because of the existence of right-half complex plane eigenvalues of A" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001873_cec.2009.4983189-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001873_cec.2009.4983189-Figure1-1.png", + "caption": "Fig. 1. Twin rotor multi input multi output system", + "texts": [ + " In this paper, a real-coded GA based system is proposed to select the parameters of the transfer function based on autoregressive moving average (ARMA) 4th order model essential to resemble the 1 DOF hovering motion of S 2022978-1-4244-2959-2/09/$25.00 c\u00a9 2009 IEEE the TRMS. The twin-rotor multiple-input multiple-output (MIMO) system (TRMS) is a laboratory set-up developed by Feedback Instruments Limited [22] for control experiments. Its behaviour in certain aspects resembles that of a helicopter. For example, it possesses a strong cross-coupling between the collective (main rotor) and the tail rotor, like a helicopter. A schematic diagram of he TRMS used in this work is shown in Fig. 1. It is driven by two DC motors. Its two propellers are perpendicular to each other and joined by a beam pivoted on its base that can rotate freely in the horizontal and vertical planes. The beam can thus be moved by changing the input voltage in order to control the rotational speed of the propellers. The system is equipped with a pendulum counterweight hanging from the beam, which is used for balancing the angular momentum in steady-state or with load. The system is balanced in such a way that when the motors are switched off, the main rotor end of the beam is lowered" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003736_tac.2012.2232376-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003736_tac.2012.2232376-Figure4-1.png", + "caption": "Fig. 4. 3-D contact case.", + "texts": [ + " Let be a one-form that vanishes on and that is 1 on , defined up to multiplication by a function which is 1 along . Along , the restriction of the 2-form can be made into a skew-symmetric endomorphism of (skew symmetric with respect to the scalar product over ), by duality: . Let denote the moduli of the eigenvalues of . We have the following: Theorem 22: 1) If , . At points where , the formula is convergent. 2) If , , where . 3) . Let us describe the asymptotic optimal syntheses. They are shown in Figs. 4 and 5. Fig. 4 concerns the case (everywhere contact type). The points where the distribution is not transversal to are omitted (again, they do not change anything). Hence is also transversal to the cylinders , for small. Therefore, defines (up to sign) a vector field on , tangent to , that can be chosen of length 1. The asymptotic optimal synthesis consists of: 1) reaching from ; 2) following a trajectory of ; 3) joining . The steps 1 and 3 cost , which is negligible w.r.t. the full metric complexity. To get the optimal synthesis for the interpolation entropy, one has to make the same construction, but starting from a subriemannian cylinder tangent to " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000407_j.triboint.2006.01.015-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000407_j.triboint.2006.01.015-Figure2-1.png", + "caption": "Fig. 2. Full temperature contour in the roll and strip: (a) with frictional heat generation, (b) without frictional heat generation.", + "texts": [ + " The numerical results were obtained with 50 10 grid points in the roll (20 10 in the bite segment) and 80 10 in the strip. Thermal fields have been the major concerns in cold and hot rollings. In cold rolling they are associated with roll thermal crowning as the roll experiences periodic temperature variations. Frictional and plastic deformation heat generations are the two important modes of heat source in the developed thermal fields. In an attempt to understand the contribution of each of these modes, two simulations were initially carried out: (1) with both heat generation modes included (Fig. 2a), and (2) with only plastic deformation heat generation included (Fig. 2b). In an actual cold rolling process the frictional heat generation is less than 7.5% of the total heat generated [2]. Although this is smaller than the plastic deformation heat, it could significantly alter the thermal field around the interface region. When frictional heat generation is neglected the roll essentially becomes a heat sink. Consequently, strip temperature near the interface is significantly lower than the strip mid-plane temperature i.e. the maximum strip temperature is located at the mid-plane as shown in Fig. 2b. On the other hand when frictional heat is included the maximum temperature can be near the interface as seen in Fig. 2a. This is due to a significant frictional heat for high rolling speed (S \u00bc 1e 2). Roll temperature in both cases are significantly different in the interface region and roll surface. But, core temperatures are identical for the two cases. Later we show that for lower speed (S \u00bc 1e 3) ARTICLE IN PRESS A.K. Tieu et al. / Tribology International 39 (2006) 1591\u20131600 1597 the interface temperature is less than the mid-plane temperature. This is because the roll could still act as a heat sink. Parametric analyses were performed to estimate the effects of some rolling parameters pertinent to mixed-film lubrication with O/W emulsions", + " In the last two cases the core temperatures are higher than the surface temperature (as shown Fig. 9 for S \u00bc 1e 3) whilst the opposite occurs at S \u00bc 1e 2. At all speeds the maximum temperature decreases as S is lowered. Nevertheless the results must be cautiously interpreted. At high S (40.1) a stronger hydrodynamic effect will be felt and higher lubricant pressure will reduce the component of total pressure at asperity contacts. Thus, plastic work may become the dominant heat generation mode and the thermal field will look more like Fig. 2b with an overall effect of a lower T. A coupled model for mixed-film lubrication in cold striprolling with emulsion, including thermal effects, has been developed. To model heat transfer, a variable interface heat conductance is used. A numerical analysis of the thermal field was carried out. Using the model and the numerical procedure outlined in the paper, parametric studies can be performed relatively quickly (in minutes at the most). The program has been validated against known experimental data and can be readily extended to hot rolling or used to model roll strip temperature subjected to different cooling mechanisms" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002099_j.cad.2010.08.007-Figure6-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002099_j.cad.2010.08.007-Figure6-1.png", + "caption": "Fig. 6. Meshing area and contact lines of Example C.", + "texts": [], + "surrounding_texts": [ + "For Examples B and C, three engagement points are selected on each momentary contact line from the top to the root of the worm wheel tooth. The values of k\u03c1 and \u03b8vt are calculated at every calculable meshing point. The relevant calculated results are tabulated in Tables 2 and 3, respectively. The obtained data illustrate that the values of k\u03c1 in the new contact zone, \u03a32B, are higher than those in the nominal former contact zone, \u03a32A. In \u03a32A, the values of k\u03c1 show little difference fromeach other. The same is true for\u03a32B aswell. This situation is in agreementwith the constant strength principle. On the other hand, the negative height modification is able to lead to higher values of k\u03c1 in \u03a32B. Nevertheless, both the positive height modification and the negative one do not differ much in terms of the values of k\u03c1 in \u03a32A. The values of the sliding angle reflect that the forming condition of the EHL oil film, in\u03a32B, is more ideal. However, both the positive and the negative height modifications, in general, do not differ greatly in terms of the values of \u03b8vt in \u03a32A or \u03a32B." + ] + }, + { + "image_filename": "designv11_7_0002350_s11044-011-9273-8-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002350_s11044-011-9273-8-Figure3-1.png", + "caption": "Fig. 3 Musculotendon model of contraction dynamics. C: contractile element, B: damping element, KPE: parallel elastic element, KT : tendon, LMT: musculotendon length, LT : tendon length, LM : muscle length", + "texts": [ + " The subject tries to follow the step target by means of a visual real-time visual feedback of the actual produced torque, superimposed over a mask of the target in the computer screen [16, 20] (the protocol can be visualized in Fig. 4). Raw EMG signal was initially band-pass filtered (15\u2013350 Hz), rectified, and low-pass filtered with a 2nd order digital Butterworth filter (2 Hz cut-off frequency). Input excitation signal u(t) for the muscle dynamics model was found by normalizing the collected EMG signals with MVC EMG. Muscle activation dynamics from [24] was used. Contraction dynamics is a modified version of Zajac musculotendon actuator [25] with added parallel elastic and damping elements [16] (Fig. 3). Each muscle is modeled as a system of three differential equations: a\u0307 = (u \u2212 a )(k1u + k2) \u02d9\u0303 F T = k\u0303T ( v\u0303MT \u2212 v\u0303M cos\u03b1 ) (1) \u02d9\u0303 L M = v\u0303M where a is the neural activation, u the excitation input signal, k1 and k2 time constants, FT tendon force, kT tendon stiffness, vMT musculotendon velocity, vM contractile element velocity, \u03b1 pennation angle, and LM contractile element length. The \u223c upperscript means that the variables are adimensionalized (see details of notation in [25]). vMT can be considered also as an external input, when the muscle dynamics is integrated independently of the skeletal system associated rigid body dynamics" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003259_j.cja.2013.04.006-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003259_j.cja.2013.04.006-Figure4-1.png", + "caption": "Fig. 4 Machine concept of free-form.", + "texts": [ + " (12) for the coordinate system S2 fixed on the machined arc tooth face-gear, the tooth surface equation of the transition curve on the arc tooth face-gear is r2c\u00f0hf;/2\u00de \u00bcM2hrmh \u00f013\u00de where M2h is a 4 \u00b7 4 matrix representing the transformation of the radius vector from the fabricated gear surface to the tooth surface of the arc tooth face-gear. M2h \u00bcM0aM20 \u00f014\u00de Because of the complex structure of gear cutting machines with a tool-inclining mechanism that is difficult to adjust, the arc tooth face-gear gear will be processed instead with multi-axis NC machining tools. The machine named Free-form can simulate any tool-inclining mechanism or transgender mechanism. The machine concept is shown in Fig. 4. All the required movements are implemented along or about the six NC axes of gear cutting. The six axes, namely, three translational axes and three rotational axes, provide six degrees of freedom with which to flexibly control the position and movement of the workpiece and the tool in space. The machining is performed by the instantaneous control of the relative position and movement of the tool and the workpiece, which is fully realized by an NC machine, with three translational axes X, Y, and Z and three rotational axes A, B, and C" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001350_bio.1186-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001350_bio.1186-Figure1-1.png", + "caption": "Figure 1. Schematic diagram of the FIA system. (a) Sample or blank solution; (b) H2O; (c) luminol (in 0.1 mol/L NaOH) solution; (d) KIO4 solution. P1 and P2, peristaltic pumps; S, switching valve; Y1 and Y2, confl uence points; F, fl ow cell; W, waste water; PMT, photomultiplier tube; PC, personal computer; NHV, negative high voltage.", + "texts": [ + " All the chemicals and reagents were of analytical- reagent grade and used without further purifi cation unless specifi ed otherwise. The water used was pure water (18.2 M\u03a9.cm) processed with an Ultrapure Water System (Kangning Water Treatment Solution Provider, China). The EP hydrochloride injec- tion (H12020526) was produced at Tianjin Golden Amino acid Co. Ltd (Tianjin, China). The FIA-CL cell was constructed in combination with a model IFFM-E FIA system (Xi\u2019an Remax Analytical Instrument Co. Ltd, China) for this work, as shown in Fig. 1. It consisted of two peri- staltic pumps (P1, P2), a switching valve (S), two Y-shaped mixture valves (Y1, Y2), a fl ow cell (F) and a CL detector (photomultiplier tube, PMT). All components in the fl ow system were connected with polytetrafl uoroethylene (PTFE) tubes (0.8 mm i.d.). A fl at spiral-coiled colorless silicon rubber tube (i.d. 0.8 mm; total length of the fl ow cell, 6 cm, without gaps between tubes) was used as fl ow cell and was placed in front of the PMT, which was biased at \u2212600 V for measurement" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000871_s0076-6879(78)54028-7-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000871_s0076-6879(78)54028-7-Figure3-1.png", + "caption": "FIG. 3. Schematic diagram of the mounting of cavity and discharge tube.", + "texts": [ + " The filament is then pulse-heated by capacitive discharge, vaporizing the sample which is then swept into the plasma. The resultant atomic emission is then measured using a spectrometer. Sample volumes of only 5 /xl are used, detection limits (on an absolute basis) are in the 1-50 pg range, and little or no sample preparation is required. A block diagram of the instrumental arrangement is shown in Fig. 2. The instrument is very compact, electronically sophisticated, and highly automated in its operation. The plasma source is shown schematically in Fig. 3. This analytical system was designed primarily for the determination of picogram quantities of metals in metalloenzyme preparations. To verify its H Hambidge, K. M. (1971). Anal. Chem. 43, 103. lz Kawaguchi, H., and Vallee, B. L. (1975). Anal. Chem. 47, 1029. utility for this purpose, Kawaguchi and Vallee 'z determined the metal stoichiometry in highly purified, well-characterized preparations of several zinc metalloenzymes, and compared these data to those obtained for the same material by atomic absorption spectrometry" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001004_physreve.78.066609-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001004_physreve.78.066609-Figure2-1.png", + "caption": "FIG. 2. Toppling a container. Schematic time sequence of container illustrated as a cylinder during one tipping experiment: side view top row and top view second row . a Tilt a container and flick its top with your finger so that b the container becomes vertical again, and then c , d tips part way over some more and then eventually d has sufficient energy to fall on its side. The container hardly ever falls symmetrically to the diametrically opposite side with = . See Fig. 3.", + "texts": [ + " After this bang, the container tips up onto the other side and maybe falls over. When this experiment is performed with a container that is not too tall and too thin, you can see that the container does not fall exactly onto the diametrically opposite side of the bottom rim. That is, point A on the bottom of the container that initially contacted the table and the new contact point B, that the container rocks up onto, are not exactly 180\u00b0 apart. This experiment video available online 1 is shown schematically in Fig. 2. Figure 3 shows a histogram of one particular container\u2019s orientations after we repeatedly flicked it. The distribution is strongly bimodal with no symmetric falls over many repeated trials. Note the apparent symmetry breaking with . Is this deviation from symmetric rocking due to imperfect hand release? Here we show that the breaking of apparent symmetry is consistent with the simplest deterministic theories, namely, smooth rigid body dynamics. We derive formulas for the *msriniva@princeton.edu; URL: http://www" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000222_icar.2005.1507412-Figure9-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000222_icar.2005.1507412-Figure9-1.png", + "caption": "Fig. 9. Example of kinematic structure of fully-isotropic PMSM actuated by one rotative and three linear motors (a) and its associated graph (b).", + "texts": [ + " Figure 8 presents the variation of the transmission factor 4 with the rotation angle of the moving platform. In Fig. 8-a we considered that the platform length is equal to the characteristic length r=Lc=1. In Fig. 8-b various values of platform length are considered. For 1 r 2 and y 60 ,60 the transmission factor is 40.4 2 . V. FULLY-ISOTROPIC PMSMS Fully-isotropic PMSMs can be derived from the PMs with uncoupled Sch\u00f6nflies motions, presented in the previous section, by replacing the actuated prismatic joint in leg A4 by a kinematic chain with two revolute joints (Fig. 9). These two joints have parallel axes and their direction is perpendicular to the other revolute joints of leg A4. The first revolute joint is actuated and q4 represents the rotation angle. The 4375 structural solutions set up in this way respect conditions (4-13) but the fourth actuator is not on the fixed base. Other 4375 solutions of fully-isotropic PMSMs with the four actuators mounted on the fixed base can be set up from the previous fully-isotropic solutions by replacing the kinematic chain with two revolute parallel joints in A4-leg by an extensible double parallelogram De Roberval scale-type (Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002071_s0091-0279(71)50004-1-Figure17-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002071_s0091-0279(71)50004-1-Figure17-1.png", + "caption": "Figure 17.", + "texts": [], + "surrounding_texts": [ + "It should be carried out in a systematic fashion, for the animal's compensatory adjustments usually involve more than one structure. For example, the lowering of the head is always accompanied by the extension of the neck, so that a 10 per cent body weight shift can be made to the foreleg support, thus making the forelegs support 70 per cent of the entire weight. The extension of the head and neck, when seen without further compensating changes, usually is observed when only minor pathologic lesio~s involve one or both hindlimbs. For ex ample, a ruptured anterior cruciate ligament necessitates this compen sation to remove weight from the unstable affected joint. When lesions of the posterior part of the body require substantial weight shift, we see not only an extension of the head and neck, but also a dropping back of the forelimb to a more posterior position. The more severe the condition, the more weight is shifted by the reposition ing of the forelimbs in this manner. In the severe spinal disk syndrome, in hip dysplasia, and in arthritic dogs. I have observed compensations that allow at least 90 per cent of the weight to be carried on the fore limbs. In one case of a small Terrier whose hindleg had been ampu tated by a mowing machine, a 100 per cent weight bearing by the fore legs was possible. Clinicians should also be aware that in these exaggerated compensa tory cases a learning period of three to six months is required. If a foreleg lesion should appear, and the forelegs can no longer support extra weight, a complete and sudden paralysis occurs that simulates many other, more serious conditions. The straightness of the back in the lateral stance phase is also of great importance, for the only way for a foreleg pathologic lesion to be relieved of weight is to shift it to the hindquarters. This cannot be strictly accomplished by repositioning the hindlimb farther forward, but necessitates an arching of the back. An example of this compensation is always observed in the heavier dog when one forelimb has been ampu tated. Also in the lateral view the degree of slope of the pelvis should be carefully noted- not necessarily for its functional qualities, but because a deviation from its 30\u00b0 to 45\u00b0 slope can be considered a congenital de fect. Like all congenital defects, this one rarely appears alone. In more severe hip dysplastic cases, it is not uncommon to find a 15\u00b0 to 20\u00b0 pelvic slope. Examination of the Posterior Stance In the posterior view of the normal dog, the hindlimbs extend from the lateral edges of the pelvis perpendicular to the ground. In the dog with gross weakness in the hindquarters, the hindlegs are spread farther apart in the stance position; in motion, this straddle-legged appear ance becomes even more exaggerated owing to instability. EXAMINATION OF THE CANINE LOCOMOTOR SYSTEM Figure 14. The posterior stance, showing normal and pathologic, un stable positions. Normal 67 Noting this abnormal stance and movement is important in the evaluation of hip dysplasia cases. In my experience radiographic find ipgs do not always parallel the performance in locomotion. The \"cowhock\" condition observed in the posterior view is a con genital defect often associated with other pathologic lesions. In the St. Bernard, for example, a \"cowhock\" condition commonly is associated with hip dysplasia. Chronic Luxating Patellas In chronic luxating patellas, seen more frequently in the smaller breeds, the dog tends to rotate the femur slightly laterally and the tibia medially. With this compensating body arrangement, the patella is pulled medially to the trochlea at the beginning of its motion. This alleviates the discomfort caused when the patellas transverse a portion of the rim of the trochlea. These dogs have a fairly characteristic stance and gait. The stance is \"toed-in\" and bowlegged. The animal walks with a shuffling gait becau~e of an inability fully to extend the knee joint. Clinicians examining these dogs for frequency of luxation and bony joint changes tend to remove the weight from the leg by lifting it from ground contact, then making their evaluation by extreme extension and flexion. I believe this to be a great mistake. To evaluate the patho logic changes correctly, one must examine the leg in normal weight bearing and muscle pull. This can easily be accomplished by placing one 68 WILLIAM E. Rov hand over the affected knee and the other on the dorsal pelvis area; then gently rock the dog's own weight on and off the affected limb. This examination allows the animal to align the bony structures in their compensated positions, and the patella moves in its pathologic course. A much more accurate evaluation of the accompanying lesions can be made by this procedure. ABNORMALITIES IN MOTION Osteochondritis Dissecans In the motion phase of our examination, we can observe definite pattern changes when we compare them to a calculated normal stride. One of the often described pattern changes takes place as a result of a lesion of the head of the humerus known as osteochondritis dis secans. This gait pattern is usually described as short and choppy. Most clinicians are well aware that in the examination for osteochondritis dissecans the anterior and posterior extension of the foreleg causes severe pain. The dog compensates for these painful areas, which are at the extreme ends of the stride arc, by shortening his contact point and by a premature lift point. Thus we see the short, choppy stride observed in the slower gaits of affected dogs. Un-united Anconeal Process The un-united anconeal process leads to a pattern similar to the short, choppy foreleg stride. However, in this condition the pain is elicited only when the elbow joint is in its fully extended position. This causes the dog to compensate by keeping the joint in a slightly flexed position at all times. In motion, the dog with this condition has an ap- EXAMINATION OF THE CANINE LoCOMOTOR SYSTEM 69 pearance something like that of a cat stalking a prey. This is especially observable when the condition exists bilaterally. Shifting the Weight Forward in Rear Leg Abnormalities The most common and unique ability of the dog is his capability of shifting his weight to the forelegs when posterior pathologic lesions exist. In such cases as the spinal disk syndrome, hip dysplasia, and spondylosis this ability is utilized to its fullest extent. In the stance phase the forelegs are placed more posterior, closer to the center of gravity, to support most of the body's weight. This abnormal stance and weight shift influence a greatly diflerent stride pattern. In motion, the foreleg is advanced to a shortened contact point in order to continue to bear the increased load. To keep the majority of the body's weight balanced on this supporting member while its oppo site member is being advanced, it must be extended far beyond the nor mal lift point at the posterior end of the stride arc. The hindlimbs, so as not to interfere with the foreleg motion, adopt a very shortened stride. 70 WILLIAM E. RoY In extreme cases of anterior weight shift, the affected animal has a \"seallike\" waddle. Hip Dysplasia These dogs provide the ultimate examples of the compensating changes of which the dog is capable. The severe dysplastic dog has very unstable, weak hip joints, which produce pain if called upon for any extra effort. In the lateral stance view, these animals have the maximum posterior forelimb placement, whereas the hindlimbs will be in a nor mal lateral stance position. A decrease in pelvic slope also is often observed. In the posterior view, the hindlimbs will spread abnormally far apart to compensate for the lateral instability. If these dogs are prone and wish to rise, they must literally pick themselves up by the forelimbs, because the hindlimbs are incapable of the extra propelling force. In motion the dog will walk or run with the typical stride of maxi mum anterior weight shift: a shortened contact point; a greatly in creased lift point; and a short, shuffied hindleg stride. The posterior view, in motion, is a straddle-legged, swaying, unstable movement with very little propulsive power- so weak, in fact, that if the dog is forced into a fast gait he may have to resort to using both hindlimbs together for power, producing a \"hopping\" gait." + ] + }, + { + "image_filename": "designv11_7_0001911_s0580-9517(08)70593-2-Figure6-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001911_s0580-9517(08)70593-2-Figure6-1.png", + "caption": "FIG. 6 . Rotating glass electrodes designed by Hagihara.", + "texts": [ + " This electrode and the bridge must be large enough not to polarize with the passage of 150 pamp. In practice a 3 Ib bottle of 10 cm diameter and tubing of 1 cm bore satisfied this requirement. The cell is filled with the suspending medium, all air bubbles being removed. The volume of liquid in the cell is about 20 ml. \u201cThe gold electrode is made the cathode, and the calomel cell the anode in their connexions with a Cambridge pen-recording polarograph.\u201d The design of a rotating electrode described by Hagihara (1961) is reproduced in Fig. 6. The electrode is made of platinum wire (28-32 gauge) the tip of which is melted to form a sphere approximately 1 mm in diameter. This sphere is sealed into a soft glass capilliary tube and the tip is then gently ground at an angle to expose a flat platinum surface. The surface is polished with very fine carborundum powder. The electrode is then joined to a toughened glass tube by a relatively unpliable piece of plastic tubing, so the platinum wire enters the lumen of the toughened glass tube. The lumen is then filled with mercury, so that the negative lead from the cathode can dip into the mercury and make continuous electrical connection whilst the electrode is rotated at greater than 500 rev/min" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001851_robot.2009.5152196-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001851_robot.2009.5152196-Figure2-1.png", + "caption": "Fig. 2. Parallel-wire Driven System using Seven Wires", + "texts": [ + " On the other hand, addressing the latter feature, lots of hypotheses for the principle of human\u2019s motion generation have been suggested in physiology. Feldman proposed the Equilibrium Point (EP) hypothesis which regards muscles as springs, thereby, the displacement of a equilibrium point of antagonistic muscles by variation of spring-length can control the limbs to desired posture[3]. Subsequently, Hogan expanded it into feedforward control as the Virtual Trajectory Control Hypothesis[4]. By the way, some of the authors pointed out that the internal force among wires of a parallel-wire driven robot (Fig. 2)[5] produces a potential field, thereby such system can achieve sensorless feedforward positioning with the constant internal force balancing at a desired position[6]. That study showed that the convergence at a desired position strongly depends on the wire arrangement. Because both of the muscle-tendon and a wire can only transmit tension, the analogy between the musculoskeletal system and the parallel-wire driven system can be found in terms of the driving principle. The above-mentioned EP hypothesis is based on the principle that the internal force among muscles is balanced at desired posture" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000055_978-1-4684-1500-1-Figure4.1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000055_978-1-4684-1500-1-Figure4.1-1.png", + "caption": "Figure 4.1 The velocity pro/i1e 0/ a robot,", + "texts": [ + " A continuous path trajectory can be program med so that the end effector follows a predetermined path in space over a wide selection of velocities. The linear interpola tion scheme used for continuous path steps allows a simple calculation of step velocity by dividing the number of interpo lations per step i by the frequency of interpolations f. The calculation of the point-to-point steps is more difficult and requires knowledge of the acceleration rates and slew speeds for each articulation. A typical velocity profile for a point-to-point step is shown in Figure 4.1, which portrays a linear acceleration a, followed by a slew velocity v (for steps long enough to saturate), finishing with a linear deceleration a. The calculation of the time required to move distance Sis: s Vs ts = -- +- a s> (vs)2 a The time required for a step of length S to be covered where velocity saturation is not reached is: tns = z[~r/2 S < (V~2 Because of the independence of completion times for ... ach of the articulations in a point-to-point move, a generalized motion consisting of up to six degrees of freedom requires the calculation of the time needed for the slowest articulation" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001860_tmech.2010.2057440-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001860_tmech.2010.2057440-Figure3-1.png", + "caption": "Fig. 3. Photograph of OCTA.", + "texts": [ + " (30) The actual accelerometer locations are slightly offset from the vertices of a regular octahedron because of practical considerations: It was simpler to directly screw the accelerometers onto the 2 in \u00d7 2 in square tubing that composes the accelerometerarray structure. Notice that each accelerometer and gyroscope was attached to the tubing not only with screws, but also with dowel pins, in an effort to reduce misalignments between the sensors. The size of the whole assembly is approximately 1 ft (305 mm) in each direction, as can be appreciated from its photograph in Fig. 3. The six biaxial accelerometers used are ADXL320 [43] from Analog Devices. Their range is \u00b15g, while their bandwidth is limited by an analog low-pass filter, whose cutoff frequency was set to 50 Hz. A rough static calibration of the accelerometers was performed by successively directing their axes toward gravity, perpendicular to gravity, and opposite to gravity. A linear leastsquares best-fit yielded the scale factors and offsets shown in Table I. As the main objective is to compare the robustness of the different CA methods, the accelerometer-calibration procedure was minimal" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003173_j.robot.2010.12.006-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003173_j.robot.2010.12.006-Figure1-1.png", + "caption": "Fig. 1. A typical example of multi-contact robotic system: multi-legged robot. The ground reaction forces at contacts counterbalance other wrenches on the robot, so that the robot can maintain equilibrium. Each contact force must lie in the circular Coulomb friction cone, which can be replaced by a polyhedral convex cone for avoiding the nonlinear friction constraint and simplifying the computation.", + "texts": [ + " Most often, the contact between a robot and the environment is a frictional point contact. Some robots or robotic systems may contact the environment by area contacts. For example, a biped robot walks on the ground usually using the entire soles of the feet [21]. Soft robot fingers make small contact regions with an object during grasping [34]. Such a contact area can be treated as multiple frictional point contacts on the boundary of the area. Hence, in this paper, we assume that each contact is a point contact with Coulomb friction. Herein, we take a multi-legged walking robot (Fig. 1) as an example to introduce the statics of a multi-contact robotic system. Suppose that robot makes m contacts with the environment. Through these contacts the environment exerts reaction forces on the robot and counterbalances the other wrenches (force and moment) applied to the robot, such as thewrenches resulting from gravity and inertia, whose sum is denoted bywext. Let ni, oi, and ti be the unit inward normal and two unit tangent vectors at contact i (i = 1, 2, . . . ,m)with respect to the global coordinate frame such that ni = oi\u00d7ti. They establish a local coordinate frame at contact i and the contact force can be expressed as fi = fi1 fi2 fi3 T therein, where fi1, fi2, and fi3 are the components of fi along ni, oi, and ti, respectively. To maintain stable contact, the contact force fi must satisfy the Coulomb friction constraint: fi1 \u2265 0 and f 2i2 + f 2i3 \u2264 \u00b5ifi1, (1) where \u00b5i is the friction coefficient. The above constraint defines a circular cone, as shown in Fig. 1. For simplicity, the circular cone can be replaced by an inscribed n-side polyhedral cone with side edges ei,j, j = 1, 2, . . . , n such that fi satisfying (1) can be written as a nonnegative linear combination of the side edges, i.e., fi = n\u2212 j=1 xi,jei,j with xi,j \u2265 0 for all i and j, (2) where ei,j, j = 1, 2, . . . , n are expressed in the local coordinate frame formed by ni, oi, ti as ei,j = [ 1 \u00b5i cos 2j\u03c0 n \u00b5i sin 2j\u03c0 n ]T . (3) The robot can hold in equilibrium if and only if there exist fi, i = 1, 2, ", + " Because it is relatively easier to solve an LP problem, the sum \u03c3L1 of fi1, i = 1, 2, . . . ,m was adopted as the mainstream measure of overall contact force magnitude [7,3,9,11,17,13,33], while the maximum \u03c3L\u221e was rarely mentioned [13]. The linear expression (2) of fi enables us to avoid the nonlinear constraint (1) and handle only a linear system (5). However, using the inscribed polyhedral cone will exscind some parts of the original friction cone and shrink the available feasible force domain (see Fig. 1). Then the computed minimum contact forces could be slightly bigger than the values using the nonlinear model (1). Choosing a bigger n can reduce this error but also increases the number of variables in (5) and the problem size. Since the robot\u2019s equilibrium and equilibrating contact forces are often required to be determined in real time, the trade-off between the computational efficiency and the solution accuracy is also a key issue that we need to consider in developing algorithms for Problems 1 and 2", + " Sometimes this intersection point still lies on the boundary of co S, so that s\u2217t2 just equals s0 and our algorithm needs no iteration (Fig. 7(b)). However, if \u03bb0 given by (29) is bigger than hco S(ut2), we can set \u03bb0 = hco S(ut2) as usual. Therefore, we finally choose \u03bb0 = min nT t1s \u2217 t1 nT t1u \u2217 t2 , hco S(ut2) . (30) We implemented the GJK algorithm and our algorithm in MATLAB on a laptop with an Intel Core i7 2.67 GHz CPU and 3 GB RAM. In numerical tests, we set a small tolerance \u03f5 = 10\u221210 on the distance dco S(sr) to terminate our algorithm. The friction coefficient \u00b5 = 0.2 for every contact. Referring to Fig. 1, we consider two cases of a six-leg robot walking on an uneven terrain. First, suppose that feet 1, 3, and5 aremoving forward,while feet 2, 4, and 6 remain on the ground to support the robot. The contact positions and normals are r2 = 0.010 0.300 \u22120.211 , r4 = \u22120.258 \u22120.242 \u22120.076 , r6 = 0.256 \u22120.236 \u22120.172 Y. Zheng et al. / Robotics and Autonomous Systems 59 (2011) 194\u2013207 203 n2 = \u22120.033 0.248 0.968 , n4 = \u22120.227 \u22120.446 0.866 , n6 = 0.354 \u22120.245 0.903 . Assume thatw1 ext = \u22120.4 \u22120" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003560_978-1-4613-4560-2_2-Figure8.28-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003560_978-1-4613-4560-2_2-Figure8.28-1.png", + "caption": "Fig. 8.28. The dependence of current density on overpotential (a) is of the shape of a hyperbolic sinh function (b).", + "texts": [ + " Before engaging in discussion, one should issue a reminder here. All relations derived so far cover only one, the simplest, of all possible cases: a single-step single-electron-exchange reaction. In more complex cases, important changes appear, but these will be discussed later (particularly in Section 9.1). Even from this simple case, much can still be learned. A better feel for the indications of the Butler-Volmer relation [Eq. (8.31)] is obtained by plotting i against 1]. The i versus 1] curve so obtained (Fig. 8.28a) looks much like the plot of a hyperbolic sine function. There is in fact a basis for this resemblance to a sinh function. It has been said that the symmetry factor is about ~. Let it be assumed to be ~. Then Eq. (8.31) becomes (8.36) and, since eX - e-X 2 = sinh x . 2' . h F'fJ 1= '0 sm 2RT (8.37) (8.38) The i versus sinh 'fJ curve, however, is symmetrical (cf Fig, 8.28b). A symmetry factor of t corresponding to a symmetrical barrier yields a symmetrical i versus 'fJ curve. Hence, equal magnitudes of 'fJ on either side of the zero produce equal currents; and, conversely, equal de-electronation and electronation currents should produce equal overpotentials, or current produced potentials, 'fJ" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001511_204103-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001511_204103-Figure1-1.png", + "caption": "Figure 1. Geometry of the two unequal spheres moving along their line of centres (z-direction).", + "texts": [ + " The general framework derived in the previous section is here applied to four specific swimmers: two unequal spheres moving along a straight line, two unequal spheres moving along a circumference, a scallop-like swimmer, and a deforming sphere. These simple examples illustrate reciprocal locomotion in the absence of fluid inertia; the goal is therefore to compute the net translational velocity of each swimmer as a function of Rep. For simplicity, gravity is not accounted for in these examples; the inclusion of gravity is straightforward, and its effect is discussed at the end of section 4. Consider the swimmer shown in figure 1, which consists of two unequal spheres. The spheres have radii a and b, which are different but of comparable magnitude, that is, \u03b2 \u2261 b/a = O(1). Note that \u03b2 = 1 is required to break the spatial symmetry and yield net motion. The time-dependent distance between the sphere centres, L(t), is large compared with the sphere radii, so that L = O(a/\u03b5), where \u03b5 \u2261 a/\u3008L\u3009 1, and the angular brackets \u3008\u3009 denote a time average over the period of motion. The two spheres are able to exert equal and opposite forces on each other, so that L(t) is a prescribed periodic function of time with radian frequency \u03c9" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000113_bf00043705-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000113_bf00043705-Figure5-1.png", + "caption": "Figure 5", + "texts": [ + " This means that the tension TI~ becomes unbounded at the points where wrinkles converge, irrespective of the rate of loading. Taking the scalar product of the Eq. (1.11) and the normal , to the film, one obtains T*bll = -F , (3.5) i.e., sign bll = -sign F. (3.6) The following example illustrates applications of the results given above. Small torsion of a film of revolution Let us consider a film which is stretched on a rigid smooth surface of revolution and bounded by two undeformable circumferences with radii R1 and R2 (Fig. 5), and assume that the lower circumference is fixed, while the upper circumference is turned through the torsion angle o~ about the axis y. As shown above, the wrinkles (if they occur) will form a family of geodesical lines. Thus, for a spherical film wrinkles will coincide with inclined great circles, while for a cylindrical film they will form a family of helices with constant slopes. In the last case the complete solution of the problem can be obtained if the angle of the torsion is small. Indeed, it is easy to verify that the constant principal strains a OL e~ : 2 ' e22 : - 5 ' e~2 : 0 (3" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003088_j.jmatprotec.2011.09.010-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003088_j.jmatprotec.2011.09.010-Figure2-1.png", + "caption": "Fig. 2. Geometry representation of (a) e", + "texts": [ + " / Journal of Materials Proc a r t r r w z c r z C l d t p d w t r nd A\u2032 represent the center points at the entry and exit sections, espectively. Cubic parametric Bezier curve defines a streamline in deformaion zone as follows: = R(t) = r0(1 \u2212 t)3 + r13t(1 \u2212 t)2 + r23t2(1 \u2212 t) + r3t3 (1) The matrix form of the above equation can be expressed as: = [ 1 t t2 t3 ] \u23a1 \u23a2\u23a3 1 0 0 0 \u22123 3 0 0 3 \u22126 3 0 \u22121 3 \u22123 1 \u23a4 \u23a5\u23a6 \u23a1 \u23a2\u23a3 r0 r1 r2 r3 \u23a4 \u23a5\u23a6 (2) here, r is the position vector of each particle in the deformation one and r0, r1, r2, r3 are the position vectors of the Bezier curve ontrol points. Referring to Fig. 2, streamline equations for deformation from a ound billet to an off-centric T-shaped section have been obtained. In order to express the coordinates of the points in deformation one, parameters u, q, and t are defined as follows (Chitkara and elik, 2000): 0 \u2264 u \u2264 1 u = w R w = u.R 0 \u2264 q \u2264 1 q = 2 \u21d2 = q.2 0 \u2264 t \u2264 1 t = z h z = t.h (3) Referring to Fig. 2, w = TH, R is the radius of the initially circuar billet, \u03d5 is the angle of the deforming region at entry, z is the istance between entry section and specified section and h = OO\u2032 is he length of the die. By applying the introduced parameters, the osition vector of particle, P, inside the deformation zone can be etermined as follows: P = Xi\u0302 + Yj\u0302 + Zk\u0302 = f1(u, q, t)i\u0302 + f2(u, q, t)j\u0302 + f3(t)k\u0302 X = f1(u, q, t) = u[ 0Sin + t3(2 0Sin \u2212 2F1) +3t2(F1 \u2212 0Sin )] + e5(2t3 \u2212 3t2 + 1) \u2212 e3(2t3 \u2212 3t2) = u.p(q, t) + K1(t) Y = f2(u, q, t) = u[ 0Cos + t3(2 0Cos \u2212 2F2) +3t2(F2 \u2212 0Cos )] + e6(1 \u2212 u)[2t3 \u2212 3t2 + 1] +e4[3t2(1 \u2212 t) + t3] = u.S(q, t) + K2(u, t) Z = f (t) = t3h(3c \u2212 3c + 1) + t2h(3c \u2212 6c ) + 3tc h = K (t) (4) 3 1 2 2 1 1 3 here, X, Y,Z are the coordinates of the particle and c1 and c2 are he Bezier coefficients. 0 is equal to TB shown in Fig. 2. e1 and e2 epresent the off-centric positions in X and Y directions, e3 and e4 essing Technology 212 (2012) 249\u2013 261 are the coordinates of center point at exit, and e5 and e6 are the coordinates of center point at entry. F1 and F2 are the geometry functions in term of q \u2013 which are given by: F1 = 2 sin F2 = 2 cos Referring to Fig. 2, 2 = A\u2032B\u2032 and is the angle of the deforming region at exit. The determination of an exact and accurate velocity profile is essential as it is the first step to predict the deviation of the final product and design the proper bearing. A kinematically admissible parametric velocity field has been obtained by differentiating the position vector and applying the volume constancy condition. To derive the velocity field, the following assumptions were considered and applied to the Bezier relations (Chitkara and Celik, 2000): 1" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003662_imece2012-89440-Figure12-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003662_imece2012-89440-Figure12-1.png", + "caption": "Fig. 12: The effect of electron beam scanning speed on melt pool width, a) scanning speed= 10 mm/s, b) scanning speed= 50 mm/s, c) scanning speed= 90 mm/s, 1: Thermal model, 2: Fluid flow model", + "texts": [], + "surrounding_texts": [ + "Temperature distribution and size of the molten pool in Electron Beam Melting\u00ae (EBM) was modeled by applying two models, one with considering material flow in molten pool and the other without considering it. Form the performed analyses, the following could be concluded. Increasing the electron beam scanning speed resulted in a smaller width and depth of the melt pool in both the thermal and fluid flow models. However, the two models predicted slightly different melt pool geometries. The negative temperature coefficient of surface tension is responsible for an outwards flow formation in the melt pool, which results in a melt pool with a larger width at the top surface and shallower penetration in the fluid flow model with respect to the thermal model. Moreover, the fluid flow model showed lower values of maximum temperature than those in the thermal model. A better understanding of temperature distribution through a more accurate model can be a very useful tool for adjusting the process parameters in order to control the cooling rate and managing the microstructural and mechanical properties of specimens produced through Electron Beam Melting\u00ae (EBM)." + ] + }, + { + "image_filename": "designv11_7_0001528_gt2008-50806-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001528_gt2008-50806-Figure4-1.png", + "caption": "Figure 4. Lateral misalignment method showing thermocouple locations looking down from the top. The left bearing is stationary. The right bearing moves laterally 0.127 mm for each incremental test.", + "texts": [ + "url In an effort to determine if the method of misalignment has a significant effect, additional tests were conducted using a different set of bearings without thermocouples. In these tests, two misalignment methods were used. The first method imposed a misalignment by holding both bearings fixed laterally, and rotating one bearing as illustrated in figure 5. In the second misalignment method, the same technique was used as the previous bearings, a lateral misalignment like the previous tests illustrated in figure 4. A different set of bearings was used without thermocouples because the thermocouples were extremely fragile and easily damaged. Additionally, as discussed later, there was a concern that the thermocouples affected the behavior of the bearings, and therefore may have influenced the results to some extent. Since there were no thermocouples on the bearings, it was not possible to determine when steady state temperature operation was reached. Therefore, each test was run for 40 minutes, which based upon the previous tests with thermocouples, is ample time to reach steady state operation", + " In addition, during this second set of tests, the displacement of the rotor in the vertical and horizontal directions at each end of the rotor were measured using eddy current displacement sensors to see if misalignment has an observable effect on the dynamics of the system. Figure 6 shows the temperature data for steady operation at 20,000 rpm. In general, there is an upward trend on temperature with higher misalignment, as anticipated. The exceptions to the trend are T3 and T4. One possible cause of the downward trend in T3 and T4 is their proximity to the turbine, seen in figure 4. Since T3 and T4 are adjacent to the turbine, they are affected by the temperature of the turbine outlet flow. The turbine is driven by compressed air, and as the air expands through the nozzle, it cools. At higher misalignment, more flow is required to counteract the higher 4 Copyright \u00a9 2008 by ASME =/data/conferences/gt2008/69978/ on 03/12/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use Dow torque, resulting in more turbine exhaust. The increased turbine exhaust may cool the bearing in the location where T3 and T4 are mounted. When the GFBs are misaligned, the bearings become more and more edge-loaded. The thermocouples were placed on the bearing in such a way to try to see the effect of the edgeloading in the form of increased temperature. For example, as the right hand bearing in figure 4 is moved upward in the picture, the film thickness near thermocouples T2, T4, T6, and T8 decreases, while at T1, T3, T5, and T7 it increases. Because thinner films are associated with higher heat generation, T2 should be hotter than T1, T4 hotter than T3, T6 hotter than T5, and T8 hotter than T7. In general, this result is observed. It should be noted that thermocouple T6 was damaged while increasing the misalignment after the run at 3.7E-3 radians of misalignment, so there is no data for T6 beyond that test" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001477_978-3-642-04466-3_2-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001477_978-3-642-04466-3_2-Figure2-1.png", + "caption": "Fig. 2 The angle of attack [37]. The arrow represents the direction of the flow", + "texts": [ + " As stated by Lyttle and Keys [17] one major advantage of CFD procedures is the possibility to assess how the variance of the inputs affects the resultant flow conditions. Hence, CFD has been used to analyze some concerns arising from empirical data. One of the major themes is related to the relative importance of drag and lift forces to the overall propulsive force production in swimming. Several studies were carried-out using digital models of the human hand and/or forearm and/or upper arms. Bixler and Riewald [33] evaluated the steady flow around a swimmer\u2019s hand and forearm at various angles of attack (Fig. 2) and sweep back angles (Fig. 3). The CFD model was created based upon an adult male\u2019s right forearm and hand with the Fig. 3 The sweep back angle [37]. The arrows represent the direction of the flow 0\u02da 180\u02da 270\u02da 90\u02da forearm fully pronated. Force coefficients measured as a function of angle of attack showed that forearm drag was essentially constant (CD 0.65) and forearm lift was almost zero (Figs. 4 and 5). Moreover, hand drag presented the minimum value near angles of attack of 0\u0131 and 180\u0131 and the maximum value was obtained near 90\u0131 (CD 1" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000829_bit.260221213-Figure6-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000829_bit.260221213-Figure6-1.png", + "caption": "Fig. 6 . Effect of temperature. Reactions were carried under standard conditions except for temperature. (0-0) Immobilized chloroplasts; (0-0) native chloroplasts.", + "texts": [ + " The activity of NADP reduction increased with increasing light intensity. The saturation of NADP reduction was observed over 10000 lx (30 cm lamp to vessel distance) in both native and immobilized chloroplasts. Figure 5 shows the pH profiles of native and immobilized chloroplasts. No difference in the optimum pH (8.0) for NADP reduction was observed between native and immobilized chloroplasts. Both native and immobilized chloroplasts could not reduce NADP below pH 5.0 and above pH 9.0. The effect of temperature on the activity of NADP reduction is shown in Figure 6. The optimum temperature of native and immobilized chloroplasts was 25\u00b0C. However, immobilized chloroplasts ditions except for light intensity. pH profiles of native and immobilized chloroplasts. Reactions were carried out under standard conditions except for pH. 0.1M phthalate buffer (pH 5-6) and 0.1M Tris-HC1 buffer (pH 7-9) were employed. (0-0) Immobilized chloroplasts; (0-0) native chloroplasts. were more stable than native chloroplasts at higher temperatures. Therefore, the reactions were performed at 25\u00b0C and pH 8" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003837_s00161-012-0235-z-Figure13-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003837_s00161-012-0235-z-Figure13-1.png", + "caption": "Fig. 13 Dependence of entropy and non-contact stresses", + "texts": [], + "surrounding_texts": [ + "Consider the example of entropy calculation for the tribo-fatigue system consisting of friction pair with the elliptic contact of the ratio between smaller b and bigger a semi-axes b/a = 0.574. One of the elements of the friction pair is loaded by non-contact bending. An example of such an element is the shaft in the roller/shaft tribo-fatigue system. Specific damage \u03c9 in (7) of elementary dW which can be presented as a ratio between current parameter \u03d5i j of mechanical state (stresses and strains) of a system and its limiting value \u03d5(lim) i j . Such ratios may be of two kinds: dimensional and dimensionless for stress tensor \u03c9 = 3\u2211 i, j=1 ( \u03c3i j \u2212 \u03c3 (lim) i j ) and (21a) \u03c9 = 3\u2211 i, j=1 ( \u03c3i j / \u03c3 (lim) i j ) , (21b) for stress intensity \u03c9 = \u03c3int \u2212 \u03c3 (lim) int and (22a) \u03c9 = \u03c3int / \u03c3 (lim) int , (22b) where \u03c3int = \u221a 2 2 \u221a (\u03c311 \u2212 \u03c322) 2 + (\u03c322 \u2212 \u03c333) 2 + (\u03c333 \u2212 \u03c311) 2 + 6 ( \u03c32 12 + \u03c32 23 + \u03c32 13 ) and energy \u03c9 = U \u2212 U (lim) and (23a) \u03c9 = U/U (lim) (23b) where strain energy is U = 3\u2211 i, j=1 \u03b5i j\u222b \u03b5i j =0 \u03c3i j d \u03b5i j , (24) that becomes U = 3\u2211 i, j=1 \u03c3i j \u03b5i j , (25) in case of the considered linear dependence between stresses \u03c3i j and strains \u03b5i j . According, for example, to [3], dangerous volume in a solid is the three-dimensional set of points (elementary volumes dV) where acting stresses (strains), stress intensity, or strain energy surpass the limiting and therefore produce damage: Wi j = { dV/ \u03d5i j \u2265 \u03d5(lim) i j , dV \u2282 Vk } , i, j = x, y, z. Wint = { dV/ \u03d5int \u2265 \u03d5(lim) int , dV \u2282 Vk } , WU = { dV/U \u2265 U (lim), dV \u2282 Vk } (26) where Vk . is working volume. Since \u03c9 dW should have energy dimension formulas (21\u201323a) may be used directly. In case formulas (21\u201323b) are used it is necessary apply dimension factor \u03b3(w) 1 . Consider the following expression for calculation of energy dangerous volume WU and tribo-fatigue entropy SU WU = \u222b \u222b \u222b WU (U\u2265U (lim)) dWU SU = \u222b \u222b \u222b WU (U\u2265U (lim)) dSU dWU (27) where according to (23b) d SU = \u03c9 /T = ( U \u2212 U (lim) ) /T . Note that integrals (27) are calculated only in the dangerous volume where U \u2265 U (lim) and therefore energy is absorbed to produce the damage unlike the volumes where energy is just dissipated if U < U (lim). Calculation of these integrals due to the complexity of the surface bounding the dangerous volume was performed numerically using Monte-Carlo method. The following input data were used in calculations of entropy for elliptic contact if contact pressure is p(n) (x, y) = p(c) 0 \u221a( 1 \u2212 x2/a2 \u2212 x2/b2 ) and the ratio between the bigger a and the smaller b semi-axes of contact ellipse is b/a = 0, 574: p(c) 0 = \u03c3(n) zz (Fc) \u2223\u2223\u2223 x=0,y=0,z=0 = 2, 960 MPa, p(c,lim) 0 = p0 ( F (lim) c ) = 888 MPa = 0.3p(c) 0 (28) where p(c) 0 is the maximum contact stress under the action of force Fc, p(c,lim) 0 is the contact fatigue limit (maximum contact stress under the action of limiting force F (lim) c obtained in the course of mechano-rolling fatigue tests described in [3]. The criterion of the limiting state in these tests was the limiting approach of the axes in the tribo-fatigue system (100 \u03bcm). The test base equaled to 3 \u00b7 107 cycles. Calculations of the three-dimensional stress-strain state in the neighborhood of elliptic contact for b/a = 0.574 [14,15] show that maximum value of strain energy U is related to the maximum contact pressure p(c) 0 in the following way U = max dV [U (Fc, dV )] = 0, 47p(c) 0 . (29) Therefore the limiting value of strain energy U (lim) for the action of limiting force F (lim) c is U (lim) = max dV [ U ( F (lim) c , dV )] = 0, 47p(c,lim) 0 . (30) Maximum stresses \u03c3a caused by non-contact bending in the contact area in calculations were the following \u22120.34 \u2264 \u03c3a /p(c) 0 \u2264 0.34. Tangential tractions are directed along the greater semi-axis of contact ellipse: p(\u03c4) (x, y) = \u2212 f p(n) (x, y) = \u2212 f p(c) 0 \u221a( 1 \u2212 x2/a2 \u2212 x2/b2 ) Distribution of entropy increment calculated according to (23a) shown in Figs. 8, 9, 10, and 11 could be considered as the characteristic of probability of appearance of local damage (initial cracks). The higher is the entropy increment in a point of the dangerous volume the higher is the probability of damage (crack) initiation in this point. Magnitudes of the dangerous volumes and entropy are the integral damage indicators (possible number of cracks and their sizes) of a body or a system. According to Figs. 8, 9, 10, and 11 for p0 = p(c) 0 and friction coefficient f = 0.2 maximum entropy increment is in the middle of contact surface. Maximum of entropy increment under the joint action of contact pressure and tangential tractions (friction) dS(n+\u03c4) U increases by approximately 30% comparing to the maximum of entropy increment dS(n) U under the action of contact pressure only. Joint action of friction and tensile bending stresses increase dS(n+\u03c4 +b) U by approximately 30% and compressive bending stresses increase dS(n+\u03c4\u2212b) U by approximately 60% comparing to the maximum of entropy increment dS(n) U . If friction is applied to the system, then the magnitudes of dangerous volume W (n+\u03c4) U , entropy S(n+\u03c4) U , and average entropy S(n+\u03c4) U /W (n+\u03c4) U are increased by approximately 6, 35, and 27 % comparing to W (n) U , S(n) U and S(n) U /W (n) U , respectively. If both friction and tensile bending stresses are applied to the system, then the magnitudes of dangerous volume W (n+\u03c4 +b) U , entropy S(n+\u03c4 +b) U , and average entropy S(n+\u03c4+b) U /W (n+\u03c4 +b) U are increased by approxi- mately 54, 112, and 36 % comparing to W (n) U , S(n) U and S(n) U /W (n) U , respectively. If both friction and compressive bending stresses are applied to the system, then the magnitudes of dangerous volume W (n+\u03c4 \u2212b) U , entropy S(n+\u03c4 \u2212b) U , and average entropy S(n+\u03c4 \u2212b) U /W (n+\u03c4 \u2212b) U are increased by approx- imately 31, 98, and 50% comparing to W (n) U , S(n) U and S(n) U /W (n) U , respectively. More detailed analysis of considered effects might be done using Figs. 12, 13, and 14. They show significant increase of entropy with the increase of contact pressure, friction coefficient, and stresses caused by non-contact loads. Entropy increases almost at the same level for the same absolute values of tensile and compressive non-contact stresses. This effect might be conditioned by the fact that energy U calculated according to (25) attains positive values. Main conclusion that can be made from the analysis of Figs. 8, 9, 10, 11, 12, 13, and 14 is that not only friction but also non-contact forces change greatly entropy characteristics in the neighborhood of contact area. Note that according to (23a), (25)\u2013(30) calculations were performed for the simplest case of fully applied to the tribo-fatigue system energy U . Similar calculations may be done for effective energies U (eff) taking into account damages interaction function according to (19)." + ] + }, + { + "image_filename": "designv11_7_0003346_j.applthermaleng.2013.02.028-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003346_j.applthermaleng.2013.02.028-Figure4-1.png", + "caption": "Fig. 4. Structural boun", + "texts": [ + " Because the thickness of the silicon cell was far less than its length or width, the cell was meshed with a finer segmentation and tailored with hexahedral elements to improve the accuracy of the analysis results. The elements were chosen as solid185 and solid186, which have sufficient convergences and fit both linear and nonlinear dynamics. The set of boundary conditions \u201cDisplacement\u201d of the ANSYS Workbench was used, in which the x- and y-direction displacements on the bottom edge of the soldering rods were defined to be zero and free-form deformation was allowed in the z-direction, as shown in Fig. 4. Regarding the thermal loading, because the cell warpage occurred during the cooling stage of the soldering, the numerical simulation of the thermal surface boundary conditions utilized the actual measured temperature values (Fig. 2); furthermore, it was assumed that after 6.5 s, the temperature had decreased linearly to room temperature. Because the cells were located on the preheating plate, only the soldering track had an elevated temperature, whereas the temperature of the other areas of each cell remained at the temperature of the preheating plate (150 C)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000774_robot.2007.363944-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000774_robot.2007.363944-Figure2-1.png", + "caption": "Fig. 2. An environment, corresponding face vector fields, and the graph showing how to reach the goal cell from any other cell.", + "texts": [ + " Then, beginning with Cg , search the connectivity graph to obtain a chain of cells from any cell to Cg . Any graph search algorithm can be used, with or without any optimality criteria. For example, breadth-first search can be used, with a corresponding linear time bound. The resulting directed graph defines a \u201csuccessor\u201d for every cell except the goal cell; the successor of a cell is the next cell on the route to the goal. We call every cell with a successor an intermediate cell, in distinction with the goal cell, which has no successor. See Figure 2. The remaining task is to construct local controllers that avoid obstacles, are consistent with the computed discrete plan, and satisfy the smoothness requirement. Since each node in the graph corresponds to a convex cell, consistency with the high level plan is equivalent to solving the control to facet problem: that is, all integral curves must exit from a particular facet in finite time while avoiding all other facets. We will construct such controllers by defining a vector field over the cell, as well as one corresponding to each face" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000344_j.triboint.2006.05.012-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000344_j.triboint.2006.05.012-Figure1-1.png", + "caption": "Fig. 1. Hole-entry journal bearing system (a) symmetrical configurat", + "texts": [ + " The Reynolds equation governing the flow of lubricant in the bearing clearance space in non-dimensional form for laminar flow is given as [15,20] q qa h\u0304 3 F\u0304 2 qp\u0304 qa \u00fe q qb h\u0304 3 F\u03042 qp\u0304 qb \u00bc O q qa 1 F\u0304 1 F\u0304 0 h\u0304 \u00fe qh\u0304 qt\u0304 , \u00f01\u00de where F\u0304 0; F\u0304 1; and F\u0304 2 are the cross-film viscosity integrals and given by the following relations by using nondimensional terms m\u0304 \u00bc m=mr and z\u0304 \u00bc z=h as F\u03040 \u00bc Z 1 0 1 m\u0304 dz\u0304; F\u03041 \u00bc Z 1 0 z\u0304 m\u0304 dz\u0304; F\u03042 \u00bc Z 1 0 z\u0304 m\u0304 z\u0304 F\u0304 1 F\u0304 0 dz\u0304. ion, (b) asymmetrical configuration, (c) worn bearing geometry. ARTICLE IN PRESS R.K. Awasthi et al. / Tribology International 40 (2007) 717\u2013734720 The geometry of the worn zone is shown schematically in Fig. 1(c). Dufrane et al. [8] assumed an abrasive wear model with the worn arc at a radius larger than the journal. Based on the visual observation, they considered that the footprint created by the shaft is almost exactly symmetrical at the bottom of the bearing. They further assumed that the wear pattern is uniform along the axial length of the bearing. The maximum defect represents 50% of the radial clearance of the bearing. The change in the bush geometry is expressed as [5,8] qh\u0304 \u00bc d\u0304w 1 sin a for abpapae, (2a) qh\u0304 \u00bc 0 for aoab or a4ae" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002132_cdc.2010.5718000-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002132_cdc.2010.5718000-Figure2-1.png", + "caption": "Fig. 2. 2D SpiderCrane gantry cart", + "texts": [ + " The form of the total energy of the system is given as H\u0304 (q, p) = 1 2 p\u22a4M\u0304\u22121 (q)p + V\u0304 (q), (2) with M\u0304 = M\u0304\u22a4 > 0 the mass matrix, given by M\u0304(q3) = mr +m 0 mL3 cos(q3) 0 0 0 mr +m mL3 sin(q3) 0 0 mL3 cos q3 mL3 sin(q3) mL2 3 0 0 0 0 0 I1 0 0 0 0 0 I2 where mr is the ring mass, m the mass of the load and L3 the (fixed) length of the cable attached to the load. The potential energy is given by V\u0304 (q2, q3) = (mr +m)gq2 \u2212mgL3 cos(q3) , and the input matrix is G\u0304 = 1 0 0 1 0 0 0 0 0 0 . We refer to [8] for a detailed description of the modeling issues. We can see that the gantry part is decoupled from the pulley mechanism, as shown in Figure 2 and Figure 3. Hence, we can concentrate on the gantry part and our objective is to position the payload, which is suspended by a cable from the ring mass mr on which two actuated forces u = col(u1, u2) act. The (reduced) inertia matrix is then M\u0303(q3) = mr +m 0 mL3 cos q3 0 mr +m mL3 sin(q3) mL3 cos(q3) mL3 sin(q3) mL2 3 with the (reduced) input force matrix G\u0303 = 1 0 0 1 0 0 . In order to simplify the dynamic equations we apply a partial linearization that transforms the system into Spong\u2019s Normal Form, see [17] for details" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003560_978-1-4613-4560-2_2-Figure8.91-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003560_978-1-4613-4560-2_2-Figure8.91-1.png", + "caption": "Fig. 8.91. A linear analogue to the po tential-energy barrier for electron tunneling shows that the ratio of tan y to tan y + tan -+ -+ (J is equal to the ratio of energies /::\"c to /::\"\u00a30, the former being equal to the symmetry fac tor f3. This gives the symmetry factor new physical meaning.", + "texts": [ + " Whether tunneling can occur or not can be expressed, for the electronation reaction, by a parameter+ if Eo , which is the difference (R + A) - (I + L - fJ\u00bb. To make tunneling possible, if Eo must be \"zeroed.\" The way the original if Eo gets squeezed to zero is by stretching the H+-H20 bond through a critical distance such that the proton is at a distance X* from the metal. That is, the energy of the state M(e) + H+ -H20 must be raised to a value at which electron tunneling begins to occur, i.e., at the intersection point of the potential energy curve of (Fig. 8.91). Let the critical stretching energy be ife. How much stretching energy ife must be put in to zero if Eo and thus make tunneling possible? It appears that the ratio ife/ifEo (cf Fig. 8.90) is of fundamental importance in charge transfer theory. Is it a new quantity or a familiar quantity in a different garb? Some geometry is indicated. Consider the linear analog of Fig. 8.90. This figure is an extreme simplificationt of the potential-energy-distance relations when there is a vibrational stretching of the H+-O bond in the system M(e) + H+-OH2 or the M-H bond in the system M-H + H20. It is concerned with proton stretching as a precondition for electron tunnel ing. It is obvious (Fig. 8.91) that ife AB tan y if Eo AB(tan y + tan 0) tan y (8.151) tan y + tan 0 But tan y/(tan y + tan 0) is none other than the symmetry factor {3 of Eq. (8.87). This is perhaps a surprising realization. The ratio ife/ifEo which is so crucial to the fundamental picture of charge transfer according to + To emphasize that the discussion pertains to zero-field conditions, a subscript 0 is used thus: LIEo. It will be noted that if the initial state involves a particular electronic state (e.g., the ground state), then that state is considered to be maintained throughout the passage of the electron" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000932_macp.200700387-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000932_macp.200700387-Figure5-1.png", + "caption": "Figure 5. X-ray patterns of Vhq-crosslinked elastomer in the heating and cooling process. In (a), the wide-angle reflection is associated with the mesogenic side groups within the smectic layers (arrow 1), and the small-angle reflection is due to the smectic layers (arrow 2).", + "texts": [ + " Additionally, the spontaneous distortion due to the helical mechanoclinic effect, which has already been discussed theoretically, was confirmed in neither the Vhq- nor Vrod-crosslinked elastomer in the present observations, because the crosslinking in the unwound SmC state prevented such distortion.[29] To trace the origin of the difference in reversible deformation between the Vhq- and Vrod-crosslinked elastomers, their molecular alignments in heating and cooling were analyzed by X-ray scattering measurements. The X-ray patterns of the uniaxially-deformed Vhq-crosslinked elastomer at various temperatures are shown in Figure 5. The geometry of the X-ray measurement is also shown in the Figure. Two characteristic reflections, namely, a wideangle reflection associated with mesogenic side groups within smectic layers (arrow 1) and a small-angle reflection due to smectic layers (arrow 2), are observed in the X-ray pattern taken at room temperature [Figure 5(a)]. An azimuthal intensity profile, which was achieved by scanning the X-ray intensity, as displayed along the angle b [see Figure 5(a)], is shown in Figure 6(a). The profile of the small-angle reflection indicates two maxima at the meridian position (at 180 and 3608), because the layer normal was parallel to the direction of the uniaxial mechanical field during the sample preparation. The broad www.mcp-journal.de 301 Figure 6. Analysis of the X-ray pattern of the Vhq-crosslinked elastomer taken at room temperature [Figure 5(a)]. (a) Azimuthal intensity profiles showing the wide-angle reflection ( ) and small-angle reflection (*). (b) Schematic figure describing the molecular alignment of the Vhq-crosslinked elastomer. 302 distribution of the wide-angle profile is due to the liquidlike arrangement of mesogens within the smectic layer. In addition, the wide-angle profile composed of four peaks reveals that the local directors of the mesogens were averagely inclined at an angle of uM with respect to the layer normal. Since the wide-angle profile is well fitted to a Gaussian distribution [see the solid line indicated by arrow 1 in Figure 6(a)] on the assumption that the mesogens were inclined at uM, we are able to estimate both the macroscopic order parameter S\u00bc (1 2)<3cos2ai 1>\u00bc 0", + " While keeping this symmetry during the sample preparation, where successive phase transformations occurred from the isotropic phase of the gel to the tilted smectic phase of the dry network, the mesogens became tilted and were ordered on a cone around the director, whereas the layer normal stayed parallel to the direction of uniaxial deformation. The molecular tilting was not uniform, macroscopically, which caused domain boundaries in the tilted smectic phase of the uniaxially-deformed elastomer. The polydomain structure was chemically fixed in the tilted smectic phase of the dry network because of the crosslinking. A typical X-ray scattering pattern of SmA was observed at 50 8C and is shown in Figure 5(b), where the layer reflection is located at the meridian and the mesogenic reflection at the equator. By comparing the X-ray patterns in Figure 5(a) and (b), we are able to recognize that uM Macromol. Chem. Phys. 2008, 209, 298\u2013307 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim decreases with increasing temperature in the temperature region of the tilted smectic phases and becomes almost 08 at the SmC -to-SmA phase transition temperature. Since the SmA-to-isotropic phase transformation occurs with a further increase in temperature, only halos are observed at 95 8C [Figure 5(c)]. In the cooling shown in parts (c)-(e) of Figure 5, the reverse change in molecular alignment is confirmed. As shown in Figure 5(d), the layer reflection appears at the meridian and the molecular reflection simultaneously emerges at a wide angle at the equator during the isotropic-to-SmA phase transformation. With decreasing temperature, the distribution of the wide-angle reflection seemingly becomes broader because of the increase in uM. They then revert to the original X-ray pattern at room temperature (Figure 5(e)). The X-ray patterns of the Vhq-crosslinked elastomer indicate that the molecular alignment at room temperature is memorized after exposure to the isotropic state. In addition, note that mesogens become tilted during the SmA-to-SmC phase transformation in the Vhq- crosslinked elastomer. This implies that the flexibility of the crosslinker allows the mesogens to tilt with respect to the layer normal. To determine whether the reversibility of molecular alignment correlates to the reversible shape change of the Vhq-crosslinked elastomer, we quantitatively estimated the molecular arrangement during reversible deformation" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000293_0021-9797(81)90153-3-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000293_0021-9797(81)90153-3-Figure3-1.png", + "caption": "FIG. 3. Schematical drawing of a small bubble at the surface of a solution, r, Bubble radius; r0, radius of the film formed at its top.", + "texts": [ + " Average Diameter of Bubbles in the Top Layer of the Steady-State Foam of AmOH-H20 at Different AmOH Concentrations Concentration of AmOH Gas l o w rate Bubble diameter (mole/dm 3) (dm3/hr) (2r mm) 10 -3 30 1.37 10 -a 40 1.59 5\" 10 -z 30 1.60 5' 10 3 40 1.49 10 -2 30 1.43 10 -2 40 1.37 3' 10 2 30 1.26 3\" 10 -2 40 1.28 Journal of Colloid and Interface Science, VoL 80, No. 1, March 1981 For these froths Under s teady-state conditions, each gas bubble reaches the surface as an individual entity. Such a gas bubble at the solution surface is shown schematically in Fig. 3. The bubble is deformed and a film having a radius, r0, that is different f rom the bubble radius, r , is formed at its interface. Within the limit of very small bubbles the dependence be tween r0 and r is given by the following equation (13): r0 _ 1.155r P - P i g [1] r o- where P is the solution density, Pl is the density of the gas in the bubble, g is the accelerat ion due to gravity, and o- is the surface tension of the solution. For the stat ionary froths that we studied the bubble radii are sufficiently low for gravitational deformations to be neglected" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003258_cyber.2012.6392571-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003258_cyber.2012.6392571-Figure1-1.png", + "caption": "Figure 1. Tilt-rotor UAV with E-frame (x, y, z) and B-frame (xb, yb, zb). Vertical component of the thrusts fL and fR provide lift and horizontal component provides forward motion [6].", + "texts": [ + " The Tilt-rotor has two rotors mounted on the lateral sides of its airframe, which can be tilted to provide lift and forward thrust. Some examples of the Tilt-rotor aircraft are the Arizona State University\u2019s HARVee [3], Compigne University\u2019s BIROTAN [4], large-scale versions like Boeing\u2019s V22 Osprey [1] and Bell\u2019s Eagle Eye [2]. One clear advantage of Tilt-rotors over other multi-rotor UAVs is that they require only two motors, leading to a reduction in weight, volume and energy consumption. Moreover, with the help of two rotors it can move faster than the single rotor fixed-wing UAV. The two rotors (rotors 1 and 2 in Figure 1) rotate in opposite directions, thereby canceling the reaction torques. This keeps the UAV stable. The control methods of a Tilt-rotor are altitude control, forward motion and pitch control, lateral motion and roll control, and yaw control. Altitude control is achieved by varying the speed of both rotors simultaneously. Changing the speed of the rotors leads to roll control. For example, if we increase the speed of the right rotor (rotor 2) and decrease the speed of left rotor (rotor 1), then the UAV will roll to the left and also move towards the left" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002318_j.conengprac.2011.06.012-Figure7-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002318_j.conengprac.2011.06.012-Figure7-1.png", + "caption": "Fig. 7. Synoptic scheme of the real process.", + "texts": [ + " The fatty acid (oleic acid) and the ester ebullition temperatures are approximately 300 1C. The chosen alcohol (1-butanol) is characterized by an ebullition temperature of 118 1C. Consequently, heating the reactor to a temperature slightly over 100 1C will result in the vaporization of water only (which is evacuated through the condenser). The reactor is heated by circulating a coolant fluid through the reactor jacket. This fluid is, in turn, heated by three resistors located in the heat exchanger (Fig. 7). The reactor temperature control loop monitors temperature inside the reactor and manipulates the power delivered to the resistors. It is, also, possible to cool the coolant fluid by circulating cold water through a coil in the heat exchanger. Cooling is, normally, done when the reaction is over, in order to accelerate the reach of ambient temperature. The system can be considered as a single input\u2013single output (SISO) one. The input is the heating power P(W). The output is the reactor temperature" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001631_s12283-010-0041-4-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001631_s12283-010-0041-4-Figure1-1.png", + "caption": "Fig. 1 Schematic of apparatus used to measure the softball impact force, left; diagram showing ball impact location, lower right", + "texts": [ + " For the stiffness measurement, the magnitude and rate of the displacement in the quasi-static test are 5 and 10,000 times lower, respectively, than under typical game conditions [5]. Given the known rate dependence of the modulus of the common polyurethane softball [10], the relevance of the quasi-static stiffness ks to e is far from obvious. The second focus of this paper is to report on an apparatus to measure a dynamic stiffness of the ball kd and to determine experimentally the relevance of kd and ks to determining the BBCOR. Balls were projected onto a fixed solid cylindrical surface, as depicted in Fig. 1, from which the impact force was measured. The half cylinder was intended to represent the shape of a softball bat, having a diameter of 57 mm (2.25 in.). The impact force was measured from an array of three load cells (PCB model 208C05), placed between the half cylinder and a rigid wall. Data from the load cells were summed and collected at 200 kHz, from which an impulse curve, as shown in Fig. 2, was obtained. To ensure uniform temperature and moisture content the balls were stored at 22 \u00b1 1 C (72 \u00b1 2 F) and between 45 and 55% relative humidity for at least 14 days prior to testing. The balls rested for at least 2 min between impacts to minimize the effect of internal frictional heating. Each ball was impacted no more than 40 times so that ball degradation effects would be small [11]. Balls were projected at speeds ranging from 26.8 to 49.2 m/s (60\u2013110 mph) using an air cannon. The balls travelled in a sabot, which separated from the ball prior to impacting the half cylinder. The sabot helped control ball speed and ball orientation. As shown in Fig. 1, the balls were impacted on the four regions of the ball with the largest spacing between the stitches. Ball speed before and after impact was measured using infrared light screens, placed as shown in Fig. 1. The centre of mass displacement of the ball may be found by dividing the impact force by the ball mass and integrating over time twice. A representative ball force\u2013 displacement curve of a fixed cylinder impact at three speeds is shown in Fig. 3. The oscillations during the loading phase were observed for both fixed and free-cylinder impacts. The oscillations, therefore, are likely to be related to vibrations in the ball. To derive the ball stiffness, it was assumed that the ball behaved as a non-linear spring during the loading phase according to F = kxn, where F and x were the force and displacement of the spring, respectively, and k was the spring constant" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001676_demped.2009.5292784-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001676_demped.2009.5292784-Figure4-1.png", + "caption": "Fig. 4. Experimental setup.", + "texts": [ + " This occurs on the simulated IM, since the negativesequence impedance does not vary with the motor load, making the negative-sequence current practically constant, for a given voltage unbalance. With the objectives of validating the simulation results and evaluating the effects of voltage unbalance on the motor torque and vibrations, experimental results were obtained from a laboratory setup. This setup is composed by a standard 5.5 kW IM supplied by variable-output autotransformers. This IM is coupled to another IM driven by a commercial torque-controlled variable speed drive, who acts as a programmable load (Fig. 4). The autotransformers have the possibility of independently regulate the output voltage, allowing the adjustment of the unbalance level ( )vk . Two phase currents and two line voltages were measured in order for the instantaneous power to be calculated and the motor torque to be estimated. The measured signals were processed in a PC. Motor vibrations were measured using a piezoelectric accelerometer, mounted in the vertical (radial) direction on the motor non-drive end bearing. The acceleration signal was analogically filtered and acquired to be processed in the PC" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000809_1.2959095-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000809_1.2959095-Figure2-1.png", + "caption": "Fig. 2 Free body diagram. The center of mass is assumed to be coplanar with the shoulder and hip joints. It can be argued that the location of the center of mass a small distance above or below the plane of the joints makes little difference to the dynamics. The shoulder and hip joints are assumed to be pairs of intersecting revolutes that are, respectively, parallel to the x axis of the body and orthogonal to the plane of the leg. The body reference frame is centered on the center of mass and aligned as shown. The principal axes of inertia are assumed to coincide with the x, y, and z axes.", + "texts": [ + "url=/data/journals/jmroa6/27973/ on 04/23/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use e d i s p w I a s b p c h s M f n W m f a i t f m a s s e s a t f w f p v e t a v p f F r s v J Downloaded Fr nces between the magnitudes of the force components and in the urations of the stances of the legs of each pair, the resultant mpulses of each lateral pair of legs are very nearly identical, upporting the assumption. Their data also indicate that the imulse from a leg has no significant lateral component, consistent ith the representation of Fig. 2. mpact Energy It is notable that animals can run over diverse surfaces without ny noticeable effect on their gait and at very nearly the same peed. This seems anomalous since the coefficient of restitution etween the foot and the ground must vary considerably and unredictably. The reason for this capability is very simple when one onsiders the way the foot works when running. Consider the system shown in Fig. 3. We model the system as aving only one leg in contact with the ground and consisting of a mall mass, m, representing the foot, connected to a large mass, , representing the rest of the system by a spring" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003888_j.proeng.2012.04.019-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003888_j.proeng.2012.04.019-Figure1-1.png", + "caption": "Fig. 1. Experimental apparatus", + "texts": [ + " The shuttlecock rotates about the shuttlecock\u2019s major axis in actual flight, and the experiments were performed on shuttlecocks with and without rotation (spin). Furthermore, the effect of the flow passing through the gap between slots (stiffeners) located at leg portion of the shuttlecock skirt on aerodynamic characteristics is also demonstrated. Therefore, the shuttle was set up in the wind tunnel to examine the fluid force that acted on the shuttlecock, and the flow field was made visible with the measurement of the fluid force. Figure1 shows the experimental apparatus used to estimate forces acting on shuttlecocks in a wind tunnel. The wind tunnel experiment was carried out by a low-turbulence wind tunnel at Tohoku University, Japan. The test section was octagonal, 0.29 m wide by 0.29 m high, and experiments were performed in the middle of the open part of the test section. The origins of coordinates X, Y, and Z were defined as the center of mass of a shuttlecock, and the distance of the center of mass from nose tip X0 was 31" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001555_iros.2008.4650574-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001555_iros.2008.4650574-Figure4-1.png", + "caption": "Fig. 4. Schematics of a 3-PPS parallel mechanism", + "texts": [ + " To realize this analysis, we will study the degeneracy of a 6-dimensional matrix composed of the screws applied on the platform by the legs [20] and will give for the first two mechanisms (the 3-PPS and the 3-RPS) simple analytical expressions characterizing the singularity loci obtained by the use of the T&T angles. We will show for the other two mechanisms that the singularity loci can be represented by a polynomial of high order (of degree 24). Moreover, for each mechanism, the maximal reachable workspace taking into account the singular configuration will be represented as a function of the design parameters. A. Singularity Loci of 3-PPS Parallel Mechanisms Referring to Fig. 4, the directions of the actuated prismatic joints are vertical, while the directions of the passive prismatic joints are horizontal. Each leg applied two constraint wrenches on the platform, Ri1 and Ri2, which in this case are pure forces through point Bi which are perpendicular to the sliding direction of the second prismatic joint. Thus, as shown on Fig. 4, for this manipulator, Ri1 and Ri2 are two forces located at point Bi and directed along the vertical axis z and perpendicular to the plane of the legs, respectively. The system of screws degenerates if the determinant of the Jacobian J, of which the lines are composed of the coordinates of the screws Rij (j = 1, 2), vanishes. After simplification, this determinant can be written as: ( )\u03b8\u03b8 cos1cos 8 27det +=J . (17) Disregarding \u03b8 = \u03c0, (13) leads us to the only remaining possibility for Type 2 singularities: \u03b8 = \u00b1\u03c0/2" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002696_j.1467-8659.2012.03165.x-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002696_j.1467-8659.2012.03165.x-Figure3-1.png", + "caption": "Figure 3: A graph representation of an example set of partial mappings. The nodes are (colored) points on the surface and the edges are mappings. As illustrated, all connected components of the graph have to be cliques by definition.", + "texts": [ + " Equivalently, we can cut the surface at all boundaries of all partial matches (Fig. 1c). Because the resulting tiles are obtained by cutting as much as possible, we call them \u201cmicrotiles\u201d. Yet another characterization is to form a graph with all points of S as nodes, and transformations from F annotating edges that connect equivalent points (shown schematically in Fig. 1e). Microtiles are maximal connected subsets of S that have cliques with the same edge annotations. This means, all microtiles in the same clique are always exchanged with each other as a whole (c.f. Fig. 3). Microtiles have some interesting further properties: First, the construction is unique and canonical: it does not require any choices or parameters in addition to the input correspondences. Furthermore, microtiles are disjoint and different types of tiles do not have partial correspondences among each other or themselves, only global symmetries are possible. Finally, unions of microtiles have the intersection of c\u00a9 2012 The Author(s) Computer Graphics Forum c\u00a9 2012 The Eurographics Association and Blackwell Publishing Ltd", + " The sets P identify the part of S the functions f act upon. Equivalence of points: Given a set of mappings F , we can now say that two points x,y \u2208 S are equivalent or similar, if there is a mapping f \u2208 F , which maps x to y: x\u2261 f y :\u21d4 \u2203(P, f ) \u2208 F : x \u2208 P and f (x) = y (2) We require that this relation be an equivalence relation. This means, we must choose F in a way this induced point-wise relation is: \u2022 Reflexive: (S, id) \u2208 F \u2022 Symmetric: x\u2261 f y\u21d2 y\u2261g x for some g \u2208 F \u2022 Transitive: x\u2261 f y and y\u2261g z\u21d2 x\u2261h z for some h \u2208 F This is illustrated in Figure 3 where points on a surface are mapped based on partial symmetries. Having an equivalence relation of such mapping means that if we construct a graph with the surface points as nodes and the mappings between them as edges, then each connected component of this graphs will be a clique. The vertices in each clique form an equivalence class with respect to F . The equivalence classes given by the set of mappings already provide a decomposition of the input into sets of points. However, there are usually infinitely many such classes (or cliques), which makes this kind of decomposition impractical", + " After all transformations are processed the table encodes all detected partial r-symmetries for the shape. Extraction: We extract a segmentation of the input scene into microtiles by region growing starting at an arbitrary (non-processed) element and expanding the current tile with elements that have the same set of symmetry transformations. We use the table we computed in the previous step to look up the transformations that map the geometry to r-symmetric parts of the surface. After the initial segmentation, we compute the equivalence classes of points (the cliques discussed in Section 3 and Figure 3). We transform the voxels that belong to a given microtile, and search in the overlapping voxels for the equivalent microtile instance. We have implemented a simple prototype of the algorithm outlined above. We follow the method of [BWS10] and use a volumetric grid to discretize the symmetry information: cubes of side length h are annotated with transformations. We have applied our prototype implementation to a few scenes to visualize the structure of the decomposition. For the tests we set the radius of symmetry to 0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000272_j.cma.2005.11.014-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000272_j.cma.2005.11.014-Figure1-1.png", + "caption": "Fig. 1. Geometry of a single contacting asperity in form of elliptic paraboloid.", + "texts": [ + " Theories of isotropic surfaces are not applicable to the important practical case of ground surfaces which are strongly anisotropic. Bush, et al. [7] presented the random theory of strongly anisotropic rough surfaces which will be briefly described here. In the model the cap of each asperity is replaced by elliptic paraboloid with summit n1 above the point (x0 = 0, y0 = 0) on the mean plane. The plane z = h intersects the paraboloid in an ellipse which has semi-axes of lengths (in a local deformed stage) A and B with one its principal radii of curvature at angle b = 0 to the positive x-axis (see Fig. 1). Let us consider a rough surface whose heights above the mean plane of of the surface are defined by z(x,y), where x, y are the Cartesian coordinates in the mean plane. Defining n1 \u00bc z; n2 \u00bc oz ox ; n3 \u00bc oz oy ; n4 \u00bc o 2z ox2 ; n5 \u00bc o 2z oxoy ; n6 \u00bc o 2z oy2 ; \u00f01\u00de the joint probability density of the normally distributed variables ni (i = 1,2, . . . , 6), each being the sum of a large number of independent variables with zero expectation, is p\u00f0n1; n2; . . . ; n6\u00de \u00bc 1 \u00f02p\u00de3D1=2 exp 1 2 Mijninj ; \u00f02\u00de where Mij is the inverse of the positive-defined covariance matrix Nij Nij \u00bc E\u00bdn2 1 E\u00bdn1n2 ", + " (17) we obtain the joint probability density function of summits as psum\u00f0x1;x4;x6\u00de \u00bc l2ffiffiffiffiffi 2p p m04m40 m02m20 3=2 jx4x6j exp\u00f0 X=2\u00de. \u00f018\u00de In the model a cap of each asperity is replaced by a paraboloid having the same height and principal curvatures as the summit of the asperity. The asperities are parameterised by their height n1 and the semi-axes a and b of the ellipse obtained from the intersection of the asperity and a plane at height h above the point (x0,y0) on the mean plane of the rough surface as shown in Fig. 1. The equation for an elliptic paraboloid asperity of summit height n1 above the point x0 and y0 is n1 z n1 h \u00bc \u00f0x x0\u00de2 a2 \u00fe \u00f0y y0\u00de 2 b2 . \u00f019\u00de Differentiating the above equation with respect to x and y yields the following relationships between the curvature and the semi-axes a and b, see Eq. (1) n4 \u00bc 2\u00f0n1 h\u00de a2 ; n6 \u00bc 2\u00f0n1 h\u00de b2 . \u00f020\u00de Using Eqs. (13) and (20), the semi-axes of the ellipse a and b can be expressed as functions of x1, x4 and x6 by the following expressions: a2 \u00bc 2\u00f0x1 ffiffiffiffiffiffiffiffiffiffi m00l p h\u00de x4 ffiffiffiffiffiffiffiffiffiffi m40l p ; b2 \u00bc 2\u00f0x1 ffiffiffiffiffiffiffiffiffiffi m00l p h\u00de x6 ffiffiffiffiffiffiffiffiffiffi m04l p " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003013_s11340-012-9600-x-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003013_s11340-012-9600-x-Figure1-1.png", + "caption": "Fig. 1 Schematic and photograph of experimental setup for the piston secondary motion measurement system", + "texts": [ + " In this study, the experimental technique was expanded to capture the piston lateral and rotational motion distinctly by using three laser displacement sensors under non-firing conditions. This is the first time that the secondary motion of the piston has been fully captured for all the modes and that the frequency of each mode has been determined. These results are important because they will enable better understanding of the nature of the secondary motion of the piston and the influence of each mode on the piston slap. Hardware Implementation Construction of Measurement System An experimental rig was designed and fabricated as shown in Fig. 1, and a 126 cc four-stroke motorcycle engine block is used in this study. The geometric and physical properties of the piston assembly are shown in Fig. 2 and Table 1. The piston assembly does not allow firing, and the crankshaft of the piston assembly was driven by an AC motor (MarelliMotori MAA80 MB4) controlled by a variable frequency controller (Emerson Commander SK). Piston Motion Measurement A measurement system consisting of three laser displacement sensors (Keyence LK-G152) is located at the front of the piston assembly, and the three laser spots are aimed at three different locations on piston crown", + " Spectral Analysis of the Experimental Rig Spectral analysis was carried out on the experimental rig to determine the vibration level under the operating conditions in order to determine the effect of the induced vibration of the experimental rig components such as the bearing housing, pulley, V-belt, and steel base plate on the piston motion. The vibration level of the experimental rig was measured using five accelerometers (Dytran 3055B2T), with two accelerometers (A1 and A2) mounted on the bearing housing, two accelerometers (A3 and A4) on the cylinder block, and one accelerometer (A5) mounted on the steel base plate, as shown in Fig. 1. The accelerometers mounted on the bearing housing and cylinder block measure the acceleration level in the x and y directions, and the accelerometer mounted on the steel base plate measures the acceleration level in the z direction. All the accelerometers are connected to the LMS Scadas Mobile data acquisition system and the LMS Test Lab post-processing software. The measurement of the experimental rig was carried out at an AC motor driving speed of 500 rpm (8.33 Hz), which is the highest operating speed of the piston motion study" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002407_j.comgeo.2010.06.003-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002407_j.comgeo.2010.06.003-Figure5-1.png", + "caption": "Fig. 5. Line\u2013line angular constraints.", + "texts": [], + "surrounding_texts": [ + "We use the four basic building blocks just presented to complete the development of the infinitesimal theory. In this section, we present the rows of the rigidity matrix associated with each of the 21 body-and-cad constraints. In all figures, body i is represented by the green tetrahedron and body j by the purple cube." + ] + }, + { + "image_filename": "designv11_7_0003651_s11012-013-9833-5-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003651_s11012-013-9833-5-Figure4-1.png", + "caption": "Fig. 4 The kinematotropic 7R mechanism. Cylinders represent revolute joints and the basis vectors of global coordinate system are colored red (Color figure online)", + "texts": [ + "3 A further analysis shows that V ( I 4,1 7R ) = R 24 \u2229 V ( I 4 7R ) = ( V ( I 4 7R )) and V ( I 7,1 7R ) = R 24 \u2229 V ( I 7 7R ) = ( V ( I 7 7R )) . Hence the singular varieties of the complex varieties V(I 4 7R) and V(I 7 7R) are actually the smooth real varieties that we are interested in. Finally we check that the 2 motion modes intersect at the initial configuration: ( V ( I 4,1 7R ) \u222a V ( I 7,1 7R )) = V ( I 4,1 7R + I 7,1 7R ) = V ( I 4,1 7R ) \u2229 V ( I 7,1 7R ) = V ( I init 7R ) . 5.3 Kinematotropic 7R mechanism Let us consider the 7R mechanism given in Fig. 4. This mechanism has been previously proposed as an exam- 3Note that the mechanism can be over and underconstrained at the same time! ple of single loop kinematotropic mechanism in [28]. The constraint equations for this mechanism are then p1 = ( e1,R(a)e3) = 0 p2 = ( e2,R(a)e3) = 0 p3 = ( R(a)e1,R(b)e3) = 0 p4 = ( R(a)e2,R(b)e3) = 0 p5 = ( R(b)e1,R(c)e3) = 0 p6 = ( R(b)e2,R(c)e3) = 0 p7 = ( R(c)e1,R(d)e3) = 0 p8 = ( R(c)e2,R(d)e3) = 0 p9 = ( R(d)e2,R(e)e3) = 0 p10 = ( R(d)e3,R(e)e3) = 0 p11 = ( R(e)e1,R(f )e3) = 0 p12 = ( R(e)e2,R(f )e3) = 0 p13 = ( R(f )e2, e1) = 0 p14 = ( R(f )e3, e1) = 0 p15" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000055_978-1-4684-1500-1-Figure10.1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000055_978-1-4684-1500-1-Figure10.1-1.png", + "caption": "Figure 10.1 The architecture of the VLSI tactile sensor is revealed. A sheet of conducive plastic is placed in surface-to-surface contact with a custom designed VLSI circuit. Each element within the array has its own computing element, hence this sensor can be used to detect both presence and form.", + "texts": [ + " The most common sensors used by robots are tactile units that determine if an item is present or not. The simplest version is the microswitch, which makes or breaks a circuit when the switch is operated by a component arriving at the sensing station. Another version uses a matrix of wires, covered by a plastic skin, that approximates to the human 'hand' and deter mines not only presence, but also position. Provided the infor mation about the item is in the robot's memory, the item is identified. The force sensor shown in Figure 10.1 has a microcomputer at every node of the matrix. It uses a custom designed, very large scale integration (VLSI) device to perform transduction, tactile image processing and communication. Forces are trans duced using a conductive plastic technique in conjunction with metal electrodes on the surface of the integrated circuit. Tactile sensors are often used to indicate what happens within the gripper as it operates. For instance, the sensor can be used to inform the robot that the gripper has closed on an object, or that it has closed too far and therefore (by deduc tion) the object was either not there or has been crushed, or has fallen out of the gripper" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003177_j.cirp.2013.03.083-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003177_j.cirp.2013.03.083-Figure2-1.png", + "caption": "Fig. 2. Principle of the new bevel gear measurement standard.", + "texts": [], + "surrounding_texts": [ + "Nominal data of bevel gear flanks are defined by a grid of points, where an elementary sketch (Fig. 1) reflects the ideal tooth surface. The nominal points spread out over the entire flank surface. Each of these points is described by its x-, y- and z-coordinates as well as the normal direction of the surface in this point, given by nx, ny and nz. If the real gear tooth will be substituted by a sphere (Fig. 3), the nominal grid points will cover a certain part of this sphere surface. At first glance, it appears not too difficult to calculate two grids of points on a sphere. But there are some bevel gear parameters to be considered in order to design and position the grid points in a useful way. Theoretically, the extension of the grid pattern in the diagonal direction should be smaller than the diameter of the sphere (Fig. 4a, two-dimensional view and Fig. 4b, three dimensional view from above). ll plate was manufactured with 260 mm in diameter (Figs. 2 and On the ball Plate 12 spheres are mounted in an angular distance 8, each made of ceramic Al2O3 with a diameter of 20 mm and a dness deviation of <0.1 mm. The centres of the spheres are tioned on the plate forming a circle of 238 mm in diameter. This otype is not calibrated yet by the PTB. bjectives of first measurements he purpose of the first prototype (Fig. 8a) and the measurets carried out were to prove the suitability of this type of (b) 3D-view from above: both grids projected to the sphere surface. ball ith itch on ickt of and For in a iece of a that the vel eds oth lly. asic ing h a eter The inclination of the pattern shows a theoretical pitch angle of 258. The points below the equator line include normal directions comparable to an undercut situation. Bevel gears usually do not show undercut. Therefore, another rotation angle of both grids towards the upper pole point is required (Fig. 5a). Additionally, many bevel gears provide a spiral angle (Fig. 6). This spiral angle can be simulated by another rotation of the grids around the upper pole point (Fig. 5b). The coordinates of the nominal points need to be converted to a Fig. 7 illustrates the theoretical nominal data for the entire plate, corresponding to the standard introduced in Section 3 w 12 spheres as imaged in Fig. 8a. Besides the introduced idea to calibrate flank form and p measurements by positioning bevel-gear-like grid patterns spherical surfaces, another calibration task covering tooth th ness measurements is imaginable [6]. Today, the measuremen the tooth thickness on a bevel gear is one of the most difficult intensively discussed problems in bevel gear metrology [7]. this purpose, the mid-grid reference points can be positioned way that their normal directions (with respect to the workp coordinate system) agree with the mid-grid reference points real bevel gear. The advantage of these point placements is they simulate the same probing conditions as required for tooth thickness measurement on the corresponding real be gear. But for this issue, the bevel gear measurement standard ne to be calibrated and the algorithms for the interpretation of to thickness deviations on bevel gears need to be verified officia Again, with the first prototype standard presented here the b feasibility of the concept (algorithms, point accessibility, prob behaviour) was tested only." + ] + }, + { + "image_filename": "designv11_7_0002316_j.cirp.2011.03.060-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002316_j.cirp.2011.03.060-Figure2-1.png", + "caption": "Fig. 2. Genesis of specific topography deviations (like in Fig. 4), caused by varying distances of the grid points from the rotary axis: (a) transversal plane through one tooth; (b) axial plane through a bevel gear.", + "texts": [ + " For the various visualisations in this Section 3, an ideal pinion with a tooth thickness deviation of 20 mm was used, whereas in Section 4 an ideal pinion with an additional profile and lead crowning of 10 mm was investigated. Since a bevel gear is an artefact with rotational symmetry, several standards define the tooth thickness and its deviation as an angular deviation of a certain flank point. Therefore, to simulate a given tooth thickness deviation, the ideal grid points of both flanks are rotated in opposite directions around the gear axis such that at the reference radius rpitch the tooth is 2 10 mm = 20 mm thicker (in circular measure) than the ideal tooth (Fig. 2a). Since the distance of each individual grid point relative to the gear\u2019s rotary/ symmetry axis varies, the deviations between original points and rotated points differ over the entire flank (see Figs. 2b and 4). The deviations of the individual grid points depend on the chosen definition of deviation type (see Sections 3.2\u20133.4) [7]. The deviation between a nominal point and a \u2018measured\u2019 point can be evaluated in different ways. The simplest calculation is the vectorial (or Euclidean) distance deuclid between both points (see Fig", + " But, the positioning uncertainty of the measuring device directly affects this deviation [8,9]. Therefore, it will mostly be used for geometry measurements, where the normal direction of a datum point is unknown. Fig. 4 shows the resulting deviations of one bevel gear tooth (grey grid: ideal surface; black grid: evaluated actual surface, based[()TD$FIG] on single point \u2018measurements\u2019). The \u2018measured\u2019 surface appears to be tilted to the ideal surface, with higher deviations at the topland and at the outer end of the tooth (heel) resulting from the simulation of \u2018measurement\u2019 points (Fig. 2). Another, more common method to calculate geometrical deviations requires the knowledge of all normal directions Ndatum at the nominal points (Fig. 3), which is fulfilled in most applications of gear metrology. It projects the vectorial deviation to the normal direction at the \u2018measured\u2019 point. The scalar product dproj = Deuclid Ndatum is in all cases smaller than or equal to the vectorial deviation deuclid. Table 1 compares the vectorial deviations of Fig. 4 at the flank corner points with the corresponding deviations in normal directions" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003064_j.ccr.2011.02.002-Figure7-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003064_j.ccr.2011.02.002-Figure7-1.png", + "caption": "Fig. 7. Schematic representation of a composite electrochemical-TIRF configuration. A home-made single compartment electrochemical cell with a transparent gold working electrode is fixed above TIRF objective of a Nikon TE200-E fluorescence microscope. The excitation source (a 633 nm laser) is filtered and totally internally reflected causing an evanescent wave which excites fluorophore tagged protein. T i p", + "texts": [ + " n the surface potential of conductance maximum and half wave potential is subject les, nearly all published works have confirmed that this coincidence is high (within where an evanescent wave is used to excite fluorophores in a restricted region of sample immediately adjacent to the surface, we have reported the application of redox coupled FRET to the direct imaging of electrochemically driven redox changes in Cy5 labelled azurin immobilized on alkyl-terminated thiol SAMs [129,133,134]. Within these experiments, a single compartment electrochemical cell containing degassed buffer and consisting of a functionalized transparent thin film gold working electrode, reference electrode and Pt gauze counter electrode is assembled on an inverted TIRF microscope (Fig. 7). Surface confined voltammetry confirms electroactive surface coverages to be \u223c5 \u00d7 1010 molecules/cm2 at these surfaces, with associated midpoint redox potentials as expected. Time resolved fluorescence imaging is then carried out with the simultaneous application of a triangular potential wave to the working electrode wherein the fluorescence emission from the surface bound protein adlayers is found to be modulated (being typically some 40\u201360% higher at potentials cathodic of the midpoint potential)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002376_j.fusengdes.2011.01.018-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002376_j.fusengdes.2011.01.018-Figure5-1.png", + "caption": "Fig. 5. Schematic diagram of the Stewart structure.", + "texts": [ + " The force fbearh x and the moment mbearh y re equal to zeros and suppressed in the equation since the force bearh x acting on the base frame causes no deformation and the oment mbearh y does not exist around the axis of the bearing ouse. . Stiffness modeling of parallel mechanism To evaluate the stiffness of the parallel mechanism, the paralel structure is decomposed into the basement frame, the bearing ouse in the base, the U-joint in the base, the hydraulic limb and he up joint in the end-effector (Fig. 5). The basement frame is onsidered as rigid structure. The bearing house and the U-joint orm the base of Stewart platform, and each has configurationndependent stiffness, while the stiffness of the base of the Stewart latform is configuration-dependent as a function of the orientaion of the hydraulic limb. The stiffness of the hydraulic limb is also onfiguration-dependent as a function of its length. The up-joint in he end-effector is considered as rigid. 3.1. Stiffness evaluation of base in parallel mechanism The composition of the base by the bearing house and the U-joint is in a serial form" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000855_s0022112006003326-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000855_s0022112006003326-Figure2-1.png", + "caption": "Figure 2. (a) An edge-on view of one set of two-dimensional fluid phases: an 8CB monolayer in coexistence with an 8CB trilayer. 8CB is a cyano-biphenyl molecule that forms a smectic (layered) liquid crystal at room temperature in bulk. (b) A top view of such a layer, defining the domain \u2126 , the boundary \u2202\u2126 , the outer monolayer \u2126c and the normal n\u0302. See de Mul & Mann Jr (1998).", + "texts": [ + " In three dimensions, slippage is perhaps seen in entangled polymers or in complex fluids. Figure 1 shows a time-lapse set of Brewster Angle Microscopy (BAM) images that demonstrate the large aspect ratio of the typical bola that results from shearing a cyano-biphenyl liquid-crystal (8CB) Langmuir layer and its subsequent relaxation to a circular domain. Amazingly, these bola may be sheared to be several orders of magnitude longer than they are wide yet do not rupture. It is the physics behind this observation that we wish to model, explain and quantify Figure 2 shows a cartoon of the cyano-biphenyl liquid crystal (8CB) studied by de Mul & Mann Jr (1998) that provides a guide in developing our theory of domain behaviour. We assume that one phase is a localized domain, \u2126 , and that its complement, \u2126c, is a second phase which extends to infinity. The domain boundary \u2202\u2126 will be parameterized by arclength s with a right-handed orientation and with an outward pointing normal n\u0302. Both phases behave as two-dimensional fluids. Each fluid can be characterized by a set of visco-elastic parameters, in direct analogy with the three-dimensional case (Goodrich 1981; Gaines Jr 1966; Mann Jr 1985; Mann Jr, Crouser & Meyer 2001)", + " With our non-dimensionalization, we find that at the surface, normal viscous stress \u223c surface tension, \u03b7\u2032 T\u2217 \u223c \u03c3H, where \u03c3 is the surface energy (which may depend upon whether it is inside or outside the domain) and H is the mean curvature of the surface. We can solve for the magnitude of the surface curvature, H \u223c \u03bb \u03c3 (L\u2217)2 . (2.6) For L\u2217 \u03bb/\u03c3 (2.7) we discover that the radius of curvature of the surface is much larger than the typical domain size; typically \u03bb/\u03c3 \u2248 10 nm so we are looking at domains 10\u20131000 times larger than this length scale. Consequently, we consider the case of a flat surface with the subfluid occupying the region z < 0 and the Langmuir layer domain \u2126 contained in the x, y coordinate plane, z = 0, as illustrated in figure 2. 2.1.3. Tangential stress balance in the Langmuir layer domain For a flat surface, the Langmuir layer evolution equations simplify drastically. Balancing the tangential stresses on the surface yields a force applied by the subfluid on the domain \u2126 . The non-dimensional stress tensor for our viscous, incompressible Newtonian fluid is T = \u2212P I + \u2207u + (\u2207u)T . (2.8) The tangential stress at the surface acts as a two-dimensional body force, Fs , (specifically, a force per unit area) acting on the Langmuir layer, Fs = \u2212k\u0302 \u00b7 T \u00b7 (I \u2212 k\u0302k\u0302) = \u2212[uz \u0131\u0302 + vzj\u0302 ]", + " The parameter can also be adjusted to be as small as desired by increasing the viscosity of the substrate, which is possible with water/glycerol mixtures (Mann et al. 1995). Henceforth we assume that inertial effects and viscous dissipation in the Langmuir layer are subdominant, so the dominant balance is between the surface pressure, the applied stress from the subfluid, and the line tension. Balancing the forces with the pressure, we see that \u2207\u22a5\u03a0 = Fs + F , (2.12) which means the Langmuir layer is in hydrostatic equilibrium. To describe the line tension we develop an intrinsic coordinate system on the surface near the boundary of the domain (see figure 2b). Let \u0393 (s, t) be a position vector for the boundary of the domain, \u2202\u2126 , parameterized by the arclength s. We choose a right-handed orientation; that is, moving along \u2202\u2126 counterclockwise with \u2126 to the left corresponds to increasing s. Let t\u0302 be the corresponding tangent vector. Differentiating with respect to arclength yields d t\u0302/ds = \u03ba n\u0302, where n\u0302 is the outwardpointing normal vector and \u03ba is the curvature of \u2202\u2126 (negative for convex \u2126). We define the signed distance from \u2202\u2126 along n\u0302 as d with d < 0 in the interior of \u2126 and d > 0 in the exterior (\u2126c)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003981_s12283-013-0122-2-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003981_s12283-013-0122-2-Figure1-1.png", + "caption": "Fig. 1 The experimental setup used to assess the impact characteristics of the racket", + "texts": [ + "0108 kg m-2 around the COM (measured by swinging the racket about an axis at its handle and measuring the frequency of oscillation, see Brody [25] for a full description). An accelerometer\u2014 attached to the handle\u2014and proprietary software were used to find the location of the racket node (using the same approach as Cross [6]) which was located 0.2 m from the COM (0.547 m from the butt). 2.2 Experimental setup The impact experiment was performed using a modified BOLA ball launcher (fitted with a barrel to minimise scatter), a set of light gates (Fig. 1) and six Prince ITF approved tennis balls. The light gates measured the inbound and outbound ball velocity in a direction perpendicular to the racket face. The racket was pin supported to approximate the freely supported condition [2]. The pin support could be raised or lowered to alter the impact position of the ball on the racket face. The six tennis balls were used in rotation during testing to prevent excessive wear. A high speed video camera (Vision Research, Phantom V4.3) was used to align the BOLA\u2019s barrel with the racket\u2019s geometric stringbed centre (GSC, 0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003710_icosc.2013.6750908-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003710_icosc.2013.6750908-Figure1-1.png", + "caption": "Figure 1. Quadrotor configuration", + "texts": [ + " dynamical model of a quadrotor. Section III gives an overview of the PSO and presents the PID controller design method using PSO. In section IV, first the PD decentralized control structure for the stabilization of the quadrotor is presented then PSO design method is used and simulation results are presented. Section V concludes the paper. A. The quadrotor is a small UAV with four propellers mounted on the end of two perpendicular arms and actuated by four DC motors. A basic configuration of quadrotors is shown in Fig. 1. Each rotors pair of the same arm rotates in same direction; one pair rotates clockwise, while the other rotates counter clockwise. The quadrotor moves by adjusting the angular velocity of each rotor. We consider the dynamical state model of a quadrotor in [5] given by: \u2126 \u2126 where: 978-1-4799-0275-0/13/$31.00 \u00a92013 IEEE and are respectively the roll angle and corresponding angular velocity; and are respectively the pitch angle and corresponding angular velocity; and are respectively the yaw angle and corresponding angular velocity; , , and are the Cartesian position coordinates" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003534_978-1-4419-6022-1-Figure3.15-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003534_978-1-4419-6022-1-Figure3.15-1.png", + "caption": "Fig. 3.15 Current biasing circuit", + "texts": [ + " This current is not really affected by the applied voltage (VCE), as shown in the figure. What really affects IC is the base current, IB. As mentioned briefly in Question 3.1, VBE is also almost constant regardless of the input voltage and current. However, VBE is a function of temperature (just like in the Zener diode), which means that we can utilize it as a temperature sensor. Again, this feature will be discussed further in the next chapter. In addition to the apparent use of a transistor for current amplification, a transistor can also be used for a current biasing circuit (Fig. 3.15). The left-hand side is essentially a voltage divider, and its output flows towards the base. By adjusting VB (and thus IB), the current flowing through Rload (collector current IC) can be regulated. Integrated circuits that provide constant current source are built upon the current biasing circuit. The transistors described previously are in fact an old type of transistor, called the biopolar junction transistor (BJT). They are still being used today, especially for analog circuits, which are essential components for physical sensors and biosensors" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002448_s0263574710000433-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002448_s0263574710000433-Figure2-1.png", + "caption": "Fig. 2. A spatial 3-DOF parallel mechanism HALF\u2217: (a) CAD model; (b) kinematical scheme.", + "texts": [ + " Section 4 investigates the parameter identification based on the minimal linear combinations of error parameters, and then measurement strategy is developed accordingly. Section 5 shows the procedure of error compensation. The experimental work and results are presented in Section 6. Conclusions are given in the last section. Figure 1 shows a 5-axis hybrid milling machine developed in Tsinghua University, which is composed of a 3-DOF parallel mechanism and a 2-DOF serial table. The prototype of the parallel mechanism to be calibrated is called HALF\u2217 introduced in refs. [19] and [20]. As shown in Fig. 2, the mobile platform is linked to the base through two identical PRU limbs and a PRC limb. Here, R, U, and C represent the revolute, universal, and cylindrical joints, respectively, and P with underline represents an active prismatic joint. When the P joints are active, the mobile platform can translate in the O-YZ plane and rotate about the y-axis. The kinematics of http://journals.cambridge.org Downloaded: 12 Mar 2015 IP address: 129.137.165.251 the mechanism was introduced in detail in ref. [19]", + "251 where \u03b4Xj is the measuring noise (the resolution or accuracy of the measuring instruments in Table I), gij is the element of row i and column j of the matrix G. The parameter \u03b4pi in Eq. (19) is defined as the anti-disturbance index of the ith combination of error parameters. From the analysis, we can see that this index reflects the information of both identification matrix and the noise resource, and there is an independent index for each combination. Therefore, the index is specific and has practical significance. For the mechanism shown in Fig. 2(a), there are only two translational DOFs, and the difference between absolute position and relative position can be eliminated by the translation of coordinate. Thus, we just need to improve its relative accuracy. Considering the relative accuracy, Eq. (9) can be rewritten as \u03b4X1 \u2212 \u03b4X0 1 = ( J1 \u2212 J0 1 ) \u03b4 P1, (20) where \u03b4X0 1 is the output position error at reference configuration 0, and J0 1 is the Jacobian matrix at reference configuration 0. In the whole workspace (\u221282.5 mm \u2264 y \u2264 82.5 mm, \u2212165 mm \u2264 z \u2264 0 mm), we choose the pose where y = 0 and z = 0 as the reference configuration 0, and get 3136 configurations stepping by 3 mm", + " (21) By decomposing the identification matrix W 3136\u00d79 using the QR decomposition algorithm to get the upper triangle matrix R, and analyzing the columns of matrix R using the four theorems of the minimal linear combinations, six minimal linear combinations of error parameters can be developed as \u03b4 p1r = [\u03b4d \u2212 \u03b4r \u03b4\u03b11 \u03b4\u03b12 \u03b4s1 \u2212 \u03b4s2 + r\u03b4\u03b2 \u03b4l1 \u03b4l2]T. Correspondingly, Eq. (20) should be rewritten as \u03b4X i 1 \u2212 \u03b4X0 1 = ( J i 1r \u2212 J0 1r ) \u03b4 P1r , (22) which is the error-mapping function under relative measurement of configuration i. For the mechanism shown in Fig. 2(b), there is only a rotational DOF. Considering the measurement costs and the feasibility of experimental work, we improve the output pose accuracy at the zero configuration to satisfy the application requirement first, then choose the relative measurement and take the zero configuration as the reference. Then, Eq. (10) can be rewritten as \u03b4\u03b8 \u2212 \u03b4\u03b80 = ( J2 \u2212 J0 2 ) \u03b4 P2, (23) where \u03b4\u03b80 is the output pose error at reference configuration 0, and J0 2 is the Jacobian matrix at this configuration. In the whole workspace (\u221225\u25e6 \u2264 \u03b8 \u2264 90\u25e6, \u2212165 mm \u2264 z \u2264 0 mm), we choose the pose where z = 0 and \u03b8 = 0 as the reference configuration 0 and get 3984 configurations through \u03b8 and z stepping by 5\u25e6 and 3 mm, respectively" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003847_piee.1970.0052-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003847_piee.1970.0052-Figure4-1.png", + "caption": "Fig. 4", + "texts": [ + " 3, with the two branches represented, respectively, by /, =fi() and i2 = /2(<\u00a3). Then / 0 (^ ) , fJ4>), and Fe((f>) which appear in Hysteresis loop in inverted position i = f() Plots of characteristic polynomials fo() and Fe() (b) M) Plots of characteristic polynomials fo() and g() (a) M4>) (b) g() Plots of characteristic polynomials fo() and fe((f>) W fo(.4>) (b) f{ eqns. 7, 8 and 10, and which we shall call the characteristic polynomials, can be obtained from the experimental points. From eqn. 8, (ID This gives a pair of curves as in Fig. 4. If, instead, we use eqn. 7, and (12) . . . (13) where #() is a double-valued function which is simpler than that of the hysteresis loop. Both functions/o(0) and g() are shown in Fig. 5, and, from eqn. 13, / , - l 2 If we use eqn. 10, we obtain the polynomials/0() ; shown in Fig. 6. Since the flux EF, then E - EF is positive, eE-EplkT -+ =, and PE -+ O. Hence, at OaK, all energy states with energy less than EF are completely populated, and all states with energy greater than EF are empty. At the absolute zero, the energy EF is like a cutoff energy, and it is known as the Fermi energy. The distribution of the number of electrons with an energy Eat OaK is shown in Fig. 8.72. Another way of looking at the Fermi energy is to consider a situation of T> OaK and to set E = EF in Eq. (8.143). Then, eE-EFlkT = 1, and PE=EF = t. In other words, the Fermi energy is the energy level which is half populated by electrons at T > OaK. The distribution function at T> OaK is shown (the full line) in Fig. 8.72. It will be seen that the distribution function takes values in between zero and unity only in a relatively narrow energy range kT around the Fermi energy. It is only electrons occupying these energy states that need to be reckoned with as free electrons. For, when PE = 1, all the energy states in the metal are filled, the electrons have no states to move into in the metal, and hence they cannot be taken as free. When PE = 0, the energy state E will have a probability of occupation of zero and hence can be ignored" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002959_j.actaastro.2013.10.022-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002959_j.actaastro.2013.10.022-Figure2-1.png", + "caption": "Fig. 2. Speed and thrust vectors definition.", + "texts": [ + " The instantaneous mass consumption (\u0394m) and the thrust magnitude (T) are motorrelated constants. The r and v variables are respectively the magnitude of the radius (distance between the Earth center and launcher center of mass) and speed vectors. The latitude (\u03b4), the longitude (\u03bb), the flight-path heading (\u03c7) and the flight-path inclination (\u03b3) are angles describing the orientation of the radius and speed vectors. The radius vector and its corresponding angles are presented in Fig. 1 while the speed vector is presented in Fig. 2. Angles \u03d1 and \u03c6 are the in-plane angle and out-of-plane thrust orientation angles respectively (Fig. 2). This representation has discontinuities over the poles (\u03b4\u00bc 7901) but they are not harmful to the sun-synchronous orbit studied later in this work (Section 4). In these equations, the variables gr and g\u03b4, representing the gravitational acceleration, set the model of the Earth. Most of space launcher guidance functions are designed with either a uniform gravity over a flat Earth or a gravity proportional to the inverse of the square of the radius over a spherical Earth [2]. That being said, launches for high inclination orbits, like the orbit studied as part of this work, are expected to reach high latitudes where the Earth's ellipticity has a significant impact on the gravity [18]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001345_j.ijmecsci.2008.10.008-Figure6-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001345_j.ijmecsci.2008.10.008-Figure6-1.png", + "caption": "Fig. 6. Geometry of a crack moving under a stationary load.", + "texts": [ + " (3), is modified, since the crack propagates relatively faster as the local hardness is lower if the stress field is identical [23]. The modified Paris\u2019 formula is as follows: da dN \u00bc C Hb Hl \u00f0DK\u00den (4) where Hb and Hl are the Knoop hardness number at the bulk material and the local Knoop hardness number, respectively. Hearle and Johnson [24] calculated the mode II stress intensity factors at each end of the crack in the half-space, where the stress field over the whole crack is known. The crack geometry used for the calculation of the stress intensity factor is shown in Fig. 6. The corresponding stress intensity factor at the leading tip (KL) is as follows: KL \u00bc ffiffiffiffiffiffi 2 pL r Z L 0 tc\u00f0xL x\u00de L x x 1=2 dx (5) where L is the crack length, tc the net shear stress, and xL the position of the leading tip. The net shear stress (tc) is the stress available to cause the stress intensities at the crack tip. The driving force for crack propagation in rolling contact has been postulated to be related to the maximum shear stress, and it was experimentally verified [7,23]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002071_s0091-0279(71)50004-1-FigureII-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002071_s0091-0279(71)50004-1-FigureII-1.png", + "caption": "Figure II. The hindlimb in normal stance.", + "texts": [], + "surrounding_texts": [ + "these are added, we find that the center of gravity moves from the center to the middle chest area, because the head is much heavier than the tail. If we place the forelimbs on one pair of scales and the hindlimbs on another, we find that in the normalstance the dog bears 60 per cent of his weight on the front limbs. Mathematically, the hindlimbs have the advantage, because now our 60 pound dog bears 18 pounds on each forelimb and 12 pounds on each hindlimb (Fig. 8). The dog's capacity for shifting his center of gravity anteriorly seems to be almost unlimited. Just by extending his head and neck, he can shift 70 per cent of his weight to the front legs. Normally, this is done when he wishes to increase forward motion. However, it can be done when there are pathologic lesions involving the posterior area. A mathematical calculation shows the advantage of this ability; with 70 per cent of the weight on the forelimbs, the 60-pound dog (when stand ing) would bear only nine pounds on each hind limb. When a severe pathologic problem develops in the posterior area, such as arthritis in the hip and knee joints, the dog must compensate for this weakness. He then shifts his center of gravity as far forward as possible, making necessary other adjustments to prevent posterior paralysis. His compensation is to adjust his front leg position nearer to the center of gravity (Fig. 9). With this type of compensation, it is not unusual, clinically, to see a dog with severe hip dysplasia, protrusion of a spinal disk, or severe arthritis carry 90 per cent of its weight on the forelimbs. When the vet erinary clinician sees patients that shift the greatest percentage of their weight forward, he should take note, for eventually the forelimbs will be unable to support this added burden. Occasionally, pathologic le sions develop in the forelimbs, and the dog becomes prostrate. Because of its apparent suddenness, this condition often is misdiagnosed as a spinal or circulatory lesion, when in fact it is a chronic lesion- now be coming acute because the front legs cannot support the entire weight of the dog. The shift of the forelimbs posteriorly, as we have described, in volves a relearning process in order to walk in this fashion. In my experience, it is acquired in from 3 to 6 months. Unless a clinician is aware of this ability-and the time interval involved-one can be con fused when seemingly hopelessly paralyzed dogs whose owners have re fused to put to sleep, or which have been put in walking carts, will start to walk again. LIMB PLACEMENT Normal Stance Since we know that the dog has great adaptability in limb position ing in pathologic conditions, it is imperative to have some reference points to determine the normal forelimb placement when there is a 60-40 weight distribution. The scapula, even though it rotates at its ends, has a relatively fixed point at its center, and this point can be used in the determina tion of the normal position of the forelimbs. To locate the position of the foreleg in a 60-40 weight position, the examiner should visually bisect the spine of the scapula and drop an imaginary \"plum line\" through this point. Its \"bob\" should parallel the point at which the metacarpal pad contacts the ground (Fig. 10). The position of the hindlimbs appears to be less important in the distribution of body weight. In the abnormal \"show\" stance, or in the more \"comfortable\" stance where the great trochanter is directly above the metatarsal pad contact, the 60-40 weight pattern seems to be main tained (Fig. 11 ). EXAMINATION OF THE CANINE LOCOMOTOR SYSTEM 63 We have discussed some of the differences in motion in the biped and quadriped, but one particular difference becomes most important in diagnosing pathologic states. In motion, the biped moves his center of gravity by leaning forward; he starts to fall, and stops this fall by advancing a limb. How far he has advanced his center of gravity will dictate the degree of advancement of the limb to control the fall. Thus a sprinter starts with his body at a greatly exaggerated angle; he then stops this fall on his first step by extending the limb to an exaggerated point. In the biped this distance, known as a \"stride,\" can be varied greatly and at will. In the dog, the strides of the fore- and hindlimbs have a very predictable normal pattern in the walking and running gaits, an exception be!ng the leaping gait. This predictable stride is of great advantage in the diagnostic examination. To picture the normal stride of the front leg of the dog, one can draw an imaginary line from the spine of the sea pula to the ground. This is the anterior contact point. The limb will stay in contact with the ground until the anterior half of the body has passed over this point, thus terminating the stride (Fig. 12). The hindlimb also has a calculable stride of great importance. In motion, the hindlimb is extended to the middle ofthe body and is placed in contact with the ground a split second after the forelimb has been lifted. The hindlimb then stays in contact with the ground to about an equal distance past the normal stance position (Fig. 13). In anteroposterior views of limb placement, normal variations will occur between the two basic shapes of dogs. Long legged, deep chested dogs-mostly the hunting breeds, where endurance necessi tates the conservation of energy- walk by placing one limb in a direct line with the limb of the opposite side (single tracking). This type of movement requires much less energy because the dog's body is stable, with no rolling of weight from side to side. These dogs are capable of running for many miles before showing signs of fatigue." + ] + }, + { + "image_filename": "designv11_7_0002128_s12239-010-0023-3-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002128_s12239-010-0023-3-Figure5-1.png", + "caption": "Figure 5. Geometry of solid element. Figure 6. Geometry of shell element.", + "texts": [ + " The mesh density is nearly between 25 and 50 mm. The shell elements with Belytschko-Tsay formulation are used for the structures of the whole bus. A solid element is used for the tilting platform of the rollover simulation. (a) Solid element model A solid element is used for the 3-D modeling of solid structures. The element is defined by 8 nodes that have the following degrees of freedom at each node: translations, velocities, and accelerations in the nodal x, y, and z directions. The geometry of this solid element is shown in Figure 5 with Nodes (I, J, K, L, M, N, O, P) and degrees of Freedom (UX, UY, UZ, VX, VY, VZ, AX, AY, AZ). (b) Shell element model This shell element is a four-node element with both bending and membrane capabilities. Both in-plane and normal loads are permitted. The element has 12 degrees of freedom at each node: translations, accelerations, and velocities in the nodal x, y, and z directions and rotations about the nodal x, y, and zaxes. The geometry of this shell element is shown in Figure 6 with Nodes (I, J, K, L) and degrees of Freedom (UX, UY, UZ, VX, VY, VZ, AX, AY, AZ, ROTX, ROTY, ROTZ)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003592_978-3-319-06698-1_33-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003592_978-3-319-06698-1_33-Figure3-1.png", + "caption": "Fig. 3 A Watt I six-bar linkage that reaches six task positions", + "texts": [ + " Finally, 5,735 nonsingular solutions were found after tracking a total of 51,000 paths. The computation took about 7h. The solution set and parameters from the regeneration run provided a parameter homotopy for the synthesis equations. The base pivots were specified to be A = \u22123.976225 \u2212 0.623063i and B = \u22122.024139 \u2212 1.285906i . This computation took about 5min and yielded 5,556 nonsingular solutions of which 243 were suitable to analyze and 43 were defect-free. Example solutions are listed in Table 4. Solution 1 is shown in Fig. 3. The chapter derives the synthesis equations forWatt I six-barmechanisms that guides a body through N task positions. For N = 8, we were unable to solve this problem using polynomial continuation but did obtain solutions via repeated trials ofNewton\u2019s method. For the simpler problem of six positions with specified ground pivots, we computed a complete solution using polynomial regeneration. This gives a set of 5,735 solutions that serve as the start points for a parameter homotopy to solve any particular case in about 5min on a 64 core parallel computer" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001695_s10409-009-0241-y-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001695_s10409-009-0241-y-Figure1-1.png", + "caption": "Fig. 1 Definition of the state variables u, w, q and \u03b8 and sketches of the reference frames. The insect is shown during a perturbation (u, w, q and \u03b8 are zero at equilibrium)", + "texts": [ + " [1\u20134], we make the rigid body approximation: the wingbeat frequency of the insect is assumed to be much higher than that of the natural modes of motion of the insect, and the insect is treated as a rigid body of six degrees of freedom (in the present case of symmetric longitudinal motion, only three degrees of freedom), with the action of the flapping wings represented by the wingbeat-cycleaverage forces and moment. Reference [6] has shown that the rigid body assumption is applicable to droneflies. This model of the droneflies is sketched in Fig. 1. Let oxyz be a non-inertial coordinate system fixed to the body. The origin o is at the center of mass of the insect and axes are aligned so that the x-axis is horizontal and points forward at equilibrium. The variables that define the motion (see Fig. 1), are the forward (u) and dorsal-ventral (w) components of velocity along x- and z-axis, respectively, the pitching angular-velocity around the center of mass (q), and the pitch angle between the x-axis and the horizontal (\u03b8). oExE yEzE is a coordinate system fixed on the earth; xE-axis is horizontal and points forward. Let c be the vector of control inputs. It has been observed that freely-flying droneflies and hoverflies and many other insects control the longitudinal motion mainly by changes in geometrical angles of attack and changes in the fore/aft extent of the flapping motion [7,8]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002468_1077546310372848-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002468_1077546310372848-Figure1-1.png", + "caption": "Figure 1. Simple spur gear pair application (Seybert et al., 1991).", + "texts": [ + " The sensitivity of the system to gyroscopic effects obviously affects the extent to which the modal transformation is affected. Consequently, for a full modal speed-sweep analysis, the transformation matrices must be calculated for each rotational speed step within the desired range. This results in an increase in computer processing requirements for a method originally intended to reduce them. The first application of this methodology is a simple system of two identical shafts connected by a spur gear pair, similar to the one depicted in Figure 1, which was used to validate this methodology (Stringer et al., 2008). It was selected because of its readily available system parameters, which appear a number of times in the literature (Lim and Singh, 1991; Choy et al., 1993). The system consists of two identical spur gears at the midpoint of identical shafts, each connected to a gearbox by a pair of rolling-element bearings. Since the two substructures are the same, the complexity of the modal analysis in equation 18 is greatly reduced. The system parameters used in the model can be found in Stringer (2008)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000351_1.2185661-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000351_1.2185661-Figure1-1.png", + "caption": "FIG. 1. Young diagram for the cylinder/fluid/air interface.", + "texts": [ + " \u00a9 2006 American Institute of Physics. DOI: 10.1063/1.2185661 I. INTRODUCTION In his celebrated article in 1805,1 Thomas Young related a pressure jump across a curved fluid/fluid interface to a \u201csurface tension\u201d within the interface; he then went on to assume an analogous tension in solid/fluid interfaces, and asserted a force balance of all tensions at a triple solid/fluid/ fluid interface within the tangent plane to the solid, as a condition for equilibrium. That led him to the \u201cYoung diagram\u201d Fig. 1 relating the three tensions 0 liquid/air , 1 solid/air , 2 solid/liquid at the triple interface; by balancing the components of these forces in the tangent plane of the solid, Young found the formula cos = 1 \u2212 2 0 1 for determining the \u201ccontact angle\u201d . He concluded that the contact angle depends only on the physical properties of the materials, and in no other way on the conditions of the problem. This result remains basic to all of capillarity theory. In Ref. 2, Finn points out that 1 is not in general correct, as it leads to contradictory statements; nevertheless, an independent reasoning supports Young\u2019s assertion that depends only on the materials", + " The force of gravity in the vertical direction is FG = \u2212 mg 6 per unit length; we obtain the buoyant force by integrating the vertical component of the action of the pressure p= gy = g u0+h normal to the surface: FB = \u2212s0 s0 gy cos ds 7 = \u2212 0 0 g u0 + r cos \u2212 r cos 0 cos rd 8 = gr \u00b12 sin 0 2 g 1 \u2212 cos 0 + r 0 \u2212 r 2 sin 2 0 , 9 where we have taken the pressure at the fluid surface at infinity to be equal to zero. The \u00b1 in Eq. 9 stems from Eq. 4 , which defines u0 as u 0 = \u00b1 2 / g 1\u2212cos 0 ; the positive sign corresponds to configurations with 0 0 and the negative sign to configurations with 0 0. We next must determine the forces arising from surface tension effects. There are three interfaces abutting on the contact point, and according to Young,1 there are corresponding surface tensions 0, 1, and 2 acting in the directions indicated in Fig. 1. According to Young, the tangential components of these forces sum to zero and we are left with a net normal force; the vertical projection of this is F \u02c6 = \u2212 2 0 sin cos 0. 10 This result is open to question in light of the material in Ref. 2. We will test that point in what follows. It has been recognized for some time that conceptual difficulties can arise in interpretations of the Young diagram; see Refs. 3 and 4. In Ref. 2, Finn asserts that the diagram suffers from a basic conceptual error in according \u201csurface tension\u201d forces to the solid/fluid interfaces" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002182_robio.2009.4913121-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002182_robio.2009.4913121-Figure2-1.png", + "caption": "Fig. 2 Configuration of ASTERISK limb", + "texts": [ + " A limb mechanism robot is a working mobile robot consisting of multiple limbs which can be used as both legs Proceedings of the 2008 IEEE International Conference on Robotics and Biomimetics Bangkok, Thailand, February 21 - 26, 2009 978-1-4244-2679-9/08/$25.00 \u00a92008 IEEE 915 for locomotion and arms for manipulation depending on present situations. The limb mechanism robot \u201cASTERISK\u201d has 6 limbs attached to the body radially at even interval, as shown in Fig.1. This arrangement gives the robot homogeneous mobility and manipulation ability in all horizontal directions. According to Fig.2, each limb consists of 4 rotational joints; thus the robot has 24 degree of freedom. The ranges are symmetric on both sides of the body, that allows the same workspace even in up and down directions. The total length of the robot when the limbs are stretched is 840 mm, the height of the body is 78 mm, the total weight is 4 kg, and the normal standing posture height is 180 mm. In the followings we use term leg instead of limb because this paper only discusses locomotion. From its features and torque provided, we chose smart actuator module Dynamixel DX-117 by ROBOTIS as joint actuators" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002492_detc2011-48306-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002492_detc2011-48306-Figure2-1.png", + "caption": "Figure 2: Temperature Unit", + "texts": [ + " The aim of the project, chosen as the case study, was to develop a watch system based on the idea to develop a mechanical watch and an instrument, which can be attached to Downloaded From: http://proceedings.asmedigitalcollection.asme.org/pdfaccess.ashx?url=/data/conferences/idetc/cie2011/70722/ on 07/13/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use 7 Copyright \u00a9 2011 by ASME the watch (see Figure 1). The instrument contains advanced functions used for alpine skiing. An additional two external units wirelessly transmit heart rate information and temperature information to the instrument attached to the watch. In this case study, we focus on the external temperature unit showed in Figure 2. It is noteworthy that one of the authors was involved as a development engineer in this specific project. The case study was built up on the experience gained by participating in the development team backed up by documentanalysis, and interviews with the project managers for the mechanical, electronics and software development. Due to limitations of describing the development process as a whole, we deem it necessary to only select small fragments from the design process to illustrate the selected challenges" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003286_s00707-013-0822-5-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003286_s00707-013-0822-5-Figure1-1.png", + "caption": "Fig. 1 Basic wear-fatigue test patterns. a Mechano-rolling fatigue, b mechano-sliding fatigue, c fretting fatigue, d rolling friction (rolling fatigue), e sliding friction (sliding fatigue), f mechanical fatigue", + "texts": [ + " On the other hand, this model allows studying the significant change of contact boundary conditions due to volume deformation of the system\u2019s elements by non-contact forces (back effect in tribo-fatigue [1\u20136]). The latter effect will be discussed further. Consider the example of calculation of contact pressure with regard to non-contact (volume) deformation. As an object of study, let us take a roller/shaft system that is acted upon by contact FN and non-contact Fb forces (Fig. 2). This model is used in wear-fatigue tests for contact-mechanical fatigue (Fig. 1a) [33,34]. For this model, the problem of the influence of the non-contact load value on contact pressure changes will be solved. From Fig. 1a, it is seen that the surfaces of contacting bodies are bounded by the second-order surfaces; therefore, to determine the contact pressure, one could confine oneself to Hertz\u2019s theory. Yet, since during long fatigue loading the cases of contact of bodies with arbitrary-shape surfaces are most probable, it is preferable to use more general methods of numerical modeling for contact pressure calculation. Our calculation uses the matrix inversion technique, whose description can be found, for example, in [17]", + " This means that for the contact to be maintained in the entire computational domain, tensile forces must be applied at such points of the grid. Such partition elements are excluded from the proposed contact region (pressures in them are assumed to be equal to zero), and Eq. (43) is being solved for an updated grid. The process as described here is repeated until at some step the obtained values of pi j become non-negative. Numerical modeling of contact interaction will be performed for the following parameters: v1 = v2 = 0.3, E1 = E2 = 2.01 \u00d7 1011 Pa, R11 = 0.005 m, R12 = 0.05 m, R21 = 0.01 m, R22 = \u2212 0.01 m (see Fig. 1a). A contact load will be assigned by (a) the force FN = 2,000 H and (b) the bodies approach \u03b4 = 2.723 \u00d7 10\u22125m, corresponding to the mentioned value of FN following Hertz\u2019s theory. The ratio of the contact ellipse half-axes a/b = 0.89. Computational domain sizes are 1.5a \u2264 x and y \u2264 1.5a where a = 5.296 \u00d7 10\u22124m. The domain was partitioned into 21 \u00d7 21 square elements. Compare the contact pressure distribution (Fig. 3) obtained as a result of iterative solution of system (43) with the analytical solution according to Hertz theory for the distribution of the form p (x, y) = p0 \u221a 1 \u2212 x2 a2 \u2212 y2 b2 , (44) Errors will be estimated by the following formulae: \u03b5i = pH i \u2212 pi pH 0 , \u03b5max = max i |\u03b5i | , \u03b5avg = 1 n n\u2211 i=1 |\u03b5i |, (45) where the superscript H means Hertz solution" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002189_ijrapidm.2010.036116-Figure7-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002189_ijrapidm.2010.036116-Figure7-1.png", + "caption": "Figure 7 POM-trumpf laser deposition head (a) schematic; (b) actual (see online version for colours)", + "texts": [ + " Although this process could successfully produce the Ti components to serve the full life and technically proved as good as the machined components, it was a commercial failure which led to the closure of the company. Direct metal deposition (DMD) developed at Michigan University, USA and marketed through Precision Optical Manufacturing Inc. (POM) uses optical feedback to ensure the integrity of deposition (Mazumder et al., 2000). Trumpf, a German laser company, adopted this process for their laser. This machine shown in Figure 7 is known as TrumaForm DMD 505. Its laser deposition head has a very high powder utilisation of over 90%. It is mounted onto a 6-axis robot so that the cladding can be done not only in planar layers but also over a freeform surface. Apart from repair, this machine can be used for cladding and hard facing over a contoured surface. All these popular systems do not have material addition and subtraction occurring at the same platform seamlessly. Electron beam welding has been in use for very demanding nuclear and aerospace applications" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000805_tmag.2007.893297-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000805_tmag.2007.893297-Figure1-1.png", + "caption": "Fig. 1. Schematic representations of armature unit.", + "texts": [ + " Therefore, we considered deforming the shape of the outlet edge at the armature in order to reduce the cogging force of the outlet edge. This paper presents the results of 3-D numerical analysis by the finite-element method (FEM) of the cogging force exerted by the outlet edge. Moreover, we deformed the shape of the armature to decrease the cogging force at the outlet edge, and the results were examined using 3-D numerical analysis by the FEM. The armature arrangement of the stationary discontinuous armature PM-LSM is given schematically in Fig. 1. The mover is accelerated by the short armature unit (accelerator) and is then driven by its own inertia. Since the velocity of the mover decreases, the mover enters the next armature unit which is installed in order to make it reaccelerate and decelerate, and Digital Object Identifier 10.1109/TMAG.2007.893297 Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. there it is reaccelerated and decelerated. However, if the mover goes through the boundary between the active part and the inactive part of the armature at stationary discontinuous armature PM-LSM, the attractive force produced between the armature\u2019s core and mover\u2019s permanent magnet fluctuates highly" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001833_siitme.2010.5649125-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001833_siitme.2010.5649125-Figure1-1.png", + "caption": "Figure 1. scheme of the synchronous machine.", + "texts": [], + "surrounding_texts": [ + "978-1-4244-8124-8/10/$26.00 \u00a92010 IEEE 237 23-26 Sep 2010, Pitesti, Romania\nused for the ordering of the invertors and synchronous machine. This system can be regarded as a hybrid dynamic system whose continuous component is the permanent magnet synchronous machine and the discrete component, the inverter of tension. In this article, we propose a modeling of this whole by a system with discrete events. This model is then simulated on Matlab/Simulink.\nI. INTRODUCTION\nPermanent magnet synchronous motor drives (PMSM) offers many advantages over the induction motor, such as overall efficiency, effective use of reluctance torque, smaller losses and compact motor size. In recent years many studies have been developed to find out different solutions for the PMSM drive control having the features of quick and precise torque response, and reduction of the complexity of field oriented control algorithms [1-3]. The DTC technique has been recognized as viable and robust solution to achieve these requirements.\nIn the existing literature, many algorithms have been suggested for the DTC control [1, 4-6]. The eight voltagevector switching scheme seems to be suitable only for high speed operation of the motor while at low speed the six voltage-vector switching scheme, avoiding the two zero voltage-vectors, seems to be appropriate for the permanent magnet synchronous motor drive The voltage vector strategy using switching table is widely researched and commercialized, because it is very simple in concept and very easy to be implemented. The stator fluxes linkages are calculated from voltage and current models PMSM drive. The DTC is increasingly drawing interest because of,\n Simplicity of its structure.\n Elimination of the current controllers.\n Inherent delays.\n Elimination of rotor position sensor.\nThe amplitude and the frequency of the controlled variables are considered. In the controlling of vector the amplitude and the position of a controlled vector of space are considered.\nThese reports are valid even during cuts which are essential for the precise ordering of couple and speed.\nII. MODELING OF THE SYNCHRONOUS PERMANENT\nThe motor considered in this paper is an interior PMSM which consists of a three phase stator windings and a PM rotor. The voltage equations in a synchronous reference frame can be derived as follows,\nsq sd\nsdssd dt\nd iru .. (1)\nsd\nsq\nsqssq dt\nd iru .. (2)\nWhere the direct and quadrate axis flux linkages are,\nfsddsd iL . (3)\nsqqsq iL . (4)\nThe electromagnetic torque of the motor can be evaluated as follows,", + "978-1-4244-8124-8/10/$26.00 \u00a92010 IEEE 238 23-26 Sep 2010, Pitesti, Romania\n qdqdqf IILLIpCe .).(. 2\n3 (5)\nThe motor dynamics can be simply described by the equation (6).\n \n .. f dt\nd JCCe r (6)\nWith:\n\u2126: rotation's speed mechanical of the PMSM\n\u03c9: rotation's speed electric.\nP: Number of pairs of poles.\nJ : Total moment of inertia brought back on the tree of the PMSM.\nf : Coefficient of viscous friction.\nCr: Resistive torque.\nf: flux produced by the permanent magnet.\nsd: d axis stator magnetic flux,\nsq: q axis stator magnetic flux,\nLsd: d axis stator leakage inductance,\nLsq: q axis stator leakage inductance,\nrs: stator winding resistance,\nCe: electromagnetic torque,\nIII. CONTROL DTC (DIRECT TORQUE CONTROL): Since Depenbrock and Isao Takahashi proposed\nDirect Torque Control for induction machines in the middle of\n1980's [9, 11], more than one decade has passed. The basic idea of DTC for induction motor is slip control, which is based\non the relationship between the slip and electromagnetic\ntorque [2]. In the 1990's, DTC for Permanent Magnet\nSynchronous Machines was developed [7, 12, 13]. Compared\nwith Rotor Field Oriented Control, the DTC has many\nadvantages such as less machine parameter dependence, simpler implementation and quicker dynamic torque response.\nThere is no current controller needed in DTC, because it\nselects the voltage space vectors according to the errors of flux\nlinkage and torque. The most common way to carry out the\nDTC is a switching table and hysteresis controller, as in [8,\n14]. Fig. 2 is a typical DTC system. It includes flux and torque estimators, flux and torque hysteresis controllers and a\nswitching table. Usually a DC bus voltage sensor and two output current sensors are needed for the flux and torque estimator. Speed sensor is not necessary for the torque and flux control. The switching state of the inverter is updated in each sampling time. Within each sampling interval, the inverter keeps the state until\nthe output states of the hysteresis controller change. Therefore, the switching frequency is usually not fixed; it changes with the rotor speed, load and bandwidth of the flux and torque controllers.\nA. Transformation abc-\u03b1\u03b2 (Clark):\nAs control DTC is a vectorial control, it is necessary to have the components of Concordia of the currents and stator tensions of the PMSM. One thus breaks up the three stator currents isabc and the three stator tensions vsabc into components direct (vs) and quadratic (vs) such as:\n \n\n \n\n \n\n \n\n\n\n \nsc\nsb\nsa\ns\ns\nx\nx\nx\nx\nx\n2\n3\n2\n3 0\n5.05.01\n3\n2\n\n (7)\nWith x = Vs or is.\nSince the model of the PMSM is expressed in the reference mark (d-q), a passage of the two-phase system (\u03b1-\u03b2) to the\ntwo-phase system (d-q) (Concordia) proves to be essential:\n s s sq sd i i i i . )cos()sin( )sin()cos( (8)\n1) Flux Estimator : The stator electric equations of the PMSM, in the reference\nmark (\u03b1-\u03b2) are given by:\n \n \n\n \n \ndt\nd irV\ndt\nd irV\ns\nsss\ns sss\n \n \n.\n.\n(9)\nWhat:" + ] + }, + { + "image_filename": "designv11_7_0002527_revet.2012.6195318-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002527_revet.2012.6195318-Figure1-1.png", + "caption": "Figure 1. Mesh generation of the studied 'IM'", + "texts": [ + " 3D effects consider external elements to field solutions, they are due to axial length, rotor slot skewing, rotor rings and stator end windings. For an appropriate definition of the coupled circuit, end- winding leakages should be considered [BIN]. In this work, 3D effects were computed and included in electrical circuit, Geometrical dimensions and physical material properties were defined, rotating air gap is considered, boundary conditions were set up with geometrical model, and mesh generation was executed for 'FEM' analysis pre-processing step Mesh generation of the studied three phase squirrel cage 'IM' is shown in Fig.1. The two dimensional flux calculations are performed to study and analyse the variation the IM mutual inductance as well as stator and rotor inductances for different rotor speeds and stator currents. Fig.2 shows a snapshot of the resulting induction machine flux distribution for 20A stator current and 25rd/s rotor speed. The flux equations can be written as follows [MRM2] : s s s r r r r s L I +M I L I +M I \u23a7\u03a6 =\u23aa \u23a8 \u03a6 =\u23aa\u23a9 (11) Where Ls : stator inductance per phase; Lr : rotor inductance per phase; Lm : mutual inductance between stator and rotor phase; M = m 3 L 2 ; Thus Stator and rotor inductances can be expressed by: s r s s r s r r \u03a6 -M IL = I \u03a6 -M IL = I \u23a7 \u23aa\u23aa \u23a8 \u23aa \u23aa\u23a9 (12) The rotor time constant is given by: r r r LT = R (13) The magnetic dispersion coefficient can be written as follows: 2 m s r L\u03c3=1L L \u239b \u239e \u239c \u239f \u239d \u23a0 (14) The mutual inductance is deduced from zero current rotor and different stator currents simulations" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001847_cdc.2010.5717905-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001847_cdc.2010.5717905-Figure1-1.png", + "caption": "Fig. 1. Mutual localization with anonymous position measures. (a) A group of robots with the associated moving frames (b\u2013e) the feature sets detected by each robot at time t.", + "texts": [ + " The novel multiple registration algorithm is introduced in Section IV, while Section V describes the particle filters for estimating the probability density functions of the agent configurations. Section VI reports experimental results, and Section VII outlines a discussion and some future work. Consider a system of n \u2265 2 agents (henceforth called robots) R1, . . . ,Rn, with n unknown (hence, it may change during the operation). Denote by N = {1, . . . , n} the robot index set, and let Ni = N/{i}. The robots move in the plane and a moving frame Fi is rigidly attached to each Ri (see Fig. 1a). We describe the localization problem from the viewpoint of a generic Ri, as in [21] and [23]. The superscripts t and 1 : t denote the value of a variable at the discrete time instant t and all its values at time instants 1, 2, . . . , t, respectively. The 3-vector describing the position and orientation of Fj w.r.t. Fi is the relative pose xj of Rj , j \u2208 Ni. We use the operators \u2295 and for the composition of poses [24]. Each robotRk, k \u2208 N , has a motion detector that provides utk, a measure of its displacement between t\u2212 1 and t. The motion detector is characterized by a probabilistic motion model p(u\u2032|u), where u\u2032 and u are, respectively, the \u2018true\u2019 and the measured displacement. In addition, each Rk is equipped with a robot detector, a sensor device that measures the relative position (typically, as bearing and distance) of other robots in Fk, without the associated identity (see Fig. 1b\u2013e). Robot Rh, h \u2208 Nk, is detected if it is placed in a perception set Dp that is rigidly attached to Fk. No assumption is taken on the shape Dp. As shown in Fig. 2, the robot detector is prone to false positives (it can be deceived by objects that look like robots) and false negatives (robots belonging to Dp which are not detected, e.g., due to line-of-sight occlusions). A probabilistic description of the robot detector is given in the form of a perception model p(z|xh xk), where z is the measured relative position of Rh in Fk, and xh xk is the relative pose of Fh with respect to Fk. In our method, p(z|xh xk) does not account for false positives/negatives, because the multiple registration algorithm provides robustness to these outliers. The measures coming from the robot detector will be generically referred to as features, as a reminder of the fact that they are anonymous and, in addition, may or may not represent actual robots. We denote by Ztk the set of features detected by Rk at time t (Fig. 1b\u2013e). Finally, each robot Rk, k \u2208 N , comes with a communication module that can send/receive data to/from any other robot Rh, h \u2208 Nk, contained in a communication set Dc rigidly attached to Fk. We will assume that Dp \u2282 Dc, so that if Rk can detect Rh it can also communicate with it. Each message sent by Rk contains: (1) the robot signature (the index k), (2) the current composition of the motion displacements u1:t k = u1 k\u2295 . . .\u2295utk incrementally obtained from the elementary measures provided by the motion detector (3) the feature set Ztk" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001502_arso.2009.5587076-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001502_arso.2009.5587076-Figure2-1.png", + "caption": "Fig. 2: Ciliary vibration drive mechanism.", + "texts": [ + " The cable of a video scope is covered by inclined cilia. Motors with eccentric mass installed in the cable excite vibration and cause up-and-down motion of the cable. When the cable move down, the tips of the cilia sticks on the floor, and the cable move forward because of the inclination. On the other T 978-1-4244-4394-9/09/$25.00 \u00a9 2009 IEEE hand, when it moves up, the tips slip against the floor, and the cable does not move back. By repetition of this process, the cable can slowly move in narrow space of rubble piles as shown in Fig. 2. B. Advantages and Disadvantages The ASC has the following advantages and disadvantages. (1) Mobility By adding the mobility to a video scope, the area of search is drastically enhanced. The ASC can enter into the space where conventional scopes could not move by negotiating with steps and slopes. It can ascend steps 20 cm high, and can climbs slopes 20 deg, when the conditions are good. (2) Controllability in narrow spaces The direction of motion in confined space can be controlled by bending the end of the scope using the original function of video scopes" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002450_s10846-010-9481-0-Figure9-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002450_s10846-010-9481-0-Figure9-1.png", + "caption": "Fig. 9 MAV autopilot", + "texts": [ + "1 Testbed and Autopilot Configuration The target MAV considered in this research is a tailless aircraft with a reflexed thin airfoil as shown in Fig. 8. It is equipped a rudder and an elevator with a vertical tail. As shown in Table 3, the MAV offers payload of 150 g, which is sufficient to carry our custom autopilot. The autopilot system consists of a flight control computer, an inertial measurement unit (IMU), a GPS receiver and a PWM generation board. The specification of the autopilot is shown in Fig. 9 and Table 4 [9]. The flight computer is based on a PXA270 400 MHz processor with 64 MB RAM and 16 MB Flash memory, weighing only 25 g. The CPU is capable of moderate navigation and control algorithms without any difficulties. The autopilot software is developed in house, written in C++ on embedded Linux 2.6 kernel. The autopilot is architected in a structured and modular manner so that it can be easily modified to integrate new capabilities such as the formation control presented in this paper. 4" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000835_iembs.2008.4650518-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000835_iembs.2008.4650518-Figure2-1.png", + "caption": "Fig. 2. Illustration of pH sensor and optical detection system", + "texts": [ + "2) has been chosen as it will show a colour change from yellow to blue over this range of measurement. It is fabricated directly onto the fabric channel by coimmobilising the dye with tetraoctyl ammonium bromide. To obtain quantitative pH measurements a paired emitterdetector LED configuration was used [11]. These LED\u2019s (Kingbright, L934SRCG) are used to measure the pH dependent (blue) colour intensity of the dye and are held over the fabric channel using a black PMMA cover which is positioned using the rubber gasket. The sensor and optical system is illustrated in Fig. 2. The detector is reverse-biased at +5 V, which charges the capacitance across it. This is discharged by the photocurrent generated upon incident light. The discharge rate is proportional to the intensity of the light reaching the detector. A digital output can be obtained by using a basic detection/timer circuit which measures the time it takes the photocurrent to discharge the voltage from +5 V (logic 1) to +1.7 V (logic 0). This is done using a Crossbow Mica2dot Mote with the data being wirelessly transmitted to a Mica2 base station connected to a laptop for analysis" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003862_ijsi-08-2013-0017-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003862_ijsi-08-2013-0017-Figure4-1.png", + "caption": "Figure 4. Typical temporal evolution and spatial distribution of the maximum principal stress over the surface of a tooth of the driven gear (for the case of perfectly aligned shafts)", + "texts": [ + " In this section, a few prototypical finite-element results pertaining to the distribution of the maximum principal stress over one of the teeth of the driven helical gear are presented and discussed in the context of the expected fatigue-life (in particular, the portion of the fatigue-life related to the crack-nucleation stage). 4.1.1 Aligned-gear case. Typical temporal evolution and spatial distribution of the maximum principal stress over the surface of a tooth of the driven gear (for the case of perfectly aligned shafts) are shown in Figure 4(a)-(d). It is seen that, as expected, the maximum principal stress displays cyclic behavior. That is, as the gears rotate, the (unengaged) tooth in question becomes progressively engaged and subsequently disengaged. Furthermore, examination of the results displayed in Figure 4(a)-(d) reveals that during this process, the location associated with the largest value of the maximum principal stress is changing with the extent of gear rotation. This observation is important since, as postulated by the fatigue-crack initiation model described in Section 3.1, fatigue-cracks are nucleated (via the operation of plastic micro-yielding phenomena) in the region associated with the highest value of the maximum principal stress. The effect of the torque transferred by the gear-pair analyzed on the largest value of the maximum principal stress, and on the corresponding value of the von Mises equivalent stress, in the subject gear-tooth (for the case of perfectly aligned shafts) is IJSI 5,1 74 shown in Figure 5" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001789_s00707-008-0132-5-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001789_s00707-008-0132-5-Figure2-1.png", + "caption": "Fig. 2 a This part illustrates the angular position \u03b2 j and span \u03b7 j of the fluid slug in the j th fluid ring. b This part illustrates a filled fluid ring with \u03b7 j = 2\u03c0", + "texts": [ + "com ME Earth\u2019s mass (kg) U\u03b2 external torque vector acting on the fluid motion (N m) u\u03b2 U\u03b2/(Ix 2) r mean radius of the fluid ring (m) R orbital radius (m) RE Earth radius (m) Rn Reynolds number, \u03c1Dr\u03b2\u0307/\u00b5 for circular fluid ring S system mass center S \u2212 X0Y0Z0 coordinate axes in the local vertical frame S \u2212 XYZ satellite body coordinate frame U j fluid frictional torque about the j th fluid ring axis of symmetry (N m) Ucj fluid control torque applied by pump in the j th fluid ring (N m) u j , ucj U j/(Ix 2), Ucj/(Ix 2) \u03b1, \u03c6, \u03b3 satellite pitch, roll and yaw angles, respectively (deg) \u03b1d , \u03c6d , \u03b3d desired or commanded satellite pitch, roll and yaw angles (deg) \u03b10, \u03c60, \u03b30 \u03b1, \u03c6, \u03b3 at \u03b8 = 0 (deg) \u03b1\u2032 0, \u03c6 \u2032 0, \u03b3 \u2032 0 \u03b1\u2032, \u03c6\u2032, \u03b3 \u2032 at \u03b8 = 0 \u03b2 j , \u03b7 j angular position and span of the fluid slug in the j th fluid ring, respectively (Fig. 2) (deg) \u03b2 je \u03b2 j at equilibrium (deg) \u03b2 \u2032 j angular speed of the fluid slug with respect to the fluid ring j (rad/s) \u03b2 \u2032 j0 \u03b2 \u2032 j at \u03b8 = 0 \u03b2 j0 \u03b2 j at \u03b8 = 0 (deg) \u03b2 \u2032 0 \u03b2 \u2032 j when \u03b2 \u2032 1 = \u03b2 \u2032 2 = \u03b2 \u2032 3 at \u03b8 = 0 \u03b7t \u03b7 j when \u03b71 = \u03b72 = \u03b73 (deg) \u03c1 fluid density (kg-m\u22123) \u03c4 j shear stress for the fluid ring j (N m\u22122) \u00b5 viscosity of the fluid (kg m\u22121s\u22121) \u03b8 angle from the reference line (deg) \u03c9i angular rate of the satellite about the body fixed i-axis (rad/s) orbit rate; (GME/R3)1/2 (rad/s) (.) j (.) for the j th fluid ring, j = 1, 2, 3 (", + " The orientation of the satellite is specified by a set of three successive rotations: \u03b1 (pitch) about the X0-axis, \u03c6 about the new roll axis (Z -axis, if \u03b1 = 0), and finally \u03b3 about the resulting yaw axis. The corresponding principal body-fixed coordinate frame for the satellite is denoted by S-XYZ. For the fluid ring j , the angle \u03b2 j denotes rotation of the fluid slug about the j-axis ( j = 1, 2, 3 corresponds to the X -axis, Y -axis, and Z -axis, respectively) with respect to the body-fixed Y -axis (Fig. 2). The resulting coordinate frame associated with this vector is denoted by SL j \u2212 X L j YL j ZL j . The system under consideration has six generalized coordinates: three for the satellite rotations: pitch(\u03b1), roll(\u03c6) and yaw(\u03b3 ), and three for the fluid rings: \u03b2 j , j = 1, 2, 3. As the fluid ring is very small compared to the satellite, its product of inertia and center of mass movement effects are ignored. We assume fully filled fluid rings (i.e., \u03b7 j = 2\u03c0) as shown in Fig. 2. The moments of inertia of the fluid ring are obtained as I f x1 = 2\u03c0\u03c1 Ar3, I f y1 = I f z1 = \u03c0\u03c1 Ar3, I f x2 = \u03c0\u03c1 Ar3, I f y2 = 2\u03c0\u03c1 Ar3, I f z2 = \u03c0\u03c1 Ar3, I f x3 = I f y3 = \u03c0\u03c1 Ar3, I f z3 = 2\u03c0\u03c1 Ar3. (1) The motion of the fluid relative to the annular ring causes energy dissipation through shear stress acting on the wall of the ring. The shear stress \u03c4 j for the fluid ring j is given as \u03c4 j = 1 8 f\u03c1V 2 = 1 8 f\u03c1r2\u03b2\u03072 j , (2) where laminar flow inside the fluid ring is assumed (Rn < 2000) [22], f = 64 Rn " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000582_j.jsv.2007.02.019-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000582_j.jsv.2007.02.019-Figure2-1.png", + "caption": "Fig. 2. Schematic drawing of the top-hat dynamometer and its attachment system. Front view and split section of the mounting assembly. The dashed lines show the location of the bolts. The thick back plate is clamped to the square bracket by four bolts on each corner of the plate. The contact tip is screwed at the end of the cylindrical shell.", + "texts": [ + " It ensures that the pin assembly tracks the deflection of the disc due to any misalignments. From a dynamical point of view, the preloading spring amounts to an extra stiffness element in parallel with the leaf springs. The rigid body mode of the bracket on leaf spring could easily be identified around 20Hz, well below the other modes of the system. The top-hat dynamometer is an axisymmetrical solid made out of a single block of Dural. A schematic drawing of this top-hat together with the attachment to the bracket is shown in Fig. 2 (transducers not shown). The dynamometer makes contact with the disc through a rounded tip. A tip made of whichever friction material is desired can be screwed to the end of the top-hat cylinder as shown in Fig. 2. The most important part of the top-hat element is the thin cylindrical shell. At its base this thin shell merges into a much thicker cylinder which contains holes for attachment. Given the thinness of the cylindrical shell (0.75mm), it can be considered as the first compliant mechanical element viewed from the contact point. This compliance is used to measure the normal and friction forces at the contact point. Following Smith [4, p. 22], arrangements of strain gauges were fitted to the cylindrical shell to measure the normal and friction forces", + " The output signals from the two Fylde amplifiers were calibrated statically by hanging known weights in both directions in turn. Besides the required calibration factors, this test confirmed that the linearity of the transducers is very good, and that the strains in the two directions are reasonably well decoupled (less than 5% within the calibrated range). Because of problems of insensitivity and bridge balancing, the accuracy of F and N cannot be guaranteed at better than 5%. To provide suitable dynamics of the pin assembly, the dynamometer was fixed to the bracket via a flexible strip as shown in Fig. 2. The top-hat cylinder is bolted to the strip at two points. The strip is then screwed to a much thicker aluminium plate. This plate allows the strip and the top-hat assembly to be fixed onto the heavy ARTICLE IN PRESS P. Duffour, J. Woodhouse / Journal of Sound and Vibration 304 (2007) 186\u2013200 189 square bracket described above. The steel strip was machined carefully to avoid sharp corners and consequential high local stresses at the regions in contact, either with the top hat or with the back plate", + " [2] shows that instability can only occur if there is a non-zero coupling between normal and tangential motion in either or both of the two uncoupled subsystems. Since the disc is almost perfectly symmetrical, such coupling can only be present if the top hat is not positioned symmetrically on the metal strip. To ensure that the coupled system has unstable zeros, asymmetry was deliberately introduced in the pin assembly by attaching the top hat on the strip about 10mm away from the middle of the strip (although it is shown in a central position in Fig. 2). The theory presented in Ref. [2,3] requires the measurement of one 2 2 mobility transfer function matrix for each subsystem. This matrix was denoted H for the pin subsystem. The velocities were measured using a laser vibrometer Polytec OFV 056 Sensor Head driven by a Polytec OFV 3001 S Controller. The structure was excited by a piezoelectric impulse hammer PCB 484B11. All the transfer functions shown here have been filtered using a low-pass filter at 30 kHz embedded in the Polytec vibrometer system" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000823_s11044-008-9122-6-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000823_s11044-008-9122-6-Figure3-1.png", + "caption": "Fig. 3 A two-link arm with both links flexible", + "texts": [ + " The eigen function used to represent the shape functions of the ith link in its j th mode of bending is given by [26]: sij = [ (sin\u03c2j + sinh\u03c2j ) \u2212 \u03c3(cos\u03c2j + cosh\u03c2j ) ]; \u03c3 = (sin \u03b4j + sinh \u03b4j )/(cos \u03b4j + cosh \u03b4j ), (44) where for j = 1 and 2, the modal constant, \u03b4j = 1.875 and 4.694, respectively [26]. The shape functions of the link in torsion s\u0304ij , as defined in (3b), can also be represented by similar trigonometric functions [30]. 6.1 Both links flexible Simulation of a two-link arm with both links flexible, as shown in Fig. 3 is performed. The arm is considered hanging freely under gravity and no external torques are applied on it. Both the links have mass, length, and flexure rigidity of 1 m, 5 Kg and 1000 Nm2. The response of the system is obtained with the following initial conditions: \u03b81 = \u221290\u25e6, \u03b82 = 5\u25e6, \u03b8\u03071 = 0 and \u03b8\u03072 = 0, and di,j = 0 and d\u0307i,j = 0, for i, j = 1,2. Simulation results, shown in Fig. 4, match exactly with those given in the literature, namely, in [13]. It is pointed out here that Cyril [13] had observed artificial damping in his simulation results, which are absent using the present formulation" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000731_jmes_jour_1978_020_048_02-Figure16-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000731_jmes_jour_1978_020_048_02-Figure16-1.png", + "caption": "Fig. 16. Squeeze-bearing pedestal", + "texts": [], + "surrounding_texts": [ + "The experimental rig was required to simulate a small gasturbine rotor running at speeds up to 4000 rev/min, supported in rolling-element bearings in series with squeeze films (Fig. la). In accordance with the recent practice of many gas-turbine manufacturers, no retainer springs are used to support the outer races of the rollingelement bearings. The arrangement of the squeeze bearing assembly is shown at C in Fig. la and in Figs lb and c. The inner element of the squeeze-film bearing was a case-hardened and ground steel ring attached to the outer race of a ballbearing. The radial rolling clearance was reduced by interference fits of both the steel ring on the outer race of the bearing, and of the inner race on the rotor shaft. As a result, no radial motion of the outer race relative to the inner race was possible and a negligible amount of pitching of the ring and outer race took place. Dogging of the squeeze-ring assembly was achieved by a simple dowel and clearance hole D, the dowel being attached to the bearing pedestal (Fig. lb). The clearance hole was situated in the squeeze ring and sufficient clearance was provided in the dogging device so as to allow the rotor to move to any part of the squeeze-film clearance space. The cast-iron pedestal consisted of two bearing lands, which were separated by a central circumferential oil-supply groove. The physical dimensions of each land were I = 10.9 111111, D = 127 mm, and c = 0.2082 mm, chosen so as to resemble a typical turbine application. A pressure transducer was fitted into the squeeze ring (Fig. lc) to measure the dynamic oil-film pressure. It was covered by a thin layer of epoxy-resin to ensure a Non-dimensional rotor radial velocity, ddd(wt) Non-dimensional rotor angular velocity, dy/d(wt) Angular measure from line of centres in direction of shaft rotation The MS. of this paper was received at the Institution on 6th December 1977 and acceptedforpublication on 14th March 1978. t School of Engineering and Applied Sciences, The University of Sussex. Graduate ofthe Institution. $ School of Engineering and Applied Sciences, The University of 8 References are given in the Appendix. continuous bearing Of the rotor shaft and mass and fitting of the squeeze-ring assemblies, drive pins and speed measurement disc, the 36 kg rotor was dynamically balanced such that the residual out-ofbalance was less than 3.6 x kgm. The rotor was driven by a drive shaft through a pin-and-wire coupling. lUter Sussex. Fellow of the Institution. Journal Mechanical Engineering Science @ IMechE 1978 Vol20 No 5 1978 at UNIV OF VIRGINIA on June 5, 2016jms.sagepub.comDownloaded from 284 B. HUMES AND R. HOLMES Journal Mechanical Engineering Science @ IMechE 1978 Displacement measurements of the rotor centre were taken from capacitive probes in the horizontal and vertical planes at positions H adjacent to the squeeze-bearing assemblies. Shrouding of the probes, to prevent oil from entering between the measuring surfaces, was achieved by the use of Perspex plates. Initial experimental tests were concerned primarily with providing qualitative information about squeeze-film performance. A known unbalance mass was applied centrally to the rotor and the supply pressure was set to a value of approximately 2 lbf/in2 (1 3.8 kN/mZ), which was sufficient to provide an adequate flow of oil through the bearing. The rotor initially rested at the base of the clearance space and, at low speeds, rolled or slid across the pedestal surface. Further increase in rotor speed resulted in visible lift, until a speed was reached when the amount of lift at the base of the clearance circle remained essentially constant, regardless of further increases in rotor speed within the range 2000-4000 rev/min. The upper part of the orbit, however, was dependent upon rotor speed and the size of the orbit increased, tending to become more and more circular, with increase in speed. The rotor was then held at constant speed and the oilsupply pressure increased in steps, the maximum supply pressure developed being approximately 13 lbf/inz (90 kN/m2). The size of the orbit decreased with increase in the oil-supply pressure and the presence of bubbles in the oil passing from the region of minimum film thickness at the base of the clearance circle suggested that oil-film rupture was occurring. Particular care was taken in photographing the experimental orbit, the squeeze rings being f i s t loaded manually until the ring touched the bearing pedestal, thus establishing the vertical and horizontal positions of the lowest point of the clearance circle. Release of the manual load allowed the rotor to resume the lifted steady-state orbit which was then recorded. 2.1 Squeeze-film pressure recordings Ultraviolet recordings were made of dynamic squeeze-film pressure when the pressure transducer was situated at Vol20 No 5 IY78 at UNIV OF VIRGINIA on June 5, 2016jms.sagepub.comDownloaded from D C negative in an absolute sense, indicating that the oil is temporarily supporting tension. This is not an unknown phenomenon, as the results of Middleton et al. (2), Patrick (3) and Dyer et al. (4) testify. Fig. 3 shows the experimental orbit corresponding to the pressure recordings of Fig. 2. The non-dimensional groups featured are those appearing in the formulation derived in the next section. The small dip within each double peak in pressure recording C coincides with the rotor centre entering the tail, T, of the orbit. There is then a reduction of film pressure as the downward motion of the rotor centre is temporarily restrained. 3 THEORETICAL TREATMENT Fig. 2. Experimental pressure recordings ( 1 division = 10 Ibf/in2 69 kN/m2) mid-land in each of four positions (at intervals of 90\u00b0) around the circumference of the bearing. A typical set of recordings is shown in Fig. 2, in which one division is equivalent to 10 lbf/in2 (69 kN/mz). Inspection of these recordings shows that the largest changes in pressure are recorded by the pressure transducer when it is situated in the lowest part (C) of the bearing, where the minimum film thickness is to be found. In general, the pressure waveforms are predominantly periodic and have a regular form. However, for case C, although the waveform appears to be essentially periodic, there also exist irregular peaks. Maximum negative pressures are about -40 lbf/in2 (-276 kN/m2), with occasional values of about -50 lbf/in2 (-345 kN/m2), and it is interesting to note that a large peak negative value immediately follows a large peak positive value. Experimental observations were also made of the axial pressure distribution for the case of the pressure transducer situated at the base of the'clearance circle. It was found that the pressure was a maximum in the central area of the bearing land, falling to a value equal to the supply pressure at the groove and to a value approaching atmospheric at the end. The most significant features of the pressure recordings are the double peak for case C and the consistent indication of large subatmospheric pressures during about half the pressure cycle for cases C and D. Indeed, this subatmospheric pressure is sometimes so low as to be 3.1 Dynamical equations Fig. 4 shows a ball-bearing squeeze-ring surrounded by its oil-film under the action of a steady load, P, due to the dead weight of the rotor that it supports. Vibration arises from a centrifugal force, P,, due to unbalance. The amplitude of any orbital motion will depend on P, P,, P, and P,. The latter two forces, P, and P,, are those arising hydrodynamically from the squeeze film, the effect of supply pressure being negligible under normal circumstances. The equations governing the motion of the bearing are then ) (1) -P, + P cos y + P, cos ( 0 2 - y) = me(& - $&) - ~ , - ~ s i n y + ~ , s i n ( w t - y ~ ) = m c ( ~ y l + 2 k . r j l ) The main problem in solving .these. equations is to decide on the functions P,, P,(& E, y, y). Squeeze films are extremely short in relation to their diameter, owing to the dimensions of the ball-bearings carrying the rotor. Hence, the short-bearing approximation can be used with justification. The oil film forces P, and Pz may be written where P,.= and P,, are the squeeze-film forces arising from a R film (l), and P,, and P2, are those arising from a full 2a film. The former are based on the assumption that the squeeze-film ruptures over the clearance region in which the squeeze-film pressure is less than atmospheric. Hence the factor b is introduced to cater for the generation of a certain amount of subatmospheric pressure. The squeezefilm forces in the subatmospheric region are then directly proportional to these subatmospheric pressures. By altering the value of b, the theoretical orbit can be adjusted to Journal Mechanical Engineering Science @ IMechE 1978 Vol20 No 5 1978 at UNIV OF VIRGINIA on June 5, 2016jms.sagepub.comDownloaded from 286 B. HUMES AND R. HOLMES ascertain whether similarity with the appropriate experimental orbit can be obtained. The component forces P I,n and P , , are given by in which p may be obtained by solving the short-bearing form of the Reynolds equation for a squeeze-film, namely, From this equation, the squeeze-film pressure, p, is given by p = 6qz (Z - z)(i case + &E sin@/cyi + E C O S ~ ) ~ Substitution into equations (3) and the use of standard integrals (5) gives where g, = - 2 ~ cOs3 e,(i - ~2 cosz e,)-2 g, = E sin 8, [3 + (2 - 5.9) cos2 ell (1 - ~ 3 - 2 x (1 - c2 C O S ~ el)-, + a( 1 + 2 ~ 3 (1 - ~2)-512 g3 = E sin 8, (1 - 2 cos2 8, + e2 cosz 0,) (1 - e2)-' x (1 - c2 cps2.0,)-2 + a(1 - $)-3'2 tan e, = --E/EW a = - + tan-'[& sin el( 1 - E ~ ) - \" ~ I The component forces P, , and P,, are obtained by putting 8, equal to zero and 0, equal to 27t in equations similar to (3), from which K 2 7tq~13 (1 + 2 ~ 3 . P I , = - * E c2 (1 - & 3 ' / 2 and 7tqRP EV P,,= -' c2 (1 - &2)3'2 3.2 Results of computations The dynamical equations (1) may be made nondimensional by writing ) (4) -9, + 9 ' 0 s w + yc COS(0f - y)= E\" - -9, -9 sin w + 9, sin (cot - w ) = EY\" + 28' w' where 9 = P/mcco2 and 9= =PJmcoZ Equations (4) were solved using the Runge-KuttaMerson step procedure and some of the results will be outlined. Journal Mechanical Engineering Science Q IMechE 1978 Vol20 No 5 1978 at UNIV OF VIRGINIA on June 5, 2016jms.sagepub.comDownloaded from THE B Viscosity (CP) VIBRATION PERFORMANCE OF SQUEEZE-FILM BEARINGS 9 9, 287 Speed (revhin) 3 100 3 100 3100 2520 2520 2520 2520 3250 3 100 0.12 31 0.12 31 0.12 50 0.15 33 0.10 0.68 0.73 Fig. No. and locus It is known from static considerations that if P, is put equal to zero, the squeeze-film exhibits no load-carrying capacity under the action of a static load, P. If, however, an unbalance load is added, it is instructive to investigate the journal-centre locus to determine whether a steadystate orbit is achieved. Consider, first, the full-cylindrical squeeze-film, with oilfilm limits of zero and 2x, that is, b = 1. Fig. 5a shows the journal-centre locus corresponding to yc = 2.26, /3 = 0.61 and 9 = 0.90; no steady-state orbit develops and the journal centre simply spirals down to the bottom of the clearance space. Now consider the half-cylindrical Locus .9 1 0.74 2 1-06 3 1.47 Fig. 7a squeeze-film, with oil-film limits of zero and 71, for which b = 0 . Fig. 5b shows the locus achieved for the same values of yc, /3 and 9. A definite load-carrying capacity is exhibited by the presence of the steady-state orbit. Fig. 5a corresponds to the case where the generation of subatmospheric pressures is permitted without limit, while Fig. 5b corresponds to the case where no subatmospheric pressures are allowed. Finally, if we consider the dynamics to be represented by values of b between 0 and 1, it could be expected that the orbit of the rotor centre will take up a position intermediate between the positions shown in Figs 5a and b. Fig. 6 shows such orbits for two further values of b of 0.40 and 0.45. Comparison of Figs. 3 and 6 shows that, for b = 0.45, fair agreement as to orbit size and disposition is obtained. The feasibility of relying on squeeze-films to support such machine elements as gas-turbine rotors is thus shown to be consistent with a theoretical analysis that allows the oil-film to generate a pressure which is considerably below atmospheric pressure before rupture. To ascertain whether b = 0.45 is representative over a range of the operating parameters, hrther comparisons of predicted and computed orbits were made. The values of the non-dimensional parameters used are shown in Table 1, in which 9, has been made greater than 9 to enable distinctive orbits to be obtained. Such a condition might arise in practice if, say, a blade were lost from a rotor. Journal Mechanical Engineering Science Q IMechE 1978 Vol20 No 5 1978 at UNIV OF VIRGINIA on June 5, 2016jms.sagepub.comDownloaded from 288 B. HUMES AND R. HOLMES The experimental and computed orbits for these sample cases are shown in Figs 7a, b and c. In each figure, three sets of orbits are shown. Set A shows the computed orbits for the case of a short n film, that is, b = 0, while set B shows the predicted orbits obtained by allowing the negative pressure to be defined by the factor b = 0-45. The corresponding experimental orbits are shown in set C and are accurate reconstructions of oscilloscope traces. For all the comparisons made, of which Figs 7a, b and c are typical, sets B showed much better agreement with the experimental sets C than did sets A. It should be pointed out, however, that the factor b probably varies depending on the application and is likely to be governed by the average pressure due to the static load. In this case, the value was about 10 lbf/in2 (69 kN/m?. A further item of interest is the way in which the force transmitted to the engine frame varies throughout one rotor revolution. The transmitted force is the resultant of the film forces, P, and P,, and may be easily computed (1). Large vibration orbits and orbits which feature a pronounced tail should be avoided in practice. In the former, the centrifugal force, and hence the transmitted force, become appreciable, while in the latter the rapid decelerations and accelerations in the vicinity of the tail lead to sudden large changes in the transmitted force to the engine frame." + ] + }, + { + "image_filename": "designv11_7_0000222_icar.2005.1507412-Figure10-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000222_icar.2005.1507412-Figure10-1.png", + "caption": "Fig. 10. Example of kinematic structures of fully-isotropic PMSM with the four actuators mounted on the fixed base.", + "texts": [ + " These two joints have parallel axes and their direction is perpendicular to the other revolute joints of leg A4. The first revolute joint is actuated and q4 represents the rotation angle. The 4375 structural solutions set up in this way respect conditions (4-13) but the fourth actuator is not on the fixed base. Other 4375 solutions of fully-isotropic PMSMs with the four actuators mounted on the fixed base can be set up from the previous fully-isotropic solutions by replacing the kinematic chain with two revolute parallel joints in A4-leg by an extensible double parallelogram De Roberval scale-type (Fig. 10). We can see that in this way the actuated revolute joint in the fourth leg can also be adjacent to the fixed base. The Jacobian matrix of the linear maping (16) of the 8750 fully-isotropic PMSMs is the identity 4\u00d74 matrix throughout the entire workspace. A one-to-one correspondence exists between the actuated joint velocity space and the external velocity space of the moving platform ( x 1v q , y 2v q , z 3v q and y 4q ). Moreover the 8750 solutions of fullyisotropic PMSMs are singularity-free throughout the entire workspace" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000395_0094-114x(80)90004-x-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000395_0094-114x(80)90004-x-Figure3-1.png", + "caption": "Figure 3. Steady state crank stress of crank rocker mechanism.", + "texts": [], + "surrounding_texts": [ + "To apply the above method of analysis in the steady state analysis of a mechanism, a computer program has been written. Several subroutines are used to carry out the series multiplications, and to form eqns (19) and (20) (from eqns (14) and (16) respectively) automatically within the computer for any value of hj and n. It may be noted here that, in spite of large size of the matrices, the last two operations take very little computer time because no multiplication is involved. The details of the computer program may be found in [10]. The following three mechanisms are selected for this section. The examples, described below, have been solved by retaining all the terms in eqn (14) and by using 13 terms in each series. Mechanism 1 A crank rocker mechanism having parameters same as those used in [1] for a similar mechanism except the damping for which the factors sr~ = 0.05j, j = 1 . . . . . 6 are used in eqn (15). Each element is treated as a single element. Mechanism 2 A slider crank mechanism having parameters same as those used in [1] for a similar mechanism except the damping for which the factors ~[ = 0.2 and ~ = 0.8j for j = 2, 3 . . . . 6 are used in eqn (15). The connecting rod is divided into two elements. Mechanism 3 Same as Mechanism 2 described above except for the following changes: connecting rod length = 7.2 in., piston weight = 8.1792 lbs; damping and the gas force are neglected. Application of the present method of analysis in mechanism 1 gives the rotation u9 (in radians) at the coupler-end of the follower in the following form ~9 = 10-3(0.0233 + 8.12 cos 02 + 3.31 cos 202 + 2.29 cos 302 +0.481 cos 402 - 1.59 cos 602 + 9.86 sin 02 + 7.5 sin 202 + 5.81 sin 302 + 4.58 sin 402 + 1.21 sin 502 +0.307 sin 602) where 02 is the crank angle. 208 % 8 RPM 6 0 0 Similar expressions are also obtained for the displacements for the other co-ordinates of the mechanism. Figures 3-5 show the variation of the bending stresses (due to the displacements alone) at the middle of the crank, follower and coupler. Sadler and Sandor [6] solved the same problem following the lumped mass parameter approach. The nature of the variation of the stresses shown in these figures will not be the same as that of the deflections shown in [6] because the displacements shown in [6] are total displacements and the rigid body displacements do not take part in straining the nember. However the nature of variation of the stress at the middle point of the follower shown in Fig. 5 is almost identical with that of the deflection at the same point found by Sadler and Sandor. The same problem has been solved considering the crank to be instantaneously clamped and the results are shown in Figs. 4 and 5 by the dotted curves. The figures show that the analysis of a mechanism by considering it a structure greatly alters the steady state characteristics and therefore should not be adopted in practice. Mechanism 3 has also been solved by this approach and the deflections of the middle point of the connecting rod for one cycle are shown by the solid curve in Fig. 6. Comparing this figure with the corresponding figure for transient response [1,7], it becomes clear that the steady state pattern may be completely different from the transient part. The dotted curve in Fig. 6 shows the deflections of the middle point of the connecting rod of mechanism 2 for the crank speed equal to 0.3 times the first natural frequency of the connecting rod considered as a linged beam. The steady state deflection in this case is found to be 0.79 in. to the value of 0.72 in. obtained by Viscomi and Ayre[7]. Almost 15 rain of computer time in IBM 7044 is needed to obtain the steady state solution by using the conventional finite element methods. This computer time is reduced to 2 min when the present method of analysis is employed. In case of mechanisms where the total number of coordinates is large, this reduction in computer time is even much greater. Conclusions A new method of analysis for obtaining the steady state displacements and stresses of a mechanism with elastic links is presented in this paper. The method of analysis is a combination of the rigid body harmonic analysis of a mechanism with a novel application of the finite element methods. Several numerical examples are solved to show the application of the method of analysis. From the numerical examples it is seen that the steady state characteristics differ from the transient characteristics considerably. It is shown that this new method is computationally more efficient than the existing finite element methods by at least an order of megnitude. The efficiency further increases when the size of the matrices is large. Compared to the conventional finite element methods, the present method of analysis has also other distinctive features[10]. The method of analysis presented here is eminently suitable for determining the stability zones and the frequency response of a flexible methanism[10]. Work in this direction has also been undertaken. References I. P. K. Nath and A. Ghosh, Kineto-elastodynamic analysis of mechanisms by finite element method. Mech. Mach. Theory 15(3), 199-211 (1980). 2. R. C. Winfrey, Elastic link mechanism dynamics. Trans. ASME, J. Engng Ind. 93, 268--272 (1971). 3. A. C. Erdman, G. N. Sandor and R. C. Oaknberg, A general method for KED analysis and synthesis of mechanisms. Trans. ASME, J. Engng Ind. 94, 1193-1205 (1972). 4. A. G. Erdman, I. Imam and G. N. Sandor, Applied KED, Proc. 2rid OSU Appl. Mech. Con[., Stillwater, Oklahama (1971). 5. 1. Imam, G. N. Sandor and S. N. Kramer, Deflection and stress analysis in high speed planar mechanisms with elastic links. Trans. ASME, J. Engng Ind. 96, 411419 (1974). 7. B. V. Viscomi and R. S. Ayre, Nonlinear dynamic response of elastic slider crank mechanism. Trans. ASME, ]. Engng Ind. 93, 251-262 (1971). 8. P. W. Jasinski, H. C. Lee and G. N. Sandor, Vibrations of elastic connecting rod of a highspeed slider crank mechanism. Trans. ASME, I. Engng Ind. 93, 636--644 (1971). 9. B. M. Bhagat and K. D. Willmert, Finite element vibration analysis of planar mechanisms. Mech. Mach. Theory 11(1), 47-71 (1976). 10. P. K. Nath, Kineto-elastodynamic analysis of high-speed mechanisms. Ph.D. Thesis, Indian Institute of Technology, Kanpur (1976). 11. F. Freudenstein, Harmonic analysis of crank and rocker mechanisms with applications. Trans. ASME, J. Appl. Mech. 81,673--675 (1959). 12. J. P. Sadler and G. N. Sandor, Kineto-elastodynamic harmonic analysis of four-bar path generating mehcanisms. Pres. l lth ASME Conf. on Mechanisms. ASME Paper No. 70-Mech-61, Columbus, Ohio, 1-4 Nov. (1970). t3. A. T. Yang, Harmonic analysis of spherical four-bar mechanisms. Trans. ASME, J. Appl. Mech. $4, 683-688 (1%2). 14. B. J. Lazan, Damping of Materials and Members in Strucutural Mechanics. Pergamon Press, New York (1%8L 15. V. V. Bolotin, The Dynamic Stability of Elastic Systems. Holden-Day, Inc., San Francisco, London, Amsterdam (1%4). 16. A. Ye. Kobrinski, Mechanisms with Elastic Couplings--Dynamics and Stability. Nauka Press, Moscow 11964): NASA Technical Translation, NASA TT F-534, June (1%9). 17. A. Ralston, A First Course in Numerical Analysis. McGraw-Hill, New York (1%5). 18. J. Denavit, R. S. Hartenberg, R. Razi and J. J. Uicker Jr., Velocity, acceleration and static-force analysis of spatial linkages. Trans. ASME, J. Appl. Mech. 32, 903-910 0%5)." + ] + }, + { + "image_filename": "designv11_7_0000352_j.mbs.2007.01.002-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000352_j.mbs.2007.01.002-Figure1-1.png", + "caption": "Fig. 1. (a) A schematic diagram of a synovial knee joint. (b) A simplified model for a synovial knee joint.", + "texts": [ + " The flow problems discussed by Stokes indicate the significant effects of couple stresses and also give the experiments measuring various material constants. The role of size effect in couple-stress fluid is evident which is not present in the non-polar fluid. The effect of couple stresses is noticeable for small values of the dimensionless couple-stress parameter s \u00bc h0\u00f0l=g\u00de 1 2 where, h0 is the typical dimension of the flow geometry. The geometry and co-ordinates of the problem are shown in Fig. 1(b), which is the simplified form of synovial knee joint (Fig. 1(a) [19]). The bone ends are covered with articular cartilage to prevent natural abrasion, which are in a sac containing fluid for lubricating two contiguous surfaces. The joint cavity is completely enclosed by a tough fibrous capsule together with the muscles, ligaments, etc. The inner lining of this capsule, the synovial membrane secretes a highly lubricating, viscous non-Newtonian fluid. This paper deals with the compression of an impermeable rigid rough plate and there is a thin layer of fluid over a thin layer of poroelastic material" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003151_0954406212468407-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003151_0954406212468407-Figure3-1.png", + "caption": "Figure 3. The two-stage planetary gearbox: (a) the planetary gearbox with four vibration sensors labeled as LS1, HS1, LS2 and HS2; (b) the structure of the second stage planetary gearbox (including four planet gears, one sun gear, and one ring gear).", + "texts": [ + " A relatively larger parameter 2 weights the correlation term more heavily and thus could produce a feature subset with less redundancy. The proposed multi-criterion algorithm for feature selection is summarized in Table 1. The planetary gearbox test rig shown in Figure 2 was designed to investigate diagnostic systems for gear faults. The test rig has a 15 kW (20 hp) drive motor, a one-stage bevel gearbox, a two-stage planetary gearbox, two speed-up gearboxes, and a 30 kW (40 hp) load motor. We study only the second stage planetary gearbox shown in Figure 3. We created two types of gear faults including crack and tooth missing using electro discharge machining (EDM). Crack may develop due to repetitive loading and impurity within the gear material. The tooth missing damage mode is very close and sometimes is equal to gearbox failure. The frontier of gearbox condition monitoring research is on early crack and/or pitting damage detection. The objective of such research work and the corresponding engineering practice is to prevent major failures of the gearbox", + " We did experiments for eight modes that include the seven types of gear faults in Table 2 and a mode of no fault. From the viewpoint of classification, it is an eight-class classification problem. For the experiment of each case, vibration data were collected with a sampling frequency of 5 kHz through two highsensitivity sensors (HS1 and HS2) mounted on the housing of the second stage planetary gearbox and two low-sensitivity sensors (LS1 and LS2) mounted on the housing of the first stage planetary gearbox (Figure 3(a)). The raw data was 10min long. It was further spliced into several time records of equal length that have to cover the lowest frequency component of interest for gear fault diagnosis. The lowest frequency is the carrier frequency of the second stage planetary gearbox. Four time records are available in one 10min raw data record. We did one experiment under 20 working conditions with varying loads and speeds. In all, there are 80 time records available for each gear mode. In this section, we apply the proposed multi-criterion fusion framework to select significant features for gear fault diagnosis" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000002_j.1600-0498.1985.tb00801.x-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000002_j.1600-0498.1985.tb00801.x-Figure1-1.png", + "caption": "Figure 1. (Based on Figure 9, Trait6 (1743)).", + "texts": [ + " were impressed alone on the bodies they would retain these motions without interfering with each other; and that if the motions a$,x were impressed alone, the system would remain at rest; it is clear that a.6,; will be the motions that the bodies will take by virtue of their action. [1743,5&51] [1758,73-751 D\u2019Alembert appears to have derived the idea for his principle from the mechanics of impact, a subject which figures prominently in his discussion of the foundations of dynamics in Part One. In the chapter \u201cOn Motion Destroyed or Changed by Obstacles\u201d he considers a \u201chard\u201d particle which strikes obliquely a fixed impenetrable wall (Figure 1). (The concept of \u201chard\u201d body is a central one in d\u2019Alembert\u2019s mechanics. A hard body is impenetrable and non-deformable. Such bodies would today be treated analytically as perfectly inelastic.) Decompose the particle\u2019s pre-impact velocity u into two components v and w parallel and perpendicular to the wall. D\u2019Alembert argues using a form of the principle of sufficient reason that w must be destroyed. (Assume the particle strikes the wall with perpendicular velocity w. Clearly no forward motion is possible" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000312_s11071-005-9016-6-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000312_s11071-005-9016-6-Figure2-1.png", + "caption": "Figure 2. Coordinate systems of a rigid body.", + "texts": [ + " The traction forces in a locomotive are usually generated by diesel engine or electric traction motors that produce torque and transmit it to the wheelset using a gear box whilst the wagons receive the traction force through pulling or pushing action of the mechanical couplers. In the locomotives the excessive traction torque can make the wheelset rotate without any longitudinal motion. This condition is referred as \u2018roll-slip\u2019 that becomes a subject of interest in the locomotive drive simulation as reported in [16]. Figure 2 shows a rigid body i in three-dimensional space represented by a coordinate system XYZ known as the inertial reference frame (IRF) with its origin fixed in space and time. The position of an arbitrary point Pi in the body i (see Figure 2) can be represented as ri = Ri + Ai u\u0304i (4) where Ri is the global position vector of the origin of the body reference frame, Ai is the transformation matrix (from the body coordinates system to the global coordinate system), and u\u0304i is the position vector of the point Pi with reference to the body coordinate system [17]. Ai , a 3 \u00d7 3 transformation matrix, and Ri and u\u0304i vectors are respectively given by Ai = \u23a1\u23a2\u23a3 1 \u2212 2(\u03b82)2 \u2212 2(\u03b83)2 2(\u03b81\u03b82 \u2212 \u03b80\u03b83) 2(\u03b81\u03b83 + \u03b80\u03b82) 2(\u03b81\u03b82 + \u03b80\u03b83) 1 \u2212 2(\u03b81)2 \u2212 2(\u03b83)2 2(\u03b82\u03b83 \u2212 \u03b80\u03b81) 2(\u03b81\u03b83 \u2212 \u03b80\u03b82) 2(\u03b82\u03b83 + \u03b80\u03b81) 1 \u2212 2(\u03b81)2 \u2212 2(\u03b82)2 \u23a4\u23a5\u23a6 (5) Ri = [ Ri 1 Ri 2 Ri 3 ]T (6) u\u0304i = [ ui 1 ui 2 ui 3 ]T (7) where \u03b8 i 0, \u03b8 i 1, \u03b8 i 2, \u03b8 i 3 are Euler parameters describing rotational coordinates \u03b8 i that define the body orientation as shown in Equation (8)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000041_6.2005-6392-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000041_6.2005-6392-Figure3-1.png", + "caption": "Figure 3. A VSCMGs system with pyramid configuration at \u03b3 = [0, 0, 0, 0]T .", + "texts": [ + " In the previous section, the simplified equations of motion, given by (2), with several assumptions were used for the adaptive control design, but in this section the complete nonlinear equations of motion, given in Eq.(1), and the acceleration steering law derived in Ref. 8 are used to predict and validate the performance of the proposed controllers under realistic conditions. The parameters used for the simulations are chosen as in Table 1. We also assume a standard four-VSCMG pyramid configuration, as shown in Figure 3. The nominal values of the axis directions at \u03b3 = [0, 0, 0, 0]T in this pyramid configuration are An s0 = [s1, s2, s3, s4] = \u23a1 \u23a2\u23a3 0 \u22121 0 1 1 0 \u22121 0 0 0 0 0 \u23a4 \u23a5\u23a6 , (46) An t0 = [t1, t2, t3, t4] = \u23a1 \u23a2\u23a3 \u22120.5774 0 0.5774 0 0 \u22120.5774 0 0.5774 0.8165 0.8165 0.8165 0.8165 \u23a4 \u23a5\u23a6 . (47) 7 of 12 American Institute of Aeronautics and Astronautics The (unknown) actual axis directions used in the present example are assumed as\u2217 As0 = \u23a1 \u23a2\u23a3 0.0745 \u22120.9932 \u22120.1221 0.9901 0.9919 \u22120.1024 \u22120.9911 \u22120.1033 0.1033 \u22120" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001982_s0022112010000364-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001982_s0022112010000364-Figure2-1.png", + "caption": "Figure 2. The model problem. The soft substrate is deformed by the hydrodynamic, electric and van der Waals intermolecular forces between the sphere and wall surfaces. Cases \u03b2 = 0 and \u03b2 = \u03c0/2 represent corkscrew and purely rolling motions, respectively.", + "texts": [ + " Appendix A provides a mathematical description of the substrate mechanics, and Appendix B analyzes the simpler problem of the elastostatic adhesion mechanism of a stationary sphere produced by surface bifurcations on the soft substrate. A rigid spherical particle of radius a and dielectric constant \u03b5s translates at constant velocity U along the x axis, and rotates at constant angular velocity \u2126 about an axis orientated at an arbitrary azimuth angle \u03b2 with respect to the translation axis, with both axes parallel to the unperturbed wall surface as depicted in figure 2, in this way representing a general drift motion on the horizontal plane. The sphere is immersed in a Newtonian incompressible fluid, which corresponds to an aqueous symmetric electrolyte of density \u03c1, equal to that of the sphere, viscosity \u00b5, ionic valency zi , ionic diffusion coefficient Di and dielectric constant \u03b5f . The clearance or minimum gap distance between the sphere and the unperturbed wall surface is \u03b4 = \u03b5a, with \u03b5 1 a small parameter. The ionic concentration in the bulk electrolyte far from the sphere is denoted by ci . The soft substrate comprises an elastic layer of thickness , dielectric constant \u03b5w , Young modulus E and Poisson coefficient \u03bd, and is bonded to a rigid motionless substrate. The ratio of the characteristic surface deflection Hc, produced by the hydrodynamic stress, to the minimum clearance \u03b4 is defined as the softness parameter, elastoviscous number or hydrodynamic compliance \u03b7 = Hc/\u03b4. The motion can be considered steady in the reference frame shown in figure 2 as long as the time scale of the sphere motion, \u03b4/U , is much longer than the viscous time scale, \u03b42/\u03bd, which is also much longer than the substrate response time scale, \u03b4/c, where c is the speed of sound in the substrate. Then, the Reynolds numbers of translation and rotation are small, ReU = \u03c1Ua/\u00b5 1 and Re\u2126 = \u03c9ReU 1, so that the flow can be described by the Stokes equations to leading order. In this formulation, \u03c9 =\u2126a/U is a kinematic parameter that measures the ratio of the rotational to the translational peripheral velocities", + "5) In these variables, a regular expansion in powers of \u03b5 yields, to leading order, the conservation equations 1 r \u2202 \u2202r (rvr ) + 1 r \u2202v\u03d5 \u2202\u03d5 + \u2202vz \u2202z = 0, \u2202P \u2202r = \u22022vr \u2202z2 , 1 r \u2202P \u2202\u03d5 = \u22022v\u03d5 \u2202z2 , \u2202P \u2202z = 0, \u23ab\u23aa\u23aa\u23ac \u23aa\u23aa\u23ad (2.6) subject to vr = \u2212 cos \u03d5 + cos(\u03d5 \u2212 \u03b3 ) V(\u03c9, \u03b2) , v\u03d5 = sin\u03d5 \u2212 sin(\u03d5 \u2212 \u03b3 ) V(\u03c9, \u03b2) , vz = \u2212r cos\u03d5 + r cos(\u03d5 \u2212 \u03b3 ) V(\u03c9, \u03b2) , (2.7) on the sphere surface z = h0(r), and vr = \u2212cos(\u03d5 \u2212 \u03b3 ) V(\u03c9, \u03b2) , v\u03d5 = sin(\u03d5 \u2212 \u03b3 ) V(\u03c9, \u03b2) , vz = \u03b7\u2207\u22a5H \u00b7 ex V(\u03c9, \u03b2) , (2.8) on the wall surface z = \u2212\u03b7H . In this formulation, \u03b8 is the physical azimuth angle (measured from the x axis as shown in figure 2), and \u03d5 = \u03b8 + \u03b3 (2.9) is a reduced angle, with \u03b3 (\u03c9, \u03b2) as a phase angle of the gap pressure distribution given by \u03b3 (\u03c9, \u03b2) = arctan ( \u03c9 cos \u03b2 1 + \u03c9 sin\u03b2 ) , (2.10) with \u2212\u03c0/2 \u03b3 \u03c0/2. For a purely rolling motion, \u03b2 = \u03c0/2 and \u03b3 = 0, so that \u03d5 = \u03b8 and the pressure distribution is dominated by the entrainment of fluid taking place along the \u03b8 = 0 axis. For corkscrew motion, \u03b2 \u2192 0 and \u03b3 \u223c arctan \u03c9, so that as \u03c9 increases the peak pressures are expected to be increasingly dominated by the lateral fluid entrainment enhanced by the rotational motion, shifting the pressure peaks towards the line \u03b8 = \u2212\u03b3 " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001568_s0091-679x(08)92009-4-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001568_s0091-679x(08)92009-4-Figure3-1.png", + "caption": "Fig. 3 Schematic of the perfusion chambers used in the microtubule sliding disintegration assay. A simple perfusion chamber can be made using a microscope slide and cover slip. A 22 40mm cover slip is affixed to the microscope slide using two thin strips of double stick tape as spacers, leaving the ends of the cover slip protruding from each side of the slide. A thin coating of valap (1:1:1 mixture of Vaseline, lanolin and paraffin wax) is placed on one side of the cover slip to make a well for loading buffers into the perfusion chamber. The other side is left open to be accessible to capillary filtration with filter paper.", + "texts": [ + " The method, described below, is routinely used to measure sliding disintegration in Chlamydomonas axonemes for an indirect assessment of axonemal 9. Phosphoregulation of Flagellar Motility 139 dynein function. It is based on the method of Okagaki and Kamiya (1986) with the modifications in buffer conditions described earlier (Habermacher and Sale, 1996, 1997; Howard et al., 1994). For these experiments, simple perfusion chambers can be made using standard microscope slides, cover slips, double stick tape, and a sealant such as valap (a 1:1:1 mixture of Vaseline, lanolin, and paraffin) (Fig. 3). Briefly, two narrow strips of double stick tape are affixed to a microscope slide, serving as spacers for a cover slip which is laid on top of the tape. One side of the cover slip is coated with a U-shaped line of valap, forming a reservoir that is used to load the perfusion chamber. Perfusion through the chamber is facilitated by adsorption from the opposite end of the chamber using strips of filter paper. Flagella are isolated from either vegetative or gametic cells by the dibucaine method described by Witman (1986). Isolated flagella can be stored on ice in a buffer containing 10mM HEPES, pH 7.4, 5mM MgSO4, 1mM DTT, 0.5mM EDTA, 5% polyethylene glycol 8000, and 25mM potassium acetate. Flagella are demembranated in buffer containing 0.5% Nonidet-P40 and added to a perfusion chamber (Fig. 3). We typically do not sonicate the flagella, as we have found no difference in sliding velocities between sonicated and unsonicated flagella. If sonication is desired, a Kontes cell disrupter set at a power of 6 for 30 s typically yields transversely fractured flagella about one-third the original length. Flagellar segments are then demembranated using the method described above and added to a perfusion chamber. Nonsticking axonemes are washed away in buffer without detergent. Microtubule sliding is initiated by addition of buffer containing 1mM ATP and 3 \u00b5g/ml subtilisin AType VIII protease" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000929_j.commatsci.2008.07.033-Figure7-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000929_j.commatsci.2008.07.033-Figure7-1.png", + "caption": "Fig. 7. Temperature distribution during discontinuous welding.", + "texts": [ + " The re-heating except for the next weld could be negligible and the workplace gradually cools to the room temperature. The thermal cycles of the three welds are similar according to the symmetry of the weld locations. The simulated thermal cycles of welds Nos. 1\u20133 from the optimal parameters of the composite heat source are presented in Fig. 6d; it could be great coherence between the simulated results and infrared results. The temperature distribution during the discontinuous welding is illustrated in Fig. 7. Note that the isotherms and welding bead are symmetrical with respect to the welding path. According to this, the transient temperature distribution varies with respect to the moving arc. A gradual change in the temperature distribution represents a typical change due to the moving heat source. The temperature near the weld bead and heat-affected zone rapidly changes with the distance from the centre of the heat source because of the locally concentrated heat source. Therefore, the highest temperature is limited to the domain of the heat sources from which lower temperature zones fan out" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003965_tmech.2014.2316007-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003965_tmech.2014.2316007-Figure5-1.png", + "caption": "Fig. 5. Three collisions by the kinematical interference of a biped robot: (a) thigh collision when the swing foot rotates, (b) foot collision because of the comparatively (relatively) small stride compared to its foot size, (c) thigh- and foot collisions when the rotated leg come back by changing a direction at next step.", + "texts": [ + " For example, the contact area between the foot sole and the ground depends significantly on the foot contact stability and foot motion during the contact, which in turn depends on the motion servo controls. In order to estimate the friction torque on the ground, the authors recommend that a database system be built based on the locomotion experience on many different terrain surfaces. Most biped robots have geometrical limitations because their legs are thicker and their feet are proportionately larger compared to a human being. Three typical examples are showing in Fig. 5. The effective rotation of a biped robot requires not only a large rotational angle but also a noncollision rotational motion. So far, the theory and trajectory planning method for a quick turn using foot slip have been explained. When the robot turns with a foot slip, it can take one of two different strategies, which differ in what is or is not done just before the turn ends. At the end of the slip-turn, if no further actions are taken, the orientation of the lower body is not aligned with that of the upper body of the robot because of the initial turning motion at the yaw joint" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003989_j.mseb.2012.03.001-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003989_j.mseb.2012.03.001-Figure5-1.png", + "caption": "Fig. 5. Test rig overview with instrumentation.", + "texts": [ + ", N} the Shannon ntropy is defined as shown in Table 1 [15]. For events with probaility around 0 or 1, P(xi) ln P(xi)2 converges to zero and the entropy s minimum, while for random signals with uniform PDF such as ure noise, the entropy is maximum. . Experiment system The experiment system consisted of a motor, a flexible coupling, olling element bearings (NSK6200), three bearing housings, a liftng tool, and a shaft with a crack. The crack was seeded by wire ut to a depth of 0.5 mm on a shaft made from SM45C (Table 2). s shown in Fig. 5, the crack was located 5 mm from the second xample of the frequency division [14]. supporting bearing, and the overhang bearing was lifted 6.5 mm 1686 D. Gu et al. / Materials Science and Engi neering B 177 (2012) 1683\u2013 1690 wideband-type sensor with a relative flat response within the frequency range of 100 kHz to 1 MHz. AE signals were pre-amplified at 60 dB, and the output from the amplifier is collected by a commercial data acquisition card with a 5-MHz sampling rate during the test. A threshold level of 30 dB, which was determined through a pre-test using a regular shaft under the same conditions, was employed for this investigation" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001850_icmech.2009.4957202-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001850_icmech.2009.4957202-Figure2-1.png", + "caption": "Fig. 2. Planar, redundantly actuated mechanism", + "texts": [ + " The fact that Oa = [6, 6F yields 8q _ [0 1 0 0 0 0 0 0] T 80a - 0 0 0 0 1 0 0 0 Since the elements of x = [XE' YE, \u00a2E]T are not independent, there are three ways to choose z (see TABLE I). E.g. if z = rYE, \u00a2El T is chosen the vector of independent coordinates results to 0 = [7j;1, 6, 7j;2, 7j;3, 6, XE]T. The matrix K == E(8X8) and matrix JT is defined as follows: where Ii = (3i - 7j;i (for i = 1,2,3). Due to space limitations the left hand side of the dynamic equations after the reducing progress are not presented here. In this example, we exemplarily present the redundantly actuated planar 3RRR robot shown in Fig. 2 [21]. This robot has only two DOFs but is controlled by three actuators. The coordinates are chosen as follows q [81, 7j;1, 82, 7j;2, 83, 7j;3, XE, YE]T, Z == X = [XE' YE]T, 0= [81, 7j;1, 82, 7j;2, 83, 7j;3F and Oa = [81, 82, 83F. The six constraint equations of the robot have the following form (for i = 1,2,3): = { XAi + lilC!}i + li2 C!}i+'ljJi - XE }. YAi + lilS!}i + li2 S!}i+'ljJi - YE In addition, we have [ 10000000]T 8q = 0 0 1 0 0 0 0 0 80 a 0 0 0 0 1 0 0 0 It can be pointed out that the matrix K == E(8X8)' Further more, det(" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003720_iros.2012.6386085-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003720_iros.2012.6386085-Figure4-1.png", + "caption": "Fig. 4. Shape and grasping points model", + "texts": [ + " Because we assign the highest priority to the reaction force control in the free subspace, we use the same parameter for all different directions. We determined kv based on the arm\u2019s reachability. We tuned mv and dv by trial and error using the real robot. We set Ku to 0.5. Using these parameters, the response of the update is more gradual than the response of reaction force control. Kzmp is diagonal(0.9 0.1) and Km is 0.9. We performed the door-opening (Fig.8) and drawer-pulling experiment (Fig.11) to evaluate the following capability to the velocity command and reference forces profiles. 1) Door and Drawer Model: Fig.4 shows the 3D shape models and grasping point models of a door and a drawer. The black lines represent x,y,z axes of the door coordinate system and the intersection is the origin of the door and drawer coordinate system. The red arrow shows grasping points. Table.I shows detailed values of the grasping points and the hand positions. All values are [m]. The hand positions are the difference between the foot middle coordinate and the hand positions used in (3). Fig.5 shows the kinematics model (\u03c8h() and \u03c8m()) of the door and the drawer" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003534_978-1-4419-6022-1-Figure8.5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003534_978-1-4419-6022-1-Figure8.5-1.png", + "caption": "Fig. 8.5 Cut-away view showing internal components of Ocean Optics USB4000 miniature spectrometer. 1 \u00bc fiber connector, 2 \u00bc slit, 3 \u00bc filter, 4 \u00bc collimating mirror, 5 \u00bc grating, 6 \u00bc focusing mirror, 7 \u00bc detector collection lens, 8 \u00bc detector (1D CCD array), 9 \u00bc filter, 10 \u00bc quartz window (optional). Accessed in August 2011 from http://www.oceanoptics.com/technical/ USB4000operatinginstructions.pdf, # Ocean Optics 2008, reprinted with permission", + "texts": [ + " Biosens Bioelectron 20:2512\u20132516 Koschwanez H, Reichert W (2007) In vitro, in vivo and post explantation testing of glucose- detecting biosensors: Current methods and recommendations. Biomaterials 28:3687\u20133703 Skoog DA, Holler FJ, Nieman TA (2006) Principles of instrumental analysis, 6th edn. Saunders College, Philadelphia Miniature Spectrometer (Section 8.2) Ocean Optics (2008) USB4000 fiber optic spectrometer installation and operation manual. http:// www.oceanoptics.com/technical/ USB4000operatinginstructions.pdf. p. 21. [Fig. 8.5] Ocean Optics (2012) CHEMUSB4-UV\u2013VIS spectrophotometer http://www.oceanoptics.com/products/chem4uvvis.asp. [Figs. 8.6 and 8.13] 138 8 Spectrophotometry and Optical Biosensor Optical glucose sensor (Section 8.3) Harborn U, Xie B, Venkatesh R, Danielsson B (1997) Evaluation of a miniaturized thermal biosensor for the determination of glucose in whole blood. Clin Chim Acta 267:225\u2013237 Luong JHT, Male KB, Glennon JD (2008) Biosensor technology: technology push versus market pull. Biotechnol Adv 26:492\u2013500 Newman J, Turner A (2005) Home blood glucose biosensors: a commercial perspective" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000120_1.2346688-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000120_1.2346688-Figure1-1.png", + "caption": "Fig. 1. The simple model of the golf swing showing the disposition of the system a before the club is released and b when the club is about to impact the ball.", + "texts": [ + " III to the standard constant-torque driven double pendulum model1,12,13 to explain why the optimum mass is, in practice, nearer 200 g. The sensitivity of the swing efficiency and driving distance to wrist-cock angle, shaft length, shaft mass, release delay, and wrist torque is also investigated. Section IV summarizes some of the observations and draws some conclusions. The discussion is extended to explain the energy transfer in triple-pendulum models of the swing. Consider the double pendulum model in Fig. 1, which shows the golf swing reduced to its simplest elements. The mass m1, representing the arms, is on a rigid massless arm of length L1 that pivots about the hub. Similarly m2 represents the club head and is on a rigid massless arm of length L2 pivoting about m1. To simplify the calculations we assume that both masses are point particles so that they have no moment of inertia about their centers of mass and are confined to the plane of the swing. We also assume that the ball, represented by m3, has a coefficient of restitution of 1", + " As the club accelerates, the required wrist torque decreases rapidly. The release of the club at the point where the required wrist torque is zero is described as a natural release. We first assume that the system is not driven, that is, there are no applied torques, the gravitational potential is neglected, and the arm-club system rotates under its own inertia. Initially, both masses orbit the hub at constant angular velocity such that R is constant \u0307= \u0307 , and the wrist-cock angle is fixed at its initial value = i as indicated in Fig. 1 a . The club is released and a short time later the mass representing the club head has swung away from the hub, as shown in Fig. 1 b , the wrist-cock angle is 180\u00b0, and the club head is about to strike the ball. To clarify the discussion we 1088 1088Am. J. Phys. 74 12 , December 2006 http://aapt.org/ajp \u00a9 2006 American Association of Physics Teachers This article is copyrighted as indicated in the article. Reuse of AAPT content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 169.230.243.252 On: Thu, 26 Feb 2015 15:33:08 shall describe the motion of the arm-club system preceding the collision with the ball as the \u201cgolf swing", + " 1 a and 1 b all motion is tangential so that radial terms in the kinetic energy and angular momentum do not need to be considered. If we equate the kinetic energy T and the angular momentum L of the system in the initial and final positions T = 1 2 m1L1 2\u0307i 2 + m2R2\u0307i 2 = 1 2 m1L1 2\u0307 f 2 + m2 L1 + L2 2\u0307 f 2 , 2 L = m1L1 2\u0307i + m2R2\u0307i = m1L1 2\u0307 f + m2 L1 + L2 2\u0307 f , 3 we can determine the angular velocities of m1 and m2 at the instant before m2 collides with m3. The angles in Eqs. 2 and 3 are defined in Fig. 1 and the subscripts i and f refer to the initial and final positions, respectively. There is one particularly interesting instance described by Eqs. 2 and 3 ; namely, when m1 is stationary at the moment that the club impacts the ball. In this case all of the kinetic energy of m1 the arms is transferred to m2 the club head and the swing is 100% efficient. When this occurs, \u0307 f =0, and Eqs. 2 and 3 simplify to m1L1 2 + m2R2 \u0307i 2 = m2 L1 + L2 2\u0307 f 2, 4 and m1L1 2 + m2R2 \u0307i = m2 L1 + L2 2\u0307 f . 5 The nontrivial solution of Eqs" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003642_s12206-013-0838-8-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003642_s12206-013-0838-8-Figure2-1.png", + "caption": "Fig. 2. A 2D Incompletely restrained wire-suspended system.", + "texts": [ + "nT T T> > >L (13) In this system, sway of payload is an issue that should be controlled since this may cause undesirable vibration of payload. Incompletely restrained wire-suspended mechanism sways with regular period. It is easily found when payload is driven by fast acceleration or when the payload\u2019s initial position is not at the equilibrium point. To get frequency of payload sway, orientation change of the payload should be expressed analytically based on dynamics of the model. This research investigates 2D model, as shown in Fig. 2. In the figure, a mass is hung by two wires, one at each end. As it is driven by less than three wires, the system is an underactuated, further it can be regarded as an incompletely restrained wire-suspended mechanism when tension solution of two wires does not exist at a certain payload movement. Since it moves in 2D space, the direction of payload sway is fixed as 0 0 1 Tp = \u00e9 \u00f9\u00eb \u00fb . (14) Then, the equation of motion is 1 1 2 2sin sinmx T Tq q= - +&& (15) 1 1 2 2cos cosmy T T mgq q= + -&& (16) ( ){ ( ) } 1 1 2 2 1 1 2 2 cos cos cos sin sin sin " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001473_j.jbiomech.2009.08.025-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001473_j.jbiomech.2009.08.025-Figure2-1.png", + "caption": "Fig. 2. Definitions of the ball deformation and the impact force.", + "texts": [ + " The absolute magnitudes of the velocity vectors were calculated from the values of their components. The local coordinate system fixed on the ball surface was defined using the three points on the ball surface to calculate the rotation. The ball rotation in each trial was calculated as the average rotation about the vertically upward axis (counterclockwise/clockwise) in five frames after impact. The coefficient of restitution in each trial was calculated using Eq. (8). The ball deformation and impact force were calculated three-dimensionally using Ishii and Maruyama\u2019s (2007) methods. In Fig. 2, the ball deformation b in the normal direction to the contact surface was calculated by subtracting the distance between the center of the ball and contact point from the radius of the ball. The absolute magnitude of the impact force |Fb| is expressed in the following equation by applying the Hertz contact theory (Greszczuk, 1982; Timoshenko and Goodier, 1970). jFbj \u00bc mbVb1R ti 0b 3=2dt b3=2 \u00f01\u00de The derivation process of Eq. (1) is shown in Supplementary materials published online. The time course of the impact force for each trial was calculated using Eq" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002287_iros.2012.6385948-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002287_iros.2012.6385948-Figure4-1.png", + "caption": "Fig. 4. Equivalent under-actuated system model: Balance previewer", + "texts": [], + "surrounding_texts": [ + "The manipulation model is concatenated with the inverted pendulum one to build the complete model composed of the manipulation and balance models shown in Figs. 3 and 4, respectively, which relies on the decoupling hypothesis described in Fig. 5. The transmission of external disturbance through the main mechanical chain involved in the manipulation task is described and the application of the resulting effort (that applies thoroughly to the rest of the body) is considered to occur at the center of mass of the robot (which is, of course, a non-physical point). The validity of this approximation decreases with high CoM accelerations, and a specific attention needs to hover the choice of the manipulation chain and of the dynamic parameters (mass, notably) involved in each description (upper/lower behavior). This model is described over a preview horizon in the way Kajita et al. previewed the inverted pendulum behavior. The controlled end-effector follows x\u0302k+1 = 1 dt dt2/2 0 1 dt \u2212Kp k \u2212dtKp k \u2212Kd k \u2212dt2 2 K p k \u2212 dtKd k x\u0302k + 0 0 Kp kx des k +Kd k x\u0307 des k + x\u0308des k + (JeH \u22121JT e )Fext k + 0 0 +J\u0307eJ \u2020 e(x\u0307 cmd \u2212 x\u0307k \u2212 dtx\u0308k) , (24) while the CoM and ZMP positions remain described by x\u0302c k+1 = Ax\u0302c k + Buk, pk = [ 1 0 \u2212 Mzc Mg \u2212 F dis k |z ] x\u0302c k+ zcF dis k Mg \u2212 F dis k |z , where we express the CoM disturbance Fdis as follows: Fdis k = MeJ\u0307eJ \u2020 e(x\u0307k \u2212 x\u0307cmd k )\u2212Mex\u0308 des k \u2212Ke k(xdes k \u2212 xk)\u2212Ce k(x\u0307des k \u2212 x\u0307k). (25)" + ] + }, + { + "image_filename": "designv11_7_0000222_icar.2005.1507412-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000222_icar.2005.1507412-Figure3-1.png", + "caption": "Fig. 3. Basic kinematic structure of PM with decoupled Sch\u00f6nflies motions and two unactuated prismatic joints in each leg (a) and its associated graph (b).", + "texts": [ + " Two consecutive joints with different indexes have perpendicular axes. The notation Pcd indicates that the direction of the translation is parallel to the plane cd. The actuated joint of each leg Ai (i=1,\u2026,4) is underlined. By various associations of the four legs Ai presented in Tables I-III we could obtain 54=625 basic structural types of PMs with decoupled Sch\u00f6nflies motions without idle mobilities from which just one solution have identical structural leg-type. This solution has 4 legs of a PPPR-type and we denote it by 4-PPPR (Fig. 3). Due to the existence of two unactuated prismatic joints in each leg, solution 4-PPPR has no great practical interest. Solutions with structural nonidentical legs could be used to overcome this disadvantage. The solution presented in Fig. 4 has 3 legs of type PRRRR and one leg of type PRRR. We can see that this solution has only one prismatic joint in each leg and this joint is actuated. No unactuated joints exist in this solution 3-PRRRR+1-PRRR- type. To simplify the notations of the elements eAi (i=1,2,3,4 and e=1,2,\u2026,n) by avoiding the double index in Fig. 3 and the following figures we have denoted by eA the elements belonging to the leg A1 (eA eA1), by eB the elements of the leg A2 (eB eA2), by eC the elements of A3 (eC eA3) and by eD the elements of A4 (eD eA4). To obey to conditions (5)-(13), the axes of revolute joints connecting legs A1 and A3 to the moving platform must be superposed and the reference point H must be situated on this common axis, as we can see in the examples presented in Figs. 3-4. The axis of revolute joint connecting the leg A2 to the moving platform could be: (i) superposed with the axis of the last revolute joint of leg A4, as in Fig. 3 and Fig. 5-a, (ii) superposed with the axis of the last revolute joints of the legs A1 and A3, as in Fig. 5-b or (iii) not superposed with the axis of another joint, as in Fig. 5-c. These different positions do not involve structural modifications of the basic solution of PMs with decoupled Sch\u00f6nflies motions. In all cases, four revolute joints are adjacent to the mobile platform and the mechanisms are fully-parallel. The other 623 basic structural solutions of PMs with decoupled Sch\u00f6nflies motions without idle mobilities and elementary legs can be obtained by analogy with the solutions presented in Figs" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001956_oceanssyd.2010.5603565-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001956_oceanssyd.2010.5603565-Figure4-1.png", + "caption": "Fig. 4 (a) Fij exerted by Ti and Tj enables the AUV to move without exerting a moment that produces the yaw motion. (b) Path tracking by controlling both F13 and Mz (a moment producing the yaw motion for heading control).", + "texts": [ + " 3) When the thruster pair (#1, #3) or (#1, #4) or (#2, #3) or (#2, #4) is faulty For these cases, H HH j i B z y x T T M F F T \u03c4 \u239f\u239f \u23a0 \u239e \u239c\u239c \u239d \u239b \u239f \u239f \u239f \u23a0 \u239e \u239c \u239c \u239c \u239d \u239b = \u239f \u239f \u239f \u23a0 \u239e \u239c \u239c \u239c \u239d \u239b \u2032\u2032 \u03b3\u03b2 10 01 (17) )dim()(rank HHB T>\u2032 (18) where, \u03b2=-a when i=1, \u03b2=a when i=2, \u03b3=b when j=3, and \u03b3=-b when j=4. Unlike the cases of Eqs. (13) and (15), the thruster forces for desired motions cannot be determined in this case because the number of thrusters is less than the number of the resultant forces and moments as shown in Eq. (18). In order to solve this control problem, we introduce Fij as shown in Fig. 4(a), which passes through the center of gravity so as not to exert a moment producing the yaw motion. Then, controlling Fij (forward velocity) and Mz (rotational velocity) can make the path-tracking possible; however, the navigation style is not of hovering AUVs but of cruising AUVs. Fig. 4(b) shows an example of path tracking when T2 and T4 are broken, i.e., T1 and T3 are active. Specifically, the thrsuter forces Ti and Tj can be obtained from the relationship: \u239f\u239f \u23a0 \u239e \u239c\u239c \u239d \u239b \u239f\u239f \u23a0 \u239e \u239c\u239c \u239d \u239b \u2212 =\u239f\u239f \u23a0 \u239e \u239c\u239c \u239d \u239b j i z ij T T baM F 12 21 sincos \u03c3\u03c3 \u03b1\u03c3\u03b1\u03c3 (19) where, \u03b1=tan-1(a/b), \u03c31=\u03c32=1 for F13, \u03c31=-1 and \u03c32=1 for F14, \u03c31=1 and \u03c32=-1 for F23, and \u03c31=\u03c32=-1 for F24. Additionally, Fij and Mz are obtained by Eqs. (11) and (12); however, \u03c9r is given by: be achieved. D. When rank(BH)>dim(TH) AND rank(BV)>dim(TV) There are two cases to be discussed: one is the case when neutral buoyancy is applied to the AUV and the other is when a slight amount of positive buoyancy is applied" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002969_j.proeng.2013.12.146-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002969_j.proeng.2013.12.146-Figure3-1.png", + "caption": "Fig. 3. (a) A plot of the local temperatures of the oil film and of the surrounding structure (separated by a thin white line) of the journal bearing for a rotational speed of 2000rpm of the journal, lubricated with SAE40 and a dynamical load with a peak force of 180kN; LP06 denotes the temperatures measured on the journal bearing test-rig LP06 shown in Fig. 4. TExp of Eq. (1) corresponds to 108\u00b0C and Toil supply to 83.2\u00b0C in this case, which yields an equivalent temperature TEHD of 101.8\u00b0C for the EHD-simulation. (b) calculated peak temperatures over an entire load cycle for three different journal bearing operating conditions, shown as green dashed line for a journal speed of 2000rpm and lubricated with SAE40, as red dotted line with a journal speed of 4500rpm and lubricated with SAE40 (this case corresponds to Fig.5) and shown as blue solid line for a journal speed of 2000rpm and lubricated with SAE20.", + "texts": [ + " It is the aim of this work to compare the results from simulation to experimental measurements from the journal bearing test-rig LP06 (see Fig. 2.(b)), consequently, journal bearings with a diameter of 76mm and a width of 34mm are considered. A dynamic (sinusoidal) load with a peak load of 180kN is applied to the test bearing with a fixed frequency of 100Hz. With carefully chosen thermal boundary conditions on the ground of physical arguments ([2] and references therein, in particular [10]), it is indeed possible to accurately simulate the different local temperatures in journal bearings. Fig. 3 shows an exemplary result from simulation in direct comparison to temperatures measured on the journal bearing test-rig LP06. It is notable that not only the peak temperature in the high load area of the journal bearing, but also the oil outflow temperature (which is directly related to the friction power losses in the bearing) is accurately calculated. As one can see from Fig. 3, a significant temperature gradient is present ranging from 82\u00b0C from the incoming lubricant to 108\u00b0C of the oil film in the high load zone. However, it is worthwhile to mention that the local temperatures change only very slowly, which allows to treat them as essentially constant over the entire load cycle. This thermal behavior can be seen in Fig. 6, where the peak temperatures in the journal bearing are shown over the entire load cycle (as shown in Fig. 3) for different operating conditions. The peak temperature in the high load area of the bearing changes only a few single degrees Celsius during the load cycle. This stable thermal behavior can be used in the following to derive a considerably simpler isothermal EHD-simulation model that is very powerful and describes accurately the friction power losses including metal metal contact for a large range of operating conditions from full film lubrication up to weak mixed lubrication. From the TEHD-results following simple relation for an equivalent temperature can be derived [2] to take into account in the EHD-simulation the temperature gradient in the journal bearing, (1) Where TExp denotes the measured bearing shell back temperature in the high load area of the journal bearing and Toil supply is the temperature of the cool supplied oil", + " As can be seen from the equation, the dominating temperature is the temperature in the high load area of the journal bearing which is corrected to consider the cool lubricant in the oil supply groove with its considerably larger viscosity. It is important to note that above relation is valid for journal bearings with a 180\u00b0 oil supply groove only; these are commonly used as e.g. main bearings in ICEs to carry the crank shaft. Exp oil supplyEHD Exp 4 T T T T In a next step, the oil film is simulated using the basic, isothermal form of the Reynolds equation [2] using the same contact model and using Eq. (1) to derive an equivalent lubricant temperature. From Fig. 3.(a) the required temperatures can be obtained, in particular TExp of Eq. (1) corresponds to 108\u00b0C and Toil supply to 83.2\u00b0C in this case, which yields an equivalent temperature TEHD of 101.8\u00b0C used in the EHD-simulation. In the following the average torque needed to motor the three journal bearings (the test bearing and two support bearings) at a given journal speed is used to compare the results from simulation to the measured data; this so called friction moment is averaged over the entire load cycle (as shown in Fig. 3.(a)) due to experimental limitations. Fig. 4.(a) and Fig.4.(b) show the comparison of the calculated friction moment with the measured friction moment on the journal bearing test-rig LP06 for two different journal speeds and two different lubricants. The results demonstrate clearly that the simulations are not only able to accurately calculate the friction power losses in journal bearings, but also that an EHD-simulation with the discussed equivalent temperature is a valid and very accurate approximation for a full TEHD-simulation at least for full film and weak mixed lubrication" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003288_1.4025234-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003288_1.4025234-Figure1-1.png", + "caption": "Fig. 1 Discretization of the rotor Fig. 2 Mechanical model of the rod-fastened rotor", + "texts": [ + " 135 / 122505-1 Copyright VC 2013 by ASME Downloaded From: http://gasturbinespower.asmedigitalcollection.asme.org/ on 05/06/2015 Terms of Use: http://asme.org/terms the calculated critical speeds of the real rod-fastened rotor agree well with the test measurement data provided by the manufacturer, mode shapes and an unbalance response of the rotor are also obtained accurately. 2.1 Framework for the Dynamic Characteristics Calculation. In Riccati TMM, the rotor is discretized to N nodes with lumped mass and N 1 elastic shaft segments as shown in Fig. 1, where Z denotes the dynamic characteristics of bearing, which will be discussed in Sec. 2.2.3. The state vector of station i consists of force vector {f}i and displacement vector{h}i, which can be expressed in the XY coordinate axis as follows: ff gi\u00bc Mx;My;Vx;Vy T i ; hf gi\u00bc x; y; h;/f gT i (1) Through force and displacement analysis, transitive relation of state vector can be established f h R i \u00bc I W 0 I i f h L i \u00fe Fu 0 i (2) f h L i\u00fe1 \u00bc U 0 S U i f h R i (3) where footnote L presents the left side of the segment and R is the right side, {W}i, {U}i, and {S}i are partitioned matrices defined as follows: Wi \u00bc 0 0 0 0 0 0 0 0 x2m zxx zxy 0 0 zyx x2m zyy 0 0 2 6664 3 7775 i \u00f0i\u00bc 0; 1; 2; 3;\u2026;N 1\u00de (4) Ui \u00bc 1 0 L 0 0 1 0 L 0 0 1 0 0 0 0 1 2 664 3 775 i \u00f0i \u00bc 0; 1; 2; 3;\u2026;N 2\u00de (5) Si \u00bc L2 2kaEI 0 L3 6kaEI 0 0 L2 2kaEI 0 L3 6kaEI L kaEI 0 L2 2kaEI 0 0 L kaEI 0 L2 2kaEI 2 6666666666664 3 7777777777775 i \u00f0i \u00bc 0; 1; 2; 3;\u2026;N 2\u00de (6) where z is the complex impedance in the xx, xy, yz, and yy direction, and ka is a correction coefficient to amend the contact stiffness, which will be further discussed in Sec" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001683_ecce.2010.5618041-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001683_ecce.2010.5618041-Figure5-1.png", + "caption": "Fig. 5. 3 HP induction machines dynamometer used for DB-DTFC", + "texts": [ + " #3 would balance a decrease in flux linkage and torque production, and #4 would yield a constant flux solution, where the flux linkage is achieved despite having lower torque production. The two options that quickly decrease flux linkage would be more desirable for a typical industrial drive because of their ability to bring the torque line back into the voltage limits. To validate the performance of the drive topology presented, an experimental test stand was constructed. The test stand utilized two mechanically coupled 3 HP induction machines. The parameters for the machines are shown in Table 1. The configuration of the DB-DTFC motor drive test stand is shown in Fig. 4. Fig. 5 shows the mechanically coupled induction machines used to perform the DB-DTFC implementation and testing. The following section provides experimental results of the proposed drive topology during steady state operation over a wide range of operating points. Fig. 6 shows the system operating at high speed with flux weakening. The operating conditions are \u03c9r = 377 rad/s (2.0 pu) and Te* = 0.5 Nm (0.04 pu) with flux linkages \u23d0\u03bbdqs * \u23d0= 0.20, 0.15, 0.10, 0.05 Volt-s. The system operates with smooth, non-oscillatory dynamics even in the deep field weakened region of 0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001766_s10409-009-0305-z-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001766_s10409-009-0305-z-Figure1-1.png", + "caption": "Fig. 1 The fish body coordinate and the global coordinate", + "texts": [ + " 2 Governing equations, feedback control strategy and swimming parameters 2.1 Governing equations The governing equations for the fluid motion are Navier\u2013 Stokes equations [5]. The dynamics equations for the selfpropelled fish are m du dt = F , dL dt = M , (1) where m is the mass of a fish; u is the velocity vector; F is the hydrodynamic force; M is the moment and L is the moment of momentum, L = \u2211 i mir i \u00d7 v i , (2) where mi is the mass of segment i,r i is the gravity center of segment i , as shown in Fig. 1. v i is the rate of change of position in the fish body coordinate.v i include two parts, i.e., v i = v f i +\u03c9i \u00d7 r i , (3) where v f i is the part determined by the given flapping rule. \u03c9i is the angular speed of segment i . Hence, L = \u2211 i mir i \u00d7 v f i + \u2211 i mir 2 i \u03c9i . (4) To get the unique solution of the moment of momentum equation in Eq. (1), the sufficient and necessary condition is \u03c91 = \u03c92 = \u00b7 \u00b7 \u00b7 = \u03c9. (5) Therefore, m du dt = F , d dt ( \u2211 i mir i \u00d7 v f i ) + d dt ( \u03c9 \u2211 i mir 2 i ) = M ", + " For a 2D fish, the rotational angular velocity only has z component. \u03c9z is the change rate of attack angle of fish body \u03b8 with time. Therefore, under the fish body coordinate system, v f = y\u0307l(xl , t) j l , (8) where yl(xl , t) is the variational rule of mass element, which is identical to Eq. (14). In the study, the non-dimensionalization is achieved by using the unit time t and the body length of fish L . 2.2 The fish body coordinate and the global coordinate In the study of self-propel process of fish, two sets of coordinate are used, as shown in Fig. 1. One is the global coordinate (x, y, z), in which the position of the gravity center of fish is defined as (x0, y0, z0). The other is the local coordinate settled on the gravity center of fish, (xl , yl , zl), which is named the fish body coordinate. The link between these two coordinate systems is the angle \u03b8 , shown in Fig. 1, which defines the orientation of xl (the generatrix) related to the x direction in the global coordinate. From Eq. (14) (2D) or Eq. (16) (3D), one can see that in the flapping process, every point on the central line is symmetric about xl . In the self-propelled swimming of a 2D fish, under the influence of total moment, between the axis xl of the fish body coordinate and the axis x of the global coordinate, there is an angle \u03b8 called the angle of attack of fish body, as shown in Fig. 1. For a 3D fish, the angle of attack of fish body has three components, which are the angles between the projection of the central line to the three planes in the global coordinate and the positive direction of axis, respectively. The fish body coordinate and the global coordinate are connected by the gravity center of fish and the angle of attack of fish body. For example, assume that at a certain time in the global coordinate, the gravity center of a 2D fish is (x0, y0), the angle of attack of fish body is \u03b8 , then in the global coordinate, an arbitrary point (xl , yl) on the body of fish in the fish body coordinate is x = x0 + xl cos(\u03b8)\u2212 yl sin(\u03b8), y = y0 + xl sin(\u03b8)+ yl cos(\u03b8), (9) where x0, y0, \u03b8 are the function of time, which is obtained by solving the control equation of motion of fish" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001237_19346182.2008.9648483-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001237_19346182.2008.9648483-Figure3-1.png", + "caption": "Figure 3. Definition of oar angles and oar forces; the oar angle measured at the oar lock (yL) can differ from the blade angle (y) due to oar bending.", + "texts": [ + " The position of the boat seat (xS) is measured by a further incremental wire potentiometer (4 cts/mm). In general, a model for virtual rowing is driven by measured variables, which reflect the rower\u2019s performance. The model output controls the displays presented to the user. In our setup, a haptic, visual, and acoustic display are integrated. Our model inputs are the three oar angles y (in the horizontal plane), d (in the vertical plane), and f (around the longitudinal oar axes), and the seat position xS (Figure 3) summarized in the vector k. The outputs are the oar forces in the horizontal and the vertical plane FO \u00bc \u00f0FOy;FOd \u00deT for the haptic display, as well as the boat velocity _xB represented by appropriate animations and sounds on the visual and the acoustic display, respectively. Furthermore, the oar angles are directly mapped to visual and acoustic dimensions shown as a virtual oar to the user. In our model, the virtual oar length (l) the rower\u2019s mass (mR), and further parameters are adjustable according to the boat type and the user" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002677_1.4001104-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002677_1.4001104-Figure1-1.png", + "caption": "Fig. 1 Schematic geometrical rep showing the two elements: an uppe and a lower rotating flat disk \u201esolid D", + "texts": [ + " APRIL 2010, Vol. 132 / 021501-110 by ASME ata/journals/jotre9/28773/ on 03/08/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use s m s s s o m e p s f t p s t 0 Downloaded Fr The aim of the current paper is to link the local effects of pinning i.e., the local kinematics to the macroscopic measureent of friction. The local kinematics are detailed in Sec. 1.2. 1.2 Contact Kinematics Due to Spin. The contact between a pherical-end pin solid B and a plane disk solid D is repreented schematically in Fig. 1 CB and CD represent two points ituated on the axis of rotation of solids B and D, respectively. The rigin is located at the center of the disk contact area. This geoetrical configuration is chosen to be the same as the one studied xperimentally in Ref. 1 . To highlight the spinning effect, the velocity components of oints AD and AB, respectively, on the surface of the plane and the pherical-end solid have to be expressed. These velocities are unction of the rotational speed of each solid D for solid D and B for solid B and the position of the axis supporting the rotaional speed", + " Moreover both velocities on surfaces D and B deend on the space variables, meaning that, in contrast with clasical rolling/sliding analysis, the local velocities are not rigorously he same all over the rubbing surfaces. \u2022 The local velocity of a given point AD of solid D is expressed as follows: VD 0 AD = VD 0 CD + ADCD \u2227 D where 0 represents a fixed frame, with VD 0 CD = 0, D = 0 \u2212 D 0 and ADCD = ADO + OCD = \u2212 x 0 \u2212 z + 0 0 RD where O represents the origin of the fixed frame 0. The velocity field at any point AD can then be written as VD 0 AD = UD VD WD = DRD 0 0 + \u2212 z D 0 x D 1 \u2022 The local speed of a given point AB of solid B depends on the tilting angle , defined in Fig. 1 as the angle between the y axis and the axis of rotation of solid B. The local speed at AB is expressed as 21501-2 / Vol. 132, APRIL 2010 om: http://tribology.asmedigitalcollection.asme.org/pdfaccess.ashx?url=/d VB 0 AB = VB 0 CB + ABCB \u2227 B with VB 0 CB = 0, B = 0 B cos B sin and ABCB = \u2212 x RB + h0 \u2212 h x,z \u2212 z and then, with h0\u2212h x ,z RB, VB 0 AB = UB VB WB = B sin . RB 0 0 + z B cos x B sin \u2212 x B cos 2 For the two solids, the velocity vector over the surfaces can be divided into three components" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003374_e2013-01781-7-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003374_e2013-01781-7-Figure2-1.png", + "caption": "Fig. 2. Release surface growing out of the release line (near midplane, green online in (a)) for the m = 3 model and St = 10\u22125. The surface is shown 0.275 units of time after starting from the release line. The free-surface flow is from the bottom to the top. Color (online) indicates the evolution time.", + "texts": [ + " In the laboratory frame of reference the triangularly-shaped region depleted of particles will rotate about the axis of the liquid bridge. This phenomenon is well-known among experimentalists [17] (their figure 3c) and has been used as a convenient indicator for a traveling hydrothermal wave. The rotating triangle changes to a pulsating triangle for a standing wave. The process by which particles that have contacted the free surface can no longer reach the depletion zone near the center is demonstrated in Fig. 2 which shows that the release surface growing out of the release line folds inwards and does not enter the depletion zone. As time proceeds, this process continues and generates a progressively complicated surface. This release surface is a contraction from a volume to a surface and hence represents an accumulation process. Even though the phenomenon has long been known, no plausible explanation for it has been given as yet. Here we offer an explanation of the depletion zone in terms of particle\u2013free-surface collisions" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000429_j.trac.2006.11.015-Figure15-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000429_j.trac.2006.11.015-Figure15-1.png", + "caption": "Figure 15. Schematic diagram of chemiluminescence (CL)detection cell. Reprinted from [78], with permission from Elsevier.", + "texts": [ + " (1) High-voltage power; (2) Pt electrode; (3) electrophoretic capillary; (4) CL solution reservoir; (5) reaction capillary; (6) photomultiplier tube (PMT); (7) reflection mirror; (8) waste-solution reservoir; (9) computer; (10) black box; (11) reaction tee; (12) glass cover; and, (13) buffer reservoir. Reprinted from [76], with permission from Wiley. 76 http://www.elsevier.com/locate/trac of saccharides. (Fig. 14) The aerosol, which was formed from mixing the CE buffer with a sheath liquid in a T-piece, was sprinkled onto the surface of porous alumina to produce the CL signal. A batch-type BL detector (Fig. 15), in conjunction with CE, was utilized by Tsukagoshi and co-workers [78,79] for the determination of biomolecules; the LODs were 10 lM for glutamate, 17 lM for glycylglycine, and 12 lM for hemoglobin, respectively. Later, Tsukagoshi et al. [80] used a batch-type BLdetection cell to detect ATP using the firefly luciferase reaction, with an LOD of 1 lM ATP. The major limitation for CL detectors is that few molecules are able to generate CL. Liquid-core waveguides (LCWs) [81\u201385] operate by using a channel as a waveguide" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003454_s10404-011-0921-3-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003454_s10404-011-0921-3-Figure3-1.png", + "caption": "Fig. 3 (Color online) Schematic of a device with a separate precharging electrode: a device schematic, b description of the precharging method with the proposed device schematic. In the image, negative (-) bias is being applied to the pre-charging electrode", + "texts": [ + " As a consequence, when the polarity of the pre-charging voltage is positive, the droplet is charged with a positive charge and driven only when a negative driving bias is applied to the next electrode. As shown in the captured image of the experiment in Fig. 2a, a droplet of 2.5-lL DI water precharged with positive pre-charging voltage (red wire) in the leftmost picture is driven to the next electrode on which the negative driving voltage (black wire) is applied. In contrast, when negative pre-charging voltage is applied, it is charged with a negative charge and guided only when a positive driving bias is applied to the designated electrode, as depicted in Fig. 2b. In Fig. 3, schematics of the device with a separate precharging electrode are shown. Instead of pre-charging the droplet by inserting an electrical wire into it, this device utilizes a small electrode in the middle of the device, along with the driving electrodes on a coplanar surface. A hole is made through the hydrophobic film and the dielectric layer, so that the droplet can touch this pre-charging electrode directly when the droplet is placed on it. Because the size of the hole (340 lm by 340 lm) is much smaller than the size of the droplet (diameter of *1.6 mm), dragging the droplet out of the hole to the next driving electrode presents no problems. As shown in Fig. 3b, the droplet is precharged by applying electrical voltage between the pre-charging electrode and the driving electrode. The precharged droplet can then be driven multiple times on the electrode array by applying the driving voltage sequentially. Figure 4 shows how the droplet is moved on the device. Multiple droplet movements were demonstrated by first pre-charging the droplet and then driving it with the successive application of voltage to the adjacent electrodes. One round of motion of the droplet on the device is shown in the image" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003312_acc.2012.6315053-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003312_acc.2012.6315053-Figure1-1.png", + "caption": "Fig. 1 Position view of the UAV and the virtual target.", + "texts": [ + " Therefore, this virtual target determination approach needs only the flight distance and not any extra information such as tracking error components (a reference point on the trajectory should be a specified length) as in Park et. al. [11,12]. If the UAV deviates from the desired trajectory, the virtual target is set at a receded point at each time step according to the flight distance to avoid repeated correction control. This study follows the basic concept of PPG trying to annul some LOS error angle from the virtual target. Assume that a UAV with a velocity of UAVV is pursuing a virtual target as shown in Fig. 1. In order to guide the UAV into the virtual target direction, the LOS vector R and the UAV's velocity vector UAVV needs to point towards in the same direction. The physics of the problem can then be expressed mathematically as 0RV =\u00d7UAV (1) The above equation can be represented in a normalized form as RVUAV UAV o RVS \u00d7 \u2261 (2) where R denotes the magnitude of the LOS vector, R and oS is assumed as the basic sliding surface vector. Along the velocity axes, UAVV and R can be expressed as ( )T UAVUAV V 00=V (3) ( )T RRR zyx=R (4) By using Eqs", + " 4) Control surface deflection limits are: ]25,25[\u2212\u2208e\u03b4 , ]20,20[\u2212\u2208a\u03b4 , ]30,30[\u2212\u2208r\u03b4 Note that, SOSM-IGC uses only an approximated lift curve slope (constant value), and three control-related dimensional stability derivatives, alk \u03b4, , emk \u03b4, , rnk \u03b4, , among many aerodynamic parameters. B. Simulation results Figure 2 shows flight path trajectory made by the UAV indicated by solid line whereas a reference trajectory denoted by a dashed dotted line. As can be seen in Fig. 2, the UAV flight trajectory almost coincides with the reference trajectory regardless of the wind turbulence. Figure 3 shows a history of the LOS error angle defined in Fig. 1. For a helical ascent motion, the LOS error angle never goes to zero because the direction of the virtual target always turns (recedes along the helical trajectory) as the UAV goes. It is observed that the LOS error angle is bounded less than 15 degrees (0.26 rad) that is almost equal to the ratio of the helical radius to the desired distance from the UAV to the target point. Load factor are periodically changes due to averaged y-axis wind as shown in Fig. 4. Such changes might affect the change of the LOS error angle" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002902_cdc.2011.6161278-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002902_cdc.2011.6161278-Figure3-1.png", + "caption": "Fig. 3. Rendering of the Balancing Cube, shown in the same orientation as in Fig. 2. The cube has six rotating arms, one on each face.", + "texts": [], + "surrounding_texts": [ + "We consider the stochastic linear time-invariant system x(k) = Ax(k\u22121) +B u(k\u22121) + v(k\u22121) (1) y(k) = C x(k) + w(k), (2) where k is the discrete time index; x(k), v(k) \u2208 R n; u(k) \u2208 R m; y(k), w(k) \u2208 R p; and all matrices are of corresponding dimensions. The process noise, the measurement noise, and the initial state x(0) are assumed mutually independent, Gaussian distributed with v(k) \u223c N (0, Q), w(k) \u223c N (0, R), and x(0) \u223c N (x0, P0), where N (m,V ) denotes a normally distributed random variable with mean m and covariance matrix V . Furthermore, the pair (A,C) is assumed detectable, (A,Q) stabilizable, and R diagonal. The latter assumption means that the measurement noise is mutually independent for any two sensors considered, which is often the case in practice. The presented state estimation method can, however, be readily extended to the case of block diagonal R by sending blocks of correlated measurements at once. Throughout this paper j is used to index a single measurement, i.e. an element of the vector y. Accordingly, Cj denotes the jth row of C and Rjj the jth diagonal element of R. We use the index set J(k), a subset of {1, . . . , p}, to denote a selection of measurements at time k. The notation [Cj ]j\u2208J(k) is used to denote the matrix constructed from stacking the rows Cj for all j \u2208 J(k); and diag[Rjj ]j\u2208J(k) denotes the diagonal matrix with entries Rjj , for j \u2208 J(k), on its diagonal. It is well-known that the optimal state estimator for the system (1), (2) with full measurements (J(k) = {1, . . . , p}) is the Kalman filter, which is restated in Sec. II-A. The constraints on the usage of measurements are set up in Sec. II-B and the corresponding Kalman filter equations for the reduced set of measurements (J(k) \u2286 {1, . . . , p}) are derived." + ] + }, + { + "image_filename": "designv11_7_0002156_robot.2009.5152525-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002156_robot.2009.5152525-Figure4-1.png", + "caption": "Fig. 4. Finger-link contact model", + "texts": [ + " A search algorithm described later and pllied to the DC motor generates the torque command to the joint. The stopper attached to the link is used to set a constant initial condition between the link and the disk. As shown in Fig. 3, the velocity, angular velocity, and direction of the ball after the release from the link are measured by image processing using a camera. Two dynamic models are presented based on the condition of contact between the ball and robot link: (1) the fingerlink contact model, and (2) the fingertip contact model. The finger-link contact model shown in Fig. 4 represents the dynamics where the ball and link keep a rolling contact condition. The fingertip contact model shown in Fig. 5 represents the dynamics where the ball is in contact with an edge of the link (fingertip). The relationship between the two contact models is illustrated in Fig. 6. The finger-link contact model is initially applied since the initial condition (see the most-left image in Fig. 3) is given under this condition. The ball is released from the link if the contact force fh acting on the ball from the link becomes zero" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003714_piee.1970.0022-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003714_piee.1970.0022-Figure4-1.png", + "caption": "Fig. 4 Cross-section of slot", + "texts": [ + " 3d-g show the pattern of the current distribution at different points in the length of the bar. (For the purposes of this illustration, a and b are presumed to be in time phase, but this is not a necessary condition fof the analysis.) In general, for the stack of conductors descending from / = 0, 2TTI (3) and, for the ascending stack, a (TTX 2TTI\\ ( T + 1 - ) (4) The mean current density at a height x and a length / will be TTX 2TT7 . . . J = 2b + a cos \u2014 cos \u2014 (5) J JL The flux density at any height will be obtained using Ampere's circuital law. From Fig. 4, integrating round the flux path shown, Hence aX 2TTI . TTX\\ Integrating over the incremental length Si to obtain the flux linkage 8, the general strand being designated by a above a point x at a length /, rx = J SIB, dx w bX2 aX2 - 3 + 2 cos ^ ~ + c o s 2 (T + a) \\2 2TT/ 2 c o s 2TTI \u2022 (9) Further, to obtain the flux linking this strand in the slot portion we must obtain the integral = Sdl o (10) where J, = Bessel function of order one of the first kind. The current densities are alternating, so let b = bQ sin cot a = a0 sin (cot + 6) Then and the e" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002034_09544100jaero606-Figure6-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002034_09544100jaero606-Figure6-1.png", + "caption": "Fig. 6 Elements of UAV communication and information link", + "texts": [ + " Aerospace Engineering at UCSF LIBRARY & CKM on May 8, 2014pig.sagepub.comDownloaded from groups through a secured communication link. Thus, it is clear that the communication flow starts from the ground control station to a UAV extends among the systems in a UAV, and further extends between the UAVs. The information flow also starts from the UAV to the ground control station and then extends to various UAVs operating in a group. The communication flow and information flow between the UAV and the ground control station are shown in Fig. 6. The UAV is commanded right from Proc. IMechE Vol. 224 Part G: J. Aerospace Engineering JAERO606 at UCSF LIBRARY & CKM on May 8, 2014pig.sagepub.comDownloaded from the take-off to climb and cruise through line of sight (LOS) communication link. If the cruise mission requirements demand UAV flight, beyond its LOS range, the UAV is controlled through the beyond line of sight (BLOS) communication link, which is achieved through a low earth orbit or a geosynchronous-satellite-based communication (SATCOM) link" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003270_amr.199-200.1984-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003270_amr.199-200.1984-Figure2-1.png", + "caption": "Figure 2. Curved layer vs flat layer for conductive polymers.", + "texts": [ + " If smooth surfaces are required for the component, the staircase effect can require sometimes substantial post-processing of the part (sanding and polishing) in order to produce smooth surfaces. All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications, www.ttp.net. (ID: 152.14.136.77, NCSU North Carolina State University, Raleigh, USA-03/05/15,19:03:23) This paper looks at the application of curved-layer FDM [3] (Fig 2) for producing plastic components with integral conductive tracks that allow for the elimination of wiring or printed circuit boards from products. This project included the development of a machine capable of constructing a part by depositing the layers of material as curved layers instead of the current flat layers. This new process could be named Curved-Layer Fused Deposition Modeling (CLFDM). The concept behind the technology is as follows: A substructure of \u2018support material\u2019 to the curved part is first created through existing flat-layer methods using a soluble support material. This support structure forms the base onto which the curved layers of product material can then be deposited by having the deposition head precisely follow the contour of the part (Fig. 2). The effect of these curved layers is to eliminate the staircase effect altogether, as well as removing the inherent lamination weakness in the direction of the layers. The bulk of the research being carried out at different universities has been related to investigating alternative materials for FDM and working with a variety of materials including ceramics and metals [4], high performance thermoplastic composites [5] and metal/polymer composites [6]. While special FDM systems have been designed for experimental deposition of different types of materials with different techniques and much work has been done on the analysis of the mechanism of deposition [7, 8], very little research has been done on depositing material as curved layer", + " The literature on RP reveals a research project in which the Laminated Object Manufacturing process was used to create curved layers [9] at the University of Dayton in the USA but the results were limited by the ability to evenly stretch a material over a curved mandrel and the small range materials that could be used. This CLFDM technology opens up an entirely new possibility of building complex curved plastic parts that have conductive electronic tracks and components printed directly as part of the plastic component. It is not possible to do this with existing flat-layer additive manufacturing technologies, particularly on parts that are curved, as the continuity of a circuit would be interrupted between the layers (Fig. 2). With curved-layer fused deposition modeling (CLFDM) this problem is removed as continuous filaments in 3 dimensions can be produced, allowing for continuous conductive circuits. The elimination of the flat printed circuit boards (PCBs) and possibly even some of the electronic components, such as transistors, that are used in most electronic products creates a whole new type of product in which the housing of the product becomes its electronic circuit. This, in turn, could revolutionize the field of product design which would no longer be constrained by having to design around flat PCBs" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002712_978-1-4419-1126-1_17-Figure17.2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002712_978-1-4419-1126-1_17-Figure17.2-1.png", + "caption": "Fig. 17.2 Schematic diagrams of the flagellum connected to the molecular motor of a bacterium. As shown in the figure, the design of this molecular motor is very similar to an artificial version with a rotor inside a stator separated by ball-bearings. This molecular structure consists of three main parts: the basal body, which acts as a reversible rotary motor; the hook, which functions as a universal joint; and the filament, which acts as a helical screw (OM: Outer Membrane; PG: Peptidoglycan layer; CM: Cytoplasmic Membrane. (Adapted from Fig. 17.1 in Minamino T. et al. Molecular motors of the bacterial flagella. Curr. Opin. Struct. Biol. 18, 693\u2013701 (2008))", + "texts": [ + " Nonetheless, this solution has limitation especially when the distance from the coils and the microscale robots increase to accommodate operation deep in the human body, especially when operating deep in the human torso. In the latter case for instance, overheating of the coils would most likely prevent their usage for such applications. Therefore, an embedded source of propulsion would become more appropriate. Each flagellum acting as a propeller is connected to a hook acting as a universal joint that connects to a molecular motor as depicted in Fig. 17.2. TheMC-1 bacterium has two bundles of such flagella providing a total thrust force for propulsion between 4.0\u20134.7 pN > 0.3\u20130.5 pN for many flagellated bacteria. Each flagellum rotates 360 degrees like a shaft in standard motor and can be reversed for backward motion. The total diameter of each molecular motor is less than 300 nm. The flagellum acting like a propeller consists of a 20 nm-thick hollow tube. As depicted in the figure, the flagellum next to the outer membrane of the cell has a helical shape with a sharp bend outside" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000583_j.cma.2008.11.014-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000583_j.cma.2008.11.014-Figure5-1.png", + "caption": "Fig. 5. Illustration for an arbitrary Cartesian basis and the corresponding rotated basis.", + "texts": [ + ", wrinkling information of a membrane is obtainable on the undeformed configuration along the inverse mapping of the deformation gradient F = ga Ga where ga is the covariant basis on the curvilinear coordinate on the mid-surface of the membrane in the deformed configuration and Ga stands for the contravariant basis on the curvilinear coordinate on the undeformed configuration. Mapping the current Green\u2013Lagrange strain on the mid-surface of the membrane E = EcmGc Gm via the original material C = CabcmGa Gb Gc Gm together with the prestress Spre \u00bc Sab preGa Gb yields the \u2018\u2018fictitious stress\u201d Sfic \u00bc Sab ficGa Gb where Ga stands for the covariant basis on the curvilinear coordinate on the mid-surface of the membrane in the undeformed configuration. These tensors can also be defined on a Cartesian basis Aa described in Fig. 5 under the state of plane stress in Voigt\u2019s notation by fSficg \u00bc fSelasg \u00fe fSpreg; fSelasg \u00bc \u00bdC fEg: \u00f01\u00de Initialize: set initial equilibrium iteration number ( =in Loop over equilibrium iteration ( 1+= nn ii ) From nominal total strains { }E and nominal co Find principal stress { }minmax , SS and principal Evaluate the state of membrane via the wrinkli TAUT NO MODIFICATION SLACK [ ] [ ]CCMOD = [ ] [ ]; \u2192= \u03d6\u03d6 CCMOD RETURN [ ]MODC Fig. 4. Flowchart for the wri Explanations are given in Appendix C. A transformation of stress and strain components from an arbitrary Cartesian basis ( ) defined on the basis Aa to a rotated one \u00f0\u0302 \u00de defined on the basis bAa in Fig. 5 by a mathematically positive angle a can be written as fbSg \u00bc TfSg; T 1fbSg \u00bc fSg; fbEg \u00bc T TfEg; TTfbEg \u00bc fEg; \u00f02\u00de where TT \u00bc c2 s2 cs s2 c2 cs 2cs 2cs c2 s2 24 35 \u00bc U1 U2 U3\u00bd ; T 1 \u00bc c2 s2 2cs s2 c2 2cs cs cs c2 s2 24 35 \u00bc n1 n2 n3\u00bd : In this equation, c stands for cosa and s represents sina, respectively. Obviously, Ui is the transformation vector that maps the stress {S} in an arbitrary Cartesian basis to the component bSi of the stress fbSg in the rotated basis. Similarly, nj is the transformation vector that transforms the strain {E} in an arbitrary Cartesian basis to the component bEj of the strain fbEg in the rotated basis", + " A variable with tilde\u2013hat \u00f0b~ \u00de is a variable on the wrinkling axes (t0, w0) that is modified by the wrinkling model whereas a variable with tilde \u00f0~ \u00de is a variable on the material axes (A1,A2) which is modified by the wrinkling model. One remark is that on the Cartesian coordinate the covariant and contravariant basis are invariant (Aa = Aa). With respect to the material basis (A1,A2), the modified Green\u2013 Lagrange strain tensor eE in Eq. (5) and its energetic conjugate which are based on the reference configuration can be described by feEg \u00bc fEg \u00fe 1 2 b\u00f02\u00fe b\u00dejjw0jj2 s2 c2 2cs T \u00bc fEg \u00fe lU2; feSg \u00bc \u00bdC feEg; \u00f06\u00de where U2 is the transformation vector of stress towards the wrinkling direction w0 as mentioned in Eq. (2) and Fig. 5 as well as Fig. 6. Obviously, l represents the amount of wrinkling, while c and s stand for cosh and sinh, respectively. The angle h is an angle of rotation that is measured counter-clockwise from the local Cartesian basis in the reference configuration (A1,A2) to an orthogonal basis formed by the wrinkling axes(t0,w0). The wrinkling direction vector in the reference configuration is given by w0 = kw0ksinhA1 + kw0kcoshA2 = w0aAa. By stretching edge cd to edge c0d0 to form the fictitious flat surface in Fig", + " DC can be explicitly shown as \u00bdDC \u00bc \u00bdC \u00bdP \u00fe R1 \u00fe R2 R3 \u00bc \u00bdC H \u00bc \u00bdC P \u00fe 2 j \u00f0U3UT 3\u00bdC P\u00deU T 2\u00bdC U2\u00f0UT 2\u00bdC fEg Salw \u00fe UT 2fSpreg\u00de \u00fe\u00f0U2UT 3\u00bdC P\u00de UT 2\u00bdC U2\u00f0UT 3\u00f0\u00bdC fEg \u00fe fSpreg\u00de\u00de \u00fe\u00f0UT 3\u00bdC U2 \u00fe UT 2\u00bdC U3\u00de\u00f0 UT 2\u00bdC fEg \u00fe Salw UT 2fSpreg\u00de !0BB@ 1CCA 2664 3775: \u00f044\u00de Eq. (44) is valid for both isotropic and orthotropic materials when the wrinkling direction w0 is available. Specifically, the vector U2 is coplanar and orthogonal to the transformation vector U1 of stress towards the uniaxial tension direction as described in Eq. (2) and Fig. 5. For isotropic case, this situation means that the first principal direction of the total stress field Selas + Spre coincides to the one of the strain field as well as the wrinkling direction. As a result, the modified stress field in Eq. (24) and the incremental constitutive tensor in Eq. (44) are tremendously simplified. This is apparent by looking at the term UT 3\u00f0\u00bdC fEg \u00fe fSpreg\u00de as the projection of the original stress field onto the shear stress direction of the wrinkling axes (t0,w0) which in turn is, for the isotropic case, the principal strain as well as the principal stress direction" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000029_bf00052515-Figure2.2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000029_bf00052515-Figure2.2-1.png", + "caption": "Figure 2.2. Forces and moments on a differential element of the bow.", + "texts": [ + " We now derive the equations of motion of bow and arrow. For simplicity we take Lo = 0; if Three situations of a bow: (a) unbraced, (b) braced and (c) fully drawn. Journal of Engineering Math., Vol. 15 (1981 ) 119-145 122 B. W. Kooi this is not the case the obtained equations have to be changed in an obvious way. The BernoulliEuler equation (which is assumed to be valid) reads M(s, t ) = W(s) { x ' y \" - y ' x \" +0o}, 0 < s < L, (2.3) where M(s, t) is the resultant bending moment at a cross section (see Figure 2.2. for sign). We recall that because the bow is symmetric with respect to the line of aim, we confine ourselves to its upper half, clamped at the origin 0. The potential energy Ap of the deformed upper half is its bending energy 1 M 2 (s, t ) d s . (2 .4) The kinetic energy Ak is the sum of the kinetic energy of the upper half of the bow, half the kinetic energy of the arrow and the kinetic energy of the concentrated mass at the tip. Then when a dot indicates differentiation with respect to time t, ~ E = J 0 l m a ~ 2 l m t l x 2 ( L , t ) + y 2 ( L , t ) } , (2", + "13) Also the dynamic boundary conditions at s = L follow from the variational procedure, they become M(L, t ) = 0, (2.14) ma~ + m t x (L, t) = 2 X(L, t ) x ' (L, t ) - y ' (L, -[)~I' (L, t ) , (2.15) _ y ( t , . . m a m tY (L , t ) = - 2 ~,(L, t ) y ' (L, t ) - x ' (i,, t-)/IT (L, t-). (2.16) b - x ( L , t) The initial conditions which complete the formulation of the problem are x ( s , O ) = x t ( s ) , y ( s , O ) = y , ( s ) , x(s , 0) = y ( s , 0) = 0, 0 < s < L . (2.17) Although it is not necessary for the computations, we look for a physical meaning of the function h(s, t). In Figure 2.2 the resultant forces and moments acting on a differential element of the bow are shown. The momentum balance in the x-andy-direct ion gives V x = ( T x ' ) ' - (Q y ' ) ' , (2.18) and V y = ( T y ' ) ' + (~9 x ' ) ' , (2.19) respectively, where T(s, t ) is the normal force and Q (s, t ) the shear force on a cross section (see Figure 2.2). If the rotatory inertia o f the cross section of the bow is neglected, the moment balance of the element gives ~I' (s, t ) = - Q(s, t) . (2.20) Journal of Engineering Math., Vol. 15 (1981) 119-145 124 B.W. Kooi Comparing equations (2.18) and (2.19), using (2.20) to replace Q by M', with (2.12) and (2.13), we find the physical meaning of X I~ ,+__(M_W0o) , 0 < s < L . (2.21) ~(s, t) = - W Substitution of (2.21) in the boundary conditions (2.15) and (2.16) yields may + m t x ( L , t ) = - T(L , t)-x' (L, t ) - y ' ( L , }-)M' (L, t) , (2" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000064_bf00537653-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000064_bf00537653-Figure1-1.png", + "caption": "Fig. 1. Deformation gradient F~i , Piola stresses tip generalized deformation gradient Uii and generalized Piola stresses ~ii", + "texts": [ + " As regards the present paper, it is further pointed out how, due to the properties of the statical and kinematical operators (including the boundary terms), the most general principles of virtual work and the associated variational principles without any subsidiary conditions can be constructed systematically. We use the Lagrangian description with the material coordinates xl and the spatial coordinates ~i, both referred to the same rectangular Cartesian reference axes with the unit base vectors el = (5~1, ($~, (~ia), where ($ij is the Kronecker delta. A rigid rotation of these axes transforms ~ into / / a n d vice versa e~ = cciiej, el ~ ~iiej; ~# = ei\" e~ = cos (ei, , (1) see Fig. 1. Here ~ij means the finite rotation which can be represented by three rotation parameters ~k in the form [2] sin ~ sin s ~/2 x~ = ~0 - - eu~ ~ + 2 ( ~ i - - ~#~) (2) where ~ - ] / ~ is the rotation angle. The following properties hold (bold face letters mean matrices): ~i~ik = o ~ k ~ , ~ i = (31j; det a = 1 ; ~ = ~-1; (3) 3~ik -=~ e,nilKmk(~l ~- --emkl~ imt)~l with el/k as permutation symbol. 31\" Ingenieur-Archiv 55 (i985) 452 Star t ing f rom the represen ta t ion ~,j = ~ , ~ = ~ k , i ~ or ~,j = - ~ % = U;i~ (4) one defines F~j =: ~ , j ; U~s = ~k~,~ = ~ ' k ~ or ~d = ~ F (5) Fi~ = ~i~U~ or F = ~ U . (6) Fu r the r one obtains f rom (4/2) ~,ldxl = F ~ l d x l ~ = U a d x ~ etc. as shown in Fig. 1. For a given general ly U is nonsymmet r ie . S y m m e t r y is achieved for a dis t inguished ro ta t ion K = a (belonging r ~ - - if) which can be calculated f rom the condit ion U = U r (U being denoted then b y U and called dist inguished general ized de format ion gradient) . I n this special case we get wi th (6) and (3/1) F~F = U~U = U~; U = I/F~F (7) the last s tep in (7/1) being due to the s y m m e t r y of U. Equa t ion (7/2) yields U and then f rom (6) there follows a = F U -~ (8) as a funct ion of the de format ion grad ien t and so changing with the place. The generahzed disp lacement gradient and the dist inguished general ized d isplacement gradient respect ively ~re defined as ~ - = ~ r or h = U - - I (9) hi~ = Ui~ - - (~0 or h = U - - I . The stresses t ---- (%~.) (Piola stresses) and ~ = (~i~) (generalized Piola stresses) can be introduced via the pseudo stress vec tor [i (force per uni t of undefo rmed e lement act ing on the deformed area e lement whose or ienta t ion in the undeformed reference configurat ion is ~ ) according to (Fig. 1) Solving for ~i~ and t~ respect ively leads to ~ = t ~ or ~ - - t a ; t~ : r~c%.~ or t : ~ . (10) r 0 = t~lcc%~ or r --- t~ ; t~ = ri~c~ or t = r a ~ (11) and calls r -- (ri]) dist inguished general ized Piola stresses. The stresses t, ~ and r are general ly nonsymmetr ic . According to the polar decomposi t ion theo rem for the deformat ion grad ien t (5/1) the unique represen ta t ion (see, f.i. Malvern [5]) = = c~ikU~j or P - - ~,: Fi: * * a ' U * (12) is val id where U* = U *~ is the posit ive definite symmet r i c r ight s t re tch and r (with propert ies (3)) describes the rigid ro ta t ion of the principal axes of Green 's s t ra in tensor which coincide wi th those of U*" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002552_iciea.2011.5975793-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002552_iciea.2011.5975793-Figure1-1.png", + "caption": "Fig. 1. Ball and beam system.", + "texts": [ + " The BBS considered in this paper is described and its models are derived, including simplified state space model and augmented state space model in Section II. Section III introduces an efficient state estimation approach, the strong tracking filter, for the case of the linear time-invariant discrete-time system. Section IV gives the design of the discrete-time LQR controller. Practical experiments are performed to illustrate the effectiveness of the STF-LQR control approach in Section V. Conclusions are drawn in Section VI. The BBS considered in this paper is shown in Fig. 1, which consists of a long beam that can be tilted by a DC servo motor together with a ball rolling back and forth on the track of the beam. The beam is supported on the both sides by two level arms. One of level arms is pined, and the other is coupled to a gear driven by the motor with a reducing gearbox. The control objective of the BBS is to turn the angle of gear \u03b8, and then the angle of the beam \u03b1, such that the ball can stay in a desired position x. When the angle is changed from the horizontal position, the gravity action will cause the ball to roll along the beam" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003404_isma.2013.6547379-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003404_isma.2013.6547379-Figure3-1.png", + "caption": "Figure 3. Movement in X direction", + "texts": [ + " By changing the control command to these motors \u03a9i, their speed will vary and the quadrotor direction is updated, accordingly the quadrotor can navigate in different directions. For instance, the quadrotor can move in the vertical Z direction by varying the speed of all propellers at the same time and by the same amount as shown in Figure 2. To command the quadrotor to move in the X direction, the speed of the front and rear propellers should be changed by the same amount and in opposite directions as shown in Figure 3. Moving the quadrotor in the Y direction can be done by changing the speed of the right and left propellers by the same amount and in opposite directions as shown in Figure 4. 978-1-4673-5016-7/13/$31.00 \u00a92013 IEEE ISMA13-2 To control quadrotor heading, the speed of all propellers is commanded by the same amount but in different directions, front and rear propellers with the same direction and right and left the propellers with opposite direction, as shown in Figure 5. The quadrotor\u2019s model, mainly includes the nonlinear aero dynamical equations of the quadrotor along with the actuators dynamics and saturation limits [10-13]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003409_s1560354711060050-Figure10-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003409_s1560354711060050-Figure10-1.png", + "caption": "Fig. 10. Geometry of the helical wave. (a) The wavelength of the traveling wave on the spheroid is (approximately) so/k cos \u03b1 where \u03b1 is the angle between e\u03b8 and the wave crest (alternatively, the angle between e\u03c6 and the direction perpendicular to the wave crest. (b) The slip velocity is decomposed into Vs \u03c6 which leads to translation, and Vs \u03b8 which leads to rotation.", + "texts": [ + "23) (a complete elliptical integral) is the arc length of the half-ellipse. We now assume that the cell has control over the orientation of the helical deformation so that it can be rotated (by, for instance, an internal helical structure) to generate helical waves passing from the north pole to south pole. If the helical deformation rotates with angular frequency \u03c9 (radians per second) then a wave crest passes a point on the spheroid every T = 2\u03c0/\u03c9 seconds. The wave speed (in the axial direction) is L/T = so\u03c9/2\u03c0k. The angle \u03b1 of the wave crest lines (see Fig. 10), measured with respect to the vector e\u03b8 is a function of both k and \u03c6 reaching a minimum at the equator and a maximum at the poles. Let us make this more explicit. In the plane (\u03b8, s) the crests appear as parallel lines given by f(\u03b8, s) = \u03b8 \u2212 2\u03c0ks = \u03c0( + 1/2) (crests). (3.24) From \u2202/\u2202\u03b8 = a sin(\u03c6)e\u03b8, e\u03b8 = (\u2212 sin(\u03b8), cos(\u03b8), 0), |\u2202/\u2202\u03b8| = a sin(\u03c6), \u2202/\u2202\u03c6 = (a cos(\u03c6) cos(\u03b8), a cos(\u03c6) sin(\u03b8),\u2212b sin(\u03c6)) = \u221a a2 cos2(\u03c6) + b2 sin2(\u03c6) \u2202/\u2202s we get that u\u0302 = 1 1 + 4\u03c02k2a2 sin2(\u03c6) (2\u03c0k\u2202/\u2202\u03b8 + \u2202/\u2202s) are the unit vectors along the crests", + "26) Step 1: identifying the parameters. Project a neighborhood of a point P \u2208 S onto its tangent plane at that point. The wavelength of the projected traveling wave at this point is so cos(\u03b1)/k, (3.27) so matching with (2.24) we have n = 2\u03c0k/(so cos(\u03b1)). Further, matching frequencies we have \u03c9 = c. Substituting these into (2.25) we have \u03c9\u03c0k\u03b52 so cos(\u03b1) (3.28) for the magnitude of the rectified velocity. Step 2: the rectified fluid velocity. It is simply Vs = |V |(cos(\u03b1)e\u03c6 + sin(\u03b1)e\u03b8) (3.29) with |V | given by equation (3.28) (see Fig. 10). This velocity is assigned to the point P . Doing this at each point defines at each point defines a constant tangential \u201cslip\u201d velocity on the surface of the spheroid. Due to axial symmetry, the e\u03c6-component contributes only to translational velocity and the e\u03b8 contributes only to the rotational velocity about the z-axis of the cell. The problem of determining the translational and rotational velocity of the cell has now been reduced to finding the translational and rotational velocities of a spheroid with a constant tangential vector field" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002696_j.1467-8659.2012.03165.x-Figure8-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002696_j.1467-8659.2012.03165.x-Figure8-1.png", + "caption": "Figure 8: A spaceship model (left) - the tiles are recognized correctly, but again, some unassigned area remains (gray). A cascade of models with increasing complexity (right) - the newly added parts create new tiles.", + "texts": [ + " We have implemented a simple prototype of the algorithm outlined above. We follow the method of [BWS10] and use a volumetric grid to discretize the symmetry information: cubes of side length h are annotated with transformations. We have applied our prototype implementation to a few scenes to visualize the structure of the decomposition. For the tests we set the radius of symmetry to 0.008 (Figure 6) or 0.016 (all other tests) of the diagonal of the bounding box of the scene. The voxel size was set to 1/512 of the diagonal (1/256 for Fig. 8). To prevent errors due to coarse discretization, classes of microtiles were computed only for microtiles larger than 32 voxels. Very small tiles usually indicate places where a finer discretization is required and we could not reliably compute the equivalence classes of such microtiles. Computing of the candidate transformations and the table that stores the set of transformations for each voxel are implemented in parallel. All test were performed on a single Intel Core 2 Quad Q9400 CPU with 4 cores running at 2", + " / Microtiles: Extracting Building Blocks from Correspondences The computed decompositions are in most regions qualitatively correct, however, the grid-discretization leads to certain variations at the boundary. We observe some unassigned area, but its diameter is below r in all of the examples. Because the voxel-discretization does not permit a 1 : 1 mapping, boundaries show some variability within voxel resolution (particularly visible at the sides of the courthouse). Furthermore, rotational patterns are numerically problematic (e.g., oversegmentation of the steps of the staircase). Similar results are obtained for the models in Figure 8. We compare our results to the previous method by Bokeloh et al. [BBW\u221709], which is computationally mostly similar but uses (as most others) simple region growing for segmentation. The method is similarly susceptible to discretization and boundary artifacts. It does not capture all symmetries, but samples prominent representatives due to the area/instance ratio heuristic employed. Global symmetries of the steps are detected, which do not affect the microtiles but are obtained implicitly with our new approach", + " Our implementation is only intended as a proof of concept, but there are some direct applications: We can determine whether two shapes are r-similar, by matching their respective microtiles. The three box-sculptures in Fig. 6 are made of the same tiles, except from the leftmost, which contains one extra, unique tile, colored violet. Similarly, the isolated tower at the left of the castle in Fig. 7 is r-similar to the castle, which contains additional tiles. A further example is demonstrated in Fig. 8 (right). A sequence of models with increasing complexity is decomposed into microtiles, revealing the redundancy in the model collection. The runtime of the decomposition is still rather large, as the algorithm performs all pairwise comparisons explicitly. Small test scenes compute in a few minutes, medium complexity scenes such as the castle require 1 hour (see Fig. 2,7). Both the number of features and the required resolution for representing the symmetries are limiting factors, and both act quadratically on the run-time" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001521_s10514-008-9106-7-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001521_s10514-008-9106-7-Figure2-1.png", + "caption": "Fig. 2 Front and back boundaries of the x-component of the ZMP. The front bound lt is a distance from the center of the support foot to the fore edge while the back bound lh is a distance from the center of the support foot to the rear edge. Fz and My denote a resultant vertical force and a moment about Y -axis acting on the foot, respectively. The ZMP along X-axis is described as Xzmp = \u2212My/Fz . The length and width of the foot are 0.21 [m] and 0.15 [m], respectively. lt = 0.134 [m] and lh = 0.076 [m] are used in the simulations and experiments", + "texts": [ + " Equation (54) states that the xcomponent of the ZMP (Xzmp) is independent of the motion along the Y -axis. Similarly the y-component of the ZMP (Yzmp) is independent of the motion along the X-axis. First, the x-component of the ZMP (Xzmp) must be in between \u2212lh and lt in the sagittal plane (Z\u2013X plane). Thus, \u2212lh \u2264 Xzmp \u2264 lt (10) where lh(> 0) denotes the length from the center of the supporting foot to the rear safety boundary while lt (> 0) denotes the length from the center of the supporting foot to the fore safety boundary, as shown in Fig. 2. Inserting (54) into (10) leads to the following inequality with respect to the range of the rate of change in angular momentum. \u2212lhmg(Z\u0308g + g) \u2264 \u2212( \u0307H0)y + n\u2211 k=1 mkgxk \u2264 ltmg(Z\u0308g + g). (11) Substituting ( \u0307HG)y + mg(ZgX\u0308g \u2212 XgZ\u0308g) for ( \u0307H0)y of (11) leads to \u2212 ltmg(Z\u0308g + g) + n\u2211 k=1 mkgxk \u2212 mg(ZgX\u0308g \u2212 XgZ\u0308g) \u2264 ( \u0307HG)y \u2264 lhmg(Z\u0308g + g) + n\u2211 k=1 mkgxk \u2212 mg(ZgX\u0308g \u2212 XgZ\u0308g). (12) It is assumed that the robot\u2019s configuration remains unchanged after impact due to the inelastic impulsive impact with the ground, the dynamic coupling effects between three planar motions, i" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001950_10402000902913345-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001950_10402000902913345-Figure3-1.png", + "caption": "Fig. 3\u2014Test bearing.", + "texts": [ + " rms = \u221a S12 + S2 [5] The AE event rate is equal to the number for every minute that the demodulated AE signal exceeds the threshold value set by the observer concerned. The rate means the condition of AE generation. The bearing used for the test was a deep-groove ball bearing (#6206 open type) with an inner diameter of 30 mm, an outer diameter of 62 mm, and a width of 16 mm, consisting of nine balls D ow nl oa de d by [ U ni ve rs ity o f C al if or ni a, S an F ra nc is co ] at 0 7: 18 2 9 Ja nu ar y 20 15 and a snap shape plastic cage as shown in Fig. 3. The inner ring, the outer ring, and the balls are made of ASTM-A295 (52100). The test rig is shown in Fig. 4. The test machine has an overhang style construction consisting of a main spindle supported on two angular contact ball bearings of #7210 series with back-to-back assembly and one deep-groove ball bearing of #6210 series. On one end of the shaft the test bearing is mounted, and to have the direct drive construction, the motor is mounted on the shaft with a coupling on the other end. Two different pure radial loads 9" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000539_1.2720866-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000539_1.2720866-Figure1-1.png", + "caption": "Fig. 1 The action of Coriolis forces: 3ND mode shapes of a bladed disk: \u201ea\u2026 blade tangential vibration; and \u201eb\u2026 blade radial vibration", + "texts": [ + " Coriolis forces are assoiated with the components of blade and disk motion along axes hich are perpendicular to the primary axis of rotation or \u201cspining\u201d of the disk on which they are carried, while the component f motion parallel to the rotation axis does not contribute to the oriolis forces F Coriolis = \u2212 m 2 r\u0307 2 here Coriolis force, F Coriolis, normal to the rotating frame veloc- ty, r\u0307 , and to the rotation vector, , causes the blade particle elocity to change direction, but not the magnitude, and is thus a eflecting force. Hence, in the investigation of the Coriolis forces\u2019 influence on ibration characteristics, we confine ourselves to study the inlane radial and tangential blade vibrations only, as there is no oupling between out-of-plane and in-plane blade vibrations due o Coriolis forces. The effects of Coriolis forces arising from si- ultaneous rotation and in-plane tangential or in-plane radial viration of the bladed disk are illustrated in Fig. 1 for the case of a hree nodal diameter 3ND mode shape. Rotating Bladed Disk System With the Effects of Coriolis orces. For rotating bladed disks, the general equation of motion or forced vibration in the time domain is known to be \u201cnonselfdjoint\u201d 5,6 and is presented as M q\u0308 t + G + D q\u0307 t + K + KS + M q t = f t 3 here, in a fixed frame of reference, q is a response of the ystem; f is the vector of applied external forces; is rotation peed; M , K , and D are mass, stiffness, and damping matries, respectively; G is a speed-dependent skew-symmetric atrix due to Coriolis forces; and KS is a speed-dependent tress stiffening matrix due to centrifugal forces; and M is a peed-dependent spin softening matrix" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000935_s1068366608030070-Figure7-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000935_s1068366608030070-Figure7-1.png", + "caption": "Fig. 7. Kinds of divisibility of surfaces and particles in the space of morphological features: (a)\u2014linear divisibility of classes; (b)\u2014 nonlinear; (c)\u2014complex; c1, c2, and c3 \u2013 morphological classes of objects.", + "texts": [ + " Several expert systems of such type are known that are used to classify wear debris by their morphological features and evaluate the current condition of friction units by output parameters of temperature, vibration, and acoustic emission gauges [37, 38]. The classification systems considered have varying potential. Production systems are capable of classifying divisible classes linearly and piece-linearly, while those based on fuzzy logic methods deal with nonlinearly divisible classes and the methods of the dimension decrease and neural networks are capable of classifying arbitrarily divisible classes (Fig. 7). However, in practice, their potential is restricted by the representativity of the parameters to be used for description of objects. To sum up the aforesaid, we can note that the practical problems of morphological analysis of friction units and wear debris can be considered for the most part solved. Numerous examples of successful realization have proved the efficiency of the methods used in 198 JOURNAL OF FRICTION AND WEAR Vol. 29 No. 3 2008 MYSHKIN, GRIGORIEV evaluation of the engineering condition of various objects of industry and transport" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000145_epepemc.2006.4778416-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000145_epepemc.2006.4778416-Figure1-1.png", + "caption": "Fig. 1 The cross-section area of the investigated real 3-phase 12/8 SRM.", + "texts": [ + " As in all kind of motors, also in the SRM a computation and prediction of performance is needed, mainly from the point of view of its efficiency [1]. The use of the SRM power-flow diagram in conjuction with the approximate equivalent circuit seems to be very simple. But in comparison with the other AC motors, SRM is always fed by inverter with nonsinusoidal current and voltage waveforms. This fact complicates the evaluation of the individual kind of losses [2]. This paper deals with investigation of losses and efficiency in real 3-phase SRM, 12/8, 3.7kW, 3000rpm. Its cross-section area is shown in Fig.1. The analysis of SRM losses is made by analytical approach of winding and iron losses. The results from analytical approaches are compared with FEM and verified by the measurement. The efficiency of SRM inverter, the efficiency of motor and the total efficiency of the whole SR drive is measured and calculated. The SR-drive losses consist mainly of: motor losses, inverter losses and wires losses. This paper is focused on the losses of the SRM in greater details. Motor losses consist of: winding loss zAPW, core losses zAPC, mechanical losses APPm and additional loss Pad", + " Analysis offlux linkage waveform Before calculation of SRM core losses it is very important to determine the flux linkage waveforms in each part of the core. The waveform of flux linkage in SRM depends on phase current waveform which depends on SRM speed and load. In the SRM only the stator winding is excited, the flux waveforms in the individual parts of core are determined by the switching sequence in the stator phase winding. The normal switching sequence for 3-phase 12/8 SRM is to excite the phases successively, it means: A, B, C, A, B, C, etc (see Fig.1). In this case, each commutation step constitutes one working stroke and each cycle constitutes a switching period Ts. Since a phase winding is excited when a rotor pole tends to the alignment, the number of periods for stator phase per revolution is equal to the number of rotor poles. Then, the switching period per phase is given as 9rNR a) r (2) where Xt is angular speed of the rotor, NR is number of rotor poles and A4 is rotor pole pitch. In this case for rated speed 3000rpm is T,=0.0025s. The stroke period T,, depends on the number of phases", + "4 there is only flux linkage waveform for phase A in stator tooth, which is reversed with period T,s but it is only positive. 0.4 Tst[Wb] 0.3 0.2 0.1 0.0 Bimst 0. 6 [T] 0.5 0.4 0.3 0.2 0.1 0.0 0 5 10 15 20 25 30 35 40 45 9 [0] a)I I 111 ulu-l-I 1-1I I-I-I II 0 0.0 -0.2 -0.4 BimsyP0.8 [T] 0.6 0.4 0.2 0.0 2 4 6 8 10 12 14 1 6 1 8 20 i-order of harmonics b) Fig. 4 a) The waveform of stator tooth flux linkage versus rotor position, b) magnitudes of flux density harmonic components. C. Statoryokeflux linkage The stator yoke of investigated SRM is possible to divide into 12 parts (see Fig. 1). The total flux linkage of the stator yoke parts is different. From the Fig. 5 it is clear, that the total flux in parts 1,4,7,10 - TsyP is nearly constant, therefore the core losses in these parts are negligible. However, in other parts of stator yoke (2,3,5,6,8,9,11,12) the flux linkage is reversed with period T', it is positive and negative and its waveform is shown in Fig.6. 0.4 Tsyl [Wb] 0.2 - 0.1 0 5 10 15 20 25 30 35 40 45 [0] a) )a) \\ 1 1 II (/10 15 20 25 30 35 45 a) 0 0 2 4 6 8 10 12 14 16 18 20 i-order of harmonics b) Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001557_j.triboint.2008.01.009-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001557_j.triboint.2008.01.009-Figure4-1.png", + "caption": "Fig. 4. Cracks initiated from edge of dent in twin-disk test: (a) Slip ratio of 5% Test conditions: Pmax \u00bc 3.2GPa; rotating speed of driving member n \u00bc 500m", + "texts": [ + " The dents made in the test pieces at the edge of the running band had a diameter of 300 mm and a depth of approximately 35 mm. The dents along the edge of the running band were made larger because flaking will not originate from the smaller dents due to the low contact pressure in ARTICLE IN PRESS T. Ueda, N. Mitamura / Tribology International 41 (2008) 965\u2013974968 this area. In the case of small dents at the edge of the running band, the tendency is for the test piece to fail by flaking due to subsurface originate fatigue at the center of the running band, where the contact pressure is high. Fig. 4 shows the condition of the edge of a dent after 50 h of testing. In Fig. 4, all of the photographs are displayed in the same orientation, i.e. the rolling direction (direction of load movement) is in the same direction. Fig. 4(a) shows the results for a driven disk test piece with dents (test condition I in Table 1) and Fig. 4(b) shows the results for a driving disk test piece with dents (test condition II in Table 1). The driven disk in Fig. 4(a) was subjected to a tangential force in the same direction as the rolling direction, while the driving disk in Fig. 4(b) was subjected to a tangential force in the opposite direction to the rolling direction. When Fig. 4(a) and (b) are compared with each other, Fig. 4(a) reveals that cracking had initiated from the trailing edge of the dent with respect to the rolling direction. Fig. 4(b) reveals that cracking had initiated from the leading edge of the dent with respect to the rolling direction. In fact, cracking initiated from the trailing edge of all eight dents in the driven disk, similar to that shown in Fig. 4(a). Conversely, cracks initiated at the leading edge of only two of the eight dents in the driving disk, similar to that shown in Fig. 4(b). Additionally, Fig. 4(c) shows that no cracks initiated at the edge of dents under conditions of zero tangential force (i.e. no slip), even after 50 h of testing. Twin-disk test results with artificial dents introduced in to the disk surface revealed: (1) tangential force (sliding) accelerates crack initiation at the edge of a dent, (2) the position of a crack initiated at the edge of a dent is affected by the direction of the tangential force (sliding direction), rather than the rolling direction (direction of load movement), and (3) cracks initiate more easily at the edge of a dent in the driven disk compared with the driving disk" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001065_09544062jmes1177-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001065_09544062jmes1177-Figure1-1.png", + "caption": "Fig. 1 Schematic representation of the region considered for mathematical formulation", + "texts": [ + " The combination of low beam power (450W) and low processing speed (1000 mm/min) leads to high beam energy level producing a keyhole mode of welding and Proc. IMechE Vol. 223 Part C: J. Mechanical Engineering Science JMES1177 \u00a9 IMechE 2009 at Purdue University on May 21, 2015pic.sagepub.comDownloaded from the effect of various beam energy levels on the weld pool geometry has to be analysed in detail. To develop the mathematical formulation for laser welding process the geometry of substrate as illustrated in Fig. 1 is considered. The figure shows a typical weld seam for a bead-on-plate configuration and the two-dimensional transverse section analysed in the present work. The laser beam is assumed to follow a three-dimensional conical Gaussian distribution with the focused spot on the workpiece surface. In the heat transfer analysis, the transient temperature field T of the laser welded sheet is a function of time t and the spatial coordinates (x, y, z) and is determined by the non-linear heat transfer equation \u03c1Cp [ \u2202T \u2202t + (\u2212vw) \u2202T \u2202y ] = k ( \u22022T \u2202x2 + \u22022T \u2202y2 + \u22022T \u2202z2 ) + Qv(x, y, z) (1) where Qv is the volumetric heat source term which varies with beam power and welding speed. k, Cp, \u03c1, and vw are the thermal conductivity, specific heat, density of the sheet material, and velocity of the workpiece, respectively. Figure 1 shows the schematic representation of the region considered for mathematical formulation. Figure 2 illustrates the thermal boundary conditions on a typical transverse section A-B-C-D (refer Fig. 1). The focused laser beam is irradiated on the top surface within a circular zone defined by the position of centre of the laser beam and its effective radius. The rest of the steel substrate surface facing air is subjected to the convection and radiative heat losses [8]. The initial condition is T (x, 0, z, t) = T0(x, y, z) (2) The essential boundary condition for the transient analysis is T (x, y, z, 0) = T0(x, y, z) (3) on the boundary S1. This condition prescribes nodal temperatures at the inlet surface S1" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002449_03093247v014313-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002449_03093247v014313-Figure5-1.png", + "caption": "Fig. 5. Simple shear with movement along a line inclined to both co-ordinate axes", + "texts": [ + " For the easy visualization of the deformation we may choose the three independent variables 4, E and (++ w), because + denotes the direction in which the body is first stretched, E the amount it is stretched and (++w) the final position of the most severely stretched fibre, or the direction of the principal finite strain (tensile). Simple shear and pure shear Simple shear (Fig. 4) is important in engineering applications because it is the deformation occurring in twisted thin tubes. The matrix representing it is where y is as shown in Fig. 4. As in the case of pure shear, the more general type ofsimple shear (Fig. 5) is represented by the product 1 - (y /2 ) sin 2+ y cos2 + cos + -sin+ -y sina 4 It can also be shown that any homogeneous two-dimensional deformation of incompressible media can be considered to be a simple shear of the type represented by equation (18) plus a rotation, and a set of equations analogous to equations (16) can be found by working out the necessary algebra. We conclude, therefore, that a homogeneous twodimensional deformation may be considered to be either a pure shear or a simple shear; it cannot be said to be one but not the other" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001677_1.4000517-Figure7-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001677_1.4000517-Figure7-1.png", + "caption": "Fig. 7 A Stephenson six-bar chain", + "texts": [ + " Since the input parameter is usually the angle between adjacent links, relative angles are used in Fig. 5. On the other hand, in a Stephenson type linkage, subbranch or full rotatability condition is complicated with the input given through a joint, i.e., C0, C, or D, not in the four-bar loop. Resolving the full rotatability problem under this input condition is the focus of this paper. This may explain why A0C0 and C0C are used as the reference links in Figs. 1 and 7, respectively. Figure 1 highlights the feature of having 2 or 8 as the input joint parameter. Figure 7 highlights the feature of having 8 or 7 as the input joint parameter. Thus, instead of presenting a lengthy discussion on all linkage inversions or input conditions, the reference is chosen differently in each example to highlight the versatility of the method, rather than the necessity of a particular reference choice. Thus, the discussion in the paper covers all possible linkage inversions or input conditions. FEBRUARY 2010, Vol. 2 / 011011-3 015 Terms of Use: http://asme.org/terms 3 w l p l o c r t c s a c a t p p o c m o l n o e t T d t c t l c g d s t a t i T a 0 Downloaded Fr Singularity There should be no dead center position in a linkage branch ith full rotatability", + " herefore, finding the dead-center positions for Stephenson linkges can be treated in three categories. 1 In the first category, the input is given through a joint in the four-bar loop Fig. 1 . The dead center positions exhibited in the I/O curve of the four-bar loop, and the branch point with the JRS boundary are the dead center positions of the Stephenson six-bar linkage. This case has been well treated 1 . In the other two categories, the input is given through a joint such as C0 or D and C Fig. 7 , not in the four-bar loop. 2 If the joint at C0 is used as the input joint, the singularity occurs when links A0A, B0B, and CD intersect at a common point 1,13 . In order to demonstrate the generality of the proposed method for any input condition disregarding the linkage structure type, the singularities will be determined through the input versus output relationship directly. Since the choice of the output joint does not affect the dead center position, 7 and 8 will be used as the input-output variable 11011-4 / Vol. 2, FEBRUARY 2010 om: http://mechanismsrobotics.asmedigitalcollection.asme.org/ on 04/21/2 pair, and hence, C0C as the reference link so that the singularities of the two categories can be dealt without excessive derivation. The relationship between 7 and 8 is governed by the following two loop closure equations of the linkage Fig. 7 . Five-bar loop C0A0ADCC0 a8 + a7ei 7 + a5ei 5 \u2212 a9e 8+ = a2ei 2 2 Five-bar loop C0B0BDCC0 a8 + a7ei 7 + a6ei 5+ \u2212 a10e i 8 = a4ei 4 3 where i, , , , , and ai denote the angular positions and link lengths of the Stephenson linkage as shown in Fig. 7. Multiplying Eqs. 2 and 3 to their complex conjugates, 2 in Eq. 2 and 4 in Eq. 3 can be eliminated. Thus, Eqs. 2 and 3 yield, respectively A1 7, 8 sin 5 + B1 7, 8 cos 5 + C1 7, 8 = 0 4 A2 7, 8 sin 5 + B2 7, 8 cos 5 + C2 7, 8 = 0 5 where A1 = 2a5a7 sin 7 \u2212 2a5a9 sin 8 + B1 = 2a5a7 cos 7 \u2212 2a5a9 cos 8 + + 2a5a8 C1 = \u2212 a2 2 + a5 2 + a7 2 + a8 2 + a9 2 \u2212 2a8a9 cos 8 + \u2212 2a7a9 cos 8 \u2212 7 + A2 = \u2212 2a6a8 sin \u2212 2a6a10 sin 8 \u2212 + 2a6a7 sin 7 \u2212 B2 = 2a6a8 cos \u2212 2a6a10 cos 8 \u2212 + 2a6a7 cos 7 \u2212 C2 = \u2212 a4 2 + a6 2 + a7 2 + a8 2 + a10 2 + 2a7a8 cos 7 \u2212 2a7a10 cos 7 \u2212 8 \u2212 2a8a10 cos 8 Substituting the half-angle formula sin 5 = 2t5/ 1 + t5 2 , cos 5 = 1 \u2212 t5 2 / 1 + t5 2 6 where t5=tan 5 /2 into Eqs", + " Each real root of the olynomial equation represents a dead center position. Example 1: The dimensions of Stephenson six-bar linkages Figs. 1 and 7 are given below a1 = 3.5, a2 = 2.82, a3 = 4.0, a4 = 2.5, a5 = 5.0 a6 = 5.23, a7 = 3.2, a8 = 1.0, a9 = 5.0, a10 = 3.04 = \u2212 36.87 deg, = 70.0 deg, = 46.0 deg = \u2212 43.69 deg The branch points and dead center positions when the input is iven through 2 of the Stephenson linkage in Fig. 1 are listed in able 1 and shown in Figs. 8 and 9. If the input is given through 8 of the Stephenson linkage in Fig. 7 with the given dimension, in Eq. 10 becomes a 66th degree polynomial, while M in Eq. 11 becomes a sixth degree polynomial in terms of t8. The real olutions of Eq. 10 that satisfy the condition of Eq. 11 are the ead center positions. The number of the extraneous roots with the iven dimensions is four. Due to the complexity of symbolic comutation, the method does not predict the maximum number of ead center positions unless the specific dimensions are given. he resulting dead center positions with 7 and 8 as the input are Table 1 Branch points and dead center positi 2 Position Input deg 2 3 4 1 36", + " 21 is equal to zero or 2 = P25 2 Q25 2 = 0 22 Thus, the dead center positions can be obtained by solving P25 2 =0 and Q25 2 0 \u2022 3 5 Let 3 be the input angle and 5 as the output angle. This is a case similar to the case of having 1 as the input. Eliminating 1 from Eq. 14 and substituting Eq. 13 into it yields the relationship between 3 and 5. That is f 3, 5 = a1 + a5 cos 5 + a4 cos 1 \u2212 n 5 + + a3 cos 3 + 1 \u2212 n 5 + 2 + a5 sin 5 + a4 sin 1 \u2212 n 5 + + a3 sin 3 + 1 \u2212 n 5 + 2 \u2212 a2 2 = 0 23 The dead-center positions occur when the discriminate of Eq. 16 is equal to zero or of Stephenson linkage of Fig. 7 with input of Output deg 2 1 = 2\u2212 8+ \u2212 3 1 = 5\u2212 8+2 \u2212 \u2212 85 6.88 295.1 59 6.56 294.65 45 3.39 240.44 97 3.47 240.54 of Stephenson linkage of Fig. 7 with input of Output deg 2 1 = 2\u2212 8+ \u2212 3 1 = 5\u2212 8+2 \u2212 \u2212 09 3.42 304.43 34 2.12 238.98 21 4.93 242.56 96 11.72 279.49 ons 8 26. 16. 77. 19. ons 7 50. 31. 89. 06. Transactions of the ASME 015 Terms of Use: http://asme.org/terms T P a a t c 5 o 4 b s c t f r l l fi l d J Downloaded Fr 3 = P35 3 Q35 3 = 0 24 hus, the dead center positions can be obtained by solving 35 3 =0 and Q35 3 0. It should be noted that, for ease of calculation, Eqs. 17 , 21 , nd 23 must be rewritten in the half-tangent-angle formula", + " This can be done by mapping the corresponding output value to the four-bar I/O curve or the linear gear constraint Figs. 8 and 6 . The full rotatability identification is illustrated with the following two examples. 4.2.1 Stephenson Six-Bar Linkages. With the same dimension as in Example 1, branch points 1\u20138, with the input given through 2 of the Stephenson linkage in Fig. 1, are list in Table 1 and shown in Fig. 8. The dead center positions with the input give through 7 or 8 of the Stephenson linkage in Fig. 7 are listed in Tables 2 and 3, respectively Fig. 9 . 4.2.1.1 Branch identification. With the branch identification discussed early, as seen in Fig. 8, the I/O curve of 2 versus 3 is ve-bar linkage with input of 5 Output deg 2 3 4 0.68 106.15 36.29 180.72 88.80 49.40 180.72 213.25 71.85 0.99 188.73 88.37 ed five-bar linkage with input of 3 Output deg 2 4 5 80.05 40.74 116.13 226.66 46.57 127.79 134.74 74.94 184.52 285.99 83.07 200.78 d fi ear FEBRUARY 2010, Vol. 2 / 011011-7 015 Terms of Use: http://asme", + "69 deg 2 252.37 deg. \u2022 Branch 7\u20138: The I/O curve in segment 5\u20136 contains branch points 5 and 6. The 2 angles at both branch points are the rotation limits of 2, i.e., 291.30 deg 2 298.52 deg. It is noted that branches 3\u20134, 5\u20136, and 7\u20138 are in the same sub-branch of the I/O curve of the four-bar loop, while branches 1\u20132 are in both sub-branches of the I/O curve due to the existence of the dead center position at 9 or 10 1 . 4.2.1.2 Full rotatability identification. If the input is given through 8 in Fig. 7, one may find that the corresponding 2 1 values at all of the four dead center positions Q1, Q2, Q3, and Q4 are in the range of 12.30 deg\u201336.22 deg . Thus, branch 1\u20132 contains four dead center positions and has no full rotatability. On the other hand, any of the other three branches contains no dead center position and has full rotatability Fig. 9 . Mapping the dead center positions onto the JRS of 2 and 3 Fig. 8 , one can observe that the dead center positions Q1, Q2, Q3, and Q4 exist only in branches 1\u20132. Any branch containing no dead center position has full rotatability. If the input is given through 7 in Fig. 7, there will be four dead center positions, P1, P2, P3, and P4. The corresponding 2 1 values at the dead center positions P1, P2, P3, and P4 are only in 12.30 deg\u2013 36.22 deg of branches 1\u20132. Thus, no full rotatability exists in branches 1\u20132. The dead center positions are the rotation limits of the input link. Mapping the dead center positions onto the JRS of 2 and 3 Fig. 8 , one can observe that no dead center positions are found in the other three branches Fig. 9 , and hence, full rotatability exists in these branches" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003490_03093247v043208-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003490_03093247v043208-Figure1-1.png", + "caption": "Fig. 1. Disc test specimen", + "texts": [ + " Its initial yield stress was found to be about 50000 lbf/in2 ( k = 28 900 lbf/in2) from tension and compression tests, rising to 80 000 lbf/in2 at a strain of 0.08. From hardness tests the flow stress was deduced to be 72 500 lbf/in2 (k = 41 700 lbf/in2). Experimental technique The residual stresses were produced in the rolling-contact disc machine described by Jefferis and Johnson (xo), with which either free rolling or a controlled traction could be obtained. This machine restricted the dimensions of the rollers to the size and shape shown in Fig. 1. The raised central rolling track is supported by sloping shoulders to achieve approximately plane-strain deformation. It was assumed that the residual stresses were confined to the rolling track and were uniformly distributed over its width. The rolling surfaces were finished to better than 10 pin c.1.a. After rolling each disc was dissected in two steps : firstly the disc was bored out to form a cylindrical shell of thickness 0.15 in for HE2OWP, 0.10 in for En 5A, and secondly the shell was cut to form the ring and strip components of width 0-25 in" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003259_j.cja.2013.04.006-Figure6-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003259_j.cja.2013.04.006-Figure6-1.png", + "caption": "Fig. 6 An arc tooth face-gear fabricated by NC machining.", + "texts": [ + " (18) are expressed as z0 \u00bc zjt\u00bc0 z1 \u00bc oz ot jt\u00bc0 z2 \u00bc 1 2 o2z ot2 jt\u00bc0 z3 \u00bc 1 6 o3z ot3 jt\u00bc0 z4 \u00bc 1 24 o4z ot4 jt\u00bc0 8>>>>< >>>>: \u00f019\u00de Table 1 presents the basic design parameters for an example of fabricating an arc tooth face-gear pair. Table 2 lists the movement parameters for each axis of a common multi-axis NC machine fabricating an arc tooth face-gear. The movement parameters of the multiple axes of an NC machine in the complete machining of an arc tooth face-gear are obtained by multi-numerical superposition. The manufactured arc tooth face-gear is shown in Fig. 6. The hobbing test is an important method with which to check the meshing condition. The arc tooth face-gear pair obtained by NC machining is inspected in a 90 hobbing machine, as shown in Fig. 7. The hobbing test inspection of the arc tooth face-gear pairs reveals good meshing, which verifies the precision of the meth- Table 2 Motion parameters in fabricating a face gear. Movement axis Constant term 1st-order Z 17.0125 119.0342 X 321.0000 0 Y 119.0322 17.0128 l 0.1402 1.0000 w 1.2998 0 od of fabricating the arc tooth face-gear and demonstrates the smooth transition between the working tooth surface and the curved tooth surface of the arc tooth face-gear" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003331_indin.2012.6301378-Figure13-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003331_indin.2012.6301378-Figure13-1.png", + "caption": "Figure 13. Inner race fault vibration signal modulation according to shaft rotation", + "texts": [ + " We can, hence, deduce that the faulty bearing is the Fan End bearing, with an Inner race fault. In this part, we will show how the HFRT is efficient for bearing fault signature characterization. There is a series of peaks around the FIRF harmonic frequencies. This is due to the amplitude modulation of the vibration signal carried by FIRF (147.7 Hz) by the shaft rotation speed which frequency is FR (29.93 Hz). lighter level and thus influences the vibration signal\u2019s amplitude. For instance, the vibration will be more intense if the load is heavier. \u201cFig.13\u201d illustrates this situation. So the vibration signal is modulated by the frequency of rotation speed of the inner ring, FR. Table IV, which lists the values of the frequencies present in the spectrum, confirms this. Figure 14. Zoomed envelope spectrum of FE signal to highlight rotation speed presence The appearance of these peaks is due to the envelope calculation. Indeed, the envelope extracts any modulation amplitude of a signal. We saw that the frequency of inner race fault FIRF itself is amplitude modulated by the frequency of rotation" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003869_s00419-012-0608-6-Figure8-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003869_s00419-012-0608-6-Figure8-1.png", + "caption": "Fig. 8 The mode shapes corresponding to frequency \u03c931 (auxiliary model)", + "texts": [], + "surrounding_texts": [ + "As mentioned earlier, in the geometrical model of the gear, the geometry of the teeth is omitted. It allows us to reduce the system\u2019s FE model size. The simplified geometrical model of the system consists of five sectors (see Fig. 1) that have the cyclic symmetry feature. Each of these segments is meshed by using standard procedures of the ANSYS software. The 3-D solid mesh is elaborated and as mentioned earlier, the ten-node tetrahedral element (solid92) with three degrees of freedom in each node is used to realize each sector. During the mesh generation process, it is assumed that the maximum length of each element\u2019s side needs to be no more than 2.7 [mm]. The developed FE model is displayed in Fig. 2, and it consists of 19,620 elements and 36,188 nodes, respectively. The particular sectors are glued as a whole at the geometrical model preparing the stage by using standard procedure of the ANSYS program. The analysed gear is mounted in the roller bearings. Such bearings typically have slight load capacity under loads perpendicular to the primary supported direction. The gear shaft neck surfaces on which the bearings are assembled are denoted \u201cbearing\u201d (see Fig. 3a). The gear mates with the other devices by the splines. The splines is simplified down to a regular cylinder of the diameter assumed as equal to the splines pitch diameter. The surface denoted \u201cjoint\u201d (see Fig. 3a) is located on the pitch diameter of the splines. Parameters of the analysed system are shown in Table 1a\u2013b. The calculation results for natural flexural oscillations taking into account angular speed of the gear are shown in the paper. In the case of circular discs and annular plates, for each solution where nodal lines are nodal diameters, one obtains two identical arrangements of straight nodal lines, rotated by an angle of \u03b1 = \u03c0/(2n) one to another, where n is the number of nodal diameters. In accordance with the circular and annular plate vibration theory [5,6,12], the particular natural frequencies of vibration are denoted as \u03c9mn , where m refers to the number of nodal circles and n is the mentioned number of nodal diameters. As the shape of the gear model is fairy elaborate, the flexural modes of the system are subject to deformation (as compared to the system without any holes) to such extent that establishing which particular node it refers to becomes rather difficult. This problem is even worse if the angular speed of the gear is varying. The problem of influence of the angular speed on the flexural gear models deformation is analysed. For the purpose of identification of these modes, an algorithm of tagging oscillation modes, which determines the correspondence between vibration of the circular disc versus disc with holes, is used. For this purpose, an auxiliary model of annular plate in the form shown in Fig. 3b is used. The geometrical dimensions of the auxiliary model were taken from the gear geometry (shown in Fig. 1). They are as follows: addendum circle diameter dz , rim mounting diameter dp, root circle diameter dw2, and thickness h p and hz (see Table 1). Dynamic analysis is performed for the auxiliary model cases rotating at predetermined angular speed, where diameter of though holes d01 (see Fig. 3b) varies as seen in Table 2. Findings are compared to each other both quantitatively and qualitatively. This method makes it possible to investigate deformations of nodal lines associated with nodal diameters and circles due to through holes and then determine correspondence between oscillation modes of solid circular disc and a plate with holes. In the final step, solutions found for the auxiliary model are compared with the solution for the system whose FEM model is shown in Fig. 2 (the principal model). As for the principal model case, the 3-D solid mesh and the ten-node tetrahedral element (solid92) are used to discretize the auxiliary models. For all models subject to analysis, the boundary conditions were applied to the nodes. For each model, 1 d f associated with node radial displacement was subtracted from the nodes found on the surface identified as a bearing (see Fig. 3a,b). Furthermore, 1 d f associated with the displacement of nodes along the centreline of each model was subtracted from the nodes found on the surface, identified as a joint (see Fig. 3a,b). For the models obtained in this way, calculations were kept conducted as long as the natural frequency \u03c918 was determined. The calculations were performed assuming that the systems rotate as angular speed of \u03b8 , within the range of 0\u20131047 [ rad/s]. During the computing process, the angular speed values were gradually increased by 80[ rad/s], which made fourteen variants of the results (the natural frequencies and corresponding natural modes), which were subject to further interpretation. The rotation effect was taken into account by determining stress distribution due to rotation, for each model during the computational step associated with static analysis (the so called pre-stress effect). This stress distribution was then included in the computation step associated with modal analysis. The results of the numerical calculations related to the procedure of identifying deformed natural modes of flexural vibration of the gear under consideration are shown below. The results displayed here relate to the determination of the correspondence between the natural frequencies \u03c916 and \u03c925 at high angular speed (\u03b8 = 1047 [ rad/s]) as well as to the correspondence between oscillation modes and the natural frequency \u03c931 at lower angular speeds (\u03b8 = 80 [ rad/s]). The results as shown in Figs. 4, 5, 6, 7, 8, 9 allow for tracking deformations of nodal lines associated with nodal circles and diameters, due to varying diameter of the through holes. With respect to the natural frequency \u03c925, there is marked difference in shapes of natural modes. When one compares the results between each other, one can notice that in order to identify correctly deformed natural modes of the flexural oscillations in the gear under consideration at lower angular speeds, larger number of auxiliary models is required to be included during calculations, as compared to the higher angular speeds. It comes from the fact that additional stresses through the centrifugal effects appear. This effect causes the gear flexural stiffness to be an apparent function of rotational speed (stiffness grows for higher speed). In the next part, results of the numerical calculations associated with the extent of the influence of the angular speed to deformation of mode shapes of oscillations. For each discussed case, both mode solutions related to nodal diameters are shown. These analysed results are sorted by the order of their occurrence. For the frequencies \u03c923 and \u03c918, the results were obtained at angular speeds of \u03b8 = 0 and \u03b8 =1,047 [ rad/s] respectively. For the other cases, results were obtained at angular speeds \u03b8 of, 0, 320, 720, and 1,047 [ rad/s], respectively. Natural frequencies for these modes are included in Table 3. To determine this mode (see Figs. 10, 11), the procedure of tagging natural oscillation modes was required. Nodal lines associated with the circle and diameter are deformed. Minor influence of the angular speed to deformation of the nodal lines is noticeable. The task of determining modes in this case was not too difficult (see Figs. 12); no procedure of tagging natural oscillation modes was required. The slight impact of the gear angular velocity on the distortion of the nodal lines is observed. For these modes (see Figs. 13, 14), procedure of tagging natural oscillation modes was required. It is noticeable that angular speed affects markedly deformation of the nodal lines. Once the angular speed of 720 [ rad/s] is exceeded, the oscillation mode takes different shape. Major deformation of mode shape attributable to the shaft vibrations is evident at this speed. Moreover, additional problem associated with some similarity of the mode being tagged to the mode associated with frequency of \u03c931, emerged during mode identification. Establishing the correspondence between these modes was a complex task (see Figs. 15, 16) due to the shape of oscillation modes similarity to the case discussed earlier. The angular speed affects deformation of nodal lines markedly. Major shape mode variations emerge at \u03b8 = 400 [ rad/s]. The identification process in this mode was not easy (see Figs. 17, 18) . One can notice that angular speed affects the deformation of nodal lines. Major variation in mode shape emerges at \u03b8 = 720 [ rad/s]. Moreover, additional annular shaft vibration emerges at the highest considered angular speed. Finding correct correspondence between the modes in this case was fairly easy (see Figs. 19). High repeatability in deformations of nodal lines on circular plate at various angular speeds is noticeable. As a consequence of the conducted analysis (see Table 3), the Campbell diagram was plotted for the gear under consideration. This is a convenient method of displaying the relationship between gear natural frequencies and transmission system excitations [4]. Excited frequencies are plotted on a vertical axis, and the gear speed of rotation is plotted on the horizontal axis (see Fig. 20). Natural frequencies achieved from numerical analysis are plotted as near-horizontal curves. The forced frequency due to the meshing is determined by the following relation (as in Ref. [4]) f = n0 \u00b7 z 60 (4) where n0 [rpm] is the rotational speed and z is the number of teeth in the gear. For this system, the gear teeth number is z = 59. Vibration resonance phenomenon occurs when forcing frequency (4) matches as to its value with some natural oscillation frequency of the gear. The points where the near-horizontal \u03c9mn curves intersect the straight line (4) indicate the speeds at which the gear resonance will be excited (see Fig. 20). For instance, the rated excitation speed for the natural frequency of \u03c923 is 764 [rpm]. It may be inferred from both the Campbell diagram and Table 3 that the rotating movement makes flexural stiffness of the gear under consideration to increase. Moreover, at speed of 3,820 [rpm], one can notice major surge associated with the mentioned earlier changing of the shape of the natural mode frequency in the case of the frequency of \u03c931. The growth of the gear transversal stiffness observed during gyrate of the gear comes from the appearance of the additional stresses in the toothed gear through the centrifugal effects. The higher rotational speed generates higher centrifugal forces, higher stress level, thereby causing the transversal stiffness of the system to increase. Moreover, the growth of the gear flexural stiffness through the gyrate effect causes reduction of the needed numerical calculations connected with identifying the proper distorted mode shapes." + ] + }, + { + "image_filename": "designv11_7_0001590_wst.2009.139-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001590_wst.2009.139-Figure1-1.png", + "caption": "Figure 1 | Schematic diagram of MFC for wastewater treatment and simultaneous generation of electricity (view from the top) (1. compartmentalized vessel;", + "texts": [ + " 2005). Though the anodic compartments described above, categorized as up-flow reactors, may apparently be scaled up without any major problems, the cathodic compartments still require significant improvements in terms of minimizing internal resistance and improving the efficiency of the cathodic reaction. The primary objective of this paper was to develop a laboratory-scale plug-flow multi-electrode MFC with immersed cathodes, and to test the prototype device using glycerol and acetate as fuels. Figure 1 shows a schematic diagram of the location of the basic elements inside the MFC constructed and the direction of liquid flow inside the anodic zone (Fedorovich et al. 2007). Thus, the MFC consists of a compartmented vessel (1) which has a cuboidal form and is equipped with an inlet (2) for input of the wastewater stream and an outlet (3) for discharge of treated wastewater. The reactor is divided into compartments by means of rectangular vertically-disposed planar elements (4) representing anodic electrodes which are manufactured from porous graphite (50% porosity) and coated with palladium" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002676_iros.2011.6094947-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002676_iros.2011.6094947-Figure2-1.png", + "caption": "Fig. 2. [Top] Structure and kinematic nomenclature for a single-segment continuum robot. [Bottom] IREP with two continuum arms constructed along with the stereo camera actuated unit.", + "texts": [ + " This paper proposes a method to estimate the configuration of a single-segment continuum robot using a visual feature descriptor that is extracted from a stereo camera system and mapped to the robot\u2019s configuration angles. Our image segmentation and descriptor extraction methods are shown to be robust to partial occlusions. We present these results by manipulating a standard laparoscopic tool in the viewing frustrum, providing different levels of partial occlusions in a realistic fashion. Although the algorithm extends to any continuum robot design, we have in mind the IREP surgical robot [24], shown on the bottom of Fig. 2. Our method uses training samples to interpolate a manifold, which is parameterized by the configuration angles of the continuum segment. This compact representation of the appearance of the robot\u2019s configuration allows us to estimate unknown configurations by extracting the feature descriptor and indexing into the manifold to determine the best angles which may have produced that descriptor. The proposed algorithm uses a feature descriptor to provide the sensitivity needed to accurately capture small changes in the configuration of a continuum robot", + " The algorithm relies on the assumption that consecutive configurations are strongly correlated and nearby in the feature descriptor\u2019s space. We tested on robot movements in all 3-dimensions and are able to recover configuration angles in the range of 1\u25e6 of accuracy. Several designs of continuum robots that bend in a circular shape have been proposed [25]. This section briefly presents the kinematics of the particular design [11] used to validate the work proposed in this paper. The multi-backbone singlesegment robot shown on the top of Fig. 2 is constructed of one centrally located passive primary backbone, and three radially actuated secondary backbones with pitch radius r and separation angle \u03b2 . By controlling the lengths of the secondary backbones, the segment can be moved throughout the workspace defined by the kinematics. The pose of the end disk of the continuum robot can be completely described by the generalized coordinates, termed configuration space, by \u03c8 = [\u03b8L,\u03b4 ]T (1) where \u03b8L and \u03b4 define respectively the angle tangent to the central backbone at the end disk, and the plane in which the segment bends" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003267_j.phpro.2012.10.063-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003267_j.phpro.2012.10.063-Figure3-1.png", + "caption": "Fig. 3. (a) tensile specimen; (b) azimuth and polar angle on building platform, according to [9]", + "texts": [ + " Similar to the struts in lattice structures, no subsequent machining was carried out after the building process. In [9], it has been shown that different geometric properties have a more or less severe influence on the mechanical properties of the single struts in lattice structures. These parameters are: polar angle of the strut in the building chamber azimuth angle of the strut in the building chamber diameter of the strut\u2019s circular cross section length of the strut These parameters can be seen in Fig. 3. The used tensile specimen is depicted in the left part of the figure. It has two fixing points, which are designed analogue to the standardized flat test specimen DIN 50125 form E. The testing geometry with its circular cross section is placed between these fixing points. The transition from the fixing point to the testing geometry was designed by a curve with a radius of 1 mm to minimize notch stresses. The specimens have been built up with a layer thickness of 50 \u03bcm and the manufacturer\u2019s standard set of process parameters" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002434_j.apm.2012.11.020-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002434_j.apm.2012.11.020-Figure1-1.png", + "caption": "Fig. 1 shows the classified geometry of bearing. Based on early literature we maintained a limit of non-circularity of (0 < G < 3) and that of misalignment as (0 < Dm < 1). The amplitude of roughness is maintained as (1 lm < At < 5 lm) and (1 lm < At < 5 lm). In order to carry out the analysis, the bearing surface is unwrapped and the film is presented in a grid.", + "texts": [ + " In this study the bearing geometry is due to combined effect of bore ellipticity, shaft misalignment and bore roughness and is quantified as hs \u00bc cf1\u00fe G cos2\u00f0h a\u00de \u00fe 20 cos\u00f0h U0\u00de \u00fe wz cos\u00f0h a U0\u00deg ht \u00fe hl \u00f01\u00de where, w \u00bc Dmwmax and wmax \u00bc 2 \u00f01 22 0 sin2 a\u00de 1 2 20 cos a h i \u00f02\u00de and, ht \u00bc At sin 2px kt \u00f03\u00de As well as, hl \u00bc Al sin 2py kl \u00f04\u00de The grid resolution is made (94 16). It means 94 nodes are taken in direction of rotation and 16 nodes are taken in the direction of axial width. Such differential node setting helps getting square grid. The Fig. 2 represents the film thickness for the bearing geometry corresponding to Fig. 1. The specific conditions applied to the corresponding geometry given in Fig. 1 are listed as ((a) G = 1.0, (b) Dm = 0.8, (c) G = 1.0, Dm = 0.8 and (d) G = 1.0, Dm = 0.8, At = 5.0 mu m and Al = 5.0 mu m). Reynolds equation is known as governing equation in lubrication performance analysis. The hydrodynamic or elastohydrodynamic action can be simulated using Reynolds equation. Mathematical model formulated to solve it takes film thickness, lubricant density, viscosity and shaft angular velocity as input parameter. The hydrodynamic pressure is the output of the simulation. Reynolds equation is case specific and takes different form in different situations" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002156_robot.2009.5152525-Figure6-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002156_robot.2009.5152525-Figure6-1.png", + "caption": "Fig. 6. Transition of the Condition of Contact", + "texts": [ + " Two dynamic models are presented based on the condition of contact between the ball and robot link: (1) the fingerlink contact model, and (2) the fingertip contact model. The finger-link contact model shown in Fig. 4 represents the dynamics where the ball and link keep a rolling contact condition. The fingertip contact model shown in Fig. 5 represents the dynamics where the ball is in contact with an edge of the link (fingertip). The relationship between the two contact models is illustrated in Fig. 6. The finger-link contact model is initially applied since the initial condition (see the most-left image in Fig. 3) is given under this condition. The ball is released from the link if the contact force fh acting on the ball from the link becomes zero. In this paper we don\u2019t discuss the case where the link contacts again with a ball once released. If the ball rolls up along the surface of the link keeping a rolling contact, and reaches the end of the link, then the condition of contact transits to the fingertip contact model" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000165_05698198108983050-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000165_05698198108983050-Figure4-1.png", + "caption": "Fig. 4-Coordinate system for flexibly mounted stator", + "texts": [ + " SEAL FACES SELF ALIGNING 2 T I L T I N E R T I A OF STATOR ACTS TO R E S I S T TRACKING OF ROTATING SEAL FACE ANGULAR MISALIGNMENT 2 . I N E R T I A OF ROTOR 0 0 ~ ~ 1 2 . I N E R T I A OF STATOR OR NOT AFFECT I T S ROTOR NOT S I G N I F I C A N I A B I L I T Y TO TRACK i UNLESS ROTOR I S STATIONARY SEAL FACE OYNAMICALLY OUT OF ANGULAR MISALIGNMENT BALANCE I Fig. 3-Dynamic characteristics of basic seal arrangements 3 . ELASTOMER STIFFNESS AND DAMPING ACT TO R E S I S T TRACKING OF STATIONARY SEAL FACE ANGULAR MISALIGNMENT Referring to Fig. 4 , 0 is a fixed point and Oxyz is a system of rotating axes attached to, ancl defined Ily motion of , the flexibly mounted stator seal face. Positive z is normal into the nominally flat face, and positive x points to~varcls the position that would give stnallest sepal-ation if angular misalignment, a, of the rotor was zero. T h e rotor is fixed to the shaft, which has constant rotation rate (spin), w,, about fixed axis Z. T h e stator does not spin about its own axis z, ' 3 ELASTOMER S T I F F N E S S AN0 OAMPING ACT TO M A I N T A I N DYNAMIC ALIGNMENT OF BOTH SEAL FACES but precesses about Z at the rate, 6 and with nutation 0", + " (see Appenclix), there will be face contact iP, J (KX w:/4/c) + K cir, 0,r, [C, + ( I - If)w:]' + C; 0: [ I41 This expression is clepenclent on a n extrapolation of the hyclrodyn~umic term beyond the conditions of \"small tilt\" for which it strictly applies. In a practical sense, the difference is not expectecl to be significant. Sin~plifying Eq. [14], For high resistance to rotor angular misalignment, high film terms and low elastomer and inertia terms are required. FLEXIBLY MOUNTED ROTOR TRACKING A MISALIGNED STATOR AT CONSTANT AMPLITUDE AND ANGULAR DISPLACEMENT T h e coorclinate system shown in Fig. 4 for the Hexibly mounted stator tnay be used for the flexibly mounted rotor if the seal rings are interchanged so the system of axes Oxjs follows the precession and nutation (but not the spin) of the rotating seal face (Fig. 7). T h e phase lag, film thickness and tilt-moment diagram is then identical to that of Fig. 5, and Eqs. [3] to [6] describing the fluid film may be usecl in this case for the flexibly mounted rotor arrangement. For steady tracking by this rotor of the misaligned stator, axes x, y, 5, and 5 must remain stationary in space ancl the rotor, therefore, must spin about fixed axis z at constant shaft speed w," + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000168_1.11032-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000168_1.11032-Figure1-1.png", + "caption": "Fig. 1 Schematic diagram of multimodule deployable manipulator system.", + "texts": [ + " Here, a neural-network-based adaptive controller is developed for this deployable manipulator system. The model includes both joint flexibilities and link flexibilities. Neural networks are used to approximate the unknown terms in the dynamic equations of the manipulator. The controller is adapted on that basis, with the objective of reducing the tracking error of the robot. The applicability and effectiveness of the neural-network control scheme for this manipulator system are tested through computer simulations. Consider the n-link deployable manipulator model shown in Fig. 1. Each manipulator module comprises two joints (degrees of freedom): one free to slew, through a revolute joint, and the other permitted to deploy (and retrieve), through a prismatic joint. The links and the joints are considered flexible. Detailed derivation of the dynamic model can be found in Ref. 2. For brevity, only the final form of equations of motion is shown in the following Mq\u0308 + V(q, q\u0307)q\u0307 + G(q) = \u03c4 (1) where M(q), V(q\u0307, q), and G(q) are system matrices. Dynamic study of this class of manipulator system has been conducted by Modi et al" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002552_iciea.2011.5975793-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002552_iciea.2011.5975793-Figure2-1.png", + "caption": "Fig. 2. BBS control test rig.", + "texts": [ + " To control the ball position at a desired position, the control law is modified as follows: u\u2217(k) = \u2212Kf [x(k)\u2212 xref ] (14) where xref=[xref 0 0 0 0]T , and xref is the reference of the ball position. For the modified system model (9), the augmented state estimation x\u0302e(k)=[x\u0302 T (k) u\u0302c(k)] T can be obtained from the STF. From (8) and (14), the control law can be described as follows: u\u2217(k) u(k) + u\u0302c(k) \u2212Kf [x\u0302(k)\u2212 xref ] (15) Thus, the following STF-LQR control law with the unmod- eled dynamics compensation can be derived from (15). u(k) = \u2212Kf [x\u0302(k)\u2212 xref ]\u2212 u\u0302c(k) (16) To validate the proposed STF-LQR approach, a BBS control test rig has been built, as shown in Fig. 2. The test rig mainly consists of four parts: a BBS introduced in Section II-A, a NetCon controller, a driver, and a configuration workstation. The NetCon controller [18] is shown in Fig. 3. It is composed of a power supply board, a main board, and an I/O board. The kernel chip of the main board is Atmel\u2019s AT91RM9200, which is a cost-effective and high-performance 180 MHz 32-bit microcontroller. The I/O board provides 12 analog-digital channels (AD00\u223cAD11), 4 digital-analog channels (DA0\u223cDA3), 2 digital input channels (DI0\u223cDI1), 2 digital output channels (DO0\u223cDO1), 3 PWM channels (PWM0\u223cPWM2) and 1 input interrupt channel" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000497_robot.2005.1570762-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000497_robot.2005.1570762-Figure1-1.png", + "caption": "Fig. 1. Particle filter tracking. (a) A set of particles (white rectangles), are scored according to how well the underlying pixels match the appearance model (left). Particles are resampled (middle) according to the normalized weights determined in the previous step. Finally, the estimated location of the target is computed as the mean of the resampled particles. (b) Motion model: The previous image and particles (left). A new image frame is loaded (center). Each particle is advanced according to a stochastic motion model (right). The samples are now ready to be scored and resampled as above.", + "texts": [ + " The multiple hypothesis tracker and the joint probabilistic data association filter (JPDAF) [6], [15] are the most influential algorithms in this class. These multi-target tracking algorithms have been used extensively. Some examples are the use of nearest neighbor tracking in [11], the multiple hypothesis tracker in [9], and the JPDAF in [22]. Recently, a particle filter version of the JPDAF has been proposed in [25]. The tracker that we will use is based on a novel multi-target particle-filter tracker based on Markov chain Monte Carlo sampling. (See [18], [19] for details.) The general operation of the tracker is illustrated in Figure 1. Each particle represents one hypothesis regarding a target\u2019s location and orientation. The hypothesis is a rectangular region approximately the same size as the ant targets. In the example, each target is tracked by 5 particles. In actual experiments we typically use the equivalent of one thousand particles per target. 0-7803-8914-X/05/$20.00 \u00a92005 IEEE. 4182 We assume that we start with particles distributed around the target to be tracked. After initialization, the principal steps in the tracking algorithm include: 1) Score: each particle is scored according to how well the underlying pixels match an appearance model" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002177_gt2009-59599-Figure7-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002177_gt2009-59599-Figure7-1.png", + "caption": "FIGURE 7: TESTED THRUST BEARING DESIGN", + "texts": [ + "org/about-asme/terms-of-use Dow Two turbochargers with bladeless compressor wheels are prepared for the test; the rotating group is presented on Figure 6. Both comprise the same center housing, turbine and compressor housings, shaft wheel assembly (SWA), seals and anti-rotating pin. The only difference is in the bearing systems. The outer bearing diameter is 11.0mm in the first and 12.0mm in the second. In addition, the radial clearances are different, as well as the thrust bearing design (see Figure 7). The tests were conducted with commercial oil, 0W30 supplied at 30 \u00baC and 100 \u00baC, and 2 bars and 4 bars oil inlet pressure. The inlet conditions were maintained over the test speed range, 500 Hz to 3000 Hz (30 - 180 krpm). As no compression work is done, the static pressure and the velocity of the gas at the turbine side create an axial load acting on the thrust bearing. Even though the turbine housing and wheel are the same; the axial load varies with gas temperature because of its effect on the gas density" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001851_robot.2009.5152196-Figure10-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001851_robot.2009.5152196-Figure10-1.png", + "caption": "Fig. 10. Geometric Parameters of 2-link Model", + "texts": [ + " Variation of potential energy with arrangement of biarticular muscles Given the internal force balancing at the desired posture \u03b8d1 = \u03b8d2 = \u03c0/2 to the muscles, we investigate the variation of the potential energy along with the arrangement of the muscles. For simplicity, the desired internal force is given as vdi = 1 (for any i) that corresponds to the desired posture. In the following, the potential aspects of two type of muscular arrangements are investigated, of which geometric parameters are depicted in Fig. 10. (a) Arrangement of muscles (b) Potential filed (P ) (c) Potential filed (P1) (d) Potential filed (P2) Fig. 11. Muscular Arrangement and Potential Fields; hi = 50, di = 20, bjx = 120, by = 10, L1, L2 = 330 (i = 1 . . . 8, j = 1 . . . 4). 1) One case that all muscles are stable: First, we introduce one of the simplest muscular arrangements, of which both of the potential are stable. In this case, the simple joint muscles are arranged to be stable. Figure 11-(a) shows the whole muscular arrangement, and the geometric parameters of this arrangement are shown in the caption" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001970_demped.2009.5292798-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001970_demped.2009.5292798-Figure1-1.png", + "caption": "Fig. 1. Squirrel Cage Equivalent Circuit.", + "texts": [], + "surrounding_texts": [ + "In order for the behavior of the sidebands around the fundamental current and their harmonics to be analyzed, simulation results for different conditions regarding load, number of broken bars, inertia of the machine-load unit and voltage distortion are obtained and presented in this section. The data and parameters of the motor used for simulation are shown in the Appendix. The sidebands around the fundamental component at frequencies (1 \u00b1 2ks)fs with k = 1,2 are shown in Fig. 3. These results correspond to a motor with three consecutive broken bars (7.5% of the bars) supplied by sinusoidal voltages and rated load. Besides these sidebands around the fundamental component, originated by rotor faults, there are others as it is shown in Fig. 4. For the one side, components at (5 \u2212 2ks)fs with k = 1,2,3,4 can be observed. Among these components, that corresponding to k = 2 shows a magnitude many times higher than the rest of them. For the other side, there are components below the 7th harmonic at frequencies (7 \u2212 2ks)fs. The magnitude of the component corresponding to k = 3 is the highest. According to these results, the components (5 \u2212 4s)fs and (7 \u2212 6s)fs are evaluated as complementary signals to the fundamental component sidebands for rotor fault diagnosis." + ] + }, + { + "image_filename": "designv11_7_0002900_icma.2013.6617997-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002900_icma.2013.6617997-Figure3-1.png", + "caption": "Fig. 3 Meshing force distribution", + "texts": [ + " We defined the surface of wave generator\u2019s outer ring as the contact surface with target170 element, and defined the surface of flexspline\u2019s inner ring as the contact surface with target174 element, and the friction coefficient was set to 0.01 [10]. At the back-end of flexspline, the flange\u2019s degrees of freedom in three directions were set to zero. The meshing force between flexspline and circular spline is difficult to evaluate. It\u2019s not only relative to the load acting on the out shaft of the reducer, but also relative to the range of meshing. Shown in Fig. 3, the meshing force distribution could be obtained from the experimental results [11-12]. According to experimental results, if we consider 2\u03d5 is approximately equal to 3\u03d5 , the meshing force in the range of 2\u03d5 could be evaluated in the form ( )max 1 2cos / 2 tan t t r t q q q q \u03c0 \u03d5 \u03d5 \u03d5 \u03b1 \u23a7 = \u2212\u23a1 \u23a4\u23aa \u23a3 \u23a6\u23a8 =\u23aa\u23a9 (1) In the same way, the meshing force in the range of 3 could be evaluated in the form: ( )max 1 3cos / 2 tan t t r t q q q q \u03c0 \u03d5 \u03d5 \u03d5 \u03b1 \u23a7 = \u2212\u23a1 \u23a4\u23aa \u23a3 \u23a6\u23a8 =\u23aa\u23a9 (2) If the moment which stands for the load acting on the output of reducer is T, the relationship between T and qt max could be represented as ( ) ( )2 1 2 max 1 24 cos / 2 2 g R t d T b q d \u03d5 \u03d5 \u03c0 \u03d5 \u03d5 \u03d5 \u03d5\u239b \u239e = \u2212\u23a1 \u23a4\u239c \u239f \u23a3 \u23a6 \u239d \u23a0 \u222b (3) ( )Rgt bdTq 2 2max 2/ \u03d5\u03c0= (4) Actually, the engaging force only acts on one side of gear, so the continuous distribution of the engaging force shown in equation (1) to equation (4) was changed into discrete distribution in the style of piecewise integral and the integration step is the teeth space" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000312_s11071-005-9016-6-Figure6-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000312_s11071-005-9016-6-Figure6-1.png", + "caption": "Figure 6. Wheel tread surface.", + "texts": [ + " This becomes difficult as the wheel and the rail surface profiles are usually complex and cannot be defined by a simple analytical expression. However in general, the surface profiles of the wheel and the rail can be seen as being generated from twodimensional curves [18] as shown in Figures 6 and 7 (for new wheels and rails with no localised damage) respectively. Wheels are described as a surface obtained by rotating a two-dimensional curve (Equation (34)) that defines the wheel profile through 360 degrees about the wheel axis as shown in Figure 6. x = x0 + r ( sw 2 ) sin sw 1 y = y0 + sw 2 z = z0 \u2212 r ( sw 2 ) cos sw 1 \u23ab\u23aa\u23ac\u23aa\u23ad (34) where sw 1 and sw 2 are the surface parameters of the wheel. In this case the parameter sw 1 represents the rotation about the wheel axis and the parameter sw 2 represents the translation in the lateral direction. Rail is described by translating a two-dimensional curve that defines the rail profile (Equation (35)) in the longitudinal direction as shown in Figure 7 x = x0 + sr 1 y = y0 + sr 2 z = z0 + f ( sr 2 ) \u23ab\u23aa\u23ac\u23aa\u23ad (35) Because of the constraint, the components of the vector of generalised coordinates q and the surface parameters s are not independent and can be written in partitioned form as follows: q = [ qT d qT i ]T (36) s = [ sT d sT i ]T (37) where qd and qi are, respectively, dependent and independent generalised coordinates, and sd and si are, respectively, dependent and independent surface parameters" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002520_j.ymssp.2011.10.017-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002520_j.ymssp.2011.10.017-Figure2-1.png", + "caption": "Fig. 2. Parallel connection of N Maxwell-slip elements.", + "texts": [ + " The elementary model will slip if the friction force of each element reaches the maximum value of the force, Wi, that it can sustain. Beyond this point the elementary friction force equals the maximum force, Wi, obtained by solving the following equation: dFi dt \u00bc 0 \u00f0slip\u00de \u00f02:3\u00de When the motion is reversed, the elementary model will stick, and it will behave again like a linear spring until the friction force reaches the maximum force, Wi. Using a parallel connection of N Maxwell-slip elements, the total friction force is equal to the sum of all elementary friction force components Ff \u00bc X N Fi \u00f02:4\u00de Fig. 2 shows the schematic of the corresponding Maxwell-slip model. The Maxwell-slip model is proven to be able to characterize the rolling (and presliding dry-) friction in a relatively simple way; however, one problem remains, the dynamic analysis of mechanical systems subjected to the aforementioned complex hysteresis phenomena is still a difficult task to perform. According to Feldman [12], a large number of signals, including vibrations of systems with geometric nonlinearities, can be converted to analytic signals in complex time" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001503_imtc.2008.4547070-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001503_imtc.2008.4547070-Figure2-1.png", + "caption": "Fig. 2. Flux density distribution of a PMSM with short circuit.", + "texts": [], + "surrounding_texts": [ + "Index Terms - Short circuit, winding, fault, Wavelet, Fourier, Drive, PMSM, fault, speed change, FEA.\nI. INTRODUCTION.\nShort circuit between turns is the most critical fault in the machine, and is quite difficult to detect and almost impossible to remove. These faults are usually short circuits between a phase winding and the ground or between two phases. It is strongly believed that such faults initiate as undetected turn-to-turn faults that develop to a major short circuit. Stator winding faults might have a destructive effect on the stator coils [1].\nThere are a number of techniques to detect turn-to-turn faults, the majority of them based on stator voltages and currents, axial flux and d-q current and voltage component analysis. Toliyat [2, 3] and Penmann [4], have examined very effectively the operation of Induction Motor drives under the conditions of loss of one phase, broken bars and shorted stator turns using winding functions. However, the models they used did not include either saturation or controller interactions. From years ago, the failure detection in a motor is studied by analyzing the stator current harmonic by means of FFT [5]. But, FFT cannot be applied in no-stationary signals [6, 7]. Fortunately, signal processing theories provide several algorithms for applications with no-stationary signals [8].\nThe Wavelet transform is a time-frequency technique of signal analysis. The main advantage of wavelet over SortTime Fourier transform (STFT) is that it uses a variablesized-regions windowing technique [9].\nCoupling between the non-linear magnetic effects and non- linear electric circuits should be token into account in order to determine the behavior of the electrical motor under fault conditions [10] be mean of FEA.\nIn this paper finite element analysis (FEA) is proposed for\nthe simulation of electrical machines with short circuit fault. FEA analysis reveals itself like an accurate an easy method to determine the interaction between non-linear effects. PMSM in a healthy state and with short circuit turns are simulated at different working points using a twodimensional (2-D) finite-element analysis software (FLUX 2D). The PMSM workbench for FEA analysis is shown in Fig. 1. Currents patterns and their harmonics contents are obtained. In addition, these harmonics of the PMSM with faults is compared with a healthy motor. The dynamic stator current was investigated by means of discrete Wavelet Transforms (DWT). The simulation is also compared with experimental results\ni\"~\n. I'l 1 .... ,PM2,@ e WF~~~~~F\nThe state space model describing the motor drive system is as follows [11]:\nV=RI+ a\u00b1-C - av = RI+L a\u00b1+ rI (1)~~~ r~~~~~)90\nWhere: I are three-phases stator currents and state variables of PMSM, V are three-phases stator terminal voltages, T is linkage flux, L represents self and mutual inductances, R are three-phases resistances, 0 is the rotor position, and (or is the rotor speed. Modeling shorted turn faults requires the introduction of an additional differential equation defining the shorted turns.\n1-4244-1541-1/08/$25.00 C 2008 IEEE\nrlwm\nwn tk FluQ0 W)", + "The equation for the shorted turns, coupled to all the other circuits in the machine is:\nO=R I + a .sh + v a .sh (2)\nWhere ish, lsh and Rsh are fault current, total flux linking and resistance of the shorted turns. Assuming the infinitely permeable characteristic of ferromagnetic materials, the rotating sinusoidal magnetomotive force (MMF) is accountable only for the air gaps. Because the stator winding is connected in series, the excitation MMF's for individual poles are the same [12]. Regardless of the air gap variations the amplitude of air gap MMF remains uniform. Fmm = Asin(p80\u00b12iZfs t) = Asin(p80\u00b1ws t) (3)\nWhere A is amplitude of MMF, t is time, O is angular position of rotor, Pn = up, u is number of harmonic (6k \u00b1 1) induced in the rotor flux by the space harmonics (slot) de stator MMF, p is pair of poles. The air gap MMF can be expressed by developing expression (4) in Fourier series for all harmonics, v of stator. The distribution of the stator MMF in the air gap will be affected with the current that will circulate through the shortcircuited turns. There exists stator slot (Z1) harmonics of order sin[vZ1 (pro \u00b1 wst)]j. Analyzing the MMF of the affected coil group can be obtained the following new frequencies [4] in the flux density as can see Fig. 3.\nBvh =A CosrPnl[lTzl]\u00b1 lTZIv( )jw5t] (4) The fault of short turns of stator phase winding leads to\ntwo main effects on the machines flux. The first is that the large current in the shorted turns leads to an increase in the local leakage flux, particularly slot leakage as shows in Fig. 3. This changes the saturation conditions of the teeth locally. Secondly, the currents induced in the shorted coils oppose the establishment of the main, air-gap flux. They thus reduce that flux and the corresponding main flux path saturation along the winding axis of the shorted coil [13].\nIf it is considered the rotor harmonic, n and s = 0 for PMSM, can be obtained the new short circuit frequency starting from the equation (4).\nfsh )~fs (5) p\nTherefore, The new frequency component appears in the stator current spectrum as a result of a fault in the stator windings, only a rise in the rotor slot harmonic frequencies can be expected because under fault conditions a greater number of flux density waves exist in the machine, and all of these waves make a contribution at the same frequencies; and there is a greater probability of flux density waves with the basic number of pole pairs now existing [4].\nIII. WAVELET TRANSFORM ANALYSIS.\nWavelet analysis [14] is capable of revealing aspects of data that other signal analysis techniques miss, like trends, breakdown points, discontinuities in higher derivatives, and also self-similarity. Also allows to denoise signal and chose bands where focus the analysis, by using properly the mother wavelet function and also the scaling function wavelet. The wavelet approach is essentially an adjustable window Fourier spectral analysis with the following general definition is continuous Wavelet transforms (CWT):\nW(a,b,X,y a' 2([)V*(t-b)[ (6)\nWhere, V*(.) is the basic wavelet function, a is the dilation factor and b is the translation of the origin.\nAlthough time and frequency do not appear explicitly in the transformed result, the variable 1/a gives the frequency scale and b, the temporal location of an event. An intuitive physical explanation of (6) is very simple: W(a, b, X, ) is", + "the 'energy' ofXof scale a at t = b. In the case of discrete wavelet transform (DWT), the dilation and translation parameters are restricted only to discrete values leading. Through digital signal processing of a signal, it is possible to obtain the wavelet transform coefficients W(a,b), on a discrete grid corresponding to the discrete time wavelet coefficients. This is achieved when a and b are assigned regularly spaced values: a=maO and b=nb,, where m and n are integer values [14]. A signal can be successively approximated by DWT with different scales. The Fig. 4 shows the decomposition or analysis filter bank for obtaining the forward DWT coefficients.\nIV. SIMULATION AND EXPERIMENTAL RESULTS.\nThe motors under analysis have been a PMSM of 6000 rpm nominal speed, 2.3 Nm nominal torque, and 3 poles pair [7]. Simulations and experiments have been carried out for motors with 4, 8 and 12 short turns of stator phase winding. The short circuit implemented (4, 8, 12 turns) is a few turns one, in relation of whole winding (144 turns of stator phase winding one).\nThe load torque for stationary conditions was always the nominal (2.3 Nm) and for non stationary conditions a speed change of \u00b1500 rpm from stationary speed has been considered. Numerical simulations were developed with the combination of a finite element software, Flux2D [15], and an electronic circuit and control simulation sotware, Matlab-Simulink. The coupling between the circuit control and the finite element model (see Fig. 1. ), automatically links local variations in magnetic flux with electrical variables and viceversa [15]. The AWT ridges algorithm are implemented in Matlab using the Wavelab850 toolbox from Stanford University [16]. A. Stationary working conditions The simulations of the PMSM in stationary conditions are shows from Fig. 6 to Fig. 8 through the stator current harmonic. The curves have been normalized to a rotor frequency for every case. The amplitudes of the stator current harmonics 1, 7, 9 are higher for a fault motor than for a healthy one. Although, at low speed the discrimination is more difficult than for the nominal speed. The harmonic 9 is bigger that others and this will shows even the short circuit at low speed with some difficult. The experimental results can be seen in from Fig. 9 to Fig. 11, for 3000, 1500 and 300 rpm, respectively. The experimental measurements performed corroborate simulations. In the practices cannot be possible to carry out tests at high speeds because the very high value of short circuit current. This current can cause irreparable damages in the stator winding, isolation and the permanent magnet.\nThe motors were driven at nominal (6000 rpm), medium (3000 rpm) and low speed (1500 and 600 rpm). Both, the simulations and the experiments were carried out under stationary and not stationary conditions. For stationary conditions, FFT has been the mathematical transform used to determine the short circuit fault stage and DWT for non stationary conditions." + ] + }, + { + "image_filename": "designv11_7_0003300_j.wear.2011.02.017-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003300_j.wear.2011.02.017-Figure1-1.png", + "caption": "Fig. 1. Schematic diagram of the model with a constant normal and oscillating tangential loading.", + "texts": [ + " Interestingly, no theoretical models for cyclic tangential loading based on the Bowden and Tabor\u2019s approach [13] of plastic failure as the source of static friction could be found in the literature. Hence, the main goal of the present study is to attempt such modeling assuming full stick contact condition as in Brizmer et al. [37,38]. The hysteretic behavior of elastic\u2013plastic spherical contact under normal load and cyclic tangential loading will be analyzed separately for the kinematic and isotropic hardening models. 2. Theoretical model Fig. 1 presents a deformable sphere of a radius R in contact with a rigid flat under combined constant normal and reciprocating tangential loading. The loading process begins by applying a normal load, P, followed by a reciprocating tangential load Q that varies in the range \u00b1Qmax (not shown in the figure). The thick and thin dashed lines show the contours of the sphere before and after the application of the normal load P, respectively. The normal load produces an initial interference \u03c90, and an initial circular contact area of a diameter d0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001677_1.4000517-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001677_1.4000517-Figure1-1.png", + "caption": "Fig. 1 A Stephenson six-bar linkage", + "texts": [ + " Its boundaries are the sinular curves of the five-bar linkage between two input joints. At ny point on the singular curve, the three passive joints of the ve-bar linkage become collinear, and the linkage has a singular onfiguration, where the linkage may lose control. The concept of heet and side of JRS offers an excellent model to explain and nderstand the interaction between loops in six-bar linkages 1,2,7,25 , and hence, the formation of branch, sub-branch, and ull rotatability of Stephenson type linkages. 2.1 Stephenson Six-Bar Linkages. A Stephenson six-bar inkage Fig. 1 contains a single-DOF four-bar loop A0ABB0A0 nd a two-DOF five-bar loop A0ADCC0A0. The branch identificaion 1 is briefly explained with the examples in Figs. 2 and 3. Consider the relationship called I/O curve between 2 and 3, hich are two joint variables in the four-bar loop Fig. 1 . Figure 11011-2 / Vol. 2, FEBRUARY 2010 om: http://mechanismsrobotics.asmedigitalcollection.asme.org/ on 04/21/2 2 shows the I/O curves in the five-bar JRS the shaded area of a Stephenson six-bar linkage. The I/O curve intersects the boundary of the JRS at branch points labeled as 1\u20136 in Fig. 2 . The JRS sheet has two sides. The branch points divide the I/O curve into segments and each segment of the I/O curve within the JRS represents a branch. Thus, Fig. 2 shows that the linkage has three branches represented by segments 1\u20132, 3\u20134, and 5\u20136", + " The branch identification can be carried ut in the way similar to that of Stephenson six-bar linkages 1,8 . 2.3 Remark. One may note that the reference links in Figs. 1, , and 7 are chosen differently, which may appear inconsistently. t is emphasized that the branch condition is irrelevant to the hoice of the input, fixed, or reference link. Therefore, the choice f the reference link or joint parameters for branch identification s based on convenience or simplicity only. This is highlighted in igs. 1 and 5. In Fig. 1, the relationship between 2 and 3 is used because 2 nd 3 are the common joint parameters between the four-bar loop nd the five-bar loop. Furthermore, the relationship between 2 nd 3 is basically governed by the four-bar loop alone, and thereore, is in the simplest form. The choice of A0C0 as the reference s arbitrary for branch identification. If branch is the only concern, ink A0A would be a good choice as the reference link. ournal of Mechanisms and Robotics om: http://mechanismsrobotics.asmedigitalcollection", + " Hence, if the sub-branch or full rotatability is also a concern, the input reference may be taken into consideration to avoid excessive derivation. Since the input parameter is usually the angle between adjacent links, relative angles are used in Fig. 5. On the other hand, in a Stephenson type linkage, subbranch or full rotatability condition is complicated with the input given through a joint, i.e., C0, C, or D, not in the four-bar loop. Resolving the full rotatability problem under this input condition is the focus of this paper. This may explain why A0C0 and C0C are used as the reference links in Figs. 1 and 7, respectively. Figure 1 highlights the feature of having 2 or 8 as the input joint parameter. Figure 7 highlights the feature of having 8 or 7 as the input joint parameter. Thus, instead of presenting a lengthy discussion on all linkage inversions or input conditions, the reference is chosen differently in each example to highlight the versatility of the method, rather than the necessity of a particular reference choice. Thus, the discussion in the paper covers all possible linkage inversions or input conditions. FEBRUARY 2010, Vol", + " Thus, the discriminant 30 of the input and output equation should vanish, which leads o a polynomial equation in terms of the input parameter only. At dead center position, the following equations must be satisfied: f i, o = 0 and i = 0 1 3.1 Singularity of Stephenson Six-Bar Linkages. The exisence of dead-center positions is affected by the choice of the nput joint and is irrelevant to the choice of the output joint. herefore, finding the dead-center positions for Stephenson linkges can be treated in three categories. 1 In the first category, the input is given through a joint in the four-bar loop Fig. 1 . The dead center positions exhibited in the I/O curve of the four-bar loop, and the branch point with the JRS boundary are the dead center positions of the Stephenson six-bar linkage. This case has been well treated 1 . In the other two categories, the input is given through a joint such as C0 or D and C Fig. 7 , not in the four-bar loop. 2 If the joint at C0 is used as the input joint, the singularity occurs when links A0A, B0B, and CD intersect at a common point 1,13 . In order to demonstrate the generality of the proposed method for any input condition disregarding the linkage structure type, the singularities will be determined through the input versus output relationship directly", + " 10 can be eliminated with Eq. 11 , which is also the coefficient f t8 with the highest order in Eq. 7 . Each real root of the olynomial equation represents a dead center position. Example 1: The dimensions of Stephenson six-bar linkages Figs. 1 and 7 are given below a1 = 3.5, a2 = 2.82, a3 = 4.0, a4 = 2.5, a5 = 5.0 a6 = 5.23, a7 = 3.2, a8 = 1.0, a9 = 5.0, a10 = 3.04 = \u2212 36.87 deg, = 70.0 deg, = 46.0 deg = \u2212 43.69 deg The branch points and dead center positions when the input is iven through 2 of the Stephenson linkage in Fig. 1 are listed in able 1 and shown in Figs. 8 and 9. If the input is given through 8 of the Stephenson linkage in Fig. 7 with the given dimension, in Eq. 10 becomes a 66th degree polynomial, while M in Eq. 11 becomes a sixth degree polynomial in terms of t8. The real olutions of Eq. 10 that satisfy the condition of Eq. 11 are the ead center positions. The number of the extraneous roots with the iven dimensions is four. Due to the complexity of symbolic comutation, the method does not predict the maximum number of ead center positions unless the specific dimensions are given", + " The following general gearing relationship 31 can be used to express the gear constrain: 4 + 5 \u2212 40 = 1 \u2212 n 5 \u2212 50 12 where 4 and 5 are the joint variables at joints D and E, 40 and 50 are the joint displacements of the reference gear position, and n is the gear ratio. With the angle definition in Fig. 5, the gear ratio is negative if both terminal gears rotate in the same direction with respect to link DE. Equation 12 can be expressed as 4 = \u2212 n 5 + 13 where = 40 if 50=0. The calculation of dead center singularity of geared five-bar linkages can be carried out in the way similar to that of Stephenson linkages. In the first category, the input is given through the of Stephenson linkage of Fig. 1 with input of Output deg 8 8 7 = \u2212 \u2212 8 7 7 = 7\u2212 8 64.64 159.03 0.01 104.02 119.65 180.00 79.75 303.42 180.43 123.08 100.59 0.58 149.60 74.07 0.19 17.57 241.24 180.72 52.47 276.14 181.00 143.24 80.43 0.00 34.02 189.65 92.55 115.77 339.44 92.40 ons 7 4.63 5.98 0.68 1.50 8.41 3.15 9.53 3.24 8.53 3.37 FEBRUARY 2010, Vol. 2 / 011011-5 015 Terms of Use: http://asme.org/terms g b I t 3 s c t s t p T s d b E c e T P 0 Downloaded Fr eared train joint A or E . The dead center positions are the ranch points, which are the intersection points between the linear /O curve, i", + "92 ournal of Mechanisms and Robotics om: http://mechanismsrobotics.asmedigitalcollection.asme.org/ on 04/21/2 4.1 Input Given to a Link of the Four-Bar Loop or Geared Train. The full rotatability of geared five-bar linkages Fig. 5 with the input given to the geared train was discussed by Ting 2 . The linear input-output I/O constraint must lie within the JRS of the five-bar loop and a unit geared ratio is required 2 unless the host five-bar contains no uncertainty singularity or dead center positions . For a branch of a Stephenson linkage Fig. 1 to have full rotatability, the following conditions must be satisfied. 1. The four-bar loop is a Class I chain and the input joint must connect the short link of the four-bar loop. This is to assure that the input link of the four-bar loop has full rotatability. 2. The I/O curve of the branch must stay within the JRS of the five-bar loop. In other words, no branch point exists in the branch. An example is shown in Fig. 13, which shows that the linkage contains four branches. Branches 3 and 4, which contain branch points, do not have full rotatability", + " In such an input condition, once the branch is determined, a branch that contains no dead center position has full rotatability. This can be done by mapping the corresponding output value to the four-bar I/O curve or the linear gear constraint Figs. 8 and 6 . The full rotatability identification is illustrated with the following two examples. 4.2.1 Stephenson Six-Bar Linkages. With the same dimension as in Example 1, branch points 1\u20138, with the input given through 2 of the Stephenson linkage in Fig. 1, are list in Table 1 and shown in Fig. 8. The dead center positions with the input give through 7 or 8 of the Stephenson linkage in Fig. 7 are listed in Tables 2 and 3, respectively Fig. 9 . 4.2.1.1 Branch identification. With the branch identification discussed early, as seen in Fig. 8, the I/O curve of 2 versus 3 is ve-bar linkage with input of 5 Output deg 2 3 4 0.68 106.15 36.29 180.72 88.80 49.40 180.72 213.25 71.85 0.99 188.73 88.37 ed five-bar linkage with input of 3 Output deg 2 4 5 80.05 40" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002258_978-3-642-19373-6-Figure5.4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002258_978-3-642-19373-6-Figure5.4-1.png", + "caption": "Fig. 5.4 Relative orientation of three intra-monomer bonds (vectors A, B and C) representing a local region of a polymer chain molecule; \u03b8 is the principal bonding (kink) angle in the discrete atomic lattice model of the molecule.", + "texts": [ + "16) Since the entropic elastic force is zero at L = L0 corresponding to a maximum of the molecular entropy, the value L0 can be referred to as a relaxed length of the molecule, which can be used for a standard linear force model of the type k(L \u2013L0). Within the continuum assumptions of Section 5.2.1, the variance parameter a for the distribution (Eq. (5.13)) cannot be elucidated, because the internal atomic structure of the polymer is not-taken account of. Furthermore, assuming a continuum range for the parameter L implies a possibility for the polymer chain to have critically small local curvature radii that may not be realized for an actual chemical bond structure of the polymer. Consider a polymer chain model of the type shown in Fig. 5.4, where the vectors A, B and C show spatial orientation of the intra-monomer bonds, such as the C\u2013 C bond in the polyethylene molecule of Fig. 5.2. The angle \u03b8 between a pair of two adjacent intra-monomer bonds, as well as the bond length, u, are basic characteristics of the chain that determine its entropic elastic properties. Another important parameter is the total number Ne of monomers on the chain under investigation. The two bonds A and B define a plane so that the next adjacent bond C can form an out-of-plane angle \u03d5 equal to one of the three possible random values corresponding to the stable energetically favorable confirmations of this local group", + " For example, at Ne = 1 000, the total number of configurations is about 4.4\u00d7 10476. A direct analysis of such vast numbers of configurations for the elucidation of the w(L) distribution form is generally intractable. A probabilistic Monte \u2013Carlo sampling approach can be employed to select a sufficiently large number of random molecular configurations N0 and to build a numerical histogram showing the approximate w(L) distribution. The sampling procedure utilizes probabilities Pi of the realization of each of the angles \u03d5i in a local group of bonds depicted in Fig. 5.4. These probabilities can be determined as asymptotic (at time t \u2192 \u221e) solutions of kinetic balance equations with a matrix of transition probabilities rij . Values of the coefficients rij can be determined using the respectable activation energy of the rotational transformations provided by a local potential of the Eq. (5.6). Since the entire approach is quasistatic, only relative probabilities are required rather than the actual dynamic rates, or probabilities per unit time. According to the transition state theory[36-42], such relative probabilities are proportional to the Boltzmann factors, rij \u223c exp ( \u2212 Eij kBT ) (5", + "17) 156 Chapter 5 Atomic Scale Monte-Carlo Studies of Entropic Elasticity Properties of Polymer Chain Molecules where Eij is the activation energy of the i \u2192 j transformation. Asymptotic solution of the kinetic equations at t\u2192\u221e can be found by solving a system of linear equations of the type P1(r12 + r13) = P2r21 + P3r31, P2(r21 + r23) = P1r12 + P3r32, P1 + P2 + P3 = 1. (5.18) Here, the last equation represents the fact that the system is always found in one of the three possible states. If there are more than three possible configurations of the local group (Fig. 5.4), the system (Eq. (5.18)) is expanded to a respectable number of the sought probabilities Pi. On the next step, the probabilities Pi are utilized during the Monte \u2013Carlo sampling procedures to render random global configurations of the polymer molecule. Example configurations are shown in Fig. 5.5, where various bonding angles \u03b8 have been utilized. In this and all further numerical examples, the 5.2 Entropic elasticity of linear polymer molecules 157 set of local angles \u03d5i and the respectable set of probabilities Pi are chosen to be {0\u25e6, 120\u25e6, 240\u25e6} and {1/3, 1/3, 1/3}" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003102_j.rcim.2013.03.002-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003102_j.rcim.2013.03.002-Figure2-1.png", + "caption": "Fig. 2. Close-loop Equation of The 3-CUP parallel manipulator.", + "texts": [ + " The subscript ij denotes the joint j (\u00bc1, 2, 3, 4, 5) on leg i (\u00bc1, 2, 3), therefore vector sij represent the axis of joint ij. Also it is important to consider C, S, and T as abbreviations of cosine, sine and tangent, respectively. For analysis convenience, note that the C joints are conformed by P and R joints, whose axes are coaxial. The P joint connected to the base is denoted as ji1, the R joint is denoted as ji2, the U joint is denoted as ji3 and j i4 (recall that the U joint is equivalent to two orthogonally intersecting R joints), and the P joint that lies on the platform is denoted as ji5 (see Fig. 2). Therefore the 3-CUP PM is also called 3-PRUP mechanism since ji1, which is part of the C joint is chosen to be the actuated joint. The legs of the parallel mechanism are evenly distributed by an angular position given by the angle \u03c8i, which is a rotation about the Z-axis (i.e. \u03c81\u00bc01, \u03c82\u00bc1201, and \u03c83\u00bc2401), and located in the XY plane by the vector ai (where a is the magnitude of ai and represents the distance from O to point Ai). Let the magnitude di of vector di represent the stroke of joint ji1, while its joint axis si1 is perpendicular to the base. The joint axes si2, si3, and si4 are chosen to intersect at point Bi (forming a non-canonical S joint). As shown in Fig. 2, the location point Bi relative to Ai is denoted by the vector di. Further, the P joints located on the platform are evenly distributed by an angular position given by the angle \u03c7i which is a rotation about the W-axis (\u03c71\u00bc01, \u03c72 \u00bc1201, \u03c73\u00bc2401), and their strokes are denoted by vectors bi with magnitude bi. Note that the axes of joints ji5 intersect at point C. The joint axis si4 is parallel to the V-axis, while the joint axis si3 is parallel to the XY plane and is perpendicular to si4. The 3- CUP PM can be considered as a non-canonical 3-PSP PM, according to [8], where it is proved that both architectures have identical mobility. The inverse kinematics problem consists in determining the actuators strokes (i.e. di) in order to configure the end-effector in a desired position and orientation. Denoting G (X, Y, Z) and H (U, V, W) as the global and platform reference frames that are located on the base and moving platform centroids, respectively (see Fig. 1), consider the loop closure equation for leg i defined in the G frame as (see Fig. 2) p\u00fe Hbi \u00bc ai \u00fe di \u00f01a\u00de where p\u00bc px py pz 2 64 3 75; bi \u00bc GRH \u22c5R\u00f0W ; \u03c7i\u00de\u22c5\u00bdbi;0;0 T ; a\u00bc aC\u03c8 i aS\u03c8 i 0 2 64 3 75 and GRH \u00bc C\u03b3C\u03b2 C\u03b3S\u03b2S\u03b1\u2212S\u03b3C\u03b1 C\u03b3S\u03b2C\u03b1 \u00fe S\u03b3S\u03b1 S\u03b3C\u03b2 S\u03b3S\u03b2S\u03b1\u00fe C\u03b3C\u03b1 S\u03b3S\u03b2C\u03b1\u2212C\u03b3S\u03b1 \u2212S\u03b2 C\u03b2S\u03b1 C\u03b2C\u03b1 2 64 3 75 \u00f01b\u00de Let GRH be the rotation matrix that defines the orientation of the platform relative to frame G and follows the X-Y-Z Euler angle convention, where \u03b1, \u03b2 and \u03b3 are their respective angular displacements [14]. The elements in Eq. (1b) are the direction cosines of u, v and w, which are defined parallel to the U, V andW axes, respectively", + " Furthermore, singular configurations (iii) \u03b2\u00bc901 and (iv) \u03b2\u00bc\u2212901 were obtained by analyzing the motion and constraint screws. In order to obtain the configuration in which the P joint represented by $15 becomes redundant due to the action of the P joint represented by $11 (this means that both screws are linearly dependent), it is necessary to determine the value of \u03b2 where the result is a loss of 1 DOF in leg 1. The branch motion-screw systems {$1}, {$2 } and {$3} of the parallel mechanism, (see Fig. 2) in the singularity configurations (i) and (ii) can be written as: $1 \u00bc $11 \u00bc 0; 0; 0; 0; 0; 1 T $12 \u00bc 0; 0; 1; 0; \u2212a; 0 T $13 \u00bc \u2212S\u03b2S\u03b3; S\u03b2C\u03b3; 0; \u2212d1S\u03b2C\u03b3; \u2212d1S\u03b2S\u03b3; a\u00f0S\u03b2C\u03b3\u00de h iT $14 \u00bc S\u03b2C\u03b3 ; S\u03b2S\u03b3; C\u03b2; \u2212d1S\u03b2S\u03b3; d1S\u03b2C\u03b3\u2212aC\u03b2; aS\u03b2S\u03b3 h iT $15 \u00bc 0; 0; 0; C\u03b2C\u03b3; C\u03b2S\u03b3; \u2212S\u03b2 T 8>>>>>>< >>>>>>: 9>>>>>>= >>>>>>; \u00f022a\u00de $2 \u00bc $21 \u00bc 0; 0; 0; 0; 0; 1 T $22 \u00bc 0; 0; 2; a ffiffiffi 3 p ; a; 0 h iT $23 \u00bc \u2212S\u03b2S\u03b3; S\u03b2C\u03b3; 0; \u2212d2S\u03b2C\u03b3; \u2212d2S\u03b2S\u03b3; aS\u03b2 2 \u00f0S\u03b3 ffiffiffi 3 p \u2212C\u03b3\u00de h iT $24 \u00bc S\u03b2C\u03b3; S\u03b2S\u03b3; C\u03b2; aC\u03b2 ffiffi 3 p 2 \u2212S\u03b2S\u03b3d2; S\u03b2C\u03b3d2 \u00fe aC\u03b2 2 ; \u2212aS\u03b2 2 \u00f0C\u03b3 ffiffiffi 3 p \u00fe S\u03b3\u00de h iT $25 \u00bc 0; 0; 0; 1 2C\u03b3\u00f0\u2212C\u03b2 \u00fe S\u03b2 ffiffiffi 3 p \u00de; 1 2 S\u03b3\u00f0\u2212C\u03b2 \u00fe S\u03b2 ffiffiffi 3 p \u00de; 1 2C\u03b3\u00f0S\u03b2 \u00fe C\u03b2 ffiffiffi 3 p \u00de h iT 8>>>>>>>< >>>>>>>: 9>>>>>>>= >>>>>>>; \u00f022b\u00de $3 \u00bc $31 \u00bc 0; 0; 0; 0; 0; 1 T $32 \u00bc 0; 0; 2; a ffiffiffi 3 p ; a; 0 h iT $33 \u00bc \u2212S\u03b2S\u03b3; S\u03b2C\u03b3; 0; \u2212d3S\u03b2C\u03b3; \u2212d3S\u03b2S\u03b3; \u2212 aS\u03b2 2 \u00f0S\u03b3 ffiffiffi 3 p \u00fe C\u03b3\u00de h iT $34 \u00bc S\u03b2C\u03b3; S\u03b2S\u03b3; C\u03b2; \u2212aC\u03b2 ffiffi 3 p 2 \u2212S\u03b2S\u03b3d3; S\u03b2C\u03b3d3 \u00fe aC\u03b2 2 ; aS\u03b2 2 \u00f0C\u03b3 ffiffiffi 3 p \u2212S\u03b3\u00de h iT $35 \u00bc 0; 0; 0; \u2212 1 2C\u03b3\u00f0C\u03b2 \u00fe S\u03b2 ffiffiffi 3 p \u00de; \u2212 1 2 S\u03b3\u00f0C\u03b2 \u00fe S\u03b2 ffiffiffi 3 p \u00de; 1 2C\u03b3\u00f0S\u03b2\u2212C\u03b2 ffiffiffi 3 p \u00de h iT 8>>>>>>>< >>>>>>>: 9>>>>>>>= >>>>>>>; \u00f022c\u00de The platform constraint-screw system {$r} is given by the null space of the motion screws of Eqs" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000005_ip-a-1:19840070-Figure30-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000005_ip-a-1:19840070-Figure30-1.png", + "caption": "Fig. 30 Locus of Ec for constant leading reactive power at constant speed", + "texts": [ + " The control link between machine and cycloconvertor is used to keep the output frequency and phase in step with rotor voltage, thus avoiding the instability inherent in doubly fed synchronous drives. In essence, speed is controlled by means of the cycloconvertor output voltage, but, by adjusting the phase shift between control voltage and induced rotor voltage, and, in effect, overexciting the rotor, the motor can be made to operate at a leading power factor. In this way the reactive power drawn by the cycloconvertor, and also the magnetising current drawn by the motor itself, can be compensated, allowing the overall system power factor to approach unity [175]. The phasor diagram of Fig. 30 indicates for the simplified equivalent circuit of Fig. 2a how Ec and P must vary with load at a given speed in order for the machine to draw constant leading reactive power, fi being the phase angle between Ex and Ec. Note, however, that because the circuit impedance and the magnitude of sEv change with slip a different locus for Ec is obtained for each speed. The static Scherbius system has been used for a few special applications, a good example being the control of a motor flywheel generator for high-power pulse generation in a thermonuclear fusion laboratory [167]", + "4 Static Scherbius drive [167-175] Unlike most other voltage-controlled drives, the torque and speed in a static Scherbius system, described in Section 6.5, are not controlled simply by the magnitude of a DC link voltage but by a three-phase control voltage of the correct frequency and phase. As in the static Kramer drive the air-gap flux is determined primarily by the stator mains supply and is therefore approximately constant. The frequency of the control voltage is determined with reference to a tachogenerator or shaft encoder so that it always remains in step with rotor speed. Fig. 30 gives some indication how, at a given speed, operating conditions are affected by the magnitude Ec and phase angle fi of the control voltage. This phasor diagram is broadly similar to that for a synchronous machine and similar conclusions can be drawn. Although the influences of /? and Ec are clearly interdependent, f} has the greater effect upon the magnitude and direction of torque, while Ec has its greater impact upon the reactive power required by the stator as a result of the rotor currents" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003736_tac.2012.2232376-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003736_tac.2012.2232376-Figure1-1.png", + "caption": "Fig. 1. Examples of kinematic systems.", + "texts": [ + " Generically, this surface (the Martinet surface) is smooth, and intersects it transversally at a finite number of points only. In this paper, as is of common usage, we say that a system is \u201ctwo-step bracket-generating\u201d when . Also, along the paper, we illustrate our results with one among the following well known academic examples: Example 1: The unicycle, or two-driving wheel robot, [28], [29], is described by the position of the point at the middle of the axis of the wheels, and the orientation of the mobile, as shown in Fig. 1(a). The kinematic model is: (2) Example 2: The car with a trailer, [28], [29], is a two-driving wheel robot with a trailer hooked to the middle point of the axis of the wheels. The distance between the robot and the trailer is assumed equal to 1. The position of the trailer is specified by the angle as in Fig. 1(b). The model is (3) Example 3: The ball rolling on a plane was also studied in [6], [9], [25]. As shown in Fig. 1(c), it is described by the coordinates of the contact point between the ball and the plane, and a right orthogonal matrix representing an orthonormal frame attached to the ball. The kinematic model is (4) Example 4: The ball with a trailer is as in example 3, where the trailer\u2019s position is known from the angle as described in Fig. 1(d). The distance between the ball and its trailer is denoted by : (5) Typical motion planning problems are: 1) for example (2), the parking problem: the non-admissible curve is , 2) for example (3), the full rolling with slipping problem, , where is the identity matrix. In Figs. 2 and 3, we show our approximating trajectories for both problems, that are in a sense universal. In Fig. 2, of course, the -scale of the trajectory is much larger than the -scale. The basic academic kinematic problems have a lot of symmetries, and most of them have finite dimensional Lie algebras" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002181_robio.2009.5420407-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002181_robio.2009.5420407-Figure1-1.png", + "caption": "Fig. 1. The target is in the vicinity of the obstacle. The left shows that robot, obstacle, and target are collinear. The right indicates that robot, obstacle, and target are not collinear.", + "texts": [ + " The Repulsive Field Function The conventional repulsive force field function can be represented as [4] [13]\u2013[17] [23] > \u2264\u2212 = ,,0 ,)11( 2 1 0 0 2 0 \u03c1\u03c1 \u03c1\u03c1 \u03c1\u03c1 \u03b2 repulseU (3) where \u03b2 is gain; \u03c1 is the minimum separation between the robot and the obstacle; 0\u03c1 is a constant and represents the influence scope of the obstacle. From (3), the corresponding repulsive force formula is driven as X UgradF repulserepulse \u2202 \u2202\u22c5\u22c5\u2212\u22c5=\u2212= \u03c1 \u03c1\u03c1\u03c1 \u03b2 2 2 0 1)11()( (4) where X\u2202\u2202 /\u03c1 can be represented as [ ]TyxX \u2202\u2202\u2202\u2202=\u2202\u2202 /// \u03c1\u03c1\u03c1 (5) Therefore, the total force acting on robot is expressed as repulseattachtotal FFF += (6) In fact, if robot is driven by totalF , the target will never be accessible. From Fig. 1, when approaching the goal, robot is close to the obstacle at the same time, whether or not the mobile robot, the obstacle, and the target are collinear. As the attractive force is getting smaller, the repulsive force is becoming bigger. Finally, robot would deviate from the object [2] [16] [18]\u2013[20] [22]. In short, target is not the global minimum of the whole potential field. The conventional potential field-based function has to be improved. As mentioned above, the target point is not global minimum", + " 3) 1>n : ( ) ( ) ,11 2 111 1 2 0 2 2 0 1 \u2212\u2212\u22c5 \u2212= \u2212\u22c5 \u2212= n goalre n goalre XXnF XXF \u03c1\u03c1 \u03b2 \u03c1\u03c1\u03c1 \u03b2 (16) where 0\u2260\u03c1 , 0\u03c1\u03c1 < , ( ) 0 11 2 0 lim = \u22c5 \u2212 \u2212 \u2192 \u03c1 \u03c1\u03c1 n goal XX XX goal (17) In (16), when 01 \u2192reF , \u21922reF constant, the goal is accessible. To verify the effectness of the improved method described in the previous section, some simulations have been performed. It is assumed that the mobile robot would run at a constant speed. The direction of mobile robot will be dependent on the direction of the total force exerting on the robot. The movement area is mm 55 \u00d7 , where there exist some circular obstacles. The distance is 0.6 m between the target and the obstacle. Two cases described in Fig.1 (a) and (b) are simulated. The starting point of movement is located in the lower-left corner. The function parameters involve 0,,, \u03c1\u03b7kn . Let 2,2 == kn , mm600 =\u03c1 . \u03b7 is determined according to the particular circumstances of the case. Simulation results are illustrated in Fig. 4(a) and (b), Fig. 5(a) and (b), Fig. 6(a) and (b). Fig. 4(a) and (b) give the snapshots of the mobile robot motion using the conventional potential function when the target is far from the obstacles. These two charts show the robot can reach the goal smoothly" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002710_oxfordjournals.jbchem.a129463-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002710_oxfordjournals.jbchem.a129463-Figure3-1.png", + "caption": "Fig. 3. Reductive titration of laccase (oxidized form) with ascorbate under anaerobic conditions. Electron \u2022equivalents on the abscissa increase from right to left. Values were calculated from the moles of ascorbate required to reduce one mole of laccas;. Values were obtained from absorbance changes at \u20ac15 m^ (O) and 330 m// (#) . x , values obtained \u2022by oxidative titration with hydrogen peroxide (Fig. 2). Concentration of ascorbate: 1 mM. Other experimental conditions as for Fig. 2.", + "texts": [ + "com /jb/article-abstract/69/1/91/2184914 by R udolph M atas M edical Library user on 22 January 2019 OXIDATION-REDUCTION TITRATIONS OF RHUS-LACCASE 95 reduced forms of both Cu(615) and Cu(330) -with hydrogen peroxide. Native laccase was fully oxdized by addition of hydrogen peroxide before reductive titration with ascorbate. The oxidized enzyme solution was titrated with 1 mM ascorbase at pH 7.0 and 25\u00b0C by measuring the decreases in absorbance at 615 m/* and 330 m^ under anaerobic conditions. As Fig. 3 shows, the curves of these values exactly corresponded to the oxidative titration curves described above (Fig. 2). There was a lag in the initial part of the titration curve for the absorbance change at 615 ran, while that at 330 m/j \u2022decreased steadily with increase in the concentration of ascorbate added. It was found that 0.18 mM ascorbate was required to reduce all the cupric ions in 0.085 mM laccase solution, that is, one mole of laccase (oxidized form) was fully reduced with about two moles of ascorbate" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003560_978-1-4613-4560-2_2-Figure8.32-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003560_978-1-4613-4560-2_2-Figure8.32-1.png", + "caption": "Fig. 8.32. The graphical representation of the electronation- and de-electronation-current densities and the approach of the Butler", + "texts": [ + " t The condition is for a one-electron transfer reaction. Y) law One does not, of course, necessarily have to go through the sinh containing version of the Butler-Volmer equation to obtain the high-field approximation for the current-overpotential law in electrodics. The Butler-Volmer equation [Eq. (8.31)] contains two terms, one of them representing the deelectronation-current density T and the other, the electronation-current density 7 - -i = i - i (8.27) where [cf Eq. (8.31)] and What happens (Fig. 8.32) when 'YJ is increased? The electronation-current ~ Volmer equation to the high-field approximation as i becomes small. density T decreases and deelectronation-current density T increases. When 'rJ is large enough, T';Y T and the Tbecomes so small that it can be dropped out of the expression. Thus, the high-field approximation of the Butler-Volmer equation (valid at 1}'s greater than about 0.10 V)t yields (8.47) The error involved in replacing the Butler-Volmer equation with (8.47) as a function of potential is shown in Table 8" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003288_1.4025234-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003288_1.4025234-Figure5-1.png", + "caption": "Fig. 5 Finite element model of the meshing between a face tooth", + "texts": [ + " The dynamic characteristics of the rod-fastened rotor may be greatly influenced by the contact effect brought by the meshing of the face tooth, and the contact effect is considered to sharply weaken the stiffness of the segment. Therefore, an investigation is implemented to determine the relationship between the equivalent stiffness and the original stiffness of the shaft segments possessing a face tooth. The investigation is based on numerical calculation, and a finite element model of the meshing between the face tooth is constructed in ANASYS software as shown in Fig. 5. To simplify the calculation process, three hypotheses are given as follows: (1) The load is transmitted through the connection of the face tooth. Without consideration of the friction force, the normal force is the only one existing in the connection area. (2) The connection segment is considered as axial symmetry, ignoring the possible differences between the material of the left and right part. (3) The stiffness is only impacted by the connection of the face tooth, ignoring influence brought by the axial force Through 3D finite element contact case analysis, correlation curves of the equivalent normal stress\u2013linear strain at a different impeller diameter are obtained as shown in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002555_s0263574712000446-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002555_s0263574712000446-Figure1-1.png", + "caption": "Fig. 1. Manipulator structure and coordinate systems affixed to it: O \u2013 base, W \u2013 wrist, S \u2013 force sensor, G \u2013 gripper (its origin is located at the gripper mass center and the orientation is the same as that of frame W ), E \u2013 end-effector (operational space frame).", + "texts": [ + "36 The force control law can be defined in the operational space taking into account the manipulator and the environment properties gathered before task execution,21 or alternatively computed on-line.26 The second approach is suitable for service robots, which perform manipulation in the unstructured environment. In general, manipulation requires three behaviors: contact with the environment, unconstrained position motion, and intermediate or transitional behavior that can be commanded for each of the directions of the operational space.21, 36 The task specified with respect to the end-effector frame (Fig. 1) has to be executed by the controller of the robotic manipulator. There are two fundamental approaches: direct force control and indirect force control.31 Here we concentrate on the latter. The indirect force controller (Fig. 2) is a manipulator controller that has two loops. The external one is forcecontrolled, and the internal one is position-controlled. For the indirect force control, the operational space controller produces the desired velocity X\u0307d represented in the operational space. This velocity is transformed into desired position \u03b8d in configuration space by the coordinate transformation block", + " Hence, the force regulator, as it is presented in the following part of this paper, was developed for a single direction of the task space. Each direction of motion in the task space is controlled by a separate force regulator. It should be noted that these motion directions do not coincide with the motions caused by single actuators. The indirect force controller in Fig. 2 can be presented as in Figs. 3 and 4 to illustrate the proposed controller development procedure description. Here, the control loop is built for a single degree of freedom in the operational space (the end-effector frame E in Fig. 1). Both force controller and controlled plant models are assumed as continuous and linear, hence represented by transfer functions. The presented control structure is an instance of the so-called cascade control well known for process control community.20 Following is the rationale for using this structure: The well-tuned inner loop of Fig. 2 (starting from coordinate transformation and ending on measurement of position) has for rigid manipulator nearly linear dynamics, which in practice can be modeled as second-order lag element" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003409_s1560354711060050-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003409_s1560354711060050-Figure4-1.png", + "caption": "Fig. 4. Sketch of a self propelled helical mechanism. Depicted the \u201cself-rotation\u201d boundary conditions, determining the SR flow. This flow generates zero force but nonzero total torque on the fluid. A counterflow with opposite torque must be added, determined by a rigid translation and rotation boundary condition. It is the RB flow that makes the spirochetes swim!", + "texts": [], + "surrounding_texts": [ + "Helically shaped organisms, how Spirochotes could self propel was a mystery to fluid mechanicists and biologists until the 1970s. The reason is that unless one applies an external force or torque a body whose shape does not change cannot move in a fluid. The Spirochetes puzzle was solved in 1976 by Howard Berg [1], who hypothesized that they have a flexible outer sheath. This is now well established [55]. Internal flagella rotate in the periplasmic space between the cell helical cylinder and the external sheath, acting as \u201croller bearings\u201d between these two surfaces. As they should, Spirochetes abide by the rules of microswimming gauge theory: every section of the outer sheath rotates about its local axis (whose direction varies from section to section). The Spirochete\u2019s shape does change, but in a subtle way, undetectable by optical microscopy. Hold the organism in place and consider this \u201cself-rotation\u201d boundary condition. For the Stokes flow (hereafter called the SR flow) determined by this boundary condition, there is no net force, but there is a nonzero net torque on the fluid. We must add a rigid body counterflow (hereafter called the RB flow) with exactly opposite torque in order to get the instantaneous free swimming flow. The combined flows, SR + RB has zero total force and torque. Thus, mathematically speaking, it is the counterflow that is responsible for the Spirochete translation velocity! For the mathematical analysis we refer to three classic papers (Wang and Jahn 1972 [52], Chwang et al. 1974 [11], Lighthill 1996 [33]). All of them model the spirochete as an infinite twisted cylindrical body, whose central line is an helix curve. Wang and Jahn use series expansions of solutions for Stokes equations, while Chwang et al. and Lighthill use a distribution singularities (stokeslets, dipoles, rotlets). In Lighthill\u2019s words, the flow is confined to \u201cdistances of less than twice the radius of the cell body\u2019s helical shape from its axis, while including a powerful jet-like interior flow through the coils . . . This strong interior jet-like flow (at an average velocity exceeding that of the organism itself) is potentially advantageous for the life-style of these bacteria. Thus, as a spirochete moves forwards, it is continuously exposed around the outside of the helix to new fluid approaching from in front, while at the same time a jet of fluid coming from behind passes through the interior of the helix. Both features should combine to bring a rather rapid flow of nutrients (as well as of chemical signals) towards the spirochete\u2019s close proximity and so help to maintain its energetic swimming movements.\u201d REGULAR AND CHAOTIC DYNAMICS Vol. 16 No. 6 2011 Lighthill argued, furthermore, that the results for a finite-length active helix (SR + RB flow) on an bounded domain should not differ qualitatively from his calculations using an infinite helix, as his solution is highly localized. For the rough estimates in Section 4 we will assume that both for he SR and RB flows the discrepancies between the solutions on bounded or unbounded flow solutions are negligible. For the RB flow this difference would imply on a (slight) change in the resistance matrix (2.3). In fact, it is common wisdom is that changes in resistance coefficients are significant only when close to a boundary [54]." + ] + }, + { + "image_filename": "designv11_7_0003350_1.j051530-Figure18-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003350_1.j051530-Figure18-1.png", + "caption": "Fig. 18 Example adopted by Ding and Yang [22].", + "texts": [ + " Figure 16g presents the result when time is t 0:50 s, when D ow nl oa de d by D re xe l U ni v L ib ra ri es o n M ar ch 1 7, 2 01 3 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /1 .J 05 15 30 the membrane is in the steady state. Figure 16h presents the static results for the same loads. It is obvious that Fig. 16h is the samewith Fig. 16g.Meanwhile, thewrinkled region shown in Fig. 16h is also in agreement with the results obtained byBlandino et al. [21], as seen in Fig. 17 (quoted from Fig. 10c in [21]). Another example of the wrinkled membrane considered in [22] is illustrated in Fig. 18. The two lower corners are fixed and the two corners at the top are applied a distributed tensile loadP t . Damping of the structure and the load\u2013time curve keep the same with the previous example. Figure 19 shows the steady state of themembrane. Similarly, the light regionmeans themembrane elements are taut, the dark region denotes the wrinkled region, and the gray region means elements are in the slack state. It can be found that the result is similar with the result obtained by Ding and Yang [22], as seen in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003801_1350650112470059-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003801_1350650112470059-Figure5-1.png", + "caption": "Figure 5. Relative deviation between the power losses produced by a modified and unmodified internal gear (Gear 1 of Table 1).", + "texts": [ + " It can be noticed that the influence of profile modifications on power losses is similar for external and internal gears. In both cases, the power losses vary from 1.3% for unmodified gears to less than 0.9% when the gears are modified. Similar results have been found for helical gears. Generally, internal gears produce lower losses than the corresponding external gears especially when the speed ratio u is close to 1 as illustrated in Figure 4 for Gear 2 in Table 1. The benefit of profile relief in terms of power losses is illustrated in Figure 5, which represents the relative deviation between the power losses produced by a modified and unmodified internal gear and shows that reductions as high as 30% can be obtained. By combining the formulae for external and internal gears, a model can be set up in order to estimate the efficiency of planetary gears. In what follows, the at RMIT UNIVERSITY on July 20, 2015pij.sagepub.comDownloaded from system under consideration is such that the driving member is the sun-gear, the carrier is the output and the ring-gear is the reaction (fixed) member" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000222_icar.2005.1507412-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000222_icar.2005.1507412-Figure4-1.png", + "caption": "Fig. 4. Example of basic kinematic structure of PMs with decoupled Sch\u00f6nflies motions 3-PRRRR+1-PRRR-type (a) and its associated graph (b).", + "texts": [ + " By various associations of the four legs Ai presented in Tables I-III we could obtain 54=625 basic structural types of PMs with decoupled Sch\u00f6nflies motions without idle mobilities from which just one solution have identical structural leg-type. This solution has 4 legs of a PPPR-type and we denote it by 4-PPPR (Fig. 3). Due to the existence of two unactuated prismatic joints in each leg, solution 4-PPPR has no great practical interest. Solutions with structural nonidentical legs could be used to overcome this disadvantage. The solution presented in Fig. 4 has 3 legs of type PRRRR and one leg of type PRRR. We can see that this solution has only one prismatic joint in each leg and this joint is actuated. No unactuated joints exist in this solution 3-PRRRR+1-PRRR- type. To simplify the notations of the elements eAi (i=1,2,3,4 and e=1,2,\u2026,n) by avoiding the double index in Fig. 3 and the following figures we have denoted by eA the elements belonging to the leg A1 (eA eA1), by eB the elements of the leg A2 (eB eA2), by eC the elements of A3 (eC eA3) and by eD the elements of A4 (eD eA4)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003741_icelmach.2012.6350105-Figure11-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003741_icelmach.2012.6350105-Figure11-1.png", + "caption": "Figure 11 - Phase diagram for vector controlled load test", + "texts": [ + " A further conclusion here is that; the inductance value may show a large variation depending on the operating conditions and in simulations this must be taken into account. IV. INDUCTANCE MEASUREMENT UNDER RUNNING CONDITIONS: WITH LOAD TORQUE odern PM Machines are generally driven by vector controlled drives. If the drive is assumed to be ideal the current flowing to the motor is a q-axis current, which produces the torque required by the load to run the machine at a particular speed. In that case the phasor diagram of this operating condition is as shown in Figure 11. In practice however, there is a current component in phase with the terminal voltage to provide for the core loss. Furthermore the vector control errors are likely to exist introducing a d-axis current component. Provided that the phasor diagram given in Figure 11 is valid, q-axis inductance Lq can be calculated from (6). -. = sin ! (\" \u2212 \"7)\u03c9' (6) In this equation terminal voltage Vt and terminal current It are easy to measure. The phasor diagram indicates that load angle \u03b4 for this operating condition is equal to power factor angle \u03b8. Power factor is relatively easy to measure. In the tests here, the power analyser voltage current and power measurements are used for this calculation. Note that the phasor diagram involves fundamental component of the variables involved" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000498_cdc.2006.377189-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000498_cdc.2006.377189-Figure1-1.png", + "caption": "Fig. 1. 3D Quanser c\u00a9 helicopter.", + "texts": [ + " Then, the above yields ek+1 = A\u0302ek (48) Using (47) in (44), the new model is( zk+1 ek+1 ) = [ (A\u0303\u2212 B\u0303K\u0303) (B\u0303K\u0303) 0 A\u0302 ]( zk ek ) Note that the stability of (A\u0303\u2212 B\u0303K\u0303) will follow from the stability of (11). To prove the stability of A\u0302, being (\u03bb I \u2212 A\u0302) = \u23a1 \u23a2\u23a2\u23a2\u23a2\u23a2\u23a3 \u03bb I \u2212 (A\u2212LC) 0 0 \u00b7 \u00b7 \u00b7 B 0 \u03bb I 0 \u00b7 \u00b7 \u00b7 0 0 I \u03bb I \u00b7 \u00b7 \u00b7 0 ... \u00b7 \u00b7 \u00b7 . . . \u00b7 \u00b7 \u00b7 ... 0 0 \u00b7 \u00b7 \u00b7 I \u03bb I \u23a4 \u23a5\u23a5\u23a5\u23a5\u23a5\u23a6 (49) by using the Schur\u2019s formula det(\u03bb I \u2212 A\u0302) = \u03bb h \u2217det(\u03bb I \u2212 (A\u2212LC)) which is stable if the observer is. Thus, the separation principle is proven. VI. EXPERIMENTAL RESULTS Consider the 3D Hover system, shown in Figure 1 [7]. The roll is defined as a body rotation around the X axis. Assuming that the pitch is zero, the following linear model can be considered,( r\u0307 r\u0308 ) = ( 0 1 0 0 )( r r\u0307 ) + ( 0 0 2.1176 \u22122.1176 )( Vr Vl ) or, by using matrix notation, x\u0307(t) = Acx(t)+Bcu(t) The experimental results are obtained by using the feedback gain designed in [7], as an LQR, u(t) = \u2212 ( 1.7453 0.3009 \u22121.7453 \u22120.3009 ) x\u0302(t) where x\u0302 is defined as x\u0302 = [r \u02c6\u0307r]T and the estimate of \u02c6\u0307r is obtained from the transfer function \u02c6\u0307r(s) = 500s s+500 r(s) Consider now a delay in the control input, such that x\u0307(t) = Acx(t)+Bcu(t \u2212 \u03c4)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000825_978-1-4020-9137-7_15-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000825_978-1-4020-9137-7_15-Figure1-1.png", + "caption": "Fig. 1 Experimental convertible coaxial UAV: Twister", + "texts": [ + " Another approach is presented in [2], where the authors present an autonomous hover flight and perform the transition to forward flight manually. Also, in [3] is presented the T-wing configuration, which is a twin-engine tail-sitter Unmanned Aerial Vehicle (UAV) that performs vertical flight, using linear control techniques to stabilize the linearized vertical dynamics. This paper contributes with the proposition of an alternative tail-sitter configuration capable of performing hover flight (see Fig. 1). A detailed mathematical model, including the aerodynamics, is obtained via the Newton-Euler formulation. In terms of control, we propose a control algorithm that achieves global stability for the longitudinal underactuated dynamics during vertical flight. The paper is organized as follows: Section 2 presents the overall equations of motion of the mini-UAV. The control design to stabilize the longitudinal dynamics, during hover mode, is described Section 3. A simulation study to observe the performance of the propose control law is provided in Section 4" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000084_s00170-005-0312-6-Figure7-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000084_s00170-005-0312-6-Figure7-1.png", + "caption": "Fig. 7 Illustration of detecting plane for a CCP", + "texts": [ + " However, in order to increase the selectivity of cutter orientation, a cone shape is then formed by this zone boundary as shown in Fig. 6. This paper is subjected in determining the mechanism of finding the collision-free zone for a finished ballend cutter. A two-stage mechanism is proposed here in finding the collision-free zone. 3.1 Determination of collision-free zone at the first stage To determine the collision-free zone at the first stage, this research paper firstly presets the original point of the local coordinate system at the contact point between cutter and surface R(u,v), as shown in Fig. 7. The XL axis of this coordinate system is the tangential direction of the tool path (assuming the tool path cuts in u direction), and the direction of normal to the surface on CC point is the ZL axis. Secondly, the detecting plane formed between YL and ZL axes makes the first checking of all adjacent surfaces of this plane. Thus, the surface coordinate system at this place is called the first detecting coordinate. Referring to Fig. 8, assuming the cutter contact point is known as Pa; the intersected curve between the detecting plane and all adjacent surfaces is computed by the linear interpolation method under certain chord deviations" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003347_tvt.2012.2188822-Figure7-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003347_tvt.2012.2188822-Figure7-1.png", + "caption": "Fig. 7. Force characteristics.", + "texts": [ + " The force depends not only on the excitation current but also on the translator position as well. Therefore, the lookup table and neural network are the most practical ways to online estimate the instantaneous force, and the look-up table is more favorable in real-time application due to the lower computation time [14], [16]\u2013[18]. In this paper, the measured force characteristics as a function of excitation current and translator position are used to develop the look-up table, as presented in Fig. 7. By ignoring the mutual coupling effects and minor error between phases induced from manufacturing, the characteristic of the single phase is used to decrease the size of the look-up table [5], [19]\u2013 [21]. Furthermore, the negative force value can be omitted from the table and predicted from the symmetrical positive force. The interpolation algorithm is used to estimate the rest values among the measured points stored in the look-up table. The effective force regions of neighboring phases are overlapped to ensure the two-phase excitation simultaneously during the phase commutation" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003762_robio.2012.6491146-Figure6-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003762_robio.2012.6491146-Figure6-1.png", + "caption": "Fig. 6. Inerter at ankle", + "texts": [ + " We can thus expect that our biped robot achieves more high-speed and energy-efficient active walking than the conventional biped robots by mimicking this PDW on level ground. Fig. 4 shows a front view of our biped robot. This robot has mechanical parameters as shown in Table I. To measure each joint angle and leg\u2019s angular velocity, this robot has rotary encoders and a gyroscope. This robot also has motors and timing belts for active walking on level ground. Fig. 5 shows the foot of our biped robot. This foot has a spring, joint damping and a rotary inerter at the ankle. Moreover, it has a toe-switch and heel-switch to detect contact conditions of the robot. Fig. 6 shows the rotary inerter at the ankle. Since the rotary inerter consists of two pinions, gears and a flywheel, we can easily modify the ankle inertia of the robot by changing the gear ratio and flywheel [10]. The inner legs are then synchronized by a mechanism of the robot, and the outer legs are also synchronized by a mechanism of the robot. Walking of this robot is thus constrained in the sagittal-plane. Fig. 7 shows a sequence of the flat-footed PDW with mechanical impedance at the ankles. We have proposed a control method that flat-footed biped robots mimic this PDW, and we have also shown its effectiveness by simulation [13]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003904_j.ast.2012.06.002-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003904_j.ast.2012.06.002-Figure1-1.png", + "caption": "Fig. 1. Definition of reference frames.", + "texts": [ + " B I is the combined matrix of inertial of the satellite platform and the point-masses of the momentum wheels. The matrices A\u2660 \u2208 R3\u00d7N have columns the s, t and g axes expressed in the body frame and the matrices I w\u2660 are diagonal with elements the values of the inertias of the momentum wheels. Thus, As = [{s\u03021}, {s\u03022}, . . . , {s\u0302N}], At = [{t\u03021}, {t\u03022}, . . . , {t\u0302N}], Ag = [{g\u03021}, {g\u03022}, . . . , {g\u0302N}], I w\u2660 = diag ([I w\u26601 , I w\u26602 , . . . , I w\u2660N ]) where \u2660 means s (the rotational axis), t and g shown in Fig. 1, {\u21c0x } means vector \u21c0 x \u2019s 3 \u00d7 1 matrix expressed in the body frame. \u03a9 = [\u03a91,\u03a92, . . . ,\u03a9N ]T is the column vector of N momentum wheels\u2019 rotation speed. Define J = B I + At I wt AT t + Ag I wg AT g = I \u2212 As I ws AT s , ha = I ws AT s \u03c9B + I ws\u03a9, h\u0307a = ga (2) where ga can be seen as a control input produced by the internal actuator, here is the momentum wheels, ha is the axial angularmomentum vector of wheels. With the previous notations hB can be rewritten as hB = J\u03c9B + Asha, thus the angular velocity is calculated by \u03c9B = J\u22121(hB \u2212 Asha)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003645_j.amc.2012.03.019-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003645_j.amc.2012.03.019-Figure1-1.png", + "caption": "Fig. 1. The physical configuration of squeeze film lubrication between two rectangular plates in the presence of a transverse magnetic field M0. The film thickness H contains height of nominal smooth part and roughness. The upper plate approaches the lower one with constant velocity dH dt .", + "texts": [ + " In Section 3, the Reynolds equation is discretized with a finite difference method, and solved using multigrid method for fluid film pressure, load carrying capacity and squeeze film time. Predictions on bearing characteristics are given for varying couple-stress, roughness parameters, Hartmann number and aspect ratio in Section 4. Final section summarises the important findings and their usefulness in designing bearings. The model consists of flow of viscous isothermal and incompressible electrically conducting couple-stress fluid between two rectangular plates in which the upper plate has a roughness structure. The physical configuration of the problem is shown in Fig. 1. The upper rough plate approaches the lower smooth plate with a constant velocity dH dt . A uniform transverse magnetic field M0 is applied in the z-direction. The upper and lower plates are separated by thickness H, then, the total film thickness is made up of two parts as H \u00bc h\u00f0t\u00de \u00fe hs\u00f0x; y; n\u00de; \u00f01\u00de where h(t) is the height of the nominal smooth part of the film region, and hs is part due to the surface asperities measured from the nominal level, which is a randomly varying quantity of zero mean, and n is the index parameter determining a definite roughness structure" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000648_bf03027056-FigureI-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000648_bf03027056-FigureI-1.png", + "caption": "Fig. I. Rotor with active auxiliary bearing (left), Electromag netic actuator (right).", + "texts": [], + "surrounding_texts": [ + "A new approach to control a rubbing rotor applying an active auxiliary bearing is presented. A two-phase control strategy has been developed, which guarantees a smooth transition from free rotor motion to the state of full annular rub, in case ofan operation state which causes rotor rubbing. The designed control system is able ofboth, avoiding high impact forces and stabilizing the rotor during rubbing. For the experimental verification of the designed control system a test rig has been realized. The experimental results show a drastic reduction of the contact forces, as well as a reduction ofthe rotor deflection.\nKeywords: Actire auxiliary bearing; Rubbing rotor; Two-phase control\n1. Introduction\nThe control of rubbing phenomena in rotating machinery is ofpractical interest for the prevention of structural damage since there is the possibility of serious failures up to complete destruction of the system if the impact forces are not taken under control. In rotating machinery, increased efficiency is often achieved by tightening operation clearances, and so, if a machine is not operating under normal conditions, the stationary and rotating elements are in danger of coming into contact. Rotor-to-stator rubs may occur under several operation states, such as a sudden increase of the unbalance, an extreme outside excitation or the passing of a resonant frequency during the speeding-up or coastdown. Auxiliary bea rings or back up bearings are used in rotor systems to prevent direct contact between rotor and casing when the rotor response is too large. Thus conventional auxiliary bearings limit large response amplitudes.\nIn this paper a control concept using an active\n'Corresponding author. Tel.: +49 89 28915199, Fax.: +49 89 28915213 E-mail address:ginzinger@anuu.mw.tum.de\nauxiliary bearing is proposed which reduces the rubbing severity. The control force is applied by the auxiliary bearing, which is attached to the foundation via two unidirectional magnetic actuators, Fig. 1.\nThe advantages of this concept are the following: If the rotor system runs in the usual way, the active auxiliary bearing does not take effect, so the original design of the rotor system can be kept to largest extent unchanged. Additionally, the auxiliary bearing does not only limit a too large response amplitude of the rotor and prevents the rotor/blades and the casing/seals from direct contact, but also effectively reduces the rubbing severity and especially avoids the occurrence of destructive rubbing instabilities.The capability of existing auxiliary bearings, i.e. as safety bearings in active magnetic bearing systems or as run-", + "dinates of the rotor, fc are the desired control forces, i c the control current to drive the actuators and p a boolean variable to activate and deactivate the control system. The activation routine observes the move ment of the rotor. In case of a sudden arising unbalance the controller can be activated automa tically if the rotor response is too large. The trajectory computation provides the target trajectory for the auxiliary bearing and should assure a smooth tran sition from free rotor motion to a state of permanent contact, which can be formulated as:\nwith arg min f(x) = value of x that minimizes f(x) , q the generalized coordinates of the rotor and the auxiliary bearing, gN the distance between the contact points and qad the target trajectory for the auxiliary bearing. The relative velocity of the contact point in tangential direction gT will not be taken in consideration in Eq. (1) because a non-sliding contact would cause a backward whirl, which is not wanted.\nIn order to define the essential geometrical varia bles a cross section of the auxiliary bearing and the rotor is shown schematically in Fig. 3. The origin of the coordinate system coincides with the center of the undeformed rotor, f r is the position vector to the center of the deformed rotor (in the cross section) and fa to the center of the auxiliary bearing. The air gap in the auxiliary bearing is called ao and f N represents the vector from the center of the auxiliary bearing to the center of the rotor. Additionally we introduce the polar angles rpa and rpr of the vectors fa and f r . The desired position of the a u x 1 a r y\n(1)_ argmin {gN qad - (ij, ij, q). '\ngN\nthrough resonance support, can be well extended from this concept by introducing active control.\nSeveral control structures have been proposed in the literature for the control of rubbing rotors. Feedback linearization was used in (Al-Hiddabi, et al.) in a drill string to suppress the lateral and torsional vibration of the system, dynamic inversion was used to track a desired bit speed. Numerical simulations showed the elimination of the torsional vibration and reduction in the lateral vibration. The problem of a Jeffcott rotor control under rubbing was treated in (Jiang, J. et aI., 2003). The author developed a controller based on stability analysis of the synchronous aunular rub to reduce the intensity of the rubbing. Feedback linearization and direct feedback were used to minimize the transient contact forces of the rotor stator system (Ulbrich, H., 1999) by activating the controller before the occurrence of the first contact.\nIn (Chavez, AI. et aI., 2005) sliding control and cross coupled feedback in a rotor system driven by a power limited motor was used to reduce the impact forces and to decrease the lateral and torsional vibrations. On the other hand, numerous interesting research publications about impacts in robotics have been published in the last decade (Brogliato, B. 1999; Brogliato, B. et aI., 1997; Tomambe, A. et aI., 2003), but the problem of controlling impacts is still open, due to sudden changes of the equations of motion when there is a switch from a state of no contact to a condition of contact.\nA control strategy has been developed, which guarantees a smooth transition from free rotor motion to the state of \"full aunular rub.\" The feedback controller assures a permanent contact with low contact forces. To keep the principal purpose in mind, the control scheme also has to limit the rotor amplitude, as a passive auxiliary bearing does.\nIn a first approach a cascade control is used, see Fig. 2, with qa the measured position of the auxiliary bearing and qad the desired one, qr are the coor\n2. Feedback control concept" + ] + }, + { + "image_filename": "designv11_7_0003057_tpas.1965.4766136-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003057_tpas.1965.4766136-Figure3-1.png", + "caption": "Fig. 3. Double-fed 3-phase induction machine.", + "texts": [ + " V/ = fl-axis flux linkage It therefore follows that = Maf Sitl 0 if - Maid sin 0 lid - B sin 20i,a T + (A - B cos 20)i3 + Maq1cos 0 i (32) T3, a(l#a - ta113) or,These equations show that, when the moving reference o axes are used, the inductances are not constant but are 3P functions of time because of the movement of fluxes with 4 respect to the reference axes. It may easily be verified that (4) and (5), and expressions similar to (7), are valid for the where vIa and lB are given by (31) and (32) flux linkages. PERFORMANCE EQUATIONS OF AN INDUCTION MACHINE Performance in Field Circuit Voltage Equations in Stator Circuit The flux linkage of the main field circuit is The induction machine is considered to be double-fed, 4,f = Lffif + Lafm [ia cos 0 + ib cos (0 - 1200) 3-phase, and ideal (shown in Fig. 3). It is assumed that + i cos (0 + 120\u00b0)] + Mf idi lid unbalance occurs on the stator side. In the following analysis, the axis of phase a of the rotor as d-axis and that Substituting ia and i6 for ia, i, and ic by using (7) and sim- of the stator as a-axis were selected (indicated in Fig. 3). plifying the result, yields Similar to synchronous machine case, the tensor trans41f= Lffif + Mat COS 0 ia - Mat sin 0 ig + Mfzdii,d. formation from phase components to the d, q, and o com- (33) ponents may be applied to induction machines. Under the (33) transformation, both the actual stator and rotor windings Similarly, the flux linkages of the d-axis and q-axis may be replaced by the imaginary d-axis, q-axis, and zerodamper circuits are sequence circuits. Both stator and rotor d-axis and q-axis circuits are centered on the d-axis and q-axis, respectively,id M=idMfd \u00b1 Maid cos 0 ia - Maid sin 0 a + Lildilid and rotate synchronously with the rotor so that their (34) relative positions are maintained" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003383_s12541-013-0061-7-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003383_s12541-013-0061-7-Figure2-1.png", + "caption": "Fig. 2 Coordinate setting for the novel twin-screw kneader", + "texts": [ + " Based on these observations and working principles of traditional twinscrew extruders, a novel continuous twin-screw kneader reactor, composed of self-cleaning, compulsory transportation and mixing and plasticizing, is proposed in this paper (see Figure 1). The core component of the novel twin-screw kneader reactor is one pair of mutually engaged screw rotors. The key to improve the overall performance of the kneader is the design, analysis and simulation of the tooth profiles of the screw rotors. Generally, the profiles were usually designed with one or several arcs and cycloids as well as lines when designing the profiles of a screw pump. The primitive profiles and its coordinate systems of the novel twin-screw kneader are shown in Figure 2. The properties of the profiles are listed in Table 1. The fixed frames are The moving frames are . \u03c3a Oa xa\u2013 ya za, ,( ) \u03c3b Ob xb\u2013 yb zb, ,( ), \u03c3f Of xf\u2013 yf zf, ,( ) \u03c3m Om xm\u2013 ym zm, ,( ), Based upon gear engagement theory,13 the correct engagement condition between the female and the male rotor is (1) In which, is the normal vector at the contact point, is the relative velocity vector at the contact point. The equation of engagement in moving frame \u03c3f between the female and the male rotors can be derived as (2) Similarly, the equation of engagement in moving frame \u03c3m can be derived as (3) The segment of profiles at the end cross section of the female rotor is given by Eq" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002696_j.1467-8659.2012.03165.x-Figure7-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002696_j.1467-8659.2012.03165.x-Figure7-1.png", + "caption": "Figure 7: More complex models: Castle (left), staircase (middle), courthouse (right) models decomposed into r-microtiles. The classes can be computed reliably only for microtiles larger than 32 voxels. The diameter of this uncertain area is smaller than r. Run-time: around 1 hour (castle), 18 min (staircase), and 40 min (courthouse). Far right: comparison to [BBW\u221709].", + "texts": [ + " Computing of the candidate transformations and the table that stores the set of transformations for each voxel are implemented in parallel. All test were performed on a single Intel Core 2 Quad Q9400 CPU with 4 cores running at 2.66GHz. Fig. 6 shows a very simple test scene composed out of boxes. The left hand side shows a scene of three different shapes, decomposed simultaneously. On the right, a simpler scene of independent boxes is decomposed. For these simple scenes, we obtain accurate results up to the resolution of the discretization. In Fig. 7, we apply the algorithm to more complex meshes of architectural objects. We depict 2- slippable tiles in gray, 1-slippable in yellow (irrespective of the class), and only show the large tiles, as explained above. The corresponding unassigned area is shown in dark gray. c\u00a9 2012 The Author(s) c\u00a9 2012 The Eurographics Association and Blackwell Publishing Ltd. 1603 Kalojanov et al. / Microtiles: Extracting Building Blocks from Correspondences The computed decompositions are in most regions qualitatively correct, however, the grid-discretization leads to certain variations at the boundary", + " Global symmetries of the steps are detected, which do not affect the microtiles but are obtained implicitly with our new approach. Our implementation is only intended as a proof of concept, but there are some direct applications: We can determine whether two shapes are r-similar, by matching their respective microtiles. The three box-sculptures in Fig. 6 are made of the same tiles, except from the leftmost, which contains one extra, unique tile, colored violet. Similarly, the isolated tower at the left of the castle in Fig. 7 is r-similar to the castle, which contains additional tiles. A further example is demonstrated in Fig. 8 (right). A sequence of models with increasing complexity is decomposed into microtiles, revealing the redundancy in the model collection. The runtime of the decomposition is still rather large, as the algorithm performs all pairwise comparisons explicitly. Small test scenes compute in a few minutes, medium complexity scenes such as the castle require 1 hour (see Fig. 2,7). Both the number of features and the required resolution for representing the symmetries are limiting factors, and both act quadratically on the run-time" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001948_20100915-3-de-3008.00018-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001948_20100915-3-de-3008.00018-Figure2-1.png", + "caption": "Fig. 2. The WOHC functionality is obtained by making a marine surface vessel emulate the behavior of a pendulum in a force field.", + "texts": [ + " A weather optimal heading control (WOHC) functionality can be obtained by making a vessel behave like a pendulum in the environmental force field. For this purpose, the vessel must comply with two basic rules: (1) Directing its heading towards a virtual pendulum suspension point. (2) Positioning itself on a circle arc surrounding the suspension point whose radius corresponds to the virtual pendulum length. These two fundamental rules will force the vessel to move along the virtual circle arc until its heading has been turned up against the mean environmental disturbance. Figure 2 illustrates the setup, where p , [ ]> denotes the position of the virtual pendulum suspension point, 0 represents the virtual pendulum length, p , [ ]> is the vessel position and signifies the required heading towards p from p. Note that it is the resultant environmental force 0 that drives the whole system. As already mentioned, the pendulum scheme has both a stable and an unstable equilibrium point, which relates to the fact that two positions on the circle arc correspond to alignment with the environmental force" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002885_s00158-012-0836-y-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002885_s00158-012-0836-y-Figure1-1.png", + "caption": "Fig. 1 Juuma\u2019s parameterized model", + "texts": [ + " These main steps form the basis of the generic model for the optimization procedure using the SAMOO algorithm. 2.1 Parametrized model Different topologies of interference fit assembly improving fatigue limit are found in the literature. Several of the authors mentioned above have suggested that the design of a hub overhanging and a shoulder fillet on a shaft substantially improves fatigue life. Dimensional parameters used by Juuma (1999, 2000) and also studied by Lanoue (2008) are reproduced in this study for the optimal design of interference fit assembly. The topology chosen is illustrated in Fig. 1 and the parameters used are defined in Table 1. According to Juumas experimental tests, the torque applied to the model is 3.8E+06 Nmm. The mechanical proprieties of the material used for the finite elements model of assembly are presented in Table 2. 2.2 Finite element model In modeling interference fit assembly using the finite element method, contact algorithm, mesh size, and simulation options must be carefully taken into consideration. First, the use of axisymmetric elements with contact is impossible when considering alternated torsional loads" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002992_s10846-013-9962-z-Figure13-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002992_s10846-013-9962-z-Figure13-1.png", + "caption": "Fig. 13 Experimental quadrotor", + "texts": [ + " Then, we placed the poles of the linearized nonlinear closed-loop dynamics at the same location of the poles of the closed-loop system (14). The resulting nonlinear control gains are KP = \u23a1 \u23a3 0.01 0 0 0 0.01 0 0 0 0.05 \u23a4 \u23a6 , KD = \u23a1 \u23a3 0.28 0 0 0 0.28 0 0 0 0.14 \u23a4 \u23a6 Finally, the integral term was carefully tuned. We followed a similar procedure to tune the Cartesian position controller as well as the vertical position controller. This is, in both cases we started with classical PD controllers. The weight of the quadrotor shown in Fig. 13 was measured using an electronic scale. The inertia was computed from the Computer Aided Design model of the quadrotor. The physical parameters of the quadrotor are summarized in the following table. Quadrotor physical parameters Parameter Value Parameter Value m (kg) 1 CQ 0.0045 g (m/s2) 9.81 (m) 0.22 r\u0304 (m) 0.127 Ixx (kg m2) 0.1 \u03c1 (kg/m3) 0.9 Iyy (kg m2) 0.1 CT 0.14 Izz (kg m2) 0.17 5.1 Outdoor Flight The experimental tests started with the implementation of the attitude controller, the reference was fixed to zero for the three angles" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003869_s00419-012-0608-6-Figure15-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003869_s00419-012-0608-6-Figure15-1.png", + "caption": "Fig. 15 The mode shapes corresponding to frequency \u03c931 (the first mode)", + "texts": [], + "surrounding_texts": [ + "As mentioned earlier, in the geometrical model of the gear, the geometry of the teeth is omitted. It allows us to reduce the system\u2019s FE model size. The simplified geometrical model of the system consists of five sectors (see Fig. 1) that have the cyclic symmetry feature. Each of these segments is meshed by using standard procedures of the ANSYS software. The 3-D solid mesh is elaborated and as mentioned earlier, the ten-node tetrahedral element (solid92) with three degrees of freedom in each node is used to realize each sector. During the mesh generation process, it is assumed that the maximum length of each element\u2019s side needs to be no more than 2.7 [mm]. The developed FE model is displayed in Fig. 2, and it consists of 19,620 elements and 36,188 nodes, respectively. The particular sectors are glued as a whole at the geometrical model preparing the stage by using standard procedure of the ANSYS program. The analysed gear is mounted in the roller bearings. Such bearings typically have slight load capacity under loads perpendicular to the primary supported direction. The gear shaft neck surfaces on which the bearings are assembled are denoted \u201cbearing\u201d (see Fig. 3a). The gear mates with the other devices by the splines. The splines is simplified down to a regular cylinder of the diameter assumed as equal to the splines pitch diameter. The surface denoted \u201cjoint\u201d (see Fig. 3a) is located on the pitch diameter of the splines. Parameters of the analysed system are shown in Table 1a\u2013b. The calculation results for natural flexural oscillations taking into account angular speed of the gear are shown in the paper. In the case of circular discs and annular plates, for each solution where nodal lines are nodal diameters, one obtains two identical arrangements of straight nodal lines, rotated by an angle of \u03b1 = \u03c0/(2n) one to another, where n is the number of nodal diameters. In accordance with the circular and annular plate vibration theory [5,6,12], the particular natural frequencies of vibration are denoted as \u03c9mn , where m refers to the number of nodal circles and n is the mentioned number of nodal diameters. As the shape of the gear model is fairy elaborate, the flexural modes of the system are subject to deformation (as compared to the system without any holes) to such extent that establishing which particular node it refers to becomes rather difficult. This problem is even worse if the angular speed of the gear is varying. The problem of influence of the angular speed on the flexural gear models deformation is analysed. For the purpose of identification of these modes, an algorithm of tagging oscillation modes, which determines the correspondence between vibration of the circular disc versus disc with holes, is used. For this purpose, an auxiliary model of annular plate in the form shown in Fig. 3b is used. The geometrical dimensions of the auxiliary model were taken from the gear geometry (shown in Fig. 1). They are as follows: addendum circle diameter dz , rim mounting diameter dp, root circle diameter dw2, and thickness h p and hz (see Table 1). Dynamic analysis is performed for the auxiliary model cases rotating at predetermined angular speed, where diameter of though holes d01 (see Fig. 3b) varies as seen in Table 2. Findings are compared to each other both quantitatively and qualitatively. This method makes it possible to investigate deformations of nodal lines associated with nodal diameters and circles due to through holes and then determine correspondence between oscillation modes of solid circular disc and a plate with holes. In the final step, solutions found for the auxiliary model are compared with the solution for the system whose FEM model is shown in Fig. 2 (the principal model). As for the principal model case, the 3-D solid mesh and the ten-node tetrahedral element (solid92) are used to discretize the auxiliary models. For all models subject to analysis, the boundary conditions were applied to the nodes. For each model, 1 d f associated with node radial displacement was subtracted from the nodes found on the surface identified as a bearing (see Fig. 3a,b). Furthermore, 1 d f associated with the displacement of nodes along the centreline of each model was subtracted from the nodes found on the surface, identified as a joint (see Fig. 3a,b). For the models obtained in this way, calculations were kept conducted as long as the natural frequency \u03c918 was determined. The calculations were performed assuming that the systems rotate as angular speed of \u03b8 , within the range of 0\u20131047 [ rad/s]. During the computing process, the angular speed values were gradually increased by 80[ rad/s], which made fourteen variants of the results (the natural frequencies and corresponding natural modes), which were subject to further interpretation. The rotation effect was taken into account by determining stress distribution due to rotation, for each model during the computational step associated with static analysis (the so called pre-stress effect). This stress distribution was then included in the computation step associated with modal analysis. The results of the numerical calculations related to the procedure of identifying deformed natural modes of flexural vibration of the gear under consideration are shown below. The results displayed here relate to the determination of the correspondence between the natural frequencies \u03c916 and \u03c925 at high angular speed (\u03b8 = 1047 [ rad/s]) as well as to the correspondence between oscillation modes and the natural frequency \u03c931 at lower angular speeds (\u03b8 = 80 [ rad/s]). The results as shown in Figs. 4, 5, 6, 7, 8, 9 allow for tracking deformations of nodal lines associated with nodal circles and diameters, due to varying diameter of the through holes. With respect to the natural frequency \u03c925, there is marked difference in shapes of natural modes. When one compares the results between each other, one can notice that in order to identify correctly deformed natural modes of the flexural oscillations in the gear under consideration at lower angular speeds, larger number of auxiliary models is required to be included during calculations, as compared to the higher angular speeds. It comes from the fact that additional stresses through the centrifugal effects appear. This effect causes the gear flexural stiffness to be an apparent function of rotational speed (stiffness grows for higher speed). In the next part, results of the numerical calculations associated with the extent of the influence of the angular speed to deformation of mode shapes of oscillations. For each discussed case, both mode solutions related to nodal diameters are shown. These analysed results are sorted by the order of their occurrence. For the frequencies \u03c923 and \u03c918, the results were obtained at angular speeds of \u03b8 = 0 and \u03b8 =1,047 [ rad/s] respectively. For the other cases, results were obtained at angular speeds \u03b8 of, 0, 320, 720, and 1,047 [ rad/s], respectively. Natural frequencies for these modes are included in Table 3. To determine this mode (see Figs. 10, 11), the procedure of tagging natural oscillation modes was required. Nodal lines associated with the circle and diameter are deformed. Minor influence of the angular speed to deformation of the nodal lines is noticeable. The task of determining modes in this case was not too difficult (see Figs. 12); no procedure of tagging natural oscillation modes was required. The slight impact of the gear angular velocity on the distortion of the nodal lines is observed. For these modes (see Figs. 13, 14), procedure of tagging natural oscillation modes was required. It is noticeable that angular speed affects markedly deformation of the nodal lines. Once the angular speed of 720 [ rad/s] is exceeded, the oscillation mode takes different shape. Major deformation of mode shape attributable to the shaft vibrations is evident at this speed. Moreover, additional problem associated with some similarity of the mode being tagged to the mode associated with frequency of \u03c931, emerged during mode identification. Establishing the correspondence between these modes was a complex task (see Figs. 15, 16) due to the shape of oscillation modes similarity to the case discussed earlier. The angular speed affects deformation of nodal lines markedly. Major shape mode variations emerge at \u03b8 = 400 [ rad/s]. The identification process in this mode was not easy (see Figs. 17, 18) . One can notice that angular speed affects the deformation of nodal lines. Major variation in mode shape emerges at \u03b8 = 720 [ rad/s]. Moreover, additional annular shaft vibration emerges at the highest considered angular speed. Finding correct correspondence between the modes in this case was fairly easy (see Figs. 19). High repeatability in deformations of nodal lines on circular plate at various angular speeds is noticeable. As a consequence of the conducted analysis (see Table 3), the Campbell diagram was plotted for the gear under consideration. This is a convenient method of displaying the relationship between gear natural frequencies and transmission system excitations [4]. Excited frequencies are plotted on a vertical axis, and the gear speed of rotation is plotted on the horizontal axis (see Fig. 20). Natural frequencies achieved from numerical analysis are plotted as near-horizontal curves. The forced frequency due to the meshing is determined by the following relation (as in Ref. [4]) f = n0 \u00b7 z 60 (4) where n0 [rpm] is the rotational speed and z is the number of teeth in the gear. For this system, the gear teeth number is z = 59. Vibration resonance phenomenon occurs when forcing frequency (4) matches as to its value with some natural oscillation frequency of the gear. The points where the near-horizontal \u03c9mn curves intersect the straight line (4) indicate the speeds at which the gear resonance will be excited (see Fig. 20). For instance, the rated excitation speed for the natural frequency of \u03c923 is 764 [rpm]. It may be inferred from both the Campbell diagram and Table 3 that the rotating movement makes flexural stiffness of the gear under consideration to increase. Moreover, at speed of 3,820 [rpm], one can notice major surge associated with the mentioned earlier changing of the shape of the natural mode frequency in the case of the frequency of \u03c931. The growth of the gear transversal stiffness observed during gyrate of the gear comes from the appearance of the additional stresses in the toothed gear through the centrifugal effects. The higher rotational speed generates higher centrifugal forces, higher stress level, thereby causing the transversal stiffness of the system to increase. Moreover, the growth of the gear flexural stiffness through the gyrate effect causes reduction of the needed numerical calculations connected with identifying the proper distorted mode shapes." + ] + }, + { + "image_filename": "designv11_7_0000723_j.ijfatigue.2008.01.003-Figure10-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000723_j.ijfatigue.2008.01.003-Figure10-1.png", + "caption": "Fig. 10. Finite element mesh used for the indent simulation.", + "texts": [ + " To evaluate the residual stress fields generated by the indentation process and the over-rolling of the dent due to the contact with another surface, a non-linear material and geometry finite element simulation was performed using the ABAQUS [15]. In an initial stage the indenter, assumed to be a rigid body, penetrates the surface to simulate the indentation process and later, the existent dent is pressed by a rigid surface, in order to simulate the over-rolling process. The experimentally obtained tensile test curve was used as material properties. The finite element model consisted of a 120 angle indenter cone penetrating a flat surface with a static normal load of 2500 N (Fig. 10). In order to simplify the analysis and take advantage of its symmetry, only a quarter part of the facing body was modeled using 16 layers of elements through the thickness. A mesh containing 6071 eight-node continuum elements (C3D8) to model the facing body was developed; contact elements were used in the surface of the disc and the indenter was modeled as a rigid body. Areas where strong stress gradients were present were refined and friction between the indenter and the facing body was not taken into account" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001093_09544062jmes923-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001093_09544062jmes923-Figure2-1.png", + "caption": "Fig. 2 Schematic of the deformed rotating shaft and local coordinates x\u2013y\u2013z", + "texts": [ + " It is shown that these resonance curves are of the hardening type. The effects of eccentricity and damping coefficient are investigated on the steady-state response of the rotating shaft. To verify the perturbation results, a numerical method is used, and a good agreement is shown. Figure 1 shows the schematic of a rotating shaft. Frame X \u2013Y \u2013Z is an inertial coordinate system.The axes x\u2013y\u2013z are local coordinates, which are the principal axes of the shaft cross-section. The axes are attached to the centre-line of the deformed shaft (Fig. 2) at position x. Displacements of a particle in arbitrary location x along X , Y , and Z axes are u(x, t), v(x, t), and w(x, t), respectively. The following assumptions are employed: (a) the shaft has uniform circular cross-section, and it spins about longitudinal axis X with a constant speed ; (b) the shaft is slender and shear deformation is neglected. Rotary inertia and gyroscopic effects are considered; (c) rotating shaft is simply supported; (d) supports O and O\u2019 of the shaft are fixed along the X -axis (Fig", + " 3), the angular velocities of the frame x\u2013y\u2013z with respect to the frame X \u2013Y \u2013Z are \u03c9 = \u03c91e1 + \u03c92e2 + \u03c93e3 = (\u03b2\u0307 \u2212 \u03c8\u0307 sin \u03b8)e1 + (\u03c8\u0307 sin \u03b2 cos \u03b8 + \u03b8\u0307 cos \u03b2)e2 + (\u03c8\u0307 cos \u03b2 cos \u03b8 \u2212 \u03b8\u0307 sin \u03b2)e3 (3) Substitution of equation (3) into equation (1) gives T = 1 2 \u222b l 0 {m(u\u03072 + v\u03072 + w\u03072) + I1[ 2 + \u03c8\u03072 sin2 \u03b8 \u2212 2( )(\u03c8\u0307 sin \u03b8)] + I2(\u03c8\u0307 2 cos2 \u03b8 + \u03b8\u03072)}dx (4) Also, the kinetic energy T e resulted from eccentricity can be computed as T e = \u2212 \u222b l 0 \u03c1A {v\u0307[e\u03be (x) sin t + e\u03c2 (x) cos t] + w\u0307[\u2212e\u03be (x) cos t + e\u03c2 (x) sin t]}dx + 1 2 \u222b l 0 \u03c1A 2[e2 \u03c2 (x) + e2 \u03be (x)]dx (5) where e\u03c2 (x) and e\u03be (x) are eccentricity distributions in two orthogonal planes. The strain along the centre-line of the shaft is e = \u221a (1 + u\u2032)2 + v\u20322 + w \u20322 \u2212 1 (6) Neglecting the shear deformation, the strain energy for a rotating shaft with the isotropic and linear material properties becomes [16] \u03b4\u03a0 = \u222b l 0 (A11e\u03b4e + D11\u03c11\u03b4\u03c11 + D22\u03c12\u03b4\u03c12 + D22\u03c13\u03b4\u03c13)dx (7) where (Fig. 2) A11 = \u222b A E dA, D11 = \u222b A G( y2 + z2)dA and D22 = \u222b A Ey2 dA = \u222b A Ez2 dA (8) In the above equation, E and G are the elasticity and shear modulus, respectively. Curvatures \u03c1i (i = 1, . . . , 3) are computed as \u03c1 = \u03c11e1 + \u03c12e2 + \u03c13e3 = (\u2212\u03c8 \u2032 sin \u03b8)e1 + (\u03b8 \u2032)e2 + (\u03c8 \u2032 cos \u03b8)e3 (9) If shear deformation is neglected, angles \u03c8 and \u03b8 can be related to the displacements (Fig. 3) \u03c8 = sin\u22121 v\u2032\u221a (1 + u\u2032)2 + v\u20322 \u03b8 = sin\u22121 \u2212w \u2032\u221a (1 + u\u2032)2 + v\u20322 + w \u20322 (10) Substituting equation (10) into equation (9), expanding outcomes in Taylor series, and retaining terms up to O(\u03b53), the curvatures are computed up to O(\u03b53)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003720_iros.2012.6386085-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003720_iros.2012.6386085-Figure5-1.png", + "caption": "Fig. 5. Definitions of \u03c6obj , \u03beh, and \u03bem", + "texts": [ + "11) to evaluate the following capability to the velocity command and reference forces profiles. 1) Door and Drawer Model: Fig.4 shows the 3D shape models and grasping point models of a door and a drawer. The black lines represent x,y,z axes of the door coordinate system and the intersection is the origin of the door and drawer coordinate system. The red arrow shows grasping points. Table.I shows detailed values of the grasping points and the hand positions. All values are [m]. The hand positions are the difference between the foot middle coordinate and the hand positions used in (3). Fig.5 shows the kinematics model (\u03c8h() and \u03c8m()) of the door and the drawer. We obtain \u03be\u0307h and \u03be\u0307m from \u03c6\u0307obj based on Fig.5. Our controller has no explicit door dynamics model and uses the force error for update of the reference forces. 1) Door \u03c6obj represents the door angle. The range of \u03c6obj is [\u221290, 0][deg]. We use a door with door-closer which requires time-variant reference forces. Note that in general the door closer holds a non-linear torque-change resulting from the closed link form and the tendency of dynamics differs depending on door angles[15]. The axis of door rotation is on the z axis of the. 2) Drawer \u03c6obj represents the drawer depth", + " (B) are the reference force in the robot controller in another experiment in the same condition as Fig.8. These forces are also projection on r. We stored the reference forces with the angle of door rotation measured by chessboard recognition. Comparing (A) and (B) shows both graphs have two peaks and the profiles are similar. 4) Force Profiles and Estimation of r: We evaluated accumulation of motion errors in the drawer-pulling experiment. We utilized \u03b4\u03b8m as the motion errors. Used drawer is Fig.5(B). We used HRP2-JSKNT. In this experiment, we set the drawer velocity to [\u22120.018, 0.018][m/s] and \u22125.00[deg/s] instead of \u03c6\u0307obj . Under the condition, we performed two experiments: (case 1) Km = 0.9z Kzmp = diagonal(0.9 0.1) (case 2) Km = 0.0z Kzmp = diagonal(0.9 0.1) Fig.10 shows \u03b4\u03b8m. Fig.11 shows the snapshots of (case 1). The motion errors in Fig.10(case 1) did not increase and the humanoid robot completed pulling motion (3,Km = 0.9 in Fig.11). The motion errors in Fig.10(case 2) increased. Therefore, the difference between the desired hand orientation and the actual hand orientation increased and the humanoid robot failed to continue pulling the drawer (3,Km = 0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002148_iemdc.2009.5075287-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002148_iemdc.2009.5075287-Figure3-1.png", + "caption": "Figure 3. The average torque of each phase in failed (light grey) and normal (black) mode. The average torque of all phases is avg T", + "texts": [ + " (4) This is a special case of fault number a. In this case of the failed winding is Neff = 0. According to (2) the effective average torque is ( )( ) ( )(1 x xeff TT y N y N y N \u2212 = \u22c5 \u2212 \u22c5 )1 . (5) The average torque avgT of all m phases according to (3) is: ( )( )( )2 11 ..avg xeff mT T y N T T m = \u2212 + + + \u22c5 (6) In case of failing a whole phase of m phases the average torque of the machine is: [ ]( ) 1 11avg x x mT m T m m \u2212 = \u2212 \u22c5 \u22c5 = T (7) The average torque xeffT of the failed phase is zero. In Fig. 3 the average torque of each phase and the average torque avg of all phases of the SRM is shown: On the one hand there is the torque with short curcuit occurrence and on the other hand there is the torque in normal operation mode without failure. T The faults number e and f are simulated with SIMPLORER\u00ae. This was done, because the short curcuit could occur in every place of the winding and the reaction of the machine could not be estimated without simulation. The simulation was done at a static moment" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001494_tmag.2008.2002621-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001494_tmag.2008.2002621-Figure2-1.png", + "caption": "Fig. 2. Horizontal force generated by an orientation change of a steel plate.", + "texts": [ + " Its thrust force can be combined with a thrust force from a linear induction motor to increase a total thrust force of the magnetically-levitated conveyance system. It Digital Object Identifier 10.1109/TMAG.2008.2002621 means that a total thrust force from both mechanisms is larger than a thrust force from one of the two. This paper explains the operating principle of the mechanism, and presents the experimental results of the noncontact steelplate conveyance system using the mechanism. The operating principle of a proposed thrust-force generation mechanism is shown in Fig. 2. The pole area of an iron-core electromagnet is parallel to the upper plane of a steel plate, and then a magnetic force is generated toward the opposite direction of the gravity force. The magnetic force is a vertical force which is toward the axis. However, in case that the steel plate has a pitch motion with an angle of rad, another magnetic force is generated on the steel plate in addition to a vertical force. This magnetic force is a horizontal force which is directed to the axis. This horizontal force is a thrust force on a steel plate proposed in the paper" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003643_robio.2011.6181649-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003643_robio.2011.6181649-Figure5-1.png", + "caption": "Fig. 5. The rebound of the ball on the table.", + "texts": [ + " The lift force is called as the Magnus effect, which can be large in the case of the large spin \u2225\ud835\udf4e\ud835\udc4f\u2225 = 3000 [rpm] and the small mass \ud835\udc5a = 2.7 [g]. The \ud835\udc36\ud835\udc37 and \ud835\udc36\ud835\udc40 are identified as 0.54 and 0.069 in [14]. As an example of the case of a top spin ball, ?\u0307?\ud835\udc4f = [\u22125.0, 0, 0]T [m/s] and \ud835\udf4e\ud835\udc4f = [0,\u22123000, 0]T [rpm], the drag and lift forces divided by the mass are calculated to 3.7 and 1.6. Since the lift force is about half of the drag one, ignoring the lift force can cause large errors in the prediction of the ball trajectory. The rebound situation of the ball on the table is illustrated in Fig. 5 (a). Define (\ud835\udc97\ud835\udc4f,\ud835\udf4e\ud835\udc4f) as the translational and rotational velocities just before the rebound and (\ud835\udc97\u2032 \ud835\udc4f,\ud835\udf4e \u2032 \ud835\udc4f) as the those just after the rebound. The variables are expressed in the base frame \u03a3\ud835\udc35 . The rebound models of the table and racket are expressed by \ud835\udc97\u2032 \ud835\udc4f = \ud835\udc68\ud835\udc63\ud835\udc97\ud835\udc4f + \ud835\udc69\ud835\udc63\ud835\udf4e\ud835\udc4f \ud835\udf4e\u2032 \ud835\udc4f = \ud835\udc68\ud835\udf14\ud835\udc97\ud835\udc4f + \ud835\udc69\ud835\udf14\ud835\udf4e\ud835\udc4f. (2) These are the algebraic equations where the (\ud835\udc97\u2032 \ud835\udc4f,\ud835\udf4e \u2032 \ud835\udc4f) is the input and (\ud835\udc97\ud835\udc4f,\ud835\udf4e\ud835\udc4f) is the output. The rebound phenomenon in the normal direction is expressed by \ud835\udc63\u2032\ud835\udc4f\ud835\udc67 = \u2212\ud835\udc52\ud835\udc5b\ud835\udc63\u2032\ud835\udc4f\ud835\udc67 with the restitution coefficient \ud835\udc52\ud835\udc5b > 0. The other equations of the other components of \ud835\udc97\ud835\udc4f and \ud835\udf4e\ud835\udc4f are derived by the conservation of momentum. If the contact is sliding, the impulse in the tangent direction is given by \ud835\udc43\ud835\udc65\ud835\udc66 = \ud835\udf07\ud835\udc43\ud835\udc67 as shown in Fig. 5 (b), where \ud835\udc43\ud835\udc67 is the impulse in the normal direction and \ud835\udf07 is the coefficient of the dynamical friction. The direction of \ud835\udc43\ud835\udc65\ud835\udc66 is the inverse of the tangent velocity \ud835\udc97\ud835\udc4f\ud835\udc47 because it is caused by the dynamical friction. Note that the impulse \ud835\udc43\ud835\udc65\ud835\udc66 is smaller than \ud835\udf07\ud835\udc43\ud835\udc67 if the contact is rolling, i.e., the tangent velocity after the rebound \ud835\udc97\u2032 \ud835\udc4f\ud835\udc47 equals to 0. By these relationships, the coefficient matrices \ud835\udc68\ud835\udc63\u2013\ud835\udc69\ud835\udf14 \u2208 \u211d 3\u00d73 are given by \ud835\udc68\ud835\udc63 = ?\u0304?\ud835\udc63(\ud835\udc4e), \ud835\udc69\ud835\udc63 = ?\u0304?\ud835\udc63(\ud835\udc4e), \ud835\udc68\ud835\udf14 = ?\u0304?\ud835\udf14(\ud835\udc4e), \ud835\udc69\ud835\udf14 = ?\u0304?\ud835\udf14(\ud835\udc4e) (3) where ?\u0304?\ud835\udc63(\ud835\udc4e) := \u23a1 \u23a31\u2212 \ud835\udc4e 0 0 1 1 \u2212 \ud835\udc4e 0 0 0 \u2212\ud835\udc52\ud835\udc5b \u23a4 \u23a6, " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003762_robio.2012.6491146-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003762_robio.2012.6491146-Figure1-1.png", + "caption": "Fig. 1. Flat-footed active walking robot", + "texts": [ + " To develop a novel biped robot achieving fast active walking based on PDW, we have studied a flat-footed passive dynamic walker with mechanical impedance at the ankles [10]. This flat-footed robot has a spring and an inerter at each ankle. We have shown that this robot achieves faster PDW than that of conventional flat-footed robots with the ankle springs using the ankle inerters. We expect that biped robots achieve fast and energy-efficient active walking by mimicking this flat-footed PDW. We have thus developed a novel biped robot that can mimic the flat-footed PDW with mechanical impedance at the ankles on level ground as shown in Fig. 1. In this paper, we show a mechanism and control method of our biped robot and its active walking performance by simulations and experiments. Fig. 2 shows a model of our biped robot. This model has flat feet that have a spring, a damper (joint damping), and an inerter at each ankle. Since this robot does not have knees, it scuffs the toe of the swing leg on the ground during the single support phase. To avoid this, we assume that the ground has footholds the same as stepping-stones. In a walking experiment, this assumption is satisfied by footholds like stepping-stones on the ground" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002448_s0263574710000433-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002448_s0263574710000433-Figure1-1.png", + "caption": "Fig. 1. The machine to be calibrated.", + "texts": [ + " The experiment has been carried out and the results are presented and analyzed in detail. The remainder of this paper is organized as follows. The next section describes the 3-DOF mechanism to be calibrated. The error modeling is presented in Section 3. Section 4 investigates the parameter identification based on the minimal linear combinations of error parameters, and then measurement strategy is developed accordingly. Section 5 shows the procedure of error compensation. The experimental work and results are presented in Section 6. Conclusions are given in the last section. Figure 1 shows a 5-axis hybrid milling machine developed in Tsinghua University, which is composed of a 3-DOF parallel mechanism and a 2-DOF serial table. The prototype of the parallel mechanism to be calibrated is called HALF\u2217 introduced in refs. [19] and [20]. As shown in Fig. 2, the mobile platform is linked to the base through two identical PRU limbs and a PRC limb. Here, R, U, and C represent the revolute, universal, and cylindrical joints, respectively, and P with underline represents an active prismatic joint" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001596_0094-114x(73)90020-7-Figure10-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001596_0094-114x(73)90020-7-Figure10-1.png", + "caption": "Figure 10. Shed mechanism of a jet loom.", + "texts": [ + " We start with the binary groups 9, I0 and I 1, 12 and compute the reaction forces in the kinematic pairs occuring in these groups. Then we solve the ternary group 3, 5, 7, 6 treating reactions in joints J and K as external forces loading member 6. At the end we compute the reaction forces in binary group 4, 8, whose member 4 is loaded at point E by the just computed reaction. The last step gives the sought driving moment acting on link 2. Example 2. A shed mechanism of a jet loom is shown schematically in Fig. 10. It consists of a cam 2 that drives a four-bar 1, 4, 3, 5 and two binary groups 6, 7 and 8,9. This mechanism is not a linkage. However, our program, slightly modified, can still be used for its kinematic analysis. The six equations describing the contour of the cam and the vector polygons OABC M.M.T. VoL 8 No. 4--D and C D E B have the same s t ruc ture as the equa t ions descr ib ing the b i t e rna ry group, Fig. I(c). Therefore , the subprogram for this group, sui tably used, solves for the mot ion of the mechan i sm I, 2, 3, 4, 5" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002605_s11431-010-0099-z-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002605_s11431-010-0099-z-Figure1-1.png", + "caption": "Figure 1 A typical two-dimensional airfoil.", + "texts": [ + " This work focused on the control system discretization and the control input constraint as well as the parameter perturbations and the time delay effects. A 4th-order fixed step Runge-Kutta (RK) algorithm was carefully utilized to simulate the close-loop responses in the time domain. These studies aimed at increasing understanding of the applications of this distinctive control strategy. 2 Aeroelastic model of the airfoil A schematic for a prototypical aeroelastic airfoil with a trailing-edge control surface is presented in Figure 1. The linear governing equations of motion can be written as 0 ( , , , ) , 0 ( , , , ) hm S k hh L h S I k M h (1) where m is the mass of the airfoil, S is the static moment about the elastic axis, Iis the inertia moment about the elastic axis, h and are the plunging and pitching coordinates, respectively, kh and k are the stiffnesses of h and , respectively, and is the representation of the flap deflec- tion degree-of-freedom (DOF). The quasi-steady aerodynamic lift and moment (per unit span length) denoted by L and M are presented as \u03c0 2 2 3 2 2 1 , 2 1 1 2 , 2 2 L L M h b L V bC a V bC V V M a b L Vb V b C (2) where \u03c0,2LC \u03c02( sin ),LC (1 2)[ sin (1 2)sin 2 ],MC cos ,e CL , CL , and CM are the aerodynamic coefficients, which can be corrected when wind-tunnel experimental data or high precision CFD data are available" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000494_wcica.2006.1713719-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000494_wcica.2006.1713719-Figure2-1.png", + "caption": "Fig. 2 he model of the rolling window", + "texts": [ + " Instead of the one-off global optimization, the rolling path planning executes local planning repeatedly and makes full use of the newest local environmental information. At each step of rolling planning, the mobile robot generates an optimal local goal based on the locally detected information by a heuristic method and plans a local path within the current rolling windows. Then it moves a step along the local path. With the rolling windows moving forward, mobile robot obtains the newer environmental information. Fig.2 is the model of the rolling window with two windows, which read a planning window and a view window with the former within the latter. The scanning angle is supposed as 360 degree and when the robot takes a step the planning window will be refreshed. So the adjacent planning window will be lapped over in some degree. This paper proposes a novel approach for complete coverage path planning of mobile robot, taking the advantages of the biologically inspired neural network approach and rolling planning" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000831_med.2008.4602258-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000831_med.2008.4602258-Figure1-1.png", + "caption": "Fig. 1. A quadrotor system (OS4 of EPFL)", + "texts": [ + " To serve the same purpose of the attitude representation, each method has its pros and cons such as the number of parameter required, and existing singularities. To avoid the singularity problem and to reduce the number of parameters used for the attitude representation, the quaternion representation is the best one. The Euler angles representation is considered as the best method when considering a minimum number of the parameters to represent the attitude. However this method suffers from the presence of a singularity for one set of values of the Euler angles. The VTOL quadrotor aircraft, named X4 or OS4, shown in Figure 1, is a mini-aircraft with four propellers (the thrust of which are considered as the inputs to the system) in cross configuration. The outputs of the system are the position (described by 3 parameters) and the attitude of the system (described by 3 parameters). Since the number of independent inputs is smaller than the number of degrees of freedom, this mini-aircraft belongs to the class of underactuated mechanical systems. In practical applications, the position in space of the UAV is generally controlled by an operator through a remotecontrol system using a visual feedback from an onboard camera, while the attitude is automatically stabilized via an onboard controller" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001424_0094-114x(75)90076-2-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001424_0094-114x(75)90076-2-Figure3-1.png", + "caption": "Figure 3.", + "texts": [ + " If the pair being unclosed is a higher pair with point contact, it must be required that the radius vectors of the contact point and unit vectors normal to the kinematic pair elements in the system S be equal in order to coordinate the motions of both halves of the contour. This enables one to compose five independent equations [7]. For the case when the higher pair elements are simple ones (two cylinders, a ball and a plane, two straight lines, etc.) it is advantageous to determine the position function in a somewhat different way. For the purpose of definition assume that elements of a higher pair M are two cylindrical surfaces in external tangency (Fig. 3). Unit vectors along the axes of the surfaces are denoted as al and a2. Let us draw the radius vector Rt (i = 1, 2) from the stationary system S~ origin to an arbitrary point of the unit vector a, action line. The radius vector of an arbitrary point of a cylinder axis may then be represented by the vector sum Rt+A, ai ( i=1,2) . To coordinate the motions of the movable links disconnected at the higher pair M, the equation a~l) + a(2) = R ~2) + A2a ~2) (12) R \u00a2') + A~a \") + h la.> \u00d7 a<~) I must be used" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003662_imece2012-89440-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003662_imece2012-89440-Figure4-1.png", + "caption": "Fig. 4: The Physical Geometry of the domain, A) Ti-6Al-4V powder layer, B) Stainless steel substrate", + "texts": [ + " Moreover, the materials property of the powder bed (mainly including thermal conductivity) is changed to the solid property by reaching the melting temperature. However, to consider the mass conservation before and after powder phase transition, the density and specific heat of the solidified zone are set same as those of the powder bed. In addition, experimental results of melt pool measurement have been used to identify average values of melt pool dimension for any of the three electron beam scanning speeds, which are then input into the modeling as known conditions. Figure 4 shows the defined geometry used in this research. A 3-mm powder layer is placed on the stainless steel substrate of 10 mm in thickness. The width and length of whole geometry are 6 mm and 10 mm, respectively. The electron beam moves along the center 5 Copyright \u00a9 2012 by ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 02/01/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use line at the top surface (Y axis). Gambit 2.4.6 is used to define and mesh the geometry" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000823_s11044-008-9122-6-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000823_s11044-008-9122-6-Figure2-1.png", + "caption": "Fig. 2 The ith flexible link", + "texts": [ + " 3, followed by the formulation of the dynamic model in Sect. 4. In Sect. 5, a recursive the forward dynamics algorithm for serial flexible robotic systems is proposed, whereas the simulation results of a flexible two link arm and a spatial Canadarm with two links flexible are reported in Sect. 6. The numerical stability of the proposed algorithm is then investigated in Sect. 7, followed by the conclusions in Sect. 8. Figure 1 shows a serial robotic system having a fixed base and n-moving bodies, which are either rigid or flexible. Figure 2 shows the ith flexible link. For simplicity, and without any loss of generality, each flexible link is assumed to vibrate in its mi th mode in bending and m\u0304i modes in torsion. Hence, the degree of freedom (DOF) of the system is, n\u0304 \u2261 n + nf\u2211 i=1 ( 3mi + m\u0304i ) , where n = nr + nf , nr and nf are the number of rigid and flexible links, respectively. For the kinematic description of the elastic deformation of each flexible link, the AMM [30, 49] is used. Thus, the deformation of any element E\u0303i lying along X\u0302i+1 axis of the link, Fig. 2, due to bending is given by the 3-dimensional vector, ui , as ui ( a\u0304i , t ) \u2261 [ ux i u y i uz i ]T , (1a) where ux i , u y i , and uz i are the projections of the deflection vector ui on the X\u0302i+1, Y\u0302i+1, and Z\u0302i+1 axes, respectively, and a\u0304i is the position vector of element E\u0303i from O \u2032 i . Thus, a\u0304i = a\u0304i x\u0302i+1, where x\u0302i+1 is the unit vector along X\u0302i+1 axis and a\u0304i is the axial distance of E\u0303i from O \u2032 i along X\u0302i+1 of the ith link. Note that a\u0304i varies from 0 to ai\u2014one of the DH parameters of the link, as defined in Appendix A", + " The term ux i results in centrifugal stiffening of the link [8, 30, 44], which is significant in the analysis of flexible multibody systems, when the angular rates of the bodies are considerably greater than their first natural frequency. The centrifugal stiffening effect becomes significant only when the flexible link rotates at a very large angular rate [12]. Hence, for a flexible link used in industrial robots and in satellites whose speed of operation are generally slow, the effect of centrifugal stiffening is neglected. Moreover, flexibility along the joint axis, Zi , is ignored due to the assumption of ith link rigid along Zi , i.e., OiO \u2032 i of Fig. 2. The above two assumptions are quite common in the literature [13, 14, 49]. For a prismatic joint, the flexibility along the Zi -axis is also ignored. Otherwise, the smooth translation along the axis is not possible. Now, using AMM, vector, ui , can be expressed in terms of space dependent eigen functions and time dependent amplitudes as ux i = { 0 for revolute joints, \u2211mi j=1 sx i,j d x i,j for prismatic joints, u y i = mi\u2211 j=1 s y i,j d y i,j for revolute and prismatic joints, uz i = {\u2211mi j=1 sz i,j d z i,j for revolute joints, 0 for prismatic joints", + " The DeNOC matrices allow one to write the matrix and vector elements associated with the dynamic equations of motion in analytical form leading to recursive forward dynamics algorithm. 4.2 Dynamic modeling of flexible robots The dynamic modeling of the flexible robot, shown in Fig. 1, is now derived using the equivalence of EL and NE methodology, as proposed for rigid robots in [7], and the DeNOC matrices for the flexible link robots derived in Sect. 4.1. The steps are outlined below: (1) Referring to Fig. 2, the position vectors of the elements, E\u0304i , E\u0303i , and payload of mass mpi on the ith link, namely, r i , r\u0303 i , and rpi are respectively given by r i = oi + b\u0304i , where b\u0304i = b\u0304izi , r\u0303 i = oi + r\u0304 i , where r\u0304 i = bizi + a\u0304i x\u0302i+1 + ui , and (16) rpi = oi + r\u0304pi, where r\u0304pi = bizi + ai x\u0302i+1 + upi, where, ai and bi are the DH-parameters of the link, as defined in Appendix A, b\u0304i is the axial distance of element E\u0304i along Zi from Oi , and a\u0304i is the axial distance of element E\u0303i along X\u0302i+1 from O \u2032 i , as shown in Fig. 2. Note that b\u0304i is the position vector of element E\u0304i along Zi from Oi , whose magnitude is b\u0304i . The term, b\u0304i , varies from 0 to bi , and a\u0304i varies from 0 to ai . Moreover, the unit vectors along Zi and X\u0302i+1-axes are denoted with zi and x\u0302i+1, respectively, and vector oi denotes the position vector of the point, Oi , of the ith frame with respect to the origin of the fixed first frame. Furthermore, vectors ui and upi are respectively the positions of the element, E\u0303i , and the payload mpi, on the deformed flexible link from its undeformed state. Vector ui is indicated in Fig. 2. Note that the payload is considered as a concentrated point mass at the tip of the link that accounts for any assembly with sensors attached to the ith link. For the nth link, it is the real load to be carried by it. (2) The kinetic energy, Ti , for the ith flexible link is then given by Ti = 1 2 \u222b bi 0 \u03c1i r\u0307 T i r\u0307 i db\u0304i + 1 2 \u222b ai 0 \u03c1i \u02d9\u0303rT i \u02d9\u0303r i da\u0304i + 1 2 mpir\u0307 T pir\u0307pi + 1 2 \u222b ai 0 \u03c1iIpi\u03b2\u0307 2 i dxi+1 + Thi, (17) where \u03c1i is the mass per unit length of the ith link, and the vectors, r\u0307 i , \u02d9\u0303r i , and r\u0307pi, are the velocities of the elements, E\u0304i , E\u0303i , and payload, respectively, which can be written from (16) as r\u0307 i = vi + \u03c9i \u00d7 b\u0304i;\u02d9\u0303r i = vi + \u03c9i \u00d7 r\u0304 i + b\u0307izi + u\u0307i ; and r\u0307pi = vi + \u03c9i \u00d7 r\u0304pi + b\u0307izi + u\u0307pi, (18) where, vi is substituted for o\u0307i , i.e., vi \u2261 o\u0307i . Moreover, \u02d9\u0304ai = a\u0307i = 0 is used in (18) due to the assumption of no extension along X\u0302i+1 axis of the ith flexible link shown in Fig. 2. Similarly, \u02d9\u0304bi = 0, as this portion of the link is assumed rigid. Furthermore, b\u0307i represents the linear joint rate in the presence of prismatic joint. However, for the revolute joint, it vanishes, i.e., b\u0307i = 0. Also, the scalar, Ipi, denotes the polar moment of inertia of the cross-section of the element, E\u0303i , belonging to the ith flexible link, whereas \u03b2i is the angular deformation of the cross-section of the element, E\u0303i , as defined after (3a). Finally, the term, Thi, represents the kinetic energy due to the hub inertia at the joint, which is given by, Thi = 1 2 \u03c9T i I hi\u03c9i , (19) where I hi is the 3 \u00d7 3 inertia tensor for the hub" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002609_icra.2011.5979602-Figure6-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002609_icra.2011.5979602-Figure6-1.png", + "caption": "Fig. 6. Measurement of coefficient of floor friction", + "texts": [ + " The size of foot is 98[mm] by 63[mm]. The distance between feet is 47[mm] at the initial standing posture. In each foot, 4 force sensors are mounted, and 3 axis acceleration/angular sensors are equipped in its body. The soles of the foot are made of POM. The robot is controlled in 1[ms] through the PC which is running RT-Linux OS. In the following experiments, two kinds of floors with different friction coefficients are used. The friction coefficients were measured using the measurement device depicted in Fig. 6. The device has a vice bench with a tiltable clump, and the tilt angle can be measured using a scale. The floorboard was clamped using the vice and a piece of plastic of the same material and size of the sole was put on the floorboard. When tilting the vice, the piece of plastic started slipping on the board. The static friction coefficient \u03bc was calculated by the following equation: \u03bc = tan \u03b8 (8) where \u03b8 is the tilting angle of the clamp. In addition, on the assumption that the piece of plastic has a constant acceleration, the dynamic friction coefficient where \u03b8 is the tilting angle of the clamp, s is the slipping length, t is the slipping time, and g(= 9" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002046_s00170-009-2065-0-Figure12-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002046_s00170-009-2065-0-Figure12-1.png", + "caption": "Fig. 12 Microlens array fabrication; a 3-D model, b without segmentation, c with segmented cross-section, d microlens arrays in a large surface", + "texts": [ + " These are fabricated as a 3\u00d73 array, and the fabrication conditions are shown in Table 3. When each layer is fabricated with one cross-sectional image, the maximum dimensional errors of the tip and height are 45 and 100\u03bcm, respectively. On the other hand, when each layer is fabricated with segmented cross-sectional images, the maximum error is reduced to about 2\u03bcm at the tip. 4.2 Microlens array Microlens arrays of 10\u00d710 have narrow gaps between the microlenses, which demonstrate the merit of fabrication with segmented cross-sections. Figure 12 shows the dimensions of a microlens (Fig. 11), and the fabrication conditions are shown in Table 4. The empty space, which is indicated by an arrow, is used to confirm the size and direction between microlenses in Fig. 12c. Fabrication with one cross-sectional image per layer results in the shape error shown in Fig. 12b. On the other hand, the microlens arrays with the same dimensions were fabricated by segmented cross-sections, as is shown in Fig. 12c. Figure 12d shows microlens arrays fabricated on large surface. 4.3 Scaffold for tissue engineering Recently, microfabrication technologies have been applied to the area of bioengineering. Scaffold fabrication with a biomaterial is currently being studied by many researchers. The scaffold is a framework in order to culture a cell [19], and it is needed to ensure a proper pore size and porosity for cell growth and for delivery of nutrients [20]. Microstereolithography is being applied to this research area owing to the possibility of shape control [6, 21]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000825_978-1-4020-9137-7_15-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000825_978-1-4020-9137-7_15-Figure3-1.png", + "caption": "Fig. 3 Forces of the vehicle", + "texts": [ + " Due to the counterrotating capabilities the yaw motion is auto-compensated, however the blade geometry is not exactly the same, therefore we handle the yaw remanent by propellers differential angular speed (see Fig. 2). 2.1 Longitudinal Dynamic Model In this section we obtain the longitudinal equations of motion of the Twister through the Newton-Euler formulation. Let I={iIx , kI z } denote the inertial frame, B={iBx , kB z } 1hobby-lobby.com/pogo.html. denote the frame attached to the body\u2019s aircraft whose origin is located at the CG and A= { iAx , kA z } represent the aerodynamical frame (see Fig. 3). Let the vector q = (\u03be, \u03b7)T denotes the generalized coordinates where \u03be = (x, z)T \u2208 2 denotes the translation coordinates relative to the inertial frame, and \u03b7 = \u03b8 describes the vehicle attitude. The general rigid-body equations of motion, based on the Newton-Euler approach [4, 5], are given by where FB \u2208 2 and B \u2208 2 are respectively the total force and torque applied to the aircraft\u2019s CG, m \u2208 denotes the vehicle\u2019s mass, = q is the body frame angular velocity, VB = (u, w)T is the translational velocity of the aircraft\u2019s center of mass, I \u2208 contains the moment of inertia about B" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003534_978-1-4419-6022-1-Figure13.19-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003534_978-1-4419-6022-1-Figure13.19-1.png", + "caption": "Fig. 13.19 Microfluidic mixers. Pure passive mixer: molecules diffuse to the other side purely by perpendicular diffusion. Pulse mixer: the fluid is supplied with pulse flow, allowing axial (i.e., parallel to the flow) diffusion. Serpentine mixer: allows both perpendicular and axial diffusions", + "texts": [ + " Because the Reynolds number is proportional to the characteristic length, d, for miniaturized systems, a small value of Re will indicate strictly laminar flow. In fact, the Re for most LOC systems are extremely low, making it almost impossible to achieve turbulent mixing of reagents as illustrated in Fig. 13.18. In LOCs, the molecules flow along the straight stream lines of a strict laminar flow. To achieve effective mixing (without the help of turbulence), the molecules must also move perpendicular to the flow (shown in Fig. 13.19 as passive mixer). This is typically achieved by molecular diffusion. While it may be possible to achieve diffusional mixing by using a very long microchannel, this method works only for molecules with very low molecular weight and not for typically highmolecular-weight biomolecules. A couple of methods have been suggested to improve this pure passive mixer. For example, the solution can also be introduced as discrete plugs of liquid, called pulse mixer (Fig. 13.19). Unlike the passive mixer, the molecular diffusion occurs parallel to the flow, i.e., axial diffusion. More effective and faster mixing can be achieved through making the discrete plugs shorter. The microchannel can also 238 13 Lab-on-a-Chip Biosensors be made as a serpentine shape, so that both perpendicular and axial diffusions occur at the same time (called serpentine mixer, Fig. 13.19). More advanced and complicated microfluidic mixers are currently being investigated. Cell phone cameras (especially those of smart phones) can be used as powerful optical detectors, as we learned from Chap. 12 laboratory task 3 (Sect. 12.11.3). The same can apply to LOC. Recent smart phones are equipped with a powerful white flash and an 8 mp or better digital camera, which can function as a powerful optical detection system for LOC. Although the number of research publications is still small, this area will surely grow rapidly" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003490_03093247v043208-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003490_03093247v043208-Figure4-1.png", + "caption": "Fig. 4 . Stress ratio plotted against depth ratio for nominally identical free-roiling aluminium-a Iloy discs", + "texts": [ + " (Note that all the results are plotted as the ratio of stress to maximum Hertz contact pressure against the ratio of depth below the surface to semi-contact width.) Discs were rolled under a load which would give rise to a maximum Hertz pressure po = 147 500 Ibf/in2 and a semi-contact width c = 0.033 in. This load was chosen to give an estimated ratio of p0 /k = 4.8, at which value theoretical residual stresses had been calculated (2). The discs were rolled at 50 rev/min for 2 min (100 loading cycles). The measured residual stresses in two nominally identical discs (B1 and B2) in free rolling are shown in Fig. 4. Since identical residual stresses would be expected in the two discs in free rolling, the results in Fig. 4 provide an assessment of the reliability of the experimental technique. The match between the two discs is encouragingly good. Average values of the results are compared with theoretical predictions in Fig. 5. The general form of the measured residual stresses is in agreement with the theoretical predictions. The depth of the maximum stresses and the total depth of residually stressed material agree closely with theory. The magnitudes of the maximum measured stresses, however, agree less closely", + " No difference in residual stresses was found even in the layer closest to the surface. Method and technique A new experimental method has been proposed for separating circumferential and axial components of residual stress in axially symmetrical cylindrical parts. It has been successfully used to determine the near-surface residual stresses induced by rolling contact in rolling discs whose stressed length in the axial direction was short (6 diameter). Measurements on two nominally identical discs in free (pure) rolling (Fig. 4) show that the repeatability of the measurements is good: within 5-10 per cent in the highly stressed regions. The importance of accounting for all stress components and stress changes during disc dissection was apparent in the course of this work. For example, to neglect the presence of the axial stress in measuring the circurnferential component leads to an underestimate of the circumferential stress by about 30 per cent. Neglecting anticlastic bending during dissection results in a 25 per cent underestimate of the stress components" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000930_0039-9140(75)80212-8-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000930_0039-9140(75)80212-8-Figure1-1.png", + "caption": "Fig. 1. Schematic diagram of rotating sample-cell assembly. 9 (Reprinted with permission from Anal. Chem., 1970,", + "texts": [ + " disks in a straight-through arrangement [this arrangement is less common than (i/)]; (ii) the Aminco-Keirs phosphoroscope, more widely used, in which the sample tube is placed in the middle of a rotating cylinder with two diametrically opposite apertures; emission light is usually collected at right angles to the excitation light. Detailed description of several types of commercial spectrophosphorimeters has been given in recent reviews. 3'5'6\"a However, important improvements of the technique have been recently reported. 7' 9-12 They 42, 639. Copyright by the American Chemical Society.) mainly concern the modification of the sample cell and the sensitivity of the detector system. Sample cell. In Fig. 1, the rotating sample-cell assembly is schematically shown, as described by Hollifield and Winefordner, 29 and modified by Zweidinger and Winefordner. 9 It consists of a Varian A60-A High Resolution Nuclear Magnetic Resonance Spectrometer Spinner Assembly mounted on a sample-compartment light-cover. The fluctuations of signal resulting from inhomogeneities in the snowed media and irregularities in the diameter of the sample tube are minimized by the rotation of the sample cell (average speed from 450 to 1400 rpm), which is generally a long thin-walled quartz tube" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000084_s00170-005-0312-6-Figure24-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000084_s00170-005-0312-6-Figure24-1.png", + "caption": "Fig. 24 Tool paths on a blade and a hub", + "texts": [ + " The CAD/CAM software is capable of parameterizing the blade curve and the hub curve and to determine the cutter contact point automatically under certain error constraint. The two factors controlling the cutter contact point are step length and tool path interval. Therefore, once an appropriate deviation is given, we can calculate the chord deviation (e) as 0.005 mm, and the cusp height (h) as 0.01 mm. After calculation by software, it is known that there are 9,834 and 9,648 cutter contact points on the hub and single blade, respectively. The numbers of their tool paths are 134 and 138, respectively, as shown in Fig. 24. When the cutter contact points on the blades and hub are determined, and after the original spindle axis orientation (TSa) and suitable clearance value (rcl 0.2 cm) are given, the collision-free cutter orientation can be acquired by using the abovementioned two stages detection methods, and through the programming usingEUKLID software. Figure 25 is the simulated diagram of collision avoidance during cutting hubs. The cone body used for collision checking is marked as the dashed line. Figure 26 is the simulated diagram on cutting blades" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003389_ut.2013.6519846-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003389_ut.2013.6519846-Figure1-1.png", + "caption": "Fig. 1. Reference frame of STARFISH AUV.", + "texts": [ + " The details of experimental design and results are discussed in section IV. In section V, we make use of yaw identification results to estimate the turning radius of the AUV at different speeds. In section VI, we show how a gain-scheduled controller can be designed using the identified parameters. Lastly, some concluding remarks are presented in section VII. Generally, the motion of an AUV can be described using six degrees of freedom differential equations of motion [10]. These equations are developed using two coordinate frames shown in Fig. 1. Six velocity components [u, v, w, p, q, r] (surge, sway, heave, roll, pitch, yaw) are defined in the body-fixed frame, while the earth-fixed frame defines the corresponding positions and attitudes [x, y, z, \u03c6, \u03b8, \u03c8]. The notation used in this paper is in accordance with SNAME [11]. When designing a controller for the AUV, we follow the conventional control philosophy which divides the AUV into three subsystems [12]. They are: (1) steering subsystem to control the heading by using rudder, (2) diving subsystem to control depth and pitch by using the elevator, and (3) speed subsystem to control vehicle speed by varying the propeller speed" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001485_acc.2009.5160064-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001485_acc.2009.5160064-Figure1-1.png", + "caption": "Fig. 1. Planar USV model schematic.", + "texts": [ + " If the resulting nonlinear optimization problem is feasible, the sliding mode controller will avoid these trajectories. If the optimization problem is infeasible, then the system is over specified and it is not possible to avoid the specified state trajectories. In this case, either the constraints on the control actuation, the constraints on the dynamic state trajectory, or both must be relaxed in order to obtain a feasible optimization problem. In this work, the three degree of freedom (DOF) planar model of a surface vessel shown in Fig. 1 is considered. This model consists of surge, sway, and yaw motion with two propeller force inputs f1 and f2. The geometrical relationship between the inertial reference frame and the vessel-based body-fixed frame is defined in terms of velocities as x\u0307 = vx cos \u03b8 \u2212 vy sin \u03b8 y\u0307 = vx sin \u03b8 + vy cos \u03b8 \u03b8\u0307 = \u03c9 (1) where (x, y) denote the position of the center of mass, \u03b8 is the orientation angle of the vessel in the inertial reference frame, (vx, vy) are the surge and sway velocity, respectively, and \u03c9 is the angular velocity of the vessel" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001982_s0022112010000364-Figure7-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001982_s0022112010000364-Figure7-1.png", + "caption": "Figure 7. Second-order pressure and stress contours for corkscrew motion. (a) The hydrodynamic pressure disturbance in the absence of intermolecular effects, \u039e = \u03a5 = 0, and the influences of intermolecular effects, with \u039e = \u03a5 = 0.5, on (b) the hydrodynamic pressure, (c) van der Waals stress, (d ) electric stress and (e) hydromolecular pressure perturbations. The dotted line represents a circle of spatial unit radius.", + "texts": [ + " In this model, the elastohydromolecular lift force is produced by the combined action of the intermolecular and hydrodynamic stresses on the substrate, which ultimately modify the compliant gap geometry and the hydrodynamic flow through that region as shown by the contours of the pressure and stress disturbances in figures 6 and 7. 5.1.1. Influences of rotation and of rotation-axis orientation on the lift force Rotational motions distort the magnitude and orientation of the pressure distribution in the gap and also modify the gap geometry, as observed in figure 7. To isolate the rotational effects, the lift force (5.14) is non-dimensionalized independently of the velocity scale V(\u03c9, \u03b2), and expressed as a function of the translational hydrodynamic compliance \u03b70/V(\u03c9, \u03b2) as shown in figure 8, where intermolecular effects have been neglected for illustrative purposes. As advanced in a previous study (Urzay et al. 2007), the inverse purely rolling motion (\u03c9 = \u22121, \u03b2 = \u03c0/2) completely suppresses the production of elastohydrodynamic lift force, since a local Couette flow is induced in the gap, and the hydrodynamic pressure becomes zero to every order of \u03b70", + " Similarly, the present formulation reveals that, for the same translational velocity, particle dimensions and substrate mechanical properties, the purely rolling motion (\u03c9 = 1, \u03b2 = \u03c0/2) produces a larger lift force than the corkscrew (\u03c9 = 1, \u03b2 = 0) and translational (\u03c9 = 0) motions; during the rolling motion, the fluid entrainment of the combined rotation and translation are aligned along the \u03b8 =0 axis and both effects more strongly synergize causing a larger positive overpressure peak in the gap and therefore larger substrate deformations. In this model, no negative values of the elastohydrodynamic lift force were found for any combination of rotation and translation. 5.1.2. Influences of intermolecular effects on the lift force Figure 7 shows that the intermolecular stresses produced by the electric and van der Waals forces disturb the compliant wall and modify the net normal stress acting on the sphere. The influences of these intermolecular effects on the lift force are shown in figure 9, which values are independent of \u03c9 and \u03b2 . For negative and order-unity values of \u03a5 , or more precisely \u03a5 \u2212(48/125)1/2, which correspond to order-unity and repulsive van der Waals forces, the lift force decreases with increasing \u03b70 because of the gap-distance-augmentation effect outlined in Appendix B, by which the repulsion decreases because of the increase of the substrate compliance and the effective clearance, which dominates the elastohydrodynamic force that typically increases with increasing \u03b70" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000583_j.cma.2008.11.014-Figure7-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000583_j.cma.2008.11.014-Figure7-1.png", + "caption": "Fig. 7. Illustration for the closest projection under the definition of the energy norm k kC.", + "texts": [ + " The energy norm of the elastic strain part is introduced as 1 2 kEek2 C \u00bc 1 2 fEegT \u00bdC fEeg \u00bc 1 2 fE EwgT \u00bdC fE Ewg: \u00f014\u00de The actual elastic strain Ee is interpreted as the solution of the minimization of strain energy in the form Ee \u00bc ARG MIN 1 2 kEek2 C \u00bc ARG MIN 1 2 fE EwgT \u00bdC fE Ewg ; \u00f015\u00de where the constitutive tensor, defined by the second order partial derivative of the elastic potential in the following form C: =r2W, is assumed to be constant and positive definite. 1 2 kE ek2 C represents the energy norm of the elastic strain Ee which is geometrically interpreted as the closest projection of the total strain E on to the direction of the wrinkling strain Ewalong the definition of k kC; see Fig. 7. For this reason, the solution Ee has to fulfil the minimal energy norm 1 2 kE ek2 C for wrinkled membranes. In this section, a similarity between wrinkling and perfect plasticity is discussed. For a hypoelastic\u2013plastic model, an additive decomposition of the strain tensor E into an elastic part Ee and a plastic part Ep is assumed; for more details about perfect plasticity, see [2] and [35]. Under usual service conditions, membranes are deformed within small elastic strain regime. For this reason, the rate-independent \u2018\u2018hypoelastic\u2013plastic model\u201d, which is typically used when elastic strains are small compared to plastic strains, is considered as a suitable choice" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001403_gt2009-59226-Figure17-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001403_gt2009-59226-Figure17-1.png", + "caption": "Fig. 17 Experimental and simulation results with shroud Tangential direction drain, without back plate", + "texts": [], + "surrounding_texts": [ + "The calculation model is shown in Fig. 12. The revolutions of the gears were set to the same as the experiment. The bearings were modeled to cylindrical shape that filled the space between the rollers of the bearing. On the axial surface of the cylinder, the revolution of a bearing holder was assigned. The flow rate of the oil supply for the bearings was modeled to constant leakage from the surface of the cylinder that had the simplified shape of the bearing rollers. Figure 13 shows the calculation cells of the unshrouded gears. In these calculation cells, in order to simulate the oil supply in the into-mesh direction of the gears, the size of the cells around the meshing part was made small until the flow in the minimum space between the gears could be calculated. The bottom surface of cell block #4 was set on a constant pressure boundary and other surfaces of the block were set on a non-slip wall. In the calculation case with the shrouds, the velocity out of the shrouds is low and influence of the casing wall is nearly isolated. Therefore, with regard to the simulation with the nloaded From: http://proceedings.asmedigitalcollection.asme.org/pdfaccess.ashx shrouds, to reduce calculation time, cell block #4 was omitted and the outer surfaces of blocks #1, #2, #3 were set on constant pressure boundaries except for wall boundaries on the back of the gears. Other calculation conditions were set the same as Table 2. The CPU times with single CPU in 10 rotation of the input gear were 8.9 days in unshrouded case and 5.2 days in shrouded case." + ] + }, + { + "image_filename": "designv11_7_0003383_s12541-013-0061-7-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003383_s12541-013-0061-7-Figure1-1.png", + "caption": "Fig. 1 Assembly drawing of the novel kneader reactor", + "texts": [ + "11,12 But these mechanisms can be improved by changing the profiles of twin-shaft kneaders based on the gear engagement theory. For screw pumps, the fill level of the plug-flow reactor depends on the intrinsic self-cleaning properties of the reactor itself. This phenomenon is well known as the \u201ccompulsory transportation effect\u201d or \u201cpumping effect\u201d. Based on these observations and working principles of traditional twinscrew extruders, a novel continuous twin-screw kneader reactor, composed of self-cleaning, compulsory transportation and mixing and plasticizing, is proposed in this paper (see Figure 1). The core component of the novel twin-screw kneader reactor is one pair of mutually engaged screw rotors. The key to improve the overall performance of the kneader is the design, analysis and simulation of the tooth profiles of the screw rotors. Generally, the profiles were usually designed with one or several arcs and cycloids as well as lines when designing the profiles of a screw pump. The primitive profiles and its coordinate systems of the novel twin-screw kneader are shown in Figure 2. The properties of the profiles are listed in Table 1" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002977_1.1719476-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002977_1.1719476-Figure1-1.png", + "caption": "FIG. 1. Viscometer cell.", + "texts": [ + " Viscosity 11 is proportional to the roll time in the expression (1) where A is a geometric constant, (Ph-PI) is the difference in the density between the ball and the liquid, and T is the roll time. Calculation of the constant A is difficult.3 Therefore, it is usually evaluated by calibrating the vis cometer against a liquid of known viscosity. Adaptation of the rolling ball viscometer technique to high pressures requires the solution of two problems: (1) the coupling of the liquid to the pressure medium and (2) the measurement of the roll time of the ball. The coupling problem was solved by using a capillary as illustrated in Fig. 1 to retain the liquid in the viscometer cell while permitting contact with the pressure medium of compressed argon. The cell was made of fused silica tubing, precision bored to a 0.7125 em diameter and fitted with a precision ground 0.6350 cm diam ball. One end of the 6.35 em long cell was sealed and the other end was joined to a 1 mm bore capillary to give an over-all length of 11.43 em. In order to provide an expansion reservoir, the midportion of the capillary was enlarged to form a cavity having about -to the volume of the cell", + " Downloaded to IP: 132.248.9.8 On: Sun, 21 Dec 2014 20:35:41 VISCOMETER 1841 member of each pair of electrodes was grounded to the high pressure bomb and the other member was connected to the high terminal of the capacitance meter. The elec trodes were made from 0.3175 em wide Nichrome strip, silver soldered to 0.0508 cm diam lead wires. In each set, the electrodes were separated by Pyrex glass spacers 0.3175 cm wide which positioned the capacitors and insu lated them from the high pressure bomb (see Fig. 1). Teflon tubing was used to insulate the lead wires from electrical contact with the high pressure assembly. Since the change in capacitance ~C produced at each ring capaci tor by the rolling ball may be less than 1 pF, a sensitive FM capacitance meter was used to detect the presence of the ball. The FM capacitance meter consisted of a stable 455 kc oscillator and a narrow band discriminator (see Fig. 3). In operation the ring capacitors were connected via coaxial cable in parallel with the frequency determining capacitor Cl in the tank circuit of the oscillator (transistor Ql) and the detector was tuned to zero on meter M l \u2022 The small change in capacity of a ring capacitor caused by the rolling ball produced a corresponding frequency change ~F in the oscillator" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003173_j.robot.2010.12.006-Figure7-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003173_j.robot.2010.12.006-Figure7-1.png", + "caption": "Fig. 7. Choice of the initial condition for our algorithm in an incremental case. By choosing the initial point s0 as the intersection of R(wres,t2 ) and the hyperplane with normal nt1 through s\u2217t1 , fewer iterations are required by our algorithm to compute s\u2217t2 . (a) Only one iteration (left side) needed, in comparison with two (right side) if s0 is chosen as in Algorithm 1. (b) Possibly, no iteration required and s\u2217t2 = s0 (left side) because s0 chosen in this way can still be a point on the boundary of co S.", + "texts": [ + " In many cases, however, the wrench vector wi,j (defined in (5)) at contact does not always change or changes intermittently atmost, as each contact is oftenmaintained for a while, such as the contact between the feet and ground during the walking of a legged robot. In such a case, we may reduce the number N of iterations of our algorithm by utilizing some coherence between successive states. Here we denote by subscripts t1 and t2 two adjacent states and assume that wres changes from state t1 to t2. Suppose that nt1 , s \u2217 t1 , and S\u2217t1 have already been computed by our algorithmwith respect towres at t1. Note that nt1 and s\u2217t1 define a hyperplane H(nt1 , s \u2217 t1) that supports co S (see Fig. 7). Then, instead of hco S(ut2), the initial value \u03bb0 for our algorithm at t2 can be taken as \u03bb0 = nT t1s \u2217 t1 nT t1u \u2217 t2 , (29) where ut2 = wres,t2/\u2016wres,t2\u2016. In fact, this is to choose the initial point s0 = \u03bb0u at the intersection point of H(nt1 , s \u2217 t1) and R(wres,t2). Probably, \u03bb0 given by (29) is smaller than hco S(ut2), which helps determine s\u2217t2 and S\u2217t2 with fewer iterations (Fig. 7(a)). Sometimes this intersection point still lies on the boundary of co S, so that s\u2217t2 just equals s0 and our algorithm needs no iteration (Fig. 7(b)). However, if \u03bb0 given by (29) is bigger than hco S(ut2), we can set \u03bb0 = hco S(ut2) as usual. Therefore, we finally choose \u03bb0 = min nT t1s \u2217 t1 nT t1u \u2217 t2 , hco S(ut2) . (30) We implemented the GJK algorithm and our algorithm in MATLAB on a laptop with an Intel Core i7 2.67 GHz CPU and 3 GB RAM. In numerical tests, we set a small tolerance \u03f5 = 10\u221210 on the distance dco S(sr) to terminate our algorithm. The friction coefficient \u00b5 = 0.2 for every contact. Referring to Fig. 1, we consider two cases of a six-leg robot walking on an uneven terrain" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003112_2013.40500-Figure6-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003112_2013.40500-Figure6-1.png", + "caption": "FIG. 6 Normal pressure profiles at no slip with load as parameter in dry sand.", + "texts": [ + " The peak points of these curves were taken for the construction of the Mohr-Coulomb envelop, and the value of (f> was found to be very nearly equal to that determined by sliding friction experiments. The sliding friction ex periments resulted in cfy equal to 24 deg and c equal to 0 while evaluating those from torque-slip relationship when the normal pressures at wheel-soil con tact are known, gave (f) equal to 23 deg and c equal to 0. Actual, normal pressure-distribution diagrams are shown in the next series of figures. Fig. 6 illustrates the pres sure distribution in sand as a function of the polar angles under a 20 by 3-in. wheel at various loads. The slip is held constant at 0 per cent. The effect of slip on pressure distribution is shown in Fig, 7, when the soil (sand), wheel size and wheel load are kept constant, It is apparent from the latter two pressure-distribution diagrams that, as slip occurs, pressure distribution as well as sinkage become a function of slip. An increased sinkage develops higher motion resistance; therefore, the result ant of the pressure distribution will have a higher angle of inclination rela tive to the vertical" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002745_robio.2010.5723320-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002745_robio.2010.5723320-Figure1-1.png", + "caption": "Fig. 1 Difference in the distance error", + "texts": [ + " We employ a CCD camera as sensor, and we utilize brightness for determining the tau-margin. To discuss the effectiveness of the proposed sensing system, we apply it for controlling a mobile robot, and we conduct experiments in which the robot avoids an oncoming object in perfect timing. It is generally known that many animals and insects can perceive distance owing to binocular parallax. However, as the distance increases, it becomes difficult to perceive the distance accurately because of the increase in the error between the perceived distance and the actual distance. Fig. 1 shows the difference in the distance error with binocular parallax. In this figure, the actual distance from the object is denoted by Da, and the visually perceived distance is denoted by Dp. Furthermore, a\u03b8 denotes the angular direction of the actual object, and p\u03b8 denotes the angular direction of the perceived object. The error in the distance, De is given by the following equation: )tan(tan 2 pae dD \u03b8\u03b8 \u2212= (1) As a\u03b8 approaches 90 degree, De diverges to infinity. Thus, this equation implies that De increases with Da" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002079_3.59009-Figure6-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002079_3.59009-Figure6-1.png", + "caption": "Fig. 6 Modified Nyquist plot for improved power actuator.", + "texts": [ + " Passive flutter occurs between 550 and 600 KEAS as indicated by the change in the direction of closure for the trajectory from clockwise below flutter onset to counterclockwise above flutter onset. After flutter onset, two poles are present in the right half plane (one for both positive and negative frequencies). The Nyquist criterion requires two counter-clockwise encirclements of the origin to ensure that there are no zeros in the right half plane and thus indicate a stabilized system. The six plots of Fig. 5 indicate a stable system for all velocities through 800 KEAS. An enlarged Nyquist plot for the velocity of 700 KEAS is shown in Fig. 6. This figure illustrates the type of data from which a control system may be designed. The diagram shows trajectories for three values of the structural damping coefficient. The phase margin varies from 18\u00b0 for # = 0.0 to 57\u00b0 for g = 0.04. The phase lead compensation was chosen to place the flutter frequency of 8.3 Hz very near the negative real axis to give the greatest latitude on gain adjustment. The maximum possible open loop gain is determined by the crossover at 6.8 Hz. If the gain is increased so that the crossover occurs on the negative real axis, the net number of encirclements of the origin would be zero and thus the system would be unstable" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003812_20110828-6-it-1002.00031-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003812_20110828-6-it-1002.00031-Figure2-1.png", + "caption": "Fig. 2. LOS constraints.", + "texts": [ + " (2011)). Defining the augmented state vector X\u0304 = ( \u03b4x \u03b4y \u03b4x\u0307 \u03b4y\u0307 rx ry \u03c3x \u03c3y ) T , the model can be written in the form, { X\u0304k+1 = A\u0304X\u0304k + B\u0304U\u0304k, Y\u0304k = C\u0304X\u0304k + D\u0304U\u0304k, (5) with appropriately defined A\u0304 and B\u0304 (see below) and where Y\u0304 , C\u0304 and D\u0304 are to be defined next based on the specifications of LOS and soft-docking constraints. The LOS constraints confine the spacecraft to an intersection of a LOS cone, with vertex moved slightly inside the platform, and a half-plane, see lines a, b, c in Figure 2. We let \u03b3 denote the half of the LOS cone angle and we let rtol denote the distance by which the vertex of the LOS cone is moved inside the platform. The value rtol > 0 slightly relaxes the LOS constraints to mitigate ill-conditioning of the MPC problem caused by cone constraints becoming almost infeasible (as a and b come arbitrary close together at the vertex) when the docking port is approached. The half-plane constraint c, defined by a tangent line to the platform at the position of the docking port, ensures that collisions of the spacecraft with the target platform are avoided with the relaxed cone constraints" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000929_j.commatsci.2008.07.033-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000929_j.commatsci.2008.07.033-Figure5-1.png", + "caption": "Fig. 5. Temperature distribution on the cross-s", + "texts": [ + "5 mm after multiple index fitting. Based on the results of the parameters of Gauss and double ellipsoid heat source, the temperature distribution on the crosssection of weld were covered in Table 5 according to different power ratio of surface heat source. The temperature decreases as the power ratio k increases, with the weld width enhancing and the weld penetration reducing. Great coherence results when the power ratio should set to 0.6. The simulated temperature distribution on the cross-section of weld is presented in Fig. 5, comparing to the physical weld, the weld penetration and width from corrected composite heat source is much more accurate. Great importance is put on the dimension accuracy according to architectural particularity, and the structural deformation should be highly restricted. Since the thermal cycle put great effect on the welding residual stresses and deformation, it should be give close attention to the heat change during the welding process. Temperature measurements at different locations were performed to verify the computed temperature field" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003383_s12541-013-0061-7-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003383_s12541-013-0061-7-Figure4-1.png", + "caption": "Fig. 4 FE model for the flow field", + "texts": [ + " According to the equations for the endcross section of the female and the male rotors and helicoid of screw rotors, the end-cross section and the 3D model of the female and the male rotors for the novel twin-screw kneader are showed in Figure 3. A three-dimensional geometrical model of \u2018 \u2019 barrel was built according to the actual size of the twin-screw kneader prototype. Boolean subtraction was performed using this model and screw rotors, and a physical model of the flow field of the novel twin-screw kneader was developed. The FE model is shown in Figure 4. The materials to be processed in the twin-screw kneader are high-viscosity non-Newtonian liquids, which can be simulated by power law fluid model.14-16 Taking into consideration the actual conditions of material transport and the characteristics of the flow field, the following assumptions can be made: (1) the flow field is steady and isothermal. (2) Renault coefficient of a fluid in laminar flow is very low. (3) effects of body forces such as inertia force and gravity can be ignored. (4) the c'd ' c'd ' xm Ra= ym 0=\u23a9 \u23a8 \u23a7 b 'c' xm a 0 coskmf\u03c6\u2013 b 0 sinkmf\u03c6 Acosimf\u03c6+\u2013= ym a 0 sinkmf\u03c6\u2013 b 0 coskmf\u03c6 Asinimf\u03c6+ +=\u23a9 \u23a8 \u23a7 u 1 um u 2 \u2264 \u2264( ) \u03c6 um arcsin kmf b 0 cosum a 0 sinum\u2013( ) Aimf -----------------------------------------------------+= xm c 0 coskmf\u03c6\u2013 d 0 sinkmf\u03c6 Acosimf\u03c6+\u2013= ym c 0 sinkmf\u03c6\u2013 d 0 coskmf\u03c6 Asinimf\u03c6+ +=\u23a9 \u23a8 \u23a7 u 1 um u 2 \u2264 \u2264( ) \u03c6 um arcsin kmf d 0 cosum c 0 sinum\u2013( ) Aimf -----------------------------------------------------+= \u03c6 \u03c9mt= b 'c' d 'e' x x t( )cos\u03c4 y t( )sin\u03c4\u2013= y x t( )sin\u03c4 y t( )cos\u03c4+= z p\u03c4= p T 2\u03c0\u2044=\u23a9 \u23aa \u23aa \u23a8 \u23aa \u23aa \u23a7 \u221e fluid is incompressible", + " The coordinates of the central axis at the inlet of the female rotor are (x0, y0, z0) and the velocity boundary conditions of the screw rotors surfaces are expressed as (27) (28) The pressure P1 at the inlet position of the flow filed is very low. The material is extruded from the inlet and moved toward the outlet through the working area of screw rotors. Due to extrusion among material, there will be a certain pressure P2 at the outlet position, and the boundary condition for the groove can be expressed as \u0394P = P2-P1 along the direction of extrusion. The inlet boundary, velocity boundary, external surface boundary and the outlet boundary of the finite element model were set as shown in Figure 4. The overall flow field contour map for pressure is shown in Figure 5. It can be seen that the pressure increases gradually from the inlet toward the outlet. The pressure obviously increasing appears at the top of screw edge region, but it is much lower at the bottom of the groove. The pressures at the right side is little higher than that of left side along the same axial section in the flow field. It also shows that the pressures experienced by the male rotor are greater than those experienced by the female rotor" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001860_tmech.2010.2057440-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001860_tmech.2010.2057440-Figure2-1.png", + "caption": "Fig. 2. CAD drawing of OCTA.", + "texts": [ + " The robustness of the CANP method was compared with those of other CA methods through a simple experiment. The accelerometer array octahedral constellation of twelve accelerometers (OCTA) was equipped with three uniaxial gyroscopes, mounted orthogonally to one another. OCTA was shaken by hand in order to produce two types of trajectories in two different trials. In the first trial, OCTA was rotated randomly so as to produce arbitrary angular-velocity estimates. In the second trial, OCTA was rotated back and forth about its x-axis, as shown in Fig. 2, which was aligned with the vertical. The amplitudes of the rotations were approximately 180\u25e6. This produced an angular-velocity vector of varying amplitude, while roughly maintaining a constant direction. The generated angular accelerations and angular velocities ranged from 0 to 250 rad/s2 in magnitude, and 0 to 23 rad/s in magnitude, respectively. The resulting accelerometer measurements were processed according to the seven CA methods available, i.e., the CAD, CAOD, CAPF, CANS, CAAD, CAAM, and CANP methods", + " Moreover, angular-velocity measurements were obtained from the three gyroscopes. For the relatively low angular-velocity and acceleration amplitudes generated in the two experiments, gyroscope measurements are more accurate than the estimates obtained from the accelerometer signals. Taking the gyroscope estimates as a reference, the accuracy of the seven CA methods were compared, and this, for the two tested trajectories. Let us first begin by giving further details on the experimental test bed, starting with OCTAs. The geometry of OCTA is shown on Fig. 2, where it is seen that its six pairs of accelerometers are located close to the vertices of a regular octahedron. The exact coordinates of its associated vectors ei and ri , i = 1, . . . , 12, expressed in frame B are recorded as follows: [e1 e2 \u00b7 \u00b7 \u00b7 e12 ] = \u23a1 \u23a2\u23a3 1 0 \u22121 0 0 0 0 1 0 1 0 0 0 1 0 0 1 0 \u22121 0 0 0 0 1 0 0 0 1 0 1 0 0 1 0 \u22121 0 \u23a4 \u23a5\u23a6 (29) \u23a1 \u23a2\u23a2\u23a2\u23a2\u23a3 rT 1 rT 2 ... rT 12 \u23a4 \u23a5\u23a5\u23a5\u23a5\u23a6 = \u23a1 \u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a3 0.1444 0 0.0252 0.1444 0 0.0252 \u22120.1444 0.0252 0 \u22120.1444 0.0252 0 0.025 0.1444 0 0.0252 0", + " The rms values of the errors were computed for all CA methods, over the duration of the first trial. In the case of the CAD method, the rms error \u03b4\u03c9CAD ,rms was computed as \u03b4\u03c9CAD ,rms = \u221a\u221a\u221a\u221a 1 m \u2212 1 m\u2211 k=1 \u03b4\u03c92 CAD ,k (32) where m = 10 000 is the number of samples acquired in the first trial. The other rms errors were computed analogously for other CA methods, which yielded the second column of Table II. 2) Second Trial (A Trajectory About a Constant Axis of Rotation): In the second trial, OCTA was rotated repeatedly about its x-axis, as defined in Fig. 2. The resulting CAD and CANP estimates are shown in Figs. 10 and 11, respectively. The associated errors \u03b4\u03c9CAD ,k and \u03b4\u03c9CANP ,k appear, respectively, in Figs. 12 and 13. Finally, as in the first trial, the rms values of the errors of all CA methods were computed according to (32). The results appear in the third column of Table II, alongside those obtained for the first trial. Let us review each of the results obtained with the CAOD, CAD, and CANP methods. We leave aside the CAPF, CANS, CAAD, and CAAM methods because 1) their analysis is much more involved and 2) their associated error-sensitivities and computational-costs are not inferior to those of the CAD and CANP methods" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003560_978-1-4613-4560-2_2-Figure8.36-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003560_978-1-4613-4560-2_2-Figure8.36-1.png", + "caption": "Fig. 8.36. When the measuring instrument draws appreciable current, the measured cell potential V is smaller than that which the cell has in the absence of the current flow drawn by the measuring instrument. Hence, the latter should have a very high impedance.", + "texts": [ + " Thus, the concepts of polarizable and non polarizable interfaces are quantified. The value io -+ 0 is the idealized extreme of a polarizable inter face; io -+ 00 is the idealized extreme of a non polarizable interface. The concept of the polarizability drJldi also shows why instruments with high input impedance must be used by those making measurements of the potential differences across electrochemical systems or cells. Thus, an instrument which measures potential differences has itself a particular resistance R. When connected across the cell (Fig. 8.36), the instrument draws a current given by Ohm's law / = Cell potential R (8.56) The passage of such a current across an interface would produce an excess -artifactual-potential difference L11], which would mean that the potential of the interface during measurement had changed from the potential before measurement. This would be poor experimentation; one aims at measure ment of the interfacial potential difference without altering it by the process of measurement. It follows from (8.56) that one must use instruments with very high input impedance (or resistances) R" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003667_j.jsv.2012.05.028-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003667_j.jsv.2012.05.028-Figure2-1.png", + "caption": "Fig. 2. Rigid body motion: definition of the error e\u00f0t\u00de.", + "texts": [ + " In [1], the stiffnesses k(t) and kbs(t) were erroneously evaluated. The contribution of the rigid body displacement due to tip and root reliefs was not removed when stiffness was computed using FEM. Now the error is corrected. The term e(t) is added, in order to consider rigid body displacements. e(t) can be due to intentional deviations from pure involute or to profile errors. In the following it is called generically \u2018\u2018the error\u2019\u2019. x(t) is the dynamic transmission error and includes both the elastic deformations and the error e(t). Fig. 2 clarifies the method used to compute the rigid body motion e(t) due to an intentional profile modification. Considering two pairs of teeth in contact, the error introduced by each of them, namely e1\u00f0t\u00de and e2\u00f0t\u00de, can be defined as the displacement on the line of contact which would be required to get contact between modified profiles, if only one tooth pair was in contact. The resulting error e(t) is the minimum between e1\u00f0t\u00de and e2\u00f0t\u00de; this is valid for contact ratio eao2. Fig. 3 shows the behaviour of STE\u00f0t\u00de and e(t) for a gear pair having a contact ratio ea \u00bc 1:28 in the presence of profile modifications. The region 0otom=\u00f02p\u00deo0:2 (om is the meshing circular frequency) corresponds to the situation shown in Fig. 2, but in the region 0:2otom=\u00f02p\u00deo0:8 there is a rigid body displacement, i.e. e\u00f0t\u00dea0. In the original paper, the mesh stiffness along the line of action was computed as follows: k\u00f0t\u00de \u00bc 2Tg1 dg1STE\u00f0t\u00de (3) where STE was the displacement of gears along the line of action due to the application of the torque; however, the initial position in the finite element calculations corresponds to the nominal position of perfect gears in contact (e\u00f0t\u00de \u00bc 0), so that, when e\u00f0t\u00dea0 the STE measured by the finite element calculations includes a rigid body displacement, which must be removed to compute the elastic stiffness" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003714_piee.1970.0022-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003714_piee.1970.0022-Figure1-1.png", + "caption": "Fig. 1 Roebel-bar construction", + "texts": [], + "surrounding_texts": [ + "Stator windings in large alternators commonly use Roebel bars in which subconductors (strands) are transposed in the slot portion. Circulating currents may flow between the strands within a bar owing to the leakage fields in the end-winding regions. It is shown in the paper that such circulating current is not only limited by the strand resistances, but that the reactance of the slot portion to circulating current has a dominant effect. Measurements of reactance confirm the values obtained theoretically.\nList of symbols a = current density, A/m2\nb = current density, A/m2 B = flux density, Wb/m2\nE = voltage, V g = number of layers of strands or sections in depth\nof bar H = magnetic field strength, A/m j = complex operator J = current density, A/m2\nj ( \u2014 j = Bessel function of order one of first kind of TT/2\n/ = distance measured from one end of the slot portion, m\nL = bar length, m M \u2014 mutual inductance, (xH N = number of strands within bar\nin, n, p, q = numbers of strands (less than N) S = bar width equal to twice strand width, m x = distance down a slot measured from the top of\nbar, m W = slot width, m a = angle designating strand position, rad A = developed bar length from clip to clip, m fx0 = primary magnetic constant 477IO\"\"7, H/m cj> = flux, Wb p = specific resistivity, Qm oj = angular frequency for 50 Hz supply, I007rrad/s\nSubscripts it and d indicate initially upward- and downwardgoing strands, respectively, at end of slot portion.\n1 Introduction It was recognised at the beginning of this century that the a.c. resistance of a deep conductor in a slot was greater\nwhich were described by Taylor2 and Summers.3 Roebel's bar appeared to present an ideal solution, complete transposition of strands in the slot portion. Although some of the stator cores in use are not uniform since they have ducts at intervals, for the slot portion, the bar still remains an ideal solution, except that it is only applicable to single-turn coils.\nA Roebel bar of the form used in a rectangular slot is shown in Fig. J. Two stacks of strands are placed side by side in the slot, and are insulated from each other throughout the bar. At the end of the bar, all the strands are joined both together and to the next bar of the winding either by brazing or soft soldering within a box known as a clip.\nWithin the slot portion, the strands are transposed by arranging that all in one stack are inclined towards the bottom of the slot, and all in the other are inclined upwards. When a strand reaches the top or bottom of the bar, it is bent to form a crossover which carries it from one stack to the other. In a normal bar, said to have a 360\u00b0 transposition, each strand has two crossovers, and, after passing through the slot portions, is in the same position relative to the other strands that it bore when it entered the slot. Thus, each strand has the same mean depth in the slot and the same leakage reactance.\nIt has become general practice to use diamond-shaped pulled-out coils wherever possible with or without the extra transpositions suggested by Summers, but when the pole pitch becomes too great for the pull-out machines and complete coils would be awkward to handle, Roebel bars are used.\nIn 1959, Ringland and Rosenberg4 pointed out the influence that circumferential flux in the end regions might have on Roebel bars which were not transposed outside the slot portion, and they suggested that (in presumably lap-wound windings) each end of a bar would have the same stray-field conditions, and that the voltages induced in each end between the strands in parallel would be exactly in phase and would add together to drive a circulating current throughout the\nthan the d.c. value.1 By 1920 it had become common practice to divide large bars in a.c. machine stators and to transpose the insulated strands by a variety of arrangements, many of\nPaper 6008 P, first received 21st May and in revised form 12th September 1969 Mr. Macdonald is with the Department of Electrical Engineering, Imperial College of Science & Technology, Exhibition Rd., London SW7, England\nPROC. IEE, Vol. 117, No. 1, JANUARY 1970\nbar from clip to clip. They suggested a 540\u00b0 transposition in the slot portion which balanced out the slot effects and coupled the end-winding induced voltages in antiphase.\nWhile this solution may be of use in turboalternators, it is not so suitable in hydroelectric machines for the following reasons: (a) The hydroelectric machine is short compared with the\n111", + "turbo-type machine. Each crossover is about 2cm long, and the number of strands is limited by the number of crossovers that may be accommodated in the slot portion. The 540\u00b0 transposition requires a number of crossovers equal to 1^ times the number of strands; in the 360\u00b0 transposition the number of crossovers is only equal to the number of strands. Thus, the number of strands would have to be less in the 540\u00b0 transposition, and to maintain the same bar cross-section, the depth of each strand would have to be increased. This would increase the loss owing to the circulating current within each strand, one loss being decreased at the cost of increasing another. (b) Wave windings are commonly used in hydroelectric alternators and the exact balance between the end effects would not then occur. (c) Owing to the comparatively short pole pitch in hydroelectric machines, the end fields are far smaller, and the endinduced circulating current loss is far less of a problem. Other means for its elimination have been suggested,5 but normally the interest of the designer is to know the size of the loss rather than to go to the expense of eliminating it. If it can be predicted accurately, allowance may be made for it in the calculation of machine efficiency.\nInterest has therefore centred on the estimation of loss in Roebel bars owing to the currents circulating within each bar. These currents circulate from one clip to the other in the overall pattern shown in Fig. 2. The currents are caused by\nExpected pattern of circulating current\nthe oscillating leakage fields passing through the ends of each bar, and two components of loss occur. First, each strand will have a circulating current within its own depth, but since the field strength is low and the depth is small the loss is also small. Secondly, a pattern of differential voltages is set up between the strands in parallel within each bar. These voltages will drive circulating currents within the bar of a magnitude dependent on the end-leakage field and the impedance that the bar presents to the circulating current. In the paper, it is shown by two independent methods that the slot portion of the bar has a very significant effect, presenting a substantial reactance to the circulating currents.\n2 Impedance of Roebel-bar slot portion to circulating currents in terms of circular functions The pattern of circulating currents which it is expected that the end-field pattern will produce is shown in Fig. 2. The precise pattern will, as has been stated, depend both on the end-field configuration and the bar impedance to circulating currents. It is first necessary to realise that the circulating current within each bar does not link with the whole of the slot-leakage flux, since the current goes and returns through the same slot. The reactance to circulating currents will therefore only be caused by flux linked by a go-and-return path within the bar, and this will be confined to flux passing through the bar cross-section.\nFirst, an indirect approach was made. When the end-field pattern is not known in detail, a simple assumption of its character would appear to be most sensible. The simplest assumption possible was that the field was uniform over the bar depth, and mathematically convenient approximations were made on this assumption.\nUniform flux density over the bar depth would, in the absence of differential-reactance effects, give rise to a cir112\nculating current increasing linearly from the centre to the top and the bottom of the bar. It was found that analysis was facilitated by replacing this linear fdnction by a cosine function. Exact expressions could have been obtained by considering harmonics of this cosine function, but these have been neglected.\nAnalytic assemblies of circular functions were used throughout, the strand depth in the slot being expressed as a sine function, and hence functions were obtained which could be integrated directly. Although the approximations seem large, it is shown later that the method is reasonably accurate, giving an analytic solution to a problem slightly idealised from the real situation. The reactance is obtained by finding the flux and voltage resulting from the assumed current distribution.\nThe initial assumptions are:\n(a) The strands make a sinusoidal oscillation in the bar depth as in Fig. 3b rather than the actual paths shown in Fig. 3a.\nApproximation of strand shape and current distributions at different points in slot length (d) I = 0 (e) I = L/4 (/) / = L/2 (g) I = 3L/4\n(b) A sinusoidally distributed circulating-current density of uniform phase is caused to flow in the bar by circumferential and axial end-leakage fields to produce at the start of the slot portion the current density shown in Fig. 3d. (c) If the core considered is infinitely permeable and the slot is narrow, the flux crosses it parallel to the bottom. (d) The strands are thin.\nThe bar dimensions are given in Fig. 3c and the depth x of the strand shown at a point in the slot length a distance / from one end is\nX X 2nl 0)\nFor any other strand,\nX) flTTl X \u2014 \u2014 < 1 \u2014 COS I\nwhere a describes the position of the strand at the end of the slot.\nPROC. IEE, Vol. 117, No. 1, JANUARY 1970" + ] + }, + { + "image_filename": "designv11_7_0003560_978-1-4613-4560-2_2-Figure8.92-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003560_978-1-4613-4560-2_2-Figure8.92-1.png", + "caption": "Fig. 8.92. A change in electron energy al ters the energy of the initial state and pro duces a vertical shift in the potential-energy curve of eo t.\u00a2.", + "texts": [ + "160) The effect of a potential difference ,j at the potential difference iJ uthr, we have 0 \u2264 \u03c82 \u2264 \u03c0; (b) when ImDet2 \u2265 0 and u < uthr, we have 2\u03c0 \u2264 \u03c82 \u2264 3\u03c0; (c) when ImDet2 < 0, we have \u03c0 < \u03c82 < 2\u03c0. \u2022 If (0 \u2264) \u03c6 < \u03c6thr (figure 8(b)), we have \u2212\u03c0/2 < \u03c82 < \u03c0. 2. For Det3\u2212(u, \u03c6) \u2261 |Det3\u2212(u, \u03c6)| exp(i\u03c83\u2212): \u2022 If \u03c6thr \u2264 \u03c6 \u2264 \u03c0 (figure 9(a)), we can check that for u0 \u2261 uthr + 0.001 we have ImDet3\u2212(u0, \u03c6) < 0 and that it represents a point in the left sector of the two sectors with ImDet3\u2212 < 0 (see figure 9(a); further, for \u03c6 sufficiently large, there is only one sector with ImDet3\u2212 < 0). Therefore: (a) when ImDet3\u2212 \u2265 0 and u > u0, we have 0 \u2264 \u03c83\u2212 \u2264 \u03c0; (b) when ImDet3\u2212 \u2265 0 and u < u0, we have 2\u03c0 \u2264 \u03c83\u2212 \u2264 3\u03c0; (c) when ImDet3\u2212 < 0, we have \u03c0 < \u03c83\u2212 < 2\u03c0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002376_j.fusengdes.2011.01.018-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002376_j.fusengdes.2011.01.018-Figure1-1.png", + "caption": "Fig. 1. 10DOF hybrid robot for the assembly of ITER: (i) vacuum vessel and (ii) robot used for the assembly of vacuum vessel.", + "texts": [ + " atrix structural analysis . Introduction The ITER vacuum vessel sectors are made of 60 mm-thick stainess steel which are joined together by the high efficiency structural nd leak tight welds. The stringent tolerances of assembly, \u00b15 mm, re expected, while high dynamic machining force and high accuacy are required for cutting, weld repair and weld preparation. To atisfy the machining capacity of mobility and flexibility in a limted space inside the ITER vacuum vessel, a hybrid parallel robot IWR in Fig. 1) has been developed, which has ten degrees of freeom (DOF); six degrees of freedom are contributed by a Stewart arallel mechanism and the rest by the serial mechanism [1]. Generally, in the high dynamic force application of assembly of TER, the deflection of robot will be getting big and the accuracy ill be getting poor. To compensate or to limit the deflection, the tiffness of robot should be studied. This paper focuses on the stiffess modeling of the robot. The developed model can be used for ompensating the deflection of robot to reach high accuracy, and t can also be used for trajectory planning to find higher stiffness oses of the motion" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001979_j.optlastec.2010.07.011-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001979_j.optlastec.2010.07.011-Figure3-1.png", + "caption": "Fig. 3. Arrangement of the camera and the lighting.", + "texts": [ + " The size and shape of the fusion zone have thus been investigated by means of a CMOS PHANTOM v4.0 high-speed digital camera, with a maximal acquisition frequency of 32 kHz. Moreover, visualization through high-speed camera also allowed for the observation of various phenomena, such as the transfer of material, the movements of the molten pool, etc. The molten pool visualizations were obtained by placing the camera perpendicular to the direction of welding, its optical axis at a 451 angle from the vertical axis of the laser beam, as specified in Fig. 3. The principle of experimental design is to realize several tests with given combinations of welding parameters, and, for each test, to characterize the variations in the dimensions of the molten zone. The realization of an experimental design allows us, on the one hand, to quantify the factors that affect objective functions chosen beforehand (molten zone geometry), so as to understand and control the process, and, on the other hand, to create a data base that contains the numerical values of the molten zone geometry in various combinations of welding parameters" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002753_s12206-011-0803-3-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002753_s12206-011-0803-3-Figure3-1.png", + "caption": "Fig. 3. Distribution of physics-based friction coefficient at each contact grid cell within one tooth-to tooth mesh cycle as predicted by using mixed EHL model.", + "texts": [ + " Winter and Michaelis [30] proposed an important relation between friction coefficient and pressure involving the averaged friction coefficient EL\u00b5 and instantaneous friction coefficient EL i\u00b5 under full film lubrication, and the load supported by the lubricant film and total load totalP . These relations are given by ( ) 0.2 0.2 0.2 0.2 0.2 ( ) ( ) EL EL EL total EL total totali total P P f P f P PP \u03b1 \u03b1 \u00b5 \u00b5 = = = = (14) ( )0.2 .EL EL i f\u03b1\u00b5 \u00b5= (15) The friction coefficient in mixed film lubrication can be de- termined by substituting Eq. (15) into Eq. (13) to obtain ( )1.2 (1 ).ML EL BL i i if f\u03b1 \u03b1\u00b5 \u00b5 \u00b5= + \u2212 (16) It is worth noting that ML i\u00b5 is the physics-based friction coefficient at each contact grid cell. Fig. 3 illustrates the qualitative distribution of ML i\u00b5 at each contact grid cell in the contact area. It will be used in dynamic analysis later. Recall that the contact patterns are computed using a finite element-based loaded tooth contact analysis mentioned above [26]. From the loaded tooth contact results, for each contact grid, the position vectors p ir and g ir for pinion and gear can be obtained. The relative rolling velocity r iU and sliding velocity s iU of each grid cell on the tooth surface can be calculated as follows: (1) {0, ,0}Tp\u03c9=\u03c9 , (2) {0,0, }Tg\u03c9= \u2212\u03c9 , p g p g N N \u03c9 \u03c9= (17) { , , }l l l l T i ix iy izr r r r= ( ,l p g= for pinion and gear respectively) (18) (1)p p i i= \u00d7v \u03c9 r (19) (2)p g i i= \u00d7v \u03c9 r (20) s p g i i iU = \u2212v v (21) 2 p g r i i iU + = v v (22) where pN and gN are the number of teeth on the pinion and gear, (1)\u03c9 and (2)\u03c9 are the nominal speed of the pinion and gear shafts, and p\u03c9 is the angular speed of pinion", + " Using these specific cases, the numerical simulation results are performed at various speeds and torques to understand the influence of tooth mesh friction and lubricant properties on geared system dynamic behaviors. The relative sliding velocity, radius of curvature and load distribution predicted by the gear mesh model along with the lubrication and temperature information are applied to the mixed EHL friction coefficient model to determine the physics-based friction coefficient at the each contact grid cell on the tooth contact surfaces. The instantaneous physics-based coefficient of friction at each contact grid cell is shown in Fig. 3(a) as discussed earlier. For the gear dynamics simulation, one mesh cycle is divided into 21 steps throughout a tooth-totooth mesh cycle. The 21st step is the beginning of next tooth engagement cycle. The physics-based friction coefficient at each contact grid cell in these 21 steps is synthesized into an effective overall friction coefficient for each time step. This overall friction coefficient is then used in the subsequent dynamic calculation. Since the normal contact force at the grid cell iP is obtained from tooth contact analysis [26], and thus for the same grid cell, the distributed friction forces fiF can be expressed as MIX fi i iF P\u00b5= ", + " Therefore, in this study, the dynamic total mesh force and transmission error are analyzed to determine the effect of friction coefficient. Simulations are performed for the following two conditions: (1) constant friction coefficient of 0.1; and (2) using realistic physics-based time-varying friction coefficient based on the mixed EHL model. For each type of right-angle gear pairs (i.e. hypoid and spiral bevel gears) examined, the predicted dy- namic total mesh forces along three global coordinate directions illustrated in Fig. 3 and are shown in Figs. 8(a)-(c) for speed ranging from 300 to 12000 rpm. In Figs. 8(a)-(c), except for moderate change in x-direction which is the pinion transversal and gear axial direction, the hypoid gear mesh force shows very little differences between the results with timevarying friction coefficient and that with constant friction coefficient. The reason is probably because friction force does not reverse direction at the pitch point, and therefore the friction excitation has only a marginal effect on hypoid gear dynamic response" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003920_20110828-6-it-1002.01102-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003920_20110828-6-it-1002.01102-Figure3-1.png", + "caption": "Fig. 3. Graphical interpretation of the separation theorem", + "texts": [ + " Given a filter R(z) the formation dynamics are stabilized if and only if the negative feedback interconnection of F (z) with L is stable and K(z) stabilizes P (z). Next we present an alternative representation of the block diagram in Fig. 2. We have p = R\u0302(z) p+ R\u0302(z)L(q) (r \u2212 p) . (2) Now substituting for R\u0302(z) = ( INq + F\u0302 (z) )\u22121 F\u0302 (z) and multiplying by ( L(q) + F\u0302 (z) )\u22121 from left leads to p = ( INq + F\u0302 (z) )\u22121 F\u0302 (z) ( p+ L(q) r \u2212 L(q) p ) . (3) From there it follows that p = ( INq + F\u0302 (z)L(q) )\u22121 F\u0302 (z)L(q) r = Gpr(z) r. (4) Equation (4) is depicted as the first feedback loop in Fig. 3. The second feedback loop consists of the vehicles and their local controllers. For the second loop one obtains y = ( INq + P\u0302 (z) K\u0302(z) )\u22121 P\u0302 (z) K\u0302(z)p = Gyp(z) p. (5) These equations are expressed in a block diagram in Fig. 3, which does not only give a visual representation of the separation principle proved in [Fax and Murray, 2004], but also shows that in fact the only communicated signal in this scheme is the information signal p. The overall transfer function of the system from the reference input r to the output of the agents y is Gyr = GypGpr and the design parameters of the overall system are the dynamical systems F\u0302 (z) and K\u0302(z). In Fig. 3 two different types of disturbances are considered in the cooperative control framework: disturbances acting on the agents, such as output disturbances dy and disturbances on the communication dp. As a result of the decoupling shown above, an output disturbance dyi will act only in the control loop of vehicle i and will not affect the other vehicles. In contrast, a communication disturbance dpi will have an effect on the information of vehicles of which vehicle i is neighbor, as it can be considered as a change in the reference input ri", + " Several conclusions can be drawn from the results in Table 1 and Fig. 9. First, by comparing the results of F2(z) with the systematic synthesis of a robust filter F\u2217(z) the advantage of synthesizing the information flow filter in a systematic way and tuning it using mixed-sensitivity techniques are clearly to be seen. Second, both Table 1 and Fig. 9 show that tuning the information filter for fast convergence might not be advantageous as the actual positions of the vehicles become oscillatory. This can be easily explained based on Fig. 3, where the information filter acts as a prefilter for the local control loop. Hence, if the local controller K(z) is tuned for fast disturbance rejection and a very fast information filter is used, the reference command is directly passed to the local loop and may excite oscillatory modes. Note that this can be avoided by redesigning the local controller and reducing its speed of response, but this could have undesirable effects on disturbance rejection in the local loop. A solution to this problem may be found in the joint design of the information flow filter and the local formation controller" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003259_j.cja.2013.04.006-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003259_j.cja.2013.04.006-Figure1-1.png", + "caption": "Fig. 1 Tooth profile of the cutter fillet.", + "texts": [ + " A matrix is established for the transformation from the cutter coordinates to the machined workpiece coordinates. The matrix ensures the same relative position and motion for the cutter-tilt milling machine and the common multi-axis NC machine. The paper also establishes an NC machining model of the arc tooth face-gear. The model provides motion parameters for each movement axis of the NC machine, which offers precise processing parameters for NC processing. The arc tooth face-gear pair meshing condition is verified in a hobbing test. Fig. 1 is the tooth profile of a machining cutter. The working tooth surface is processed by a linear cutter edge. Because a fillet is machined with the top tooth edge of a gear shaper cutter, the tooth root fillet can be machined with a blade fillet and top tooth edge to decrease the tooth root bending stress. The fabricated gear is assumed to be a conjugate arc tooth cylindrical gear and arc a tooth face-gear to ensure the processed arc tooth face-gear can correctly mesh with an arc tooth cylindrical gear" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003223_s11249-012-0039-0-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003223_s11249-012-0039-0-Figure1-1.png", + "caption": "Fig. 1 Schematic of the optical EHL apparatus (with friction measuring devices)", + "texts": [ + " If the aforementioned non-conventional EHL film shapes and friction curves are only due to non-Newtonian fluid properties (or slip is only apparent rather than real), different bounding surfaces should have no effect on the results. Thus the aims of this work were to verify the boundary slip effect and to understand how it affects the friction and film shape of sliding EHL contacts. This study is an extension of our previous work and details of the experiments can be referred to in [19]. The main apparatus is a conventional optical EHL tester, as schematically shown in Fig. 1. Experiments were run at ultra-slow speeds, ranging from 5.7 lm/s to 5.7 mm/s, with either pure disc sliding (DS) or pure ball sliding (BS). DS and BS refer, respectively, to a moving disc of constant speed on a stationary ball, and vice versa. For DS, the friction acting on the stationary ball was measured using a torque sensor, whereas for BS, the glass disc was constrained by an inelastic string, and the friction at the EHL contact was measured using a tensiometer, as illustrated in Fig. 1. The ball was a highprecision steel ball of one inch in diameter and the reduced elastic modulus of the contact was 117 GPa. The applied load ranged from 6.6 to 52.6 N, corresponding to 0.3 to 0.6 GPa. The light source was quasi-monochromatic, which was obtained using a narrow-band interference filter of 600 nm in the central wavelength and 10 nm full-width of half-maximum. The film profiles were obtained using the multi-beam, intensity-based film measuring technique [26, 27] with a very high resolution of 1 nm and detectable minimum film thickness of 1 nm", + " The corresponding pure DS results are shown in Fig. 4b. Under the low load, the friction of the SiO2-coated disc under the DS test was the same as that of the Cr-coated disc, but there was a significant difference in magnitude for the high load. The SiO2-coated disc produced significantly higher friction than the Cr-coated disc under high load DS conditions. Note that friction was measured using different sensors, a tensiometer and a torque sensor in the BS and DS tests, respectively, as depicted in Fig. 1. The absolute values of the friction coefficient from a BS test cannot be compared directly with the kinematically equivalent DS test. The interferograms and their corresponding film profiles for the tests on the SiO2- and Cr-coated discs were extracted at two representative sliding speeds, u1 (1.92 9 10-4 m/s) and u2 (1.12 9 10-3 m/s). u1 is the lower speed at which the friction curves approach their local maxima, whereas at u2, the magnitude of friction is smaller and it is close to the end of the friction drop for the tests at the lower load, as shown in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002943_j.jbiomech.2012.08.038-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002943_j.jbiomech.2012.08.038-Figure5-1.png", + "caption": "Fig. 5. Evolution of the mechanical model during the predicted recovery for the scenario of Cyr and Smeesters (2009) (snapshots every 200 ms).", + "texts": [ + " In this study, the balance recovery is considered only in the sagittal plane using a mechanical model of the human body placed in closed loop with a controller. This mechanical model is an inverted-pendulum-plus-foot model representing the support limb (see Fig. 1a). The trailing limb is not explicitly modeled and its influence on the system dynamics is neglected. The length of the pendulum is constant for each step but can change from one step to another. The resulting trajectories of the Center of Mass (CoM) are thus circles of possibly different diameters (see Fig. 5) and can experience only instantaneous double support phases. The feedback loop is based on a Model Predictive Control (MPC) approach (Fig. 2), using an internal model which can be different and simpler than the real mechanical model. This internal model is considered for predicting future control actions over a given time horizon. Expectations about the evolution of the state of the system are expressed as a cost function. The adequate control actions are then selected by minimizing this cost function, given the current state of the system", + " It can be perceived that simulated and experimental step lengths match well, in particular for the smaller inclination angles. Fig. 4 shows the results for the extreme inclination case of Cyr and Smeesters (2009) with no limit on number of steps. Stride lengths instead of step lengths are reported to be coherent with this study. Predicted and reported stride length are of the same order. Note that the third step, reported by Cyr and Smeesters (2009) but not predicted by the model, was only observed for two out of 28 subjects. Fig. 5 shows the evolution of the mechanical model during the predicted recovery for the scenario of Cyr and Smeesters (2009). It can be seen that the CoM trajectory follows circular arcs of varying lengths. The goal of this study was to adapt a control scheme initially proposed for the locomotion of biped robots (Herdt et al., 2010) and test it against experimental balance recovery data reported in the biomechanics literature. By only inputting the subject anthropometry and timing of the foot contacts, the recovery step placements are predicted with a reasonable accuracy for different scenarios: single and shortest step recovery for different perturbation levels (lean angles) up to the maximum perturbation recoverable in one step, and multiple step recovery for the maximum recoverable perturbation" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001134_00220345800590051301-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001134_00220345800590051301-Figure1-1.png", + "caption": "Fig. 1 -Schematic drawing of the test pattern used.", + "texts": [ + "9 In this study, a new design of casting mold which is easily formed from sprue wax and nylon lines (though different from that previously reported by Vincent)9 is presented. This design has allowed some differentiation of the alloys being tested. The pattern is designed to take into account factors which may cause difficulties in obtaining complete castings. Materials and methods. The testing model was constructed of 14 gauge sprue wax and various diameters of nylon fishing line. A schematic drawing of the pattern is presented in Fig. 1. A vertical sprue 4 mm long was luted to a conical sprue form. From the top of the vertical sprue, four spokes of 14 gauge wax radiated horizontally (900 to the vertical sprue). Each spoke was 3 mm long. Again, 14 gauge sprue wax was used to form a ring around the outside of the spokes. Then six gauges of nylon fishing line, each 20 mm long, were luted with green inlay wax to the rim of the sprue wax wheel. They were positioned such that the nylon lines projected vertically, parallel to the original vertical sprue, forming a 90\u00b0 angle to the plane of the wheel to which they were attached" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001745_physreve.81.031920-Figure7-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001745_physreve.81.031920-Figure7-1.png", + "caption": "FIG. 7. Generalized hydrodynamic influence of bead II on bead", + "texts": [ + "447, respectively 19,20 . It is interesting to note that the implicit technique intrinsically accounts for these end corrections. In Sec. II A 2 we described the implicit method for two beads moving parallel and perpendicular to their center line. The equations in Sec. II A 2 can be easily extended to capture the hydrodynamic influence between beads moving at arbitrary velocities and directions. We demonstrate for the case of two beads which are parts of two different rods separated by an arbitrary angle and distance Fig. 7 . Let beads I and II be part of two separate rods. Let V1 p ,V2 p and V1 n ,V2 n be the parallel and normal translational velocities of the rods, and let 1 , 2 be their orientation angles Fig. 7 . Let v1 p ,v2 p and v1 n ,v2 n be the corresponding parallel and normal velocities of the beads of interest, and let 12 and r12 be the angle and distance between them Fig. 7 . The hydrodynamic influence of bead II on bead I can be determined as v1 pH v1 nH = V1 p V1 n \u2212 H12 v2 pH v2 nH , 7 where 031920-6 H12 = cos 12 \u2212 1 \u2212 sin 12 \u2212 1 sin 12 \u2212 1 cos 12 \u2212 1 3a 2 r12 cos 12 3a 2 r12 sin 12 \u2212 3a 4 r12 sin 12 3a 4 r12 cos 12 8 H12 is a matrix describing the hydrodynamic influence of bead II on bead I. It has two component matrices Eq. 8 . The right-side matrix determines the radial and tangential solvent field due to bead II at the location of bead I. Multiplication by the left-side matrix projects the radial and tangential solvent velocities at bead I in the directions of its parallel and normal velocities" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002060_j.talanta.2010.04.042-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002060_j.talanta.2010.04.042-Figure1-1.png", + "caption": "Fig. 1. Schematic diagram of the CL flow-through biosensor for the determination of lactose (a) lactose standard solution or samples; (b) distilled water; (c) luminol solution; (d) DPN solution; EC: enzymes reactor; V: injection valve; F: spiral glass cell; PMT: photomultiplier tube; pump1, pump2: peristaltic pump; W1, W2: waste.", + "texts": [ + " Tetraethyl orthosilicate (TEOS), cetyltrimethylammonium romide (CTAB) and calcium chloride anhydrous were obtained rom Sinopharm Chemical Reagent Co. Ltd. (Shanghai, China). otassium persulfate from Shanghai Aijian Chemical Reagent Comany, and sodium alginate, lactose, potassium hydroxide, sodium itrate, sodium periodate and nickel sulfate from Shanghai Chemcal Reagent Company. All reagents were of analytical grade and eionized and double-distilled water was used throughout. .2. Apparatus The flow system employed in this work is shown in Fig. 1. wo peristaltic pumps (Remex Analytical Instrument Co. Ltd., Xi\u2019an, hina) were used to deliver all flow streams. Polytetrafluoroethy- ene (PTFE) flow tubes (0.8 mm i.d.) were used to connect all the omponents in the flow system. Injection was done using an eightay injection valve equipped with a sample loop (90 L). CAF or AF\u2013AMNMS with immobilized enzymes was packed into a glass tube (length: 55 mm, i.d.: 3 mm). The flow cell was made by coiling 20 cm of colorless glass tube (2 mm i.d.) into a spiral disk shape and was located directly facing the window of the photomultiplier tube (PMT)", + " Then the mixture solution was mixed ith 5 mL 5.0% aqueous sodium alginate solution and the rest of rocedure was as the same as Section 2.5. The reactor with AMNMS r remodeled AMNMS was denoted respectively as sensor B or ensor C. .7. Procedures During the enzymatic reaction, a lactose molecule creates equivlent H2O2 by reacting with -galactosidase and glucose oxidase. he determination of H2O2 was based on the CL reaction of luminolPN in alkaline medium. The CL flow-through biosensor used for he determination of lactose is shown in Fig. 1. When the anayte solution passed through the immobilized bi-enzymes reactor, actose was transformed to H2O2 by enzymes. Then 90 L H2O2 prouced was injected into the carrier stream to react with luminol and PN to produce CL. The CL signal was detected by IFFS-A multifuncion chemiluminescence analyzer. The concentration of sample was uantified by the relative peak height of the CL intensity. . Results and discussion .1. Characterization of AMNMS TEM images of AMNMS and remodeled AMNMS were taken sing a JEM-2100 transmission electron microscopy (JOEC, Japan) Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000351_1.2185661-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000351_1.2185661-Figure2-1.png", + "caption": "FIG. 2. Vertical cross section of the cylinder submersed in fluid.", + "texts": [ + " Specifically, we study the two-dimensional problem of an infinite solid circular cylinder of homogenous material, floating in horizontal equilibrium in an unlimited liquid bath, in the presence of a downward vertical gravity field. We examine all possible configurations, in terms of , the sectional mass m per unit length and the radius r of the cylinder, the density of the fluid, the interfacial tensions 0, 1, 2, and the gravity force g per unit mass. A cross section of the cylinder and some notation are indicated in Fig. 2. We find immediately the geometric constraint 0 = 0 + \u2212 . 2 We assume the fluid surface u x to be asymptotically horizontal and of constant height with increasing distance from the cylinder, and we take that level to be u =0. In a vertical section, we have the capillarity equation d dx sin = g u , 3 which admits a first integral in terms of as parameter: a Electronic mail: rbhatnagar@stanford.edu b Electronic mail: finn@math.stanford.edu 1070-6631/2006/18 4 /047103/7/$23.00 \u00a9 2006 American Institute of Physics18, 047103-1 This article is copyrighted as indicated in the article" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003853_00268976.2014.903004-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003853_00268976.2014.903004-Figure1-1.png", + "caption": "Figure 1. Set-up used to study the hydrodynamic force F and torque N exerted on a colloidal particle by a swimmer.", + "texts": [ + " At the start of the simulation, the inert particle is placed at the centre of the simulation box, which we take as the coordinate origin, and the squirmer is placed at a position (\u2212d, 0,\u2212L/2). The squirmer\u2019s swimming axis is set parallel to the z-axis of the lab frame, and it is constrained to move only in one dimension, along paths of constant (x, y) coordinates. Since the squirmer is not allowed to rotate, d is constant throughout the simulation. A schematic representation of this two-dimensional set-up is given in Figure 1. As the squirmer transverses its path, we measure the hydrodynamic force F and torque N exerted on the inert particle as a function of the vertical distance z. In Figure 2, we present the results for \u03b1 = \u00b12 swimmers, for different values of the perpendicular distance d/2 = 1.4, 1.5, 1.8, and 2.4. As expected, the results are inverted when switching from pusher to puller. In addition, there is a clear fore\u2013aft asymmetry, such that the force (torque) experienced by a particle will be inverted as it passes from the front of the particle to the back", + " For d/2 2, pushers (pullers) will push (pull) the particle in both the parallel and perpendicular directions (with respect to the swimming direction), as long as the vertical distance is greater than the particle diameter |z|/2 \u2265 1; for |z|/2 \u2264 1 pushers (pullers) will pull (push) the colloidal particle in the horizontal direction, and both will exert an oscillatory force in the vertical direction. In terms of the torque exerted on the colloid, there is a clear inversion symmetry with respect to the vertical D ow nl oa de d by [ D eb re ce n U ni ve rs ity ] at 0 5: 22 2 6 A pr il 20 14 Figure 2. Hydrodynamic force F and torque N experienced by a fixed colloidal particle as a squirmer swims past it along vertical paths at a fixed perpendicular distance d/2 = 1.4, 1.5, 1.8, and 2.4 (see Figure 1). Lines are colour coded with respect to d , with darker (lighter) colours corresponding to smaller (larger) separations. Results for pushers (\u03b1 = \u22122) are on the left, for pullers (\u03b1 = +2) are on the right. Forces and torques have been scaled using the value of the Stokes force experienced by a particle moving at the same speed as the swimmer fs = 4\u03c0\u03b7aB1. separation of the particles. As the puller (pusher) swims past the particle, the rotation of the flow field around the colloid goes from a counter-clockwise (clockwise) direction to a clockwise (counter-clockwise) one" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000429_j.trac.2006.11.015-Figure11-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000429_j.trac.2006.11.015-Figure11-1.png", + "caption": "Figure 11. Cross-sectional view of: (a) detection system deposited onto interference filter. Reprinted from [60], with permission from ACS.", + "texts": [ + " Also, there is interference from scattering of the beam in these configurations. As a result, non-confocal optical arrangements, including bevelincident laser and orthogonal optical arrangements, are used; in these, the interference from the excitation light to emitted fluorescence was eliminated. In a bevel-incident laser system [57\u201362], as shown in Fig. 9 (b and c), the laser beam was positioned to minimize scatter while the fluorescence was detected perpendicular to the chip. Dandliker s group [60] used a non-focal LIF system (Fig. 11) in which the HeNe laser beam was at 45 to the chip surface, and the emitted fluorescence was then collected and focused perpendicular to the chip surface by a microlens into the photodetector. The LOD for Cy5 solution was 3.3 nM. As for the orthogonal optical arrangement [63\u201366] (Fig. 9 (d\u2013f)), the laser beam was guided by an optical fiber, inserted into the chip channel from a horizontal direction, and the emitted fluorescence was detected in the perpendicular direction with respect to the chip surface" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000084_s00170-005-0312-6-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000084_s00170-005-0312-6-Figure2-1.png", + "caption": "Fig. 2 Tool path interval for a cusp height", + "texts": [ + " Within the acceptable deviation range, the interval between the current cutter contact point and the next cutter contact point is called step length s, as shown in Fig. 1. s \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4e 2r e\u00f0 \u00de p (1) where e is the acceptable deviation (or called chord deviation) assigned by the user, s is the step length, and r is the radius of curvature on the surface. The distance between the two mutually accompanying tool paths is called tool path interval (L), which is determined by the acceptable cusp height h, radius of curvature \u03c1 and radius of cutter R, as shown in Fig. 2. L\u00bc \u03c1j j ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi f4\u00f0 \u03c1j j R\u00de2\u00f0 \u03c1j j h\u00de2 \u00bd\u03c12 2R\u03c1\u00fe \u00f0 \u03c1j j h\u00de2 2g q \u00f0 \u03c1j j R\u00de\u00f0 \u03c1j j h\u00de (2) In this equation, the upper and lower symbols represent convex and concave surfaces, respectively. Therefore, the distance between the two adjacent tool paths is referred to as the least tool path interval" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002448_s0263574710000433-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002448_s0263574710000433-Figure3-1.png", + "caption": "Fig. 3. Error vector chains: (a) two PRU limbs; (b) the PRC limb.", + "texts": [ + "org Downloaded: 12 Mar 2015 IP address: 129.137.165.251 the mechanism was introduced in detail in ref. [19]. One may see that there are no parasitic motion and no coupling between the rotation and the translation along the x-axis. In practice, the platform can tilt continuously from \u221225\u25e6 to 90\u25e6. For such a reason, by using a serial table with a rotational DOF and a translational DOF, the machine is capable of 5-face machining. According to the kinematic model of the HALF\u2217, the error vector chains are shown in Fig. 3. The nominal parameters are given as follows: |T1T2| = d = 730 mm, |PiQi | = li = 300 mm (i = 1, 2, 3), |Q1Q2| = r = 470 mm, |Q1Q2| = r = 470 mm, |Q3O \u2032 T | = r1 = 180 mm, |OT3| = r2 = 240 mm, |Oo| = h = 760 mm, \u03b1i = 0 (i = 1, 2, 3), \u03b3 = 0, \u03b2 = 0. The frame o-yz is located in the frame O-YZ and the coordinate of point o is (0, h), and (y, z) is a point in frame o-yz, then, the output position vectors can be expressed as X1 = [Y Z]T = [y z + h]T, X2 = [X Z]T = [\u2212(z + h) tan \u03b3 z + h]T. The vectors in the error vector chains can be described as follows: P i Qi = lini(i = 1, 2, 3), T i P i = R\u03b1i sie1(i = 1, 2), T 3 P3 = R\u03b13s3e3" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003869_s00419-012-0608-6-Figure14-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003869_s00419-012-0608-6-Figure14-1.png", + "caption": "Fig. 14 The mode shapes corresponding to frequency \u03c916 (the second mode)", + "texts": [], + "surrounding_texts": [ + "As mentioned earlier, in the geometrical model of the gear, the geometry of the teeth is omitted. It allows us to reduce the system\u2019s FE model size. The simplified geometrical model of the system consists of five sectors (see Fig. 1) that have the cyclic symmetry feature. Each of these segments is meshed by using standard procedures of the ANSYS software. The 3-D solid mesh is elaborated and as mentioned earlier, the ten-node tetrahedral element (solid92) with three degrees of freedom in each node is used to realize each sector. During the mesh generation process, it is assumed that the maximum length of each element\u2019s side needs to be no more than 2.7 [mm]. The developed FE model is displayed in Fig. 2, and it consists of 19,620 elements and 36,188 nodes, respectively. The particular sectors are glued as a whole at the geometrical model preparing the stage by using standard procedure of the ANSYS program. The analysed gear is mounted in the roller bearings. Such bearings typically have slight load capacity under loads perpendicular to the primary supported direction. The gear shaft neck surfaces on which the bearings are assembled are denoted \u201cbearing\u201d (see Fig. 3a). The gear mates with the other devices by the splines. The splines is simplified down to a regular cylinder of the diameter assumed as equal to the splines pitch diameter. The surface denoted \u201cjoint\u201d (see Fig. 3a) is located on the pitch diameter of the splines. Parameters of the analysed system are shown in Table 1a\u2013b. The calculation results for natural flexural oscillations taking into account angular speed of the gear are shown in the paper. In the case of circular discs and annular plates, for each solution where nodal lines are nodal diameters, one obtains two identical arrangements of straight nodal lines, rotated by an angle of \u03b1 = \u03c0/(2n) one to another, where n is the number of nodal diameters. In accordance with the circular and annular plate vibration theory [5,6,12], the particular natural frequencies of vibration are denoted as \u03c9mn , where m refers to the number of nodal circles and n is the mentioned number of nodal diameters. As the shape of the gear model is fairy elaborate, the flexural modes of the system are subject to deformation (as compared to the system without any holes) to such extent that establishing which particular node it refers to becomes rather difficult. This problem is even worse if the angular speed of the gear is varying. The problem of influence of the angular speed on the flexural gear models deformation is analysed. For the purpose of identification of these modes, an algorithm of tagging oscillation modes, which determines the correspondence between vibration of the circular disc versus disc with holes, is used. For this purpose, an auxiliary model of annular plate in the form shown in Fig. 3b is used. The geometrical dimensions of the auxiliary model were taken from the gear geometry (shown in Fig. 1). They are as follows: addendum circle diameter dz , rim mounting diameter dp, root circle diameter dw2, and thickness h p and hz (see Table 1). Dynamic analysis is performed for the auxiliary model cases rotating at predetermined angular speed, where diameter of though holes d01 (see Fig. 3b) varies as seen in Table 2. Findings are compared to each other both quantitatively and qualitatively. This method makes it possible to investigate deformations of nodal lines associated with nodal diameters and circles due to through holes and then determine correspondence between oscillation modes of solid circular disc and a plate with holes. In the final step, solutions found for the auxiliary model are compared with the solution for the system whose FEM model is shown in Fig. 2 (the principal model). As for the principal model case, the 3-D solid mesh and the ten-node tetrahedral element (solid92) are used to discretize the auxiliary models. For all models subject to analysis, the boundary conditions were applied to the nodes. For each model, 1 d f associated with node radial displacement was subtracted from the nodes found on the surface identified as a bearing (see Fig. 3a,b). Furthermore, 1 d f associated with the displacement of nodes along the centreline of each model was subtracted from the nodes found on the surface, identified as a joint (see Fig. 3a,b). For the models obtained in this way, calculations were kept conducted as long as the natural frequency \u03c918 was determined. The calculations were performed assuming that the systems rotate as angular speed of \u03b8 , within the range of 0\u20131047 [ rad/s]. During the computing process, the angular speed values were gradually increased by 80[ rad/s], which made fourteen variants of the results (the natural frequencies and corresponding natural modes), which were subject to further interpretation. The rotation effect was taken into account by determining stress distribution due to rotation, for each model during the computational step associated with static analysis (the so called pre-stress effect). This stress distribution was then included in the computation step associated with modal analysis. The results of the numerical calculations related to the procedure of identifying deformed natural modes of flexural vibration of the gear under consideration are shown below. The results displayed here relate to the determination of the correspondence between the natural frequencies \u03c916 and \u03c925 at high angular speed (\u03b8 = 1047 [ rad/s]) as well as to the correspondence between oscillation modes and the natural frequency \u03c931 at lower angular speeds (\u03b8 = 80 [ rad/s]). The results as shown in Figs. 4, 5, 6, 7, 8, 9 allow for tracking deformations of nodal lines associated with nodal circles and diameters, due to varying diameter of the through holes. With respect to the natural frequency \u03c925, there is marked difference in shapes of natural modes. When one compares the results between each other, one can notice that in order to identify correctly deformed natural modes of the flexural oscillations in the gear under consideration at lower angular speeds, larger number of auxiliary models is required to be included during calculations, as compared to the higher angular speeds. It comes from the fact that additional stresses through the centrifugal effects appear. This effect causes the gear flexural stiffness to be an apparent function of rotational speed (stiffness grows for higher speed). In the next part, results of the numerical calculations associated with the extent of the influence of the angular speed to deformation of mode shapes of oscillations. For each discussed case, both mode solutions related to nodal diameters are shown. These analysed results are sorted by the order of their occurrence. For the frequencies \u03c923 and \u03c918, the results were obtained at angular speeds of \u03b8 = 0 and \u03b8 =1,047 [ rad/s] respectively. For the other cases, results were obtained at angular speeds \u03b8 of, 0, 320, 720, and 1,047 [ rad/s], respectively. Natural frequencies for these modes are included in Table 3. To determine this mode (see Figs. 10, 11), the procedure of tagging natural oscillation modes was required. Nodal lines associated with the circle and diameter are deformed. Minor influence of the angular speed to deformation of the nodal lines is noticeable. The task of determining modes in this case was not too difficult (see Figs. 12); no procedure of tagging natural oscillation modes was required. The slight impact of the gear angular velocity on the distortion of the nodal lines is observed. For these modes (see Figs. 13, 14), procedure of tagging natural oscillation modes was required. It is noticeable that angular speed affects markedly deformation of the nodal lines. Once the angular speed of 720 [ rad/s] is exceeded, the oscillation mode takes different shape. Major deformation of mode shape attributable to the shaft vibrations is evident at this speed. Moreover, additional problem associated with some similarity of the mode being tagged to the mode associated with frequency of \u03c931, emerged during mode identification. Establishing the correspondence between these modes was a complex task (see Figs. 15, 16) due to the shape of oscillation modes similarity to the case discussed earlier. The angular speed affects deformation of nodal lines markedly. Major shape mode variations emerge at \u03b8 = 400 [ rad/s]. The identification process in this mode was not easy (see Figs. 17, 18) . One can notice that angular speed affects the deformation of nodal lines. Major variation in mode shape emerges at \u03b8 = 720 [ rad/s]. Moreover, additional annular shaft vibration emerges at the highest considered angular speed. Finding correct correspondence between the modes in this case was fairly easy (see Figs. 19). High repeatability in deformations of nodal lines on circular plate at various angular speeds is noticeable. As a consequence of the conducted analysis (see Table 3), the Campbell diagram was plotted for the gear under consideration. This is a convenient method of displaying the relationship between gear natural frequencies and transmission system excitations [4]. Excited frequencies are plotted on a vertical axis, and the gear speed of rotation is plotted on the horizontal axis (see Fig. 20). Natural frequencies achieved from numerical analysis are plotted as near-horizontal curves. The forced frequency due to the meshing is determined by the following relation (as in Ref. [4]) f = n0 \u00b7 z 60 (4) where n0 [rpm] is the rotational speed and z is the number of teeth in the gear. For this system, the gear teeth number is z = 59. Vibration resonance phenomenon occurs when forcing frequency (4) matches as to its value with some natural oscillation frequency of the gear. The points where the near-horizontal \u03c9mn curves intersect the straight line (4) indicate the speeds at which the gear resonance will be excited (see Fig. 20). For instance, the rated excitation speed for the natural frequency of \u03c923 is 764 [rpm]. It may be inferred from both the Campbell diagram and Table 3 that the rotating movement makes flexural stiffness of the gear under consideration to increase. Moreover, at speed of 3,820 [rpm], one can notice major surge associated with the mentioned earlier changing of the shape of the natural mode frequency in the case of the frequency of \u03c931. The growth of the gear transversal stiffness observed during gyrate of the gear comes from the appearance of the additional stresses in the toothed gear through the centrifugal effects. The higher rotational speed generates higher centrifugal forces, higher stress level, thereby causing the transversal stiffness of the system to increase. Moreover, the growth of the gear flexural stiffness through the gyrate effect causes reduction of the needed numerical calculations connected with identifying the proper distorted mode shapes." + ] + }, + { + "image_filename": "designv11_7_0003112_2013.40500-Figure15-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003112_2013.40500-Figure15-1.png", + "caption": "FIG. 15 Normal pressure profiles under a 20 by 3-in. wheel in sandy loam at w equal to 16 percent with 50-lb load.", + "texts": [], + "surrounding_texts": [ + "ducers, the magnitude of angular and linear displacement, torque and sinkages. The pressure cells were calibrated by a device developing a known air pressure and having a maximum capac ity of 20 psi (Fig. 4 ) .\nTests were performed in sand and in sandy loam under laboratory conditions. The soil bin used for this investigation was 40 by 5 by 2 ft in overall dimen sions and was equally divided between sand and sandy loam. During test, the sand was kept air-dry. However, in the case of the sandy loam, water was added after each complete experiment as needed to investigate the effect of soil consistency on pressure distribu tion and slip-sinkage relationship.\nSome important characteristics of the materials tested are tabulated in Table 1. Atterberg limits pertaining to sandy loam are tabulated in Table 2.\nPrior to each test run, the dry sand was leveled with a leveling board at tached to the carriage in order to as sure a reference surface for sinkage measurements. Then the wheel was loaded and the experiment was begun by driving the wheel and tow carriage simultaneously. Drag was applied to the carriage causing it to slow down relative to the wheel and produce a certain magnitude of slip. By increas ing the drag on the carriage, pressuredistribution measurements and slipsinkage measurements at higher slip were possible. This technique was em-\nployed for testing at different slips, since speed of carriage and wheel can not be controlled separately. During this procedure, pressure distribution, angular displacement, linear displace ment, torque and sinkage data were recorded con t inuous ly . The experi mental technique produced data which permitted plotting of normal pressure distribution, sinkage and torque as a function of slip between 0 and 100 percent for each type of soil and load ing condition.\nThe test procedure for sandy loam was essentially the same as for sand. The only difference existed in process ing the material. Sandy loam was mixed at each test run and at each addition of water content with a rotary tiller. Then it was raked until a smooth soil surface was obtained. After this procedure, two passes with a smooth roller, weighing 200 lb, were made. Although this resulted in an increase of soil density, it assured a more uniform soil structure, which is demonstrated by the fact that the deviations from\n1965 \u2022 TRANSACTIONS OF THE ASAE\nthe mean in moisture and density val ues are within acceptable limits. As a matter of interest, it should be noted here that deviation from mean density at least doubled when the roller passes were omitted.\nTEST RESULTS\nThe results of driving moment, pres sure distribution and slip-sinkage meas urements are presented in diagrams and chart forms.\nFig. 5 shows a typical torque vs slip relationship with wheel load as parame^ ter in dry sand. This figure also con firms that, for slip conditions in sand in excess of 30 percent, the assumption that is constant is valid. If shear strength is taken as independent of depth, the torque vs slip relationship depicted can be considered as a shear deformation diagram since torque is proportional to the tangential forces and slip to the corresponding deforma tions. The peak points of these curves were taken for the construction of the Mohr-Coulomb envelop, and the value of (f> was found to be very nearly equal to that determined by sliding friction experiments. The sliding friction ex periments resulted in cfy equal to 24 deg and c equal to 0 while evaluating those from torque-slip relationship when\nthe normal pressures at wheel-soil con tact are known, gave (f) equal to 23 deg and c equal to 0.\nActual, normal pressure-distribution diagrams are shown in the next series of figures. Fig. 6 illustrates the pres sure distribution in sand as a function of the polar angles under a 20 by 3-in. wheel at various loads. The slip is held constant at 0 per cent. The effect of slip on pressure distribution is shown in Fig, 7, when the soil (sand), wheel size and wheel load are kept constant,\nIt is apparent from the latter two pressure-distribution diagrams that, as slip occurs, pressure distribution as well as sinkage become a function of slip. An increased sinkage develops higher motion resistance; therefore, the result ant of the pressure distribution will have a higher angle of inclination rela tive to the vertical.\nAnother important factor is that the pressure distribution extends beyond the point of maximum sinkage. The ex tent of pressure distribution to the trail ing portion of the wheel is about 10 deg or less from the toe of the wheel in most of the pressure profiles reported here. This phenomenon can be at tributed to the flow of the material into the wheel rut in sands, to the rebound of the material in firm soils.\nNote that the pressure distribution in the lateral direction is also shown in the figures. Dots denote the pressure at the center of the wheel and crosses denote the pressure close to the edges of the wheel. The pressure transducers mounted at the edges of the wheel were averaged on the recording device so that the crosses represent the average value of the pressure on the two wheel edges.\n307", + "Fig. 8 shows the same information for a 20 by 5-in. wheel as was shown in Fig. 7 for the 20 by 3-in. wheel in sand. The variation in pressure across the wheel face is very significant in deed for this wheel. The pressures at the center of the wheel were found approximately twice as high, as they were observed close to the edges of wheel. In case of the narrow wheel, the variation of pressure in the lateral direction is negligible, except for those pressure-distribution diagrams which were obtained at very high slip condi tion.\nFig. 9 shows sinkage (maximum vertical deformation) as a function of slip in sand for the 20 by 3-in. wheel. Again, it is apparent that as slip oc curs sinkage rapidly increases. For sand the compaction effects are small, so that the wheel can dig itself into the ground. This process is associated with slip failure in which the wheel removes material from the contact surface and deposits it behind the wheel.\nThe next figure (Fig. 10) shows sinkage as a function of the angle of inclination of the resultant of normal pressures in sand for both wheels tested. This function may be approxi mated by a straight line having the fol lowing equation:\nz = 6.87 oc After some manipulation it may be seen that in sand the normal resultant divides the ground contact arch ap proximately into two equal parts, there by confirming the hypothesis of Tanaka (12) who assumed in general that the angular position of the resultant (N) is half that of the angle of sinkage.\nIf the vertical component of the ground reaction is evaluated by graphi cal integration, a chart plotting Nv and\nRv against W can be made. Nv is the vertical component of the normal re sultant N, while Rv is the vertical com ponent of the resultant of normal and frictional forces. It is found that Nv alone does not satisfy the equilibrium of the vertical forces. This indicates tliat frictional forces must be included to achieve equilibrium, The frictional forces were evaluated from Coulomb's equation for maximum shear stress. The agreement obtained by the inclusion of the frictional forces is shown in Fig. 11, and it can be seen that the mag nitude of the discrepancy is within an acceptable limit.\nThe tests were continued to investi gate the behavior of the wheel in a sandy loam at various moisture con tents.\nThe following illustrations refer to results obtained. Figs. 12 and 13 show typical slip-sinkage relationships for a 20 x 5-in. wheel in sandy loam mix No. 1 and for a 20 x 3-in. wheel in\nsandy loam mix No. 4, respectively. In sandy loam at low moisture contents (w < 9.0 percent) the slip-sinkage re lationships were found to be very simi lar to those obtained in sand. However, at higher moisture contents, sinkage will be independent of slip.\nAn explanation of slip-sinkage be havior of wheels in sand and in sandy loam may be given as follows: in granu lar soils (dry sand and sandy loam as low moisture content) the compaction effects are very small. Therefore, a \"soil transport\" phenomenon exists un derneath the wheel. With added water and the same compactive effort of roller and wheel, greater density can be ob tained up until the water c o n t e n t reaches the value where maximum den sity is achieved. The sandy loam type of soil is highly compactable at higher moisture contents. Movement of the moisture of the wheel-soil interface\nserves as a lubricant; therefore, the transport of soil by wheel does not occur.\nThese series of slip-sinkage tests were performed with the aim of pirir pointing the minimum amount of co^ Lesion at which sinkage may be taken as independent of slip.\nFrom the experiments, it appears that the cohesive properties of soils are re>sponsible for the dependence or inde pendence of sinkage upon slip. The number of experiments conducted sug gests that above 0.5 psi of cohesion sinkage may be regarded as independ ent of slip.\nFig. 14 shows the angular position of the resultant of the normal pressure distribution as a function of slip for a 20 x 3-in. wheel in sandy loam at 16 percent of moisture content. This curve also shows the independence of oc and slip.\nSince the sinkage and oc were found to be independent of slip, the pressuredistribution measurements were pre sented in a superimposed form. Figs.\n308 TRANSACTIONS OF THE ASAE \u2022 1965", + "clay plotted against concentration for a Grenada silt loam soil is shown in Fig. 7. These data indicate that at low concentrations (below 1,000 ppm) the percentage of clay transported from the plot was greater than 90 percent and the percentage of silt transported was less t h a n 10 p e r c e n t . As the concentration increased, the percent age of clay transported from the plot decreased and the percentage of silt transported increased. At a concen tration of 3,000 to 4,000 ppm the per centage of silt and clay transported was about equal. When the concen tration reached 20,000 to 30,000 ppm and above, the percentage of silt and clay transported was almost constantapproximately 70 percent silt and 30 percent clay. This was the approximate percentage of silt and clay in the Gren ada silt loam soil. The results indicate that, when the concentration reached between 20,000 and 30,000 ppm, the entire top layer of soil was being moved from the plot.\nEffect of Ground Cover on Runoff and Erosion Rates\nThe characteristics of runoff hydrographs and soil erosion rate graphs on the three different ground-cover condi tions studied were similar except for the rates. The rates of runoff and ero sion increased as the percentage of ground cover decreased. The rate of soil erosion increased as rainfall and runoff rates increased. Rainfall, runoff and soil erosion data from three dif-\nferent ground-cover conditions are sum marized in Table 2. Runoff and erosion rates fluctuated widely with rapid changes in rainfall intensity during the first part of the storm. There was no apparent change in erosion rates from the fluctuations in rainfall and runoff rates in the low-intensity portion of the storm's later stages. Improved manage ment corn with 60 to 90 percent cover produced no measureable erosion for this storm and produced only 0.03 in. of runoff.\nSUMMARY\nErosion rates and particle-size dis tribution throughout runoff events were determined from runoff samples col lected from unit source areas. Equip ment and procedures were developed to obtain samples of runoff at intervals throughout runoff events from V\u00b1 and 1/45-acre plots. An instantaneous total load sampling device was developed and used to obtain runoff samples from a 1/45-acre fallow plot.\nSediment concentrations were de termined from, each runoff sample. The eroded sediment was separated into sand, silt and clay.\nEleven and one-half tons per acre per hour was the highest erosion rate determined from a ^ -acre unit source area. Rates of soil movement varied in the same manner as the runoff. The peak sediment concentration occurred at about the same time or slightly be\u0302 - fore the runoff peaked.\nData indicated that the proportion of silt increased and the proportion of clay decreased as the sediment concen trations increased up to approximately 20,000 ppm. Above 20,000 ppm the particle-size distribution in the runoff samples was approximately the same as the particle-size distribution in the unit source area soil (Grenada silt loam).\nThere were vast differences in the erosion rates from fallow soil, corn under poor management practice, and corn under improved management prac tices.\nPRESSURE DISTRIBUTION UNDER RIGID WHEELS\n(Continued from page 308) 15, 16 and 17 show the superimposition of all the pressure distribution diagrams regardless of slip at 50, 100 and 150 lb of wheel load, respectively. These measurements were taken in sandy loam mix No. 4. Note that the trend of lateral-pressure distribution reverses; that is, close to the edges of the wheel higher pressures were recorded than at the center of the contact strip in a co hesive type of soil.\nIt can be stated again from the ex periments that the angular position of the resultant approximately bisects the contact angle.\nSimilarly, as was shown for sand, equilibrium considerations pertaining to the above normal pressures, esti mated frictional forces, and imposed loads are shown in Fig. 18. It is seen that the frictional forces must also be included in the description of a wheel operation in a material having cohesion, if equilibrium is to be achieved.\nCONCLUSIONS\n1 An analytically correct equation for pressure distribution must include not only soil properties and wheel geometry, as previously believed, but also the slip-sinkage relationship and tangential forces.\n2 The effect of frictional forces are significant and should be included in equilibrium equations for wheels. The frictional forces may be conveniently estimated from Coulomb's equation for maximum shear strength,\n3 Sinkage is a function of slip in granular soils; however, in cohesive soils sinkage may be taken independ\nent of slip. Further tests are necessary to confirm this statement, since tests in loam with a moisture content in ex cess of 16 percent have not be per formed.\nReferences 1 Bekker, M. G. Theory of land locomotion. University of Michigan Press, Ann Arbor, 1956. 2 Vandenberg, G. E. and Gill, W. R. Pressure distribution between a smooth tire and soil. Transactions of the ASAE 5:(2)105-107, 1962,\n3 Cooper, A. W., Vandenberg, G. E., McColly, H. F., Erickson, A. E. Strain gage cell measures soil pressure. Agricultural Engineering 38: (4) 232-235, 246, April 1957.\n4 Reaves, C. A. and Cooper, A. W. Stress dis tribution in soils under tractor loads. Agricultural Engineering 41:(1)20-21, 31 , January 1960.\n5 Sonne, W. The transmission of force be tween tractor tires and farm soils. Grundlagen der Landtechnik, 1952.\n6 Vincent, E. T. Pressure distribution on and flow of sand past a rigid wheel. 1st International Conference on the Mechanics of Soil Vehicle Systems, Torino, 1961.\n7 Trabbic, G. W. The effect of drawbar load and tire inflation on soil-tire interface pressure. M.S. thesis, Michigan State University, 1959.\n8 Capper, L. and Cassie, F. The mechanics of engineering soils. McGraw-Hill, New York, 1953.\n9 Schuring, D. On the mechanics of rigid wheels on soft soil. V.D.I., June 1961.\n10 Hegedus, E. A preliminary analysis of the force system acting on a rigid wheel. Land Loco motion Laboratory, OTAC, Report No. 74, 1962.\n11 Phillips, J. A discussion of slip and rolling resistance. 1st International Conference on the Mechanics of Soil-Vehicle Systems, Torino, 1961.\n12 Tanaka, T. The statical analysis and ex periment on the force to the tractor wheel. 1st International Conference on the Mechanics of Soil-Vehicle Systems, Torino, 1961.\n1965 \u2022 TRANSACTIONS OF THE ASAE 311" + ] + }, + { + "image_filename": "designv11_7_0000473_s11071-007-9293-3-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000473_s11071-007-9293-3-Figure1-1.png", + "caption": "Fig. 1 Picture of the experimental device", + "texts": [ + " The short bearing theory is utilized to model the nonlinear oil\u2013film forces and Muszynska nonlinear seal force is used. Nonlinear governing equations of the rotor\u2013bearing\u2013seal system are set up. In Sect. 4, by numerical method, bifurcation diagrams, waterfall plots, Poincar\u00e9 maps, spectrum plots and rotor orbits are drawn. Various nonlinear phenomena and system unstable process are analyzed. Theoretical results are compared with the ones from experiments. Finally, the conclusions for this work are given. The experimental setup is explicitly shown in Fig. 1. A direct-current motor is used to drive the rotor system. Its rated current is 41.5 A and the output power is 7.5 kW. Because higher rotating speeds of the rotor are needed in this experiment and the motor can\u2019t provide these speeds directly, a gearbox is used to increase the rotor rotating speeds. The rotating speed can be adjusted between 0 and 9,000 rpm. Couplings are used for the connection between the motor and the gearbox, the gearbox and the rotor. The compressed air is generated by the air compressor and can reach 12 bar" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000449_s0364-0213(77)80022-0-Figure8-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000449_s0364-0213(77)80022-0-Figure8-1.png", + "caption": "FIG. 8. Trigger tree signal buffer.", + "texts": [ + " In the case of a modifying watcher, W, which is a function (rather than a trigger tree), the modified signal to be propagated can be defined simply as the value W returns. But for trigger trees, which are mobs of computations not necessarily related to one-another or coordinated in any way, and where there could be quite a few relevant SCs which run in reaction to some signal, there is a question of how the modified signal is to be computed and communicated back to the channel. To solve this dilemma, each trigger tree has an associated signal buffer. depicted in Fig. 8, As the tree is about to be applied, its signal buffer is initialized to the original signal. Any SC that wishes to alter the signal does so simply by replacing the contents of its tree's signal buffer with some new value. The value in the buffer after all SCs have been run is the signal to be propagated. By definition, when a watcher modifies the signal to NIL, the signal has been blocked, and its propagation down the Channel ceases. 2.2.5 Possibilities for Channels Channels are powerful constructions, since they fracture the private communication paths among the LISP function calls which implement a theory" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001842_robio.2009.4913244-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001842_robio.2009.4913244-Figure5-1.png", + "caption": "Figure 5. Puma 560 robot manipulator", + "texts": [ + " \u2211 = + = 20 1 )()()( )( )( 1 n k i kk i k i Qnf \u03b2 \u03b1 (16) \u2022 The procedure is finished after a sufficient number of iterations or when the maximum of one of probability vectors is reached desirably to one. After sufficient iterations, the probability of optimal limit for each parameter is maximized and the value of each parameter converges to the optimum value. Here the supervisory level, using learning automata algorithm, adjusts the gains of PID controller and the width of membership functions of fuzzy controller. V. Simulation and Results In this section, we simulate our proposed method on the robust tracking design of a Puma560 robot manipulator as shown in Fig. 5 using robotic toolbox. [20] Assume that the trajectory planning problem for a weightlifting operation is considered and the Puma560 robot manipulator suffers from time-varying parametric uncertainties and exogenous disturbances. With the aim of testing in experiments the performance of the proposed controller, a rectangular reference trajectories in joint space has been selected. Also, the exogenous disturbances 1d through 6d are assumed which their values are mentioned in Table II. [21] Obviously, the parameter uncertainties and exogenous disturbances are extremely large" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003560_978-1-4613-4560-2_2-Figure8.37-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003560_978-1-4613-4560-2_2-Figure8.37-1.png", + "caption": "Fig. 8.37. The i versus 1) relation has one point of particular interest, the point of zero overpotential and zero current. It corresponds to equilibrium at the electrode surface.", + "texts": [ + "56) that one must use instruments with very high input impedance (or resistances) R. Then, the currents flowing across the electrode during measurement and therefore the disturb ances to the potential difference under measurement become negligible. Two regions of the general interfacial current-density-overpotential curve have been discussed, the exponential region far from equilibrium and the linear region near equilibrium. Now attention will be focused on one single point on the i versus 'YJ curve (Fig. 8.37). This is the unique point corresponding to equilibrium where the overpotential 'YJ and the driving force I (lX, are equal to zero; as a consequence, the net current density i is also zero and the de-electronation T and electronation 7 current densities are equal to each other, T = 7. Since, under equilibrium conditions, the individual electronation- and de-electronation-current densities are equal to the equilibrium exchange current density, i.e. (cf Section 8.2.6), (8.26) it follows that (8.57) Upon taking logarithms, A)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003919_icra.2014.6907600-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003919_icra.2014.6907600-Figure1-1.png", + "caption": "Fig. 1: Modular 9-DOF agricultural robot developed within the CROPS project [4]", + "texts": [ + " Since this approach is related to ours, a comparison with our following scheme will be in the focus of our upcoming work. In this paper, we propose to use the numerically efficient conjugate gradient method to solve the PMP as formulated by [7]. Since the optimization input is projected to the nullspace of the redundant manipulator, workspace contraints x\u0307d(t) are preserved. Real-time optimization is enabled by applying a moving horizon approach (comparable to Model Predictive Control). We implemented this approach for a 9-DOF modular agricultural robot (Fig. 1a), that has been developed at our institute for harvesting of single crops (e.g. sweet pepper or apples) or precision spraying of grapes [4]. It has 1 prismatic and 8 rotational joints, the kinematic scheme is shown in Fig. 1b. Since the workspace is 6-dimensional (3 cartesian positions and 3 rotations), the degree of redundancy is 3. For the inverse kinematics solution, an local inverse kinematics approach was presented in [4], [19], which will be the reference for our new approach. In Section II, we present the basic idea of our approach including the problem formulation, optimality criteria and an efficient numerical solution. Section III deals with different examples of cost functionals that we have used in our application" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002429_j.cma.2010.12.020-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002429_j.cma.2010.12.020-Figure3-1.png", + "caption": "Fig. 3. Pin-on-flat problem: (a) geometry and boundary conditions, (b) sketch of the parameterized here by, respectively, 5 and 6 independent shape parameters).", + "texts": [ + " The normal at the typical node Xi k is determined as the average of the normals of the two linear segments adjacent to the node, according to N i k;t \u00bc Xi k\u00fe1 Xi k 1 kXi k\u00fe1 Xi k 1k e3; \u00f030\u00de where Xi k 1 and Xi k\u00fe1 are the positions of the two neighboring nodes, e3 is the unit vector normal to the plane of analysis, and denotes the vector product. As the first example, a highly simplified two-dimensional pinon-flat problem is studied, which roughly corresponds to the pinon-disk tribological test. A hyperelastic pin is pressed into an hyperelastic block with a constant force P, cf. Fig. 3(a). The problem is analyzed in two dimensions, and plane strain conditions are assumed, as if both the contacting bodies were long in the e3-direction, perpendicular to the plane of analysis. Relative sliding in the e3-direction is assumed, and the effect of the associated friction stresses on the in-plane deformation is neglected. As a result, the deformation problem resulting from the assumption of separation of time scales (Section 2.2) is a steady-state frictionless contact problem, and the wear rate is assumed proportional to the (nominal) normal traction TN and to the sliding velocity v3, so that we have _Wi \u00bc \u00f0ji =j1\u00deKiTNv3; i \u00bc 1;2, cf", + " The hyperelastic neo-Hookean material model is adopted for both bodies with identical elastic properties: Young\u2019s modulus E = 10 MPa and Poisson\u2019s ratio m = 0.4 (quadrilateral F-bar elements [33] are used to avoid volumetric locking effects). The loading force (per unit length in the out-of-plane direction) is equal to P = 20 N/mm. The wear coefficients at both surfaces are K1 = K2 = 10 5 mm2/N, the sliding velocity is v3 = 10 mm/s, and the wear process is simulated for t 2 [0,T], where T = 9600 s. The computations have been carried out in the AceGen/AceFEM environment [34]. The adopted shape parameterization is sketched in Fig. 3(b). The shape of the boundary is described by a B-spline curve, and the positions of its control points constitute the shape parameters. In Fig. 3(b), the open circles denote the positions of the control points in the initial configuration. The modified shape is defined by the control points marked by the full circles, which are obtained by scaling the initial positions (along the dotted lines) by the values of the corresponding shape parameters. For a smooth parame- terization, quadratic B-splines are used, while a piecewise linear function (linear B-spline) is used to define the nodal parameterization, cf. Remark 3. In both cases, the parameterization preserves the symmetry with respect to the vertical axis. The mesh update scheme based on the above shape parameterization is analogous. The positions of the nodes of the block are scaled along the vertical lines, while the pin nodes are scaled along the family of lines passing through point A, cf. the dotted lines in Fig. 3(b). Fig. 4 shows the undeformed and deformed finite element mesh at three time instants (at the t-scale). The finite configuration changes due to both deformation and shape evolution are clearly visible. A more detailed view of the evolution of the shape of the undeformed contact surfaces is presented in Fig. 5 for the case of nodal shape parameterization (20 and 15 shape parameters for the pin and block, respectively). The instability of the time integration scheme is observed when the time step is too large, cf" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000686_j.actaastro.2008.08.003-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000686_j.actaastro.2008.08.003-Figure1-1.png", + "caption": "Fig. 1. Geometry of orbit motion and proposed solar controller configuration.", + "texts": [ + " The performance of the proposed control laws are tested in the presence of parameter uncertainties and external disturbances. In addition, the effects of various system parameters on the performance of the controllers are studied. Finally, Section 5 concludes with the major findings of the present investigation. The proposed system model comprises of a satellite with two-oppositely placed light-weight solar flaps along the satellite Y-axis and its center of mass O moving in an elliptic orbit about the earth\u2019s center E (Fig. 1). The center of mass of the satellite lies on the system center of mass O. The mass of the solar flaps and other accessories are assumed to be negligible. For the system under consideration, an orbital reference frame O-XoYoZo is selected such that the Yo-axis always points along the local vertical, the Xo-axis lies normal to the orbital plane, and the Zo-axis represents the third axis of this right handed frame taken. The body-fixed coordinate frame is represented by O-XYZ. For solar flap-j, we consider its axis nj initially aligned with the Z-axis is rotated by an angle j about the Xaxis (normal to the orbit plane Y\u2013Z)", + ", t = a = d = 0, s = 1; no transmission, no absorption, no diffusion, only specular reflection), the preceding expression (3) simplifies to where s j is the unit vector of the incoming light from the sun on the solar flap-j and can be written in the satellite body-fixed reference frame as s j=[sin sin(i\u2212 s)]i\u0302+[\u2212 cos cos( + L ) \u2212 sin cos(i\u2212 s) sin( + L )] j\u0302+[cos sin( + L ) \u2212 sin cos(i\u2212 s) cos( + L )]k\u0302 (5) The vector normal to the solar flap-j, n j can be written in terms of the satellite body-fixed reference frame as n j = [\u2212 sin j ] j\u0302 + [cos j ]k\u0302, j = 1, 2 (6) Thus, the torque exerted by the solar flap-j on the satellite is derived as Ts j = r j \u00d7 Fs j = (\u22121) j+12 s pA jr j | s j \u00b7 n j |( s j \u00b7 n j ) \u00d7 [cos j ]i\u0302, j = 1, 2 (7) Assuming the cross-sectional area of the flap and the distance between the system center of mass O and the center of pressure for both the solar flaps being the same (i.e., Aj = A, rj = r), the total solar torque about the satellite body axes is Ts = Ts1 + Ts2 = 2 s pAr [| s1 \u00b7 n1|( s1 \u00b7 n1) cos 1 \u2212 | s2 \u00b7 n2|( s2 \u00b7 n2) cos 2] (8) Considering be the orientation of the satellite with respect to the inertially fixed axis YI (Fig. 1), we can write = L + \u0307 = \u0307L + \u0307 \u0308 = \u0308L + \u0308 (9) where = t is the orbital angle, and = /a3 is the mean orbital rate. Substituting L = \u2212 into Tg and Ts [Eqs. (2) and (8)], and writing the derivatives with respect to true anomaly , and applying the following relations \u0307 = \u0307 \u2032 \u0308 = \u0307 2 \u2032\u2032 + \u0308 \u2032 (10) \u0307 = \u221a a(1 \u2212 e2) R2 \u0307 2 = R3 (1 + e cos ) \u0308 = \u2212 2 R3 e sin (11) and further replacing R by semi-major axis a and eccentricity e, using the relation R = a(1 \u2212 e2) (1 + e cos ) = 1/3(1 \u2212 e2) 2/3(1 + e cos ) (12) the resulting governing equation of motion of the system are obtained as follows: (1 + e cos ) \u2032\u2032 = Tg( , ) + Ts( , , e, j , ( ), ( )) + 2e sin \u2032 (13) where Tg( , ) = \u2212 3 2K sin 2( \u2212 ) Ts( , , e, j , ( ), ( )) =C ( 1\u2212e2 1+e cos )3 { sin2( + + 1) 1 cos 1 \u2212sin2( + + 2) 2 cos 2 } ( ) = 1 \u2212 sin2 sin2(i \u2212 s) ( ) = \u2212tan\u22121(tan cos(i \u2212 s)) j = sgn(sin( + + j )), j = 1, 2 K = Iy \u2212 Iz Ix , C = 2 s pAr Ix 2 , = a3 (14) and the function sig( ) denotes signum function" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001195_tnn.2007.899181-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001195_tnn.2007.899181-Figure4-1.png", + "caption": "Fig. 4 NN classification i = f1 . . . 4g.", + "texts": [ + " This section presents the control law, whose aim is to reduce the error between the desired and actual state of the system, by finding the right configuration to apply. As established previously, the NN is defined to provide the relation between every configuration and the system state variations. Consequently, the learned NN performs the classification of the configurations depending on the input vector . Definition: Given an input vector , it belongs to the class denoted if is the component of maximum value of the output vector (Fig. 3) if (8) An example of the classification performed by an NN with two inputs and four classes is given as follows (Fig. 4). This classification is used to choose the configuration which reduces the best tracking error, which is written as follows: (9) where is the desired state and the process state. Then, by applying this vector to the network input, we obtain an output vector whose component of maximum value gives the class of . Knowing this class, we can deduce the matching configuration and the associated control vector. Step 1) Compute the position error . Step 2) Compute the network output with as input. Step 3) Determine the maximal element of to deduce the right class to choose" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002546_ipec.2010.5542008-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002546_ipec.2010.5542008-Figure4-1.png", + "caption": "Fig. 4. IVMS of open phase.", + "texts": [ + " The phase V flux is increased and the phase W flux is decreased at this position. Furthermore, these fluxes are changed with different rates (time-derivatives of flux are different). As a result, the influence voltage caused by the flux change occurs in the open phase U. In the same way, IVMS is generated in the open phase U corresponding to the rotor position. However, IVMS does not occur at d=90[deg] because the timederivatives of flux v and w are completely the same in this position (Fig. 3 (d)). Figure 4 (a) and (b) show the winding circuit of PMSM. IVMS is generated depending on the characteristics of the magnetic saturation and the mutual inductance of the PMSM. These characteristics determine the sensitivity of IVMS (Fig. 4 (a)). Even if the mutual inductance is negligibly small, IVMS is generated as the neutral point voltage, as shown in Fig. 4 (b). It may be a very low value in this case. For example, if the difference in inductance between Lv and Lw is 10% (Lv=90%, Lw=100%), the neutral point voltage is expected to be about 2.6% ( =Lw/(Lv+Lw)0.5) of DC voltage. If 12V DC source is applied to the inverter, IVMS occurs with peak of about 0.32V. This is a high enough value to use to estimate the position. To accurately estimate the position, PMSM inductance must change at least 5%. The initial rotor position detection using IVMS has been used in several products [8]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001660_raad.2010.5524544-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001660_raad.2010.5524544-Figure1-1.png", + "caption": "Fig. 1. Differentially driven mobile robot, Ti - radius of the wheel, 2bi - distance between wheels, ai - distance between wheel axis and center of mass of the robot, [Xi YilT - robots position, ()i - robots orientation, [Xsi Ysi]T - position of the center of mass of the robot.", + "texts": [], + "surrounding_texts": [ + "Index Terms-mobile robots, trajectory tracking, collision avoidance, artificial potential function\nI. INTRODUCTION\nCooperative robotics is currently area of interest for many researchers [2], [5], [6], [7], [9]. Recent development in multiagent systems, mechanics, computer sciences, electronics - especially in communication caused that multirobot systems have great potential to solve many practical problems. Su pervision, surveillance, exploration, mapping and many other tasks can be executed effectively by the group of autonomous, cooperating robots. In this paper problem of trajectory tracking in the environment with static, convex obstacles is investigated. Similar algorithm was presented in [1] but its computational requirements are higher then for method presented in this paper.\nIn section II model of the multi-robot system is presented. Next control algorithm is shown. In section IV stability of the system is described. Simulation results that illustrate effective ness of presented algorithm int the next section are shown. Concluding remarks end the paper.\nII. MODEL OF THE ROBOTS\nModel of the kinematics of the i-th robot (i = 1 , . . . N), where N - number of robots, is given by:\n[ i: 1 \ufffd [ \ufffd\ufffd:; \ufffd 1 [ \ufffd 1 ' (1)\nwhere Xi, Yi, (h represent position and orientation coordinates of the center of the i-th robot, and U i = [Uvi uwif is input vector of linear and angular velocity controls, respectively.\nModel of the dynamics of the differentially driven mobile platform is given by the following equation:\n(2)\n978-1-4244-6886-7/10/$26.00 \u00a92010 IEEE 451\nwhere Mi is mass matrix, Ci (eli) - Coriolis matrix, Di - damping matrix, Gi - gravitational force vector, Wwi = [WLi WRi]T - robot wheels velocity vector, Ti = [TLi TRif - input torque vector.\nMi is symmetric positive definite, constant matrix:\nMi = [ mlli m12i ] , m12i ml li (3)\nwhere ml li = br;(mi b; + Ii), m12i = br;(mi b; - Ii), , 2 2 '2 . mi = mei +2 mwi, Ii = mei ai +2 mei ai +2 mwi bi + Iei +2 I m i, mci - mass of the body of the i-th robot, mwi - mass of the wheel, lei - moment of inertia of the i-th robot body about vertical axis through center of mass, IWi - moment of inertia of the wheel with the rotor of motor about the wheel axis, I m i - moment of inertia of the wheel with the rotor of the motor about the wheel diameter, ri - robot wheel radius, ai - distance between center of mass of the robot [X si Y si]T and wheel axis, 2 bi - distance between robot's wheels.\nCoriolis matrix C( eli) can be written:\nh I 2 w ere Ci = 2bi ri mei ai. Damping matrix Di is as follows:\nD, = [ d1 0 1i 0 ] \u2022 d22i '\nwhere dUi and d22i are nonnegative damping coefficients.\n(4)\n(5)\nGravitational vector Gi = [0 of when robots move on the horizontal plane.\nTransformation between linear and angular velocity vector Wi and robot wheel velecity vector Wwi is as follows:\nWwi = Bi Wi , (6)\n[ .l. h 1 Bi = r, \ufffdh . (7) .l. r, r,\nwhere\nTransformation between force and torque for the platform Ti = [Fi Ti]T and whell torques Ti is given by the Eq.:\n(8)", + "W. Kowalczyk et al\u00b7 Trajectory Tracking for Multiple Unicycles in the Environment with Obstacles\nwhere\n(9)\nNotice that B i = Br. Model (2) can be rewritten as follows:\nM i'ro i + C i (q i) Wi + D i Wi = B(Ti (10)\nwhere M i = B iMiBi, C i = B iCi (q i)Bi, and D i = B iDiBi.\nIII. CONTROL ALGORITHM\nReference path for the i-th robot is given by the vector qdi = [Xdi Ydi]T. Reference orientation can be computed using reference linear velocity: Bdi = at a n 2c (Ydi' Xdi) where a t a n 2c (\u00b7 , .) is continuous version of the a t a n 2(\u00b7 , .) function described in [4]. Let's define qi = [Xi Yi]T - position vector for the i-th robot. One can write position tracking error as follows:\n(11)\nA. Dynamics feedback linearization\nThe dynamics of the robot can be linearized by the follow ing control feedback:\n(12)\nwhere V i is a new control input. Substituing (12) into (2) one obtains equation of linearized robots dynamics in the form of integrator in the form:\n(13)\nFor the linearized dynamics of the robot the following linear control law can be proposed:\n(14)\nwhere kw is posItIve definite diagonal gain matrix. New control U i = [Uvi Uwi]T is computed using VFO (Vector Field Orientation) method [4].\nB. Vector Field Orientation Algorithm\nLets introduce the convergence vector:\n[ hxi 1 [ kpEx\ufffd + Xd\ufffd 1 hi = hy\ufffd kpEYi + i;di , h o\ufffd ko eat + Ba\ufffd\n(15)\nwhere kp, ko > \u00b0 are control gains for position and orientation, respectively.\nModified position errors:\nEYi = eyi + Wyi\n(16)\n(17)\nwhere W i = [Wxi wyi]T is collision avoidance term that will be described further in this paper; ea i = Ba i - Bi is auxiliary orientation error. Auxiliary orientation variable Ba i is given by the Eq.: Ba i = at a n 2c (hyi' hxi). Control law for the i-th mobile platform is as follows: U i = [Uvi uW i]T:\nUvi = hxi cos Bi + hyi sin Bi Uwi = h O i\nThe following assumptions are imposed.\n(18)\nAssumption 3.1: Desired trajectories do not intersect APF areas of obstacles and robots do not interact when tracking is executed perfectly.\nAssumption 3.2: If robot position is in the repel area then reference trajectory is frozen:\n(19)\nwhere C is the time value before robot gets to the repel area. Higher derivatives of qdi (t) are kept zero until robot leaves the repel area [3].\nAssumption 3.3: When ea i E (\ufffd + 7rd - 8, \ufffd + 7rd + 8), where 8 is a small positive value, d = 0 , \u00b1 1 , \u00b1 2 , ... , then auxiliary orientation variable Ba i is replaced by Ba i = Ba i + sgn (ea i - (\ufffd + 7rd) ) E, where E is a small value that fulfills condition E > \u00b0 and sgn(\u00b7) denotes the signum function.\nAssumption 3.4: When robot reaches a saddle point ref erence trajectory is disturbed to drive robot out of local equilibrium point. In the saddle point the following condition is fulfilled: Ilhill =0 , (20 )\nwhere hi = [hxi hyi t. In this case Ba i (t ) is frozen: Ba i (t ) = Ba i (C ) , C. Artificial Potential Function\nCollision avoidance behaviour is based on the artificial po tential functions (APF). All physical objects in the environment like robots and static obstacles are surrounded with APF's that raise to infinity near objects border rj (j - number of the robot/obstacle) and decreases to zero at some distance Rj, Rj > rj.", + "19th International Workshop on Robotics in Alpe-Adria-Danube Region - RAAD 2010 \u00b7June 23-25, 2010, Budapest, Hungary\n20\n1 5\n\ufffd -\", 10 >\n,r\ufffd 5\n00 ,R\n0 . 5 1. 5 2 2. 5 11m]\nthat gives output Ba ij (lij) E (0 , 1). Distance between the i-th robot and the j-th object is as follows: lij = 11 Y rn Zcn Zrn \u00fe Ycn > Y rn Zcn < Zrn 2 Ycn< Y rn Zcn < Zrn \u00bc Tan 1 jZcn Zrnj jYcn Y rnj cn \u00bc Sin 1 Rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u00f0Ycn Yrn\u00de2 \u00fe \u00f0Zcn Zrn\u00de2 q 8>>< >>: (8) where Ycn, Zcn represent a certain dispersion point n within COL2, the position of cutter\u2019s center with radius R is (Yrn, Zrn)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000478_tec.2007.902674-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000478_tec.2007.902674-Figure1-1.png", + "caption": "Fig. 1. Cross section of the PMIG.", + "texts": [ + "kanazawa-it. ac.jp). Digital Object Identifier 10.1109/TEC.2007.902674 2) The inrush current can be significantly reduced by synchronizing the phase of a grid voltage with that of an internal voltage (induced in the primary winding by the PM rotor) [5]. Thus, containing a PM rotor improves both the steady-state and transient performance of an IG. This paper investigates how the built-in PM rotor affects the equivalent circuit parameters of the PMIG and explains the reason for the increased power density. Fig. 1 shows the cross section of a 4-pole PMIG (rated at 2.2 kW, 200 V, 9 A, and 60 Hz) [2]\u2013[5] that was used for this investigation. Fig. 2 shows the calculated and experimental output power characteristics of the PMIG. The details of the calculation method are given in [2]. In this figure, a comparison with a 0885-8969/$25.00 \u00a9 2007 IEEE conventional IG is also shown to justify the superiority of the PMIG. The main dimension and employed material of the IG are the same as those of the PMIG analyzed, except for the presence of the PM rotor", + " As can be seen from this table, xm12 and r\u20322(= \u03b22r2) of the PMIG are smaller than those of the IG. The reason for the decreased xm12 is that the reluctance of the squirrel cage rotor is increased by containing the PM rotor. In addition, the decreased r\u20322 is due to a reduction in \u03b2. The reduced \u03b2 means an increase in E2 because E1 of the PMIG is almost equal to that of the IG as in Table I. In the case of the PMIG, the squirrel cage rotor is uniformly excited from the inside by the PM rotor as shown in Fig. 1. Consequently, the magnetic fluxes interlinked with the From the previously mentioned results and (1), it can be seen that the reduced \u03b2 (i.e., the increased E2) leads to the increase in Pout of the PMIG. IV. CONCLUSION This paper has investigated the effects of the built-in PM rotor on the equivalent circuit parameters of the PMIG. As a result, it was shown that containing the PM rotor inside the squirrel cage rotor reduces the effective turns ratio and provides a higher power density. REFERENCES [1] W" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002940_cssc.201200349-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002940_cssc.201200349-Figure3-1.png", + "caption": "Figure 3. (a) Facile fabrication process for I2-free ssDSSCs using conductive polymers as HTMs. i) Solid-state polymerizable monomer crystal formation with complete penetration by drop casting and drying of DBProDOT or DBEDOT solutions. ii) Simple SSP of DBProDOT penetrated the cell at room temperature. iii) SSP of DBEDOT penetrated the cell at 60 8C. iv) Application of the counter electrode on the nanocrystalline TiO2 layer. (b) Cross-sectional SEM images of the TiO2 photoelectrode with HTMs and the magnified interface between the OM film and nanocrystalline TiO2 layer.", + "texts": [ + " Despite the ordered structure of PProDOT and steric bulkiness, the activation energy of the oligomerized carbocations is less than that of the dimerized carbocations, mainly because of the formation of a stable delocalized structure in the oligomer.[20] Formation of HTMs for I2-free ssDSSCs at room temperature The I2-free ssDSSCs were constructed with fluorine-tin-oxide(FTO)-coated glass, an interfacial TiO2 layer, an N719-dye-adsorbed nanocrystalline TiO2 layer, pore-filled PProDOT as an HTM, and a Pt-coated FTO counter electrode (Figure 3 a). A conventional compacted TiO2 layer (CC-TiO2) was used as a control sample, whereas an organized mesoporous TiO2 (OMTiO2) layer was introduced to reduce the interfacial resistance and improve light transmittance. The 550 nm-thick, transparent OM-TiO2 layer was synthesized through a sol\u2013gel process using an amphiphilic graft copolymer (see the Supporting Information for details) as an interfacial layer.[27, 45, 46] After casting an ethanol solution containing DBProDOT on the dye-adsorbed TiO2 photoelectrode, SSP occurred to produce PProDOT at room temperature. The cross-sectional scanning electron microscopy (SEM) images of the TiO2 photoelectrode (Figure 3 b) clearly show the deep penetration of PProDOT into the 11 mmthick nanocrystalline TiO2 layer to result in improved interfacial contact of the electrode/HTM. The 550 nm-thick OM-TiO2 layer also had good interfacial contact on the FTO glass without defects. As shown in Figure 4 a and b, the OM-TiO2 layer exhibited high porosity with good interconnectivity compared to the uniformly dense CC-TiO2 layer. The average pore diameter was approximately 40\u201370 nm. After in situ SSP of DBProDOT in the TiO2 pores, the nanocrystalline TiO2 layer was completely filled without defects (Figures 4 c and d and S8)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001269_1.3197178-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001269_1.3197178-Figure2-1.png", + "caption": "Fig. 2 Residual displacements used in tangential problem", + "texts": [ + " 3 Normal and Tangential Problems in Elastoplasticity Both normal and tangential displacements of a surface point due to a cuboid of uniform plastic strain should be carefully considered when solving EP contact problem in the stick/slip regime. The normal displacement was given in an integral form by Chiu 26 , which was analytically integrated in Ref. 5 . It is also given MARCH 2010, Vol. 77 / 021014-110 by ASME 6 Terms of Use: http://www.asme.org/about-asme/terms-of-use i m c s T p 4 v w m a o i T w a v 0 Downloaded Fr n terms of Galerkin vectors in Ref. 27 . The knowledge of noral displacements, see Fig. 1, is sufficient for most frictionless ontact problems. For frictional contacts the tangential problem, ee Fig. 2, must be solved to correctly define shears in stick-zones. angential displacements induced by plasticity are useful in this roblem, but have not yet been studied nor considered. Maxwell\u2013Betti Reciprocal Theorem Consider two independent loads applied to an elastic body of olume and of boundary . The first state u , , , f i exists ith initial strains \u00b0. The second state is undefined for the moent and will be noted u , , , f i . The reciprocal theorem, lso know as Maxwell\u2013Betty theorem, expresses an equilibrium f works between both states" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002128_s12239-010-0023-3-Figure12-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002128_s12239-010-0023-3-Figure12-1.png", + "caption": "Figure 12. Concerned points on each bay of bus frame in correlation with survivor space.", + "texts": [ + " The maximum side wall displacement is a constrained function, and the weight of the whole bus is an objective function. The optimization problem can be formulated as: Minimize : F(xi) = W0 + Wi.xi Subject to : y1(xi) \u2013 150 0 y2(xi) \u2013 400 0 xi : is the vector of design variables W0 : is the unvarying of the whole bus while considering 16 design variables Wi : is the weight constant for each part that is considered y1, y2, : are the constrained functions for the side wall displacements in the upper and lower area versus the survivor space (see Figure 11 and Figure 12). Using the Design of Experiments to perform the optimization analysis, the LS-DYNA/ MPP971 was used for the sampling process while the Excel tool was used for the regression technique. The 16-variable problem is very expensive. Therefore, in this paper, the optimization problem was made simple by considering 16 variable correlations upon energy absorption. The members of the window pillars and the side wall bars are shown in Figure 11. During the rollover, after the corner (where the lateral and roof are connected) is impacted, the window pillars were first affected followed by the side wall bars", + " The thickness values of the window pillars and the side wall bars at x=2 are the values that are found after redistributing the energy absorption ability. Therefore, the sampling value range was considered about x=2. LSDYNA/ MPP971 was used for simulation of each sampling step. The results of the sampling process for the upper constraint, shown in Table 10, and the lower constrain, shown in Table 11, which correlate to each design value, was the maximum displacement of the bus\u2019s superstructure at the points, see Figure 11 and Figure 12. 5.4. Regression Analysis The Excel tool was used to perform the regression processes. The results of the regression for the upper and lower constraints are shown in Figure 13 and Figure 14, respectively. The maximum displacement of the bus\u2019s frame for the lower area was a monotonically decreasing power function, y1 = 508.1 x\u22120.4029 [mm], with an R-squared value of 0.9992 and a standard error of 0.0094. The maximum displacement of bus frame for the upper area also was a monotonically decreasing power function, y2 = 160" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000193_13506501jet89-Figure6-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000193_13506501jet89-Figure6-1.png", + "caption": "Fig. 6 Experimental apparatus", + "texts": [ + " Figure 5 shows the aerostatic porous journal bearing used in the experiment. A porous bush made of graphite was adhered to the back metal by epoxy. To avoid pneumatic hammer instability, the surface-restricted layer was formed by putting epoxy adhesive on the bearing surface and then wiping it off by supplying pressurized air into the porous bush. In this experiment, two types of aerostatic porous journal bearings were prepared: one with a narrow width of the feed groove (L1/L \u00bc 0.5) and the other was wide (L1/L \u00bc 0.8). Figure 6 shows the experimental apparatus to measure the whirling instability of a rotor. The rotor was supported by two aerostatic porous bearings that had almost the same surface-restriction ratio. The rotor weight was supported by an aerostatic thrust bearing. The rotor was driven by blowing air jets at turbine buckets located at the upper and lower parts of the rotor. The whirling amplitude of the rotor was measured by two displacement probes installed in the x and y directions. As mentioned earlier, to calculate pressure distributions in the bulk of the porous material, the surface-restricted layer, and the bearing clearance, the permeabilitiesof theporousmaterialand the restricted layer have to be determined so that the theoretical Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002664_bf03266743-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002664_bf03266743-Figure2-1.png", + "caption": "Figure 2 \u2013 Cruciform joint specimen", + "texts": [], + "surrounding_texts": [ + "Welding in the World, Vol. 54, n\u00b0 9/10, 2010 \u2013 Peer-reviewed Section\nstrength difference, i.e. the consideration of mean and residual stresses [9, 10], of the thickness infl uence and of the weld quality.\nAn important infl uence on the fatigue strength of welded joints is the realized weld quality, which depends on manufacturing conditions. Of prime importance is the weld geometry, for example, the misalignment, the weld toe and the weld root geometry (rootside drop-thru).\nIn the railway vehicle industry, manufacturing conditions correspond to good workmanship with respect to shop fabrication. An open question is the infl uence on the fatigue strength of such welded components, especially relating to the fatigue strength level in the IIW Recommendations.\nIn order to clarify this subject, special fatigue tests were carried out with different welded specimens made by several railway vehicle manufacturers of bogies (Bombardier, Siemens, and ALSTOM). For these fatigue tests, specimens of typical welded joints with significantly different notch effect were selected, i.e. butt weld specimens with relatively low notch effect and cruciform joints with relatively high notch effect.\nThese specimens were made under typical industrial conditions so that they represented the weld quality level of this industrial fi eld. Before the fatigue testing of these specimens, the weld quality was checked on the basis of the criteria of DIN EN 15085 [11], which are based on the general weld quality standard DIN EN ISO 5817 [12].\nThe shape and size of the investigated welded specimens are presented in Figures 1 and 2. The material for both of these specimen types is the normal structural steel S355J2 (1.0577), with the yield strength of 355 N/ mm\u00b2 and the ultimate tensile strength of 520 N/mm\u00b2, according to DIN EN 10025-2 [13]. The thickness of the\nspecimens is the mean structural thickness for bogie frames (t = 10 mm). The fabrication of the investigated specimens was carried out under normal conditions for the railway vehicle industry. All specimens were manually welded with the metal active gas process. Table 1 contains details of the welding process. The parameters of the welding process were documented. The specimens were made by the cutting of long, welded plates. Therefore, the residual stresses are very low and the fatigue strength of the specimens is dependent on the mean stress.\nThe butt welds were welded with two weld passes and on temporary backing by 2 manufacturers (single V-butt joint) and, from both sides of the plate, by one manufacturer (double V-butt joint). The cruciform joints were produced with 4 fi llet welds with a single pass. The throat thickness of the fi llet welds was specifi ed as a = 5 mm in order to obtain the same thickness for weld seam and plate cross-section. However, all manufacturers have realized a signifi cantly higher throat thickness for the fi llet welds (as presented in Table 2 and Figure 3) which contain the metallographic sample of a cruciform joint specimen. The throat thickness was determined by metallographic samples. Therefore, the determined throat thicknesses include the degree of welded penetration. The non-welded inner gap of these specimens is named the root face length g (also referred to as root gap, see 3.2.2). The values of Table 2 are mean values. Hence, direct conclusions to single test results are conditionally possible.\nFor railway applications, the relevant criteria of weld quality are given in DIN EN 15085 [11], which is based on the general weld quality standard DIN EN ISO 5817 [12]. This means that DIN EN 15085 [11] and DIN EN ISO 5817 [12] contain identical limits for weld quality criteria in relation to weld quality levels.\nThe weld quality inspection was carried out by the Institute of Welding of Technical University Braunschweig, referring to the criteria of DIN EN ISO 5817 [12] and, in", + "Welding in the World, Vol. 54, n\u00b0 9/10, 2010 \u2013 Peer-reviewed Section\naddition, to the angular distortion which is reported in [14]. This inspection included:\n\u2013 visual inspection of all specimens,\n\u2013 liquid penetration test,\n\u2013 radiographic examination of butt joints,\n\u2013 surface inspection of cruciform joints and\n\u2013 measurement of weld contour by laser triangulation of the specimens.\nThe details which follow outline the results of these quality controls:\n\u2022 Butt welds\n\u2013 weld toe angle \u2265 150\u00b0 (angle between the plane surface and a plane tangential to the weld run surface at the toe of the weld, according to imperfection No. 1.12 in DIN EN ISO 5817)\n\u2013 misalignment \u2264 0.1 \u00d7 t\n\u2013 angular distortion \u2264 1\u00b0\n\u2013 porosity \u2264 2 %; max. \u2264 0.2 \u00d7 t\nTable 1 \u2013 Filler metal and shielding gas for the fabrication of specimens\nManufacturer A Manufacturer B Manufacturer C\nThroat thickness of fi llet weld a [mm] 6.8 7.2 7.6\nRoot face length g [mm] 8.6 7.1 7.7", + "Welding in the World, Vol. 54, n\u00b0 9/10, 2010 \u2013 Peer-reviewed Section\n\u2013 clustered porosity \u2264 4 %; max. \u2264 0.2 \u00d7 t\n\u2013 outer transition radius \u2265 1.0 mm\n\u2013 no continuous undercut or lack of fusion (results of visual inspection and liquid penetration test)\n\u2013 short intermittent undercut \u2264 0.05 \u00d7 t (accuracy of measurement \u2264 0.1-0.2 mm\n\u2022 Cruciform joints\n\u2013 misalignment \u2264 0.1 \u00d7 t\n\u2013 angular distortion \u2264 1\u00b0\n\u2013 determination of throat thickness a > 5 mm\n\u2013 outer transition radius \u2265 0.7 mm\n\u2013 no continuous undercut or lack of fusion (results of visual inspection and liquid penetration test)\n\u2013 short intermittent undercut \u2264 0.05 \u00d7 t (accuracy of measurement \u2264 0.1-0.2 mm)\nThe summarized results of these quality controls are\n\u2013 most of the specimens quality level B according to DIN EN ISO 5817\n\u2013 some butt joints quality level C (weld toe angle)\n\u2013 some cruciform joints quality level C (misalignment, angular distortion)\n\u2013 for both specimen types small, exceeding the limit for quality level B\nThe butt welds with quality level C (4 specimens) deviate only marginally in the weld toe angle (148\u00b0) from the limit of quality level B (150\u00b0) of DIN EN ISO 5817. The quality level C of the cruciform joints (8 specimens) is related to weld toe angle, misalignment and angular distortion. The deviation of these imperfections is not more than 15 %. In summary, the main quality level of the investigated specimens is B, as defi ned by DIN EN ISO 5817.\nIn addition, it is interesting to compare these quality results with the weld classes of the new Volvo Standard [15, 16] because in this standard, the quality criteria correlate better with fatigue strength than in DIN EN ISO 5817. All investigated specimens correspond to the normal quality for the fatigue strength of this standard (weld class VD). For some criteria, the high quality level is even fulfi lled.\nFurthermore, additional metallographic investigations and hardness measurements show a typical metallurgical state for such types of welded joints and no noticeable problems.\nThe fatigue tests were carried out by Fraunhofer Institute for Structural Durability and System Reliability LBF, Darmstadt, and are presented in [17]. These tests were executed under the following conditions:\n\u2013 per joint type, 3 \u00d7 9 specimens were tested by axial loading with constant amplitude and with stress ratio R = 0,\n\u2013 the failure criterion of fatigue strength was the rupture of the specimen,\n\u2013 N = 107 cycles of tests were the maximum. Thereafter, unbroken specimens were tested with higher load amplitude.\nThe test results are shown in Figures 4 to 7 and in Table 3. These results are based on the evaluation of all fatigue tests per joint type.\nFor the butt welds, the slope of the S-N curve as k = 4.4 is the mean value of the slopes which was determined by an individual evaluation of the specimens per manufacturer. This process corresponds to the general experiences for the test evaluation of fatigue tests with the relative fl at slope of the S-N curve. Whereas for the cruciform joints, the slope of the S-N curve was calculated as k = 3.5 and the standard deviation of the" + ] + }, + { + "image_filename": "designv11_7_0000964_j.mechmat.2008.09.004-Figure11-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000964_j.mechmat.2008.09.004-Figure11-1.png", + "caption": "Fig. 11. A pure sear, loading surface for the case of allowing for the Bauschinger effect.", + "texts": [ + "2) give the absolute value of distance to this plane: h m \u00bc ffiffiffi 2 p sS \u00fe Dh m \u00bc ffiffiffi 2 p sS Dhm \u00bc 2 ffiffiffi 2 p sS S0 sin b; b1 6 b 6 p=2: \u00f06:3\u00de The equation of plane (line) in S1S3-plane from the range b1 6 b 6 p/2 with distance in Eq. (6.3) has the form: S1 cos b\u00fe S3 sin b\u00fe 2 ffiffiffi 2 p sS S0 sin b \u00bc 0: \u00f06:4\u00de The envelope curve of the set of lines in Eq. (6.4) is the circle, S2 1 \u00fe \u00f0S3 S0\u00de2 \u00bc R2; R \u00bc 2 ffiffiffi 2 p sS; whose center is situated at point A1 in Fig. 10. Since the loading surface is symmetrical above S3-axis, it is clear that, in three-dimensional space, we have S2 1 \u00fe S2 2 \u00fe \u00f0S3 S0\u00de2 \u00bc 8s2 S : \u00f06:5\u00de Therefore, the loading surface (Fig. 11) consists of three parts: the cone constituted by boundary planes (b = b1) located on the endpoint of the vector ~S, the initial sphere (3.23), and the sphere determined by Eq. (6.5). The subsequent yield stress, SS, in opposite direction to the vector ~S can be calculated from Eq. (6.3) as SS = h m(b = p/2): SS \u00bc S0 2 ffiffiffi 2 p sS; \u00f06:6\u00de where S0 P ffiffiffi 2 p sS. Eq. (6.6) gives the positive value of SS for S0 P 2 ffiffiffi 2 p sS, which corresponds to the so-called Bauschinger negative effect when a plastic deformation occurs even during unloading (Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003276_tasc.2013.2283238-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003276_tasc.2013.2283238-Figure3-1.png", + "caption": "Fig. 3. Analysis result of magnetic flux density contours of HTS rotor at (a) unsaturated and (b) saturated conditions. (a) Unsaturated (air-gap magnetic flux density: 0.4 T). (b) Saturated (air-gap magnetic flux density: 1.1 T).", + "texts": [ + " In order to verify the abovementioned idea, electromagnetic field analysis is carried out. Fig. 1 is modeled for 2-D finiteelement analysis (FEA). A normal conducting (copper) stator (three-phase, four-pole, distributed windings, star connection) is considered, and the rotor windings are made of HTS tapes. The air-gap length between the stator and the rotor is 0.3 mm. At present, the analysis is only available for the static condition of the rotor due to the difficulty in the characterization of the HTS. Fig. 3 shows the examples of analysis results of magnetic flux density contours. As can be seen in Fig. 3(a), clear four magnetic poles are formed at the steady (no saturation) mode (air-gap magnetic flux density: 0.4 T). On the other hand, when the rotor core is in the starting (saturation) mode (1.1 T), doubled magnetic poles, i.e., 8, further add to the four magnetic poles. This shows one of the evidences for the saturation mode reluctance torque. In other words, the reluctance torque is autonomously generated with the aid of the magnetic condition of the rotor core. Fig. 4 shows the schematic diagram of the magnet torque, the reluctance torque, and the total torque waveforms" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003331_indin.2012.6301378-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003331_indin.2012.6301378-Figure2-1.png", + "caption": "Figure 2. A schematic of rolling element bearing", + "texts": [ + " !! !!!!!! !\"# ! (1) \u2022 Outer race fault frequency: !!\"#! !! ! !! !!!!!! !\"! ! (2) \u2022 Inner race fault frequency: !!\"#! !! ! !! !\"!!!! !\"# ! (3) \u2022 Ball fault frequency: !!\"! !! !!! !! !! !! !! ! !\"#! ! (4) Where FR is the rotation speed of the inner race (with the hypothesis: the inner race rotates, and the outer race is at rest), NB is the number of balls, DB is the ball diameter, DP is the ball pitch diameter, \u03b8 is the ball contact angle. A schematic view of rolling element bearing is given in \u201cFig.2\u201d. In the following part, two approaches are given to analyze the vibration signal from a machine: the time domain techniques used for inspection, and frequency domain techniques used for diagnosis. Time domain techniques could provide an overall understanding of the vibration level as well as the distribution of the vibration data. Thus, a global assessment of the machine condition can be conducted for inspection. Some among of them we focus on are: 1) RMS (root mean square) It can provide an overall indicator of the vibration energy" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000111_j.msea.2006.05.113-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000111_j.msea.2006.05.113-Figure3-1.png", + "caption": "Fig. 3. The distribution of residual (a) x-direction and (b) z-direction stresses, and of (c) the residual y-direction displacement. Modeling parameters: laser beam scanning rate = 10 m/s, thickness of each powder layer = 0.5 mm, initial porosity of the powder bed = 33%, and no chamber preheating.", + "texts": [ + " Since the temperature gradient in the part being fabricated nduce the stress and displacement fields via the thermal strain, th, which is calculated according to the temperature field btained in the thermal analysis through the following equation. \u03b5th} = T [ \u03b1 \u03b1 \u03b1 0 0 0 ]T (6) where is the coefficient of thermal expansion (CTE), T = T - TREF, and TREF is the strain-free temperature. Thus, the total strain is defined as {\u03b5} = {\u03b5el} + {\u03b5pl} + {\u03b5th} (7) where \u03b5el, \u03b5pl and \u03b5 are elastic, plastic and total stain, respectively. Since the effects of the stress and displacement fields on the temperature field are negligibly small, the sequential fieldcoupling method is used for the thermo-mechanical simulation in the present study. Fig. 3 shows the residual X- and Z-direction stress distribution and Y-direction warping in the MMLD model forming from porcelain and nickel powders. The residual X-stresses in nickel near the nickel/porcelain interface are tensile, while the corresponding stresses in porcelain are compressive. Tensile Zstresses are present in the central region of the specimen, while compressive Z-stresses are located at edges. The warping is concave upward, and is apparently due to different amounts of deformation between the top and bottom surfaces during the MMLD process" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001065_09544062jmes1177-Figure25-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001065_09544062jmes1177-Figure25-1.png", + "caption": "Fig. 25 Temperature distribution during the welding process at two different workpiece thickness (a) 1.6 and (b) 2.0 mm", + "texts": [ + " It is seen that temperature decreases as the thickness of the workpiece increases. It is also noted that the HAZ in the x- and z-directions decreases as the workpiece thickness increases (refer Figs 24(a) and (b)). Particularly, the HAZ in z-direction (0.7 mm) is higher when compared to x-direction (0.5 mm) for the 1.6 mm thick sheet. Both the peak temperature and the temperature gradient decrease as the workpiece thickness increases; this is because the heat transfer rate is higher in high thickness workpiece compared to low thickness workpiece (refer Fig. 25). The relationship between the peak temperature values and the temperature gradient is non-linear in nature. Figure 26 shows the effects of beam incident angle on the temperature profiles for the laser power of 450W and welding speed of 1000 mm/min. It is noted that there is a slight variation in the peak temperature value as the analysis performed between lower beam incident angle (5\u25e6) and higher beam incident angle (15\u25e6). The peak temperature values attained at low beam incident angle and high beam incident angle are approximately 2417 and 2371 \u25e6C, respectively (Figs 26(a) to (c))" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003867_j.powtec.2012.11.027-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003867_j.powtec.2012.11.027-Figure1-1.png", + "caption": "Fig. 1. Dependence of the normalized density field N, at normalized times \u03c4=0.3 and \u03c4=0.49, on the normalized spatial coordinates (\u03be,\u03b7) and two-dimensional contours of the same normalized density field.", + "texts": [ + " (46) and (47) become: \u2202 \u2202\u03c4 NV\u03be \u00fe 1 \u03be \u2202 \u2202\u03be \u03beNV2 \u03be \u00fe \u2202 \u2202\u03b7 NV\u03beV\u03b7 \u00bc \u2212N\u22121 \u2202N \u2202\u03be \u00f050\u00de \u2202 \u2202\u03c4 NV\u03b7 \u00fe 1 \u03be \u2202 \u2202\u03be \u03beNV\u03beV\u03b7 \u00fe \u2202 \u2202\u03b7 NV2 \u03b7 \u00bc \u2212N\u22121 \u2202N \u2202\u03b7 \u00f051\u00de \u2202N \u2202\u03c4 \u00fe 1 \u03be \u2202 \u2202\u03be \u03beNV\u03be \u00fe \u2202 \u2202\u03b7 NV\u03b7 \u00bc 0 \u00f052\u00de For the numerical integration we shall impose the initial conditions V\u03be 0; \u03be; \u03b7\u00f0 \u00de \u00bc 0;V\u03b7 0; \u03be;\u03b7\u00f0 \u00de \u00bc 0;N 0; \u03be;\u03b7\u00f0 \u00de \u00bc 1=5;1\u2264\u03be\u22642;0\u2264\u03b7\u22641 \u00f053a e\u00de as well as the boundary conditions V\u03be \u03c4;1;\u03b7\u00f0 \u00de \u00bc V\u03be \u03c4;2;\u03b7\u00f0 \u00de \u00bc 0; V\u03b7 \u03c4;1;\u03b7\u00f0 \u00de \u00bc V\u03b7 \u03c4;2;\u03b7\u00f0 \u00de \u00bc 0 V\u03be \u03c4; \u03be;0\u00f0 \u00de \u00bc V\u03be \u03c4; \u03be;1\u00f0 \u00de \u00bc 0; V\u03b7 \u03c4; \u03be;0\u00f0 \u00de \u00bc V\u03b7 \u03c4; \u03be;1\u00f0 \u00de \u00bc 0 N \u03c4;1;\u03b7\u00f0 \u00de \u00bc N \u03c4;2;\u03b7\u00f0 \u00de \u00bc 1=5 N \u03c4; \u03be;0\u00f0 \u00de \u00bc 1 10 exp \u2212 \u03c4\u22121=5 1=5 2 exp \u2212 \u03be\u22123=2 1=5 2 \" # N \u03c4; \u03be;1\u00f0 \u00de \u00bc 1=5 \u00f054a g\u00de The equations system (50)\u2013(52) with the initial conditions (53 a-e) and the boundary ones (54 a-g) was numerically resolved by using the finite differences [36]. We present in Figs. 1\u20133 the numerical solutions for the normalized density field N(\u03be,\u03b7) \u2014 Fig. 1 for the normalized velocity field V\u03be(\u03be,\u03b7)\u2014 Fig. 2 and for the normalized velocity field V\u03b7(\u03be,\u03b7) \u2014 Fig. 3 at the normalized time sequence \u03c4=0.3 and \u03c4=0.49, both three-dimensional and two-dimensional (Figs. 1\u20133) solutions, through contour curves. By analyzing these numerical solutions, it can be concluded: i) the normalized density field is of soliton-type for \u03c4=0.3 or solitonpackage-type for \u03c4=0.49 [37] (Fig. 1); ii) the normalized velocity field V\u03be is symmetric with respect to the symmetry axis of the spatio-temporal Gaussian (Fig. 2); iii) shock waves and vortices are induced at the structure periphery for the normalized velocity field V\u03b7 (Fig. 3). In Figs. 4 and5wepresent the normalized forcefield for the F\u03be component (three-dimensional dependence and two-dimensional contour Fig. 4) and the normalized force field for the F\u03b7 component (threedimensional dependence and two-dimensional contour Fig. 5). It results that the simultaneous presence of soliton \u2014 anti-solitons (Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003005_0020-7357(68)90006-1-Figure6-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003005_0020-7357(68)90006-1-Figure6-1.png", + "caption": "FIG. 6. Influence of flank land width on the force intercepts, Feo and F8 0.", + "texts": [ + " 0 5 \u2022 0 \" 0 5 5 Lf T- / 0\" / / / /\u00b0 / / = / / / / / / / / / / , 2ool, Z: / / / / l / J Y ~ k / / x \\ / / / / / / / / 2 \" , / ///i Q / ,x Fs I00 Matl: S.A.E.4135 as received Speed : 3 8 4 f t /min Rake on(lie: 0 \u00b0 I I I I I I O I Z 3 4 5 Shear plane area , A s ( i n Z x l O -3) Fie. 4. Influence of flank land width on the machinability chart, SAE 4135. and rake angle, remain constant when large tool nose forces are present. However, the intercepts of the lines of the machinability chart on the force axis increase in proportion to the wear land width (Fig. 6). It can be argued that the whole concept of the machinability chart is false as it is based upon the assumption that shearing takes place along a single plane, whereas a shear zone exists in practice. However, in spite of this, a linear relationship exists between the cutting force, Fc and the somewhat artificial shear plane area to a good approximation. E X P E R I M E N T A L S T A B I L I T Y C H A R T The simplified machine tool system consists essentially of the lathe tool-holder shown in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002278_icelmach.2012.6349905-Figure7-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002278_icelmach.2012.6349905-Figure7-1.png", + "caption": "Fig. 7. Distribution of the magnetic flux density and magnetic flux in 3M-PC PM motor.", + "texts": [ + " A finite-element-method (FEM) magnetic field analysis is performed to clarify the basic pole-changing characteristics and to verify the feasibility of a 3M-PC PM motor. Fig. 4 shows the analytical 3M-PC PM motor model. PMs are arranged in a V-shape and embedded in the rotor core. Table I shows the motor specifications of the analytical model, while Fig. 5 shows the winding connections for the pole changing of the stator. Fig. 6 shows the magnetic property in the PMs for magnetization. We verified the pole changing of the rotor by using magnetic field analysis. Fig. 7 shows the distributions of the magnetic flux density in the motor for varying pole configurations. When all the PMs are magnetized with the same polarity, the magnetic flux forms an 8-pole distribution, as shown in Fig. 7(a). When the PMs are magnetized in the polarity opposite to their adjacent pole, the magnetic flux forms a 4- pole distribution, as shown in Fig. 7(b). When all the PMs are demagnetized, the magnetic flux due to the exciting current forms a 4-pole distribution, as shown in Fig. 7(c). Variable magnetization in the PM enables pole changing of Fig. 5. Winding connections of 3M-PC PM motor. VW W (a) 8 poles (b) 4 poles -2 -1.5 -1 -0.5 0 0.5 1 1.5 -340 -290 -240 -190 -140 -90 -40 M ag ne tic fl ux d en sit y[ T] Magnetic field[kA/m] Coercive force of variable magnetized magnet = 150kA/m 1.5 1.0 Magnetic field (kA/m) M ag ne tic fl ux d en sit y (T ) -140 -90-290 -240 -190 -40-340 0.5 0 -1.5 -2.0 -1.0 - .5 Fig. 6. Magnetic property in the permanent magnet. the PM motor. Fig. 8 shows the variable characteristics of the induced voltage" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003409_s1560354711060050-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003409_s1560354711060050-Figure2-1.png", + "caption": "Fig. 2. Sketch of an external helical mechanism (from Purcell [40]) which is the most common design for current artificial microswimmer proposals.", + "texts": [ + "3) In this S1 equivariant setting only three resistance coefficients are needed. Purcell calls the attention that for a right handed helix the coefficient B < 0, implying that \u201ca helical filament does tend to move like a corkscrew in a cork when it is rotated\u201d. 2)An earlier paper by Ludwig [34] was unnoticed then. REGULAR AND CHAOTIC DYNAMICS Vol. 16 No. 6 2011 For a sphere of radius a, it is well known since Stokes that Bo = 0, Ao = 6\u03c0\u03b7a, Do = 8\u03c0\u03b7a3. (2.4) where \u03b7 is the viscosity. How does the gauge theory of microswimming comes into play here? Consider Fig. 2. The shape space has one angular coordinate \u03b8 \u2208 S1, measuring the relative rotation between propeller and cell, varying with motor\u2019s speed \u03c9m = \u03c9 \u2212 \u03a9. For a axisymmetric cell the organism translates and rotates smoothly3). The conditions of vanishing total force and total torque are Ao v + (Av + B\u03c9) = 0, Do\u03a9 + (B v + D \u03c9) = 0 . (2.5) Purcell avoids complicated hydrodynamical calculations by imposing the \u201cadditive rule\u201d for resistance matrices, correct in first order. We present highlights of his analysis in Appendix A, requiring only high school algebra: the quantities v, \u03c9, \u03a9 and the motor torque N are expressed in terms of the motor\u2019s speed \u03c9m" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003958_j.engstruct.2014.08.030-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003958_j.engstruct.2014.08.030-Figure1-1.png", + "caption": "Fig. 1. The bearing test rig.", + "texts": [ + " IbW;T \u00f0t\u00de \u00bc 1 B1B2 Z B1 Z B2 bW;T\u00f0f 1; f 2; t\u00de 2df1df2 \u00f05\u00de where |bW,T(f1, f2, t)| is the modulus of the WB map, B1 and B2 are the integration frequency bands. The frequency bands B1 and B2 need to be adapted according to the frequencies related to bearing impacts produced by defects as well the coupling between impacts, i.e. band B1 + B2, should be present. The wavelet scalograms for no-defect and defect conditions are used to find the appropriate frequency bands for integration of the WB map. The SKF bearing test rig has a coupled VSD motor driving a shaft supported on three identical bearings (FK UCP203). Fig. 1 shows the test rig under consideration. The VSD drive provides 20\u201360 Hz supply frequency. It is possible to induce a misalignment load at the non-drive end. Pre-machined shims are required to align the test bearing. No-shims provide the maximum misalignment load. It has been estimated that 0.2 mm of downward shaft deflection resulted into 64 N of resultant radial load. Tests were conducted at full speed and full load condition. The full speed and full load condition correspond to 60 Hz supply frequency and 196 N resultant radial load" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002338_ma101121f-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002338_ma101121f-Figure1-1.png", + "caption": "Figure 1. Sketch of the sample withwave vectors k and electric fieldsE, The vectors indexed with 1,2 describe the wave inside the medium, the incident (k0, Ein) and transmitted wave (k0, E) are shown as well. The rotation of sample and holder is performed with respect to the x axis (gray arrow) of the sample frame (unprimed coordinate system), which is identical with the x0 axis of the laboratory frame (primed system). Therefore, the film surface normal is always the z axis and the inclination angle is \u03b8. The angle between the electric polarization and the x axis is denoted as \u03a6. The inset depicts the shear deformation (shear angle \u03b2) and the sample holder (dark gray) in the same reference frame.", + "texts": [ + "23-25 In this study, the orientation, molecular order, and biaxiality of different mesogen parts are analyzed with respect to shear angle in an attempt to characterize the coupling of the liquid crystal director to the elastomer network. Measurement Setup.To study the three-dimensionalmolecular order of a polymer film a Bio-Rad FTS 6000 FTIR-spectrometer is provided with a custom-made tilting apparatus containing the sample holder, that enables one to rotate the sample about a horizontal axis (x axis in Figure 1) perpendicular to the propagation direction of light (z0). Consequently, a parallel incident beam has to be used instead of a focused one to avoid the conic distribution of the wave vector. Therefore, one can choose an arbitrary combination of inclination and polarization angle by the useof awire gridpolarizer and, hence, select a special combination of electric field and wave vector. To separate the spatial contributions of the absorption ellipsoid and improve fitting by overdetermining the equation system, the tilt or inclination angle of the sample \u03b8 is varied between -60 and \u00fe60 in steps of 10 , while the polarization angle\u03a6, measured from the x axis, varies between 0 and 180 in steps of 18 , determining the electric field (E) and the wave vector (k) of the incident light", + " In contrast to usual measurements, the fingerprint region is not chosen, because of the high absorbance due to the large number of bands in this region and the thickness of the sample. For each combination of \u03b8 and \u03a6 one IR spectrum in the range of [3000, 6000] cm-1 is acquired with a spectral resolution of 4 cm-1 using a photoconductive InSb detector. Three spectra collected for different polarization and inclination angles are shown in Figure 2 to illustrate the dependence of the absorbance on \u03b8 and \u03a6. The film length corresponding to the distance of the two edges of the holder is 6 mm (see Figure 1) and the width 8.8 mm. The thickness of the sample d = 450 \u03bcm is measured with a capacitive displacement transducer (Mitutoyo, Digimatic Indicator) with a tolerance of \u223c15 \u03bcm. Furthermore, shear is applied to the samples by movable metal plates on which the sample is fixed in the preferred direction using a solvent-free glue (Figure 1). The positions of the plates are controlled with a micrometer screw, while the retracting force response can be measured by a collinearly mounted force sensor (burster GmbH). Samples. The liquid crystalline elastomer (LCE) analyzed in this study is a free-standing smectic Cmain chain elastomer film, synthesized in a two step cross-linking procedure,26,27 following the route described by Donnio et al.,16 which is an advancement of K\u20acupfer and Finkelmann.28 The chemical structure including stoichiometry is shown in Figure 3", + " Since the intensity transmitted through the sample is measured, the theoretical background, that governs the propagation of light in anisotropic dielectric and nonmagnetic media, is provided first. The transmitted intensity depends on the electromagnetic wave (namely its polarization, wavelength and intensity) as well as on the properties of the medium (indicatrix and thickness). Naturally, the relative orientation of the two also plays an important role; here, this is treated in terms of the wave vectors and the film plane surface normal (compare Figure 1). The propagation equation for electromagnetic waves inside an anisotropic dielectric medium (that can be derived directly fromMaxwell\u2019s equations13) is given, where n is the indicatrix, c0 the speed of light in vacuum, k is the wave vector, \u03c9 the frequency and E the electric field of the wave. k \u00f0 k E\u00de\u00fe\u03c92 c20 n2 3 E \u00bc 0 \u00f01\u00de The boundary conditions lead to the following continuity condition (Snell\u2019s law) in terms of the wave vectors, k; the effective refractive index, n; the reference frame of the sample, y; and the angle between the surface normal (z) and the wave vector, \u03b8 (the refractive index of the surrounding medium is set to 1, for definitions see Figure 1). k 0y \u00bc sin \u03b8 \u00bc nm sin \u03b8m \u00bc kmy \u00f02\u00de where the m(0)-indexed values correspond to the quantities inside (outside) themedium.Combining eq 1 and eq 2 enables one to find theallowedpropagationdirections (k=km) insidemedium and the corresponding electric fields.12-14 Equation 1 can thus be written as - k0, y 2 0 0 0 - k0, y 2 - kz 2 k0, ykz 0 k0, ykz - k0, y 2 0 BB@ 1 CCA\u00fe \u03c92 c02 n2 8>< >: 9>= >;E \u00bc 0 \u00f03\u00de By setting the determinant of the resulting matrix in eq 3 to zero, four complex values of kz can be found, which allow nonzero solutions forE. Generally, each of these four kz values belongs to a different effective index of refraction (compare nm in eq 2). Since two of the solutions refer to forward and two to backward propagation, the incident beam is split into the two forward beams with different propagation directions and electric polarizations (Figure 1). These \u201ceigenpolarizations\u201d do not, in general, coincide with any of the sample axes.12 In the following the different eigenpolarizations, corresponding wave vectors and effective refractive indices are indexed with i, where i \u2208 {1, 2} denotes forward propagation. In order to investigate the effects of the anisotropy on the propagation direction, in Figure 4 the propagation direction obtained by the assumption of a constant effective (and real) refractive index for both eigenpolarizations is compared with the directions obtained by numerical solutions of eq 3 for reasonable values of n", + " The sum of the corresponding absorbance values could thus be used to extract the orientation distribution. The transition dipole moment matrix can be converted into a set of eigenvalues and eigenvectors; thus, instead of the elements of \u03bc, its eigenvalues (normalized by their sum) are presented together with four spherical coordinate angles, that describe the orientation of the eigenvectors of the extremal eigenvalues in ordinary spherical coordinates (the inclination \u03b8s is measured from the surface normal corresponding to the z axis, and the azimuth \u03c6s from the x axis, compare Figure 1). Since the specificity of the IR-spectral range enables one to analyze the response of differentmolecularmoieties independently from each other, in the following, the results obtained for all 4 bands are discussed. The absorption bands 2 to 4 are perpendicular to the director and show one minor and two major axes. Therefore, their clearly different minor axis has to be compared to the major axis of band 1. Furthermore, it has to be stated, that if the distribution approaches uniaxiality, only one axis can be distinguished from the other and hence no minor axis orientation is given (compare e" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000532_50008-3-Figure7.4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000532_50008-3-Figure7.4-1.png", + "caption": "Figure 7.4: Schemes of laser treatment by remelting: (a) laser melting without alloying; (b) laser alloying by remelting of alloying layer and (c) laser alloying by remelting by powder blowing.", + "texts": [ + " Cladding also enables one metal to be joined with another, but in this case, there should be no mixing between the cladding layer and substrate. Laser alloying can be realized by laser melting of the substrate previously covered with alloying material which can be placed in the melt zone by: electroplating, vacuum evaporation, pre-placed powder coating, thin-foil application, ion implantation, diffusion, powder blowing or reactive gas shroud. The basic schemes of laser pro cessing by remelting are presented in Fig. 7.4 and the scheme of longitudinal cross-section of laser track is shown in Fig. 7.5 [9]. Laser melting can be used to create supersaturated and highly alloyed materials with novel structures. Most of the beneficial effects of laser treatment can be attrib uted to specific types of solidification fine structure. The high-melt-pool temperature, resulting from a high power density of laser beam, enables the dissolution of even thermodynamically stable intermetallic phases and the formation of metastable phases due to the high cooling rates [8,9]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000077_2006-01-0358-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000077_2006-01-0358-Figure1-1.png", + "caption": "Figure 1: Ribbon style deep groove ball bearing cage employed in the FCM.", + "texts": [ + " An extension to Gupta\u2019s [5] investigation on cage instability induced by bearing clearances is also made, but in this case for ball-guided cages, by varying the ball-to-cage pocket clearance and the results are presented using the cage instability parameter proposed by Ghaisas et al. [7]. A two-dimensional flexible cage model was developed to investigate the effects of cage flexibility on bearing performance. A three-dimensional, six degree-offreedom Dynamic Bearing Model (DBM) for deep groove and angular contact ball bearings was modified to include the Flexible Cage Model (FCM). Figure 1 illustrates the ribbon style ball-guided cage used in this investigation. To include cage flexibility in the DBM, the cage pockets are represented by lumped masses and connected in the circumferential direction by a series of springs, kc, and dampers, ccd, as shown in Figure 2. Changes in the cage pocket geometry are neglected for ease in detecting contact between the balls and cage pockets, although the deflection of the spring-damper systems between cage pockets is considered to be representative of the deflection of a cage pocket during ball-to-cage pocket contact" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000070_bf02721700-Figure6-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000070_bf02721700-Figure6-1.png", + "caption": "Fig. 6. - Extinction factor a2(= ]T/IO) aS a function of the number of reflections in the cavity.", + "texts": [], + "surrounding_texts": [ + "where -To is the beam intens i ty prior to A, a 2 is the ext inc t ion fac tor of the pai r of prisms (A and F) and fl is t he misal ignment angle between the axes of P and QW. The light signal I s is conver ted into an electrical current i(t) in a photomul t ip l ier (PM). The Four ier analysis of i(t) shows, in the first approximat ion, the following components : i) a signal at the f requency ]~ propor t ional to ~o2; ii) two signals at the frequencies ]F~IM, proport ional to the modulat ion ell iptici ty (/)o and to the ell ipticity ~Po f rom which we wish to derive An; iii) a signal a t the f requency ]F depending on the misalignment angle fl and propor t iona l to q~o; iv) a signal a t t he f requency 2]~,, propor t ional to r v) a d.c. component propor t ional to a2; vi) the spec t rum of the noise. I f we assume tha t the l imiting noise is due to pho ton statistics, it can be shown t h a t t he signal-to-noise rat io (SIqR) (components ii) to vi)) is given b y the expression ]/WoeT;t W 2qb~ where Wo is the l ight power pr ior to A, e is the q u a n t u m efficiency of the P~r h is P lanek ' s constant , c is the l ight ve loc i ty and T is t h e measu r ing t ime. Equa t i on (9) shows t.hat the modu la t ion ampl i t ude r has to be re la ted t o the ext inct ion fac tor a ~ in order to opt imize the S/~tr F o r prac t ica l reasons a good choice appears to be (10) ~o ~ ~ a~, so t ha t I T is of the order of Ion ~, as follows f rom eq. (8). Equa t i on (9) takes into account only the shot noise. I n the more general case, if we assume eq. (10), the measur ing t ime T needed to achieve a g iven S~I~ can be wri t ten as ~2 SNR2 hc T - - where ~ is the ra t io between the noise in the signal s(t) and the shot noise due to photoelect ron statistics. B y insert ing the wave- length of the mos t in tense line of the argon laser spec t rum (2~ ---- 4880 A) in fo rmula (6) and express ing the magnet ic field in units of T, the l ight power Wo in W and the to t a l opt ica l p a t h L iu km, one obtains for SNI~ ~ 1 and ~ ~ 0.25 (11) T = 70 W ~ ~Bo] h. Considering the high magnetic-f ield in tens i ty t h a t we need, a realistic possibility for the f requency ]~ seems to be (12) f~i ~ 5\"10-3 H z . 2\"1. Optica~ cavity. - F r o m lo rmul~ (11), one s~es t h a t wi th Bo ~ 10 T, Wo ~ 1 W, to detect the signM wi th a SIql~ of un i ty in one day, an opt ica l p a t h L of 1 k m is needed. F o r this reason we in tend to pe r fo rm the experimen t b y placing an optical cav i ty in which the light b e a m is reflected for several hundred t imes in a mague t a few motres long. Of course this solut ion can be accepted only if the essential character is t ics of the l ight b e a m are preserved to a tolerable degree: in par t icular , we m u s t be sure t h a t the polar iza t ion s ta te of the light b e a m is not p e r t u r b e d b y the mirrors ~ 1 and ~ 2 of the cav i ty . I f ATT(m) is the a t t enua t ion of the l ight due to the reflections, one has (13) A T T ( m ) ~ I ( m ) / I : exp [ - - m / m o ] , where I ( m ) is the light in tens i ty af ter the m- th reflection and mo is the qual i ty factor , re la ted to the mirror ref lect ivi ty R b y m0 ~ 1 ( 1 - R). Tak ing into account in fo rmula (11) the reflection losses, one arrives a t measur ing t ime T of lloyex,[ /mo] (14) T ~-- 70 W M l ' \\ B o / m ' h , where W M is the l ight power (in W) prior to M1. The above expression has a m i n i m u m for m ---- 2too; as shown in fig. 2 this m i n i m u m is quite flat, leaving the possibil i ty to opt imize for other paramete rs . To m a k e Z a few ki lometres , when l is a few metres , 2mo needs to be abou t 1000, i . e . t he mi r ror ref leet ivi ty m u s t be a round 99.8 %, a value t h a t can be reached only wi th in tefferent ia l mirrors . I t can be shown t h a t in an opt ical cav i ty consisting of two spherical mirrors of t he same focal length the reflection points will be s i tua te4 on an ellipse, a fac tor which l imits the n u m b e r of separa ted reflections considerably. Be t te r use of the mi r ror surfaces is m a d e if a cylindrical a s t igma t i sm is in t roduced into the sys tem, for ins tance b y mechanica l ly deforming one of the mirrors, as suggested by H E ~ I o T et al. (s). This deformation displaces the reflection points from the original ellipse (or circle) into a more complicated pattern (a Lissajous figure). A high number of reflections will inevitably depolarize the beam, mainly for the following three reasons: the divergence of the laser beam; the residual birefringence of the dielectric layers; the scattering processes on the surfaces. The behaviour of the cavi ty has been experimental ly invest igated by mount ing a system consisting of two concave spherical interferential mirrors (*) (5) D. R. HERRIOT and H. J. SCHULTE: AJ0~0~. O~ot., 4, 883 (1965). (*) Supplied by M.T.0., Metallisations et Traitements Optiques, 11, rue Ampere, B.P.6, 91302 Massy Cedex (France). of 11 cm diameter and 10 nl focal length, at a distance of about 2 in f rom each other. One of the mirrors had a 4 nnn hole drilled in its centre, for injection of the light beam. The simplest way to extract the beam from the cavity was to use a small (4 mm diameter) mirror (M), held in position by a mechanical system giving the necessary degrees of freedom. The cylindrical ast igmatism was created by deforming one of the mirrors (see fig. 3). I n this manner we have easily obtained tip to 1000 separated reflections on a surface of 6 \u2022 6 em 2. I n fig. 4 a pho tograph of the pa t te rn of reflections on the entrance mirrors M1 is shown; the entrance angle of the light beam and the deformation amplitude of the mirror have been chosen so tha t it was possible to extract the beam easily after 500+700 reflections (see fig. 5). The qual i ty factor mo cf the (av i ty has been measured in the following way. The direct laser light beam was a t t enua ted by calibrated ol~tical filters until it was equal in intensi ty to the light emerging from the cavi ty after m reflect ions. The filters emlcloyed give a value of the a t tenuat ion in the cavity. Tho measured a t t enua t i en ATT(m) was then fit ted with the exponential of formula (13), which gave a value of mo --~ 250 \u2022 This value agrees quite well w i t h t h e spec i f i ca t ion for t h e r e f l e c t i v i t y / i v e n b y t h e m a n u f a c t u r e r (R > 99.5 %) a n d is v a l i d for b o t h l ines 2~ ~ 5 1 4 5 A a n d 22 ~ 4880 ~, of t h e a r g o n l a se r . The d e p o l a r i z a t i o n of t i m b e a m has b e e n m e ~ s u r e 4 b y o b s e r v i n g i t s inf luence on t h e e x t i n c t i o n f a c t o r of a s y s t e m of t w o c rosse4 po l a r i z e r s w i t h t h o c a v i t y m o u n t e d b e t w e e n t h e t w o p r i sms . A q u a r t e r w a v e p l a t e was u s e d to c o m p e n s a t e t h e r e s i d u a l c l l i p t i e i t y . T h e rny t r a n s m i t t e d b y t h e a n a l y s e r was d e t e c t e d b y a p h o t o m u l t i p l i e r ( E M I 9813). To e l i m i n a t e s p o t sizc osc i l l a t ions in t h e eavi ty~ wc h a v e u sed a s y s t e m of lenses to m a t c h t h e l a se r b e a m t o t h e n a t u r a l m o d e s of t h e c a v i t y . I n t h i s w a y t h e s p o t size r e m a i n e d c o n s t a n t d u r i n g t h e re f l ec t ions w i t h a d i a m e t e r of a b o u t 2 r am. To r e d u c e t h e effect of t h e t h e r m a l g r a d i e n t s in t h e a i r , t h e c a v i t y was p l a c e d ins ide a n a l u m i n i u m t u b e . T h e whole o p t i c a l s y s t e m was m o u n t e d on a 3.8 m long g r a n i t e o p t i c a l bench . F i g u r e 6 shows t h e r e su l t s of t h e m e a s - u r e m e n t s of t h e e x t i n c t i o n f a c t o r a ~ as a f u n c t i o n of t h e n u m b e r of r e f l ec t ions . W i t h o u t a n y ref lec t ions we were ab le to o b t a i n a a -~ s m a l l e r t h a n 10 -7 (*). A f t e r (*) The prism polarizes were furnished by the Karl Lambrech t Corp., 4204 Nor th Lineoh~ Avenlt~, Chicago, Ill. 60618, USA. 2too reflections (which reduce the light intensity by e~), the extinction fac tor had worsened to 2.10-% The relevance of these results lies in the fact tha t they determine the following two experimental parameters for the set-up outlined in fig. 1: a) The modula t ion ampli tude ~)o, which will take the value of about l0 -* because of formula (10). This corresponds to a Fa raday cell angle of a maximum of 10 -3 rad, a value tha t is readily obtained in the kHz frequency region. b) The intensi ty of the light impinging on the photodetector , which will be of the order of 1 [zW if the beam intensity prior to A is 1 W. Such an intensi ty is within the linear range of sensitivity of a suitable PM tube. 2\"2. L a s e r noise. - The dominant noise source in the experimental appara tus is the laser itself. We have studied the light intensity fluctuations associated with the blue line (4880 \u2022) of a 2 W argon laser (*). Since we intend to use (~) /F ~ 1.5 kHz, we have investigated the frequency region below 2.5 kHz. (~ CR2, made by Coherent Radiation, 3210 Porter Drive, Palo Alto, Cal. 94304, USA. (~) E. IACOPII~I, P. LAZEYRAS, M. MORPURGO, E. PICASSO, B. SMITtI, E. ZAVATTIN~ and E. POLACCO: Exper imental determination o/ vacuum polarization e/leers on a laser tight-beam propagating it~ a strong magnetic ]ield, CERN proposal D2 (1980). Figure 7 shows the laser noise ampli tude at 1.5 kHz as a funct ion of the light power impinging on the detector. The laser was working at full power and the required intensi ty reduct ion was obtained with neutral density filters. The shot noise limit is indicated by the dashed line; it is reached at a few tens of n W on the detector. Above this limit the noise increases proportionally to the l ight intensity. We have tested lasers also from other manufacturers (with power up to 20 W all lines) and we have found practically the same excess p lasma noise. Figure 8 shows the comparison between the Fourier spectrum of laser light and the Four ier spectrum of light f rom a stochastic source (in this case an incandescent lamp) between 0 and 2.5 kHz. In both cases the PiV[ cathode current was fixed at 100 nA, corresponding to the expected working intensity of about 1 FW at 4880 A. The to ta l laser noise exceeds, at this intensity level, the theoret ical shot noise limit by 15 dB and this means tha t the ~ of formula (11) takes the value of 70. I n an effort to decrease this excess noise, two different methods have been employed, one working on the principle of light intensi ty stabilization (IS) and the other by common-mode rejection (C~R). I n the first method, one monitors the light intensity in a side branch derived by a 4 % beam splitter. The photocurren t is amplified and applied as a correct ion vol tage to a Pockels cell, moun ted between a quarter wave plate and polarizer prism. Wi th an a.c. coupled feedback loop, a noise reduction of about" + ] + }, + { + "image_filename": "designv11_7_0002327_iccme.2012.6275613-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002327_iccme.2012.6275613-Figure1-1.png", + "caption": "Fig. 1 Configuration of the system", + "texts": [], + "surrounding_texts": [ + "Our proposed microrobot has two motion mechanisms. One is a spiral jet motion, and the other is a fin motion. Spiral jet motion can move by rotating its body. Fin motion can move by vibrating its body. It's like a fin of the fish. We developed driving systems to realize wireless automatically locomotion of the microrobot. Proposed driving system is shown in Fig. I. This system is composed of large 3 axes helmholtz coil system and high sensitive magnetic field sensor. Large 3 axes helmholtz coil can generate uniformed magnetic field to do locomotion of the robot. High sensitive magnetic field sensor can detect position of the robot by calculating inverse problem based on theoretical magnetic field and sensor signal which is generated magnetic field by magnet in the robot. Based on the position of the microrobot, the microrobot can change orientation and velocity by" + ] + }, + { + "image_filename": "designv11_7_0002327_iccme.2012.6275613-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002327_iccme.2012.6275613-Figure2-1.png", + "caption": "Fig. 2 Large 3 axes helmholtz coil system", + "texts": [ + " This system is composed of large 3 axes helmholtz coil system and high sensitive magnetic field sensor. Large 3 axes helmholtz coil can generate uniformed magnetic field to do locomotion of the robot. High sensitive magnetic field sensor can detect position of the robot by calculating inverse problem based on theoretical magnetic field and sensor signal which is generated magnetic field by magnet in the robot. Based on the position of the microrobot, the microrobot can change orientation and velocity by Developed Large 3 axes helmholtz coil systems are shown in Fig. 2 and its specification is shown in Table I. We evaluated magnetic flux density which is generated by the coil system. This result is shown in Fig. 3. Experimental results indicated that this coil system can generate uniformed magnetic field about 0.075 meters in the center. So, the robot can stable motion in this area. III. SPIRAL JET MOnON We developed spiral jet motion to implement safety and high propulsive force of the robot. Model of the spiral jet motion is shown in Fig. 4. This robot has neodymium magnet in own body" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003309_0954406213490465-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003309_0954406213490465-Figure5-1.png", + "caption": "Figure 5. 3-DOF PUMA560 robot. 3-DOF: three-degrees-of-freedom.", + "texts": [ + "comDownloaded from In this case, smoothed QC3C and FQC3C are obtained as uQC3 \u00bcM\u00f0x1\u00dek z2 \u00fe 2 z1j j \u00fe z0j j 2=3 1=2 z1 \u00fe z0j j 2=3sign\u00f0z0\u00de ( ) z2j j \u00fe 2 z1j j \u00fe z0j j 2=3 1=2 \u00fe 0 BBBB@ 1 CCCCA \u00f041\u00de and uFQC3 \u00bcM\u00f0x1\u00deuf z2 \u00fe 2 z1j j \u00fe z0j j 2=3 1=2 z1 \u00fe z0j j 2=3sign\u00f0z0\u00de ( ) z2j j \u00fe 2 z1j j \u00fe z0j j 2=3 1=2 \u00fe 0 BBBB@ 1 CCCCA \u00f042\u00de In order to verify the effectiveness of the proposed fuzzy quasi-continuous HOSM controllers, its overall procedure is simulated for a PUMA560 robot in which the first three joints are used. The PUMA560 robot is a well-known industrial robot that has been widely used in industrial applications and robotic research. The explicit dynamic model and parameter values necessary to control the robot are given by Armstrong et al.32 The three-degrees-of-freedom (3-DOF) PUMA560 robot is considered with the last three joints locked. A kinematic description of the robot is given in Figure 5. In this simulation, the parameters of the PUMA560 robot are taken from Armstrong et al.32 These parameters are used to build the nominal dynamic model. As the robot dynamic equation described in equation (1), f \u00f0q, _q\u00de is a function of the positions and velocities that denotes unmodeled at Nat. Taichung Univ. of Sci. & Tech. on May 14, 2014pic.sagepub.comDownloaded from dynamics including friction terms and external disturbances and so on. Therefore, the uncertainties used in this article can be described by f \u00f0q, _q\u00de \u00bc 8:1 _q1 \u00fe 10:02 sin\u00f03q1\u00de \u00fe 10:2\u00f0 _q1\u00de 14:2 _q2 \u00fe 13:2 sin\u00f02q2\u00de \u00fe 8:1 sin\u00f0 _q2\u00de 10:1 _q3 \u00fe 12:15 sin\u00f0q3\u00de \u00fe 10:15 sin\u00f0 _q3\u00de 2 64 3 75 \u00f043\u00de Matlab/Simulink is used to perform all simulations with the sampling time set at 10 3s" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000648_bf03027056-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000648_bf03027056-Figure3-1.png", + "caption": "Fig. 3. Contact kinematics.", + "texts": [ + " The trajectory computation provides the target trajectory for the auxiliary bearing and should assure a smooth tran sition from free rotor motion to a state of permanent contact, which can be formulated as: with arg min f(x) = value of x that minimizes f(x) , q the generalized coordinates of the rotor and the auxiliary bearing, gN the distance between the contact points and qad the target trajectory for the auxiliary bearing. The relative velocity of the contact point in tangential direction gT will not be taken in consideration in Eq. (1) because a non-sliding contact would cause a backward whirl, which is not wanted. In order to define the essential geometrical varia bles a cross section of the auxiliary bearing and the rotor is shown schematically in Fig. 3. The origin of the coordinate system coincides with the center of the undeformed rotor, f r is the position vector to the center of the deformed rotor (in the cross section) and fa to the center of the auxiliary bearing. The air gap in the auxiliary bearing is called ao and f N represents the vector from the center of the auxiliary bearing to the center of the rotor. Additionally we introduce the polar angles rpa and rpr of the vectors fa and f r . The desired position of the a u x 1 a r y (1)_ argmin {gN qad - (ij, ij, q)", + "\" The feedback controller assures a permanent contact with low contact forces. To keep the principal purpose in mind, the control scheme also has to limit the rotor amplitude, as a passive auxiliary bearing does. In a first approach a cascade control is used, see Fig. 2, with qa the measured position of the auxiliary bearing and qad the desired one, qr are the coor 2. Feedback control concept bearing is chosen in a way that the contact point coincides with the point of the surface of the rotor which is farthest from the origin of coordinate system, fig. 3. This means that qJa desired = qJr (2) tion: (6) where fc is the control force, K p, K D and K1 are coefficients and e the tracking error: Furthermore the desired polar radius IrN desired I is needed to determine the desired position of the auxiliary bearing according the equation (3) (7) The coefficients of the control law are chosen for the linearized system for both operation states (separated or in contact) and were optimized using numerical simulations. Note that in case of contact the integral part of the controller is set to zero" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003499_s11771-013-1495-x-Figure7-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003499_s11771-013-1495-x-Figure7-1.png", + "caption": "Fig. 7 Model with seven teeth", + "texts": [ + " [6\u20137], in which all degrees of freedom of the gear are fixed, and the torque on the pinion about its rotation axis is applied. We would like to take this method as the loaded analysis, not a loaded meshing simulation. To achieve this, we give an angular displacement on the coupling point of pinion, which is about the rotation axis, so the gear can rotate with the pinion by the contact ratio; the torque is applied on the coupling point of gear, and the degree of freedom about its rotation axis should be released, as shown in Fig. 7. J. Cent. South Univ. (2013) 20: 354\u2013362 359 When the contact ratio is larger than two, it means that there are three teeth in contact at the same time. In this situation, a seven teeth model is required, because five teeth are not enough to research transmission errors and load distribution factor. 3.2.1 Outputs for transmission errors of face-gear drive During the loaded meshing simulation, the loaded transmission error is computed at every rotation position. The angular displacements of the pinion and gear are recorded at any moment of simulation" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002567_j.triboint.2012.10.025-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002567_j.triboint.2012.10.025-Figure2-1.png", + "caption": "Fig. 2. Schematic view of the four bar linkage used for the experimental tests.", + "texts": [ + " Oil lubrication is not used, nonetheless the interface between the seal lip and the shaft cannot be assumed to be perfectly dry as some oil residue, due to the mounting and installation of the system, might have been present. Same procedure was adopted for the loading through the wedge. The experimental apparatus conceived for these experiments comprised the housing, a leverage system for moving the probing shaft or the wedge, and the seal. The leverage system used to apply the radial force is shown in Fig. 2; such leverage is based on a self-balanced four-bar linkage with compliant hinges. A compliant design type was Wedge Heating system Radial lip seal Housing to the shaft, (b) force applied to the wedge. The radial lip seal is positioned in the necessary because the friction in traditional revolute joints, although small, could have affected the precision of the measurements. Also visible in Fig. 1 is the electric resistance employed to reach the desired temperature regime. This resistance was positioned circumferentially close to the oil side of the seal, and a thermocouple measured the temperature under the lip, with a resolution of 0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000934_taes.1974.307798-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000934_taes.1974.307798-Figure3-1.png", + "caption": "Fig. 3.", + "texts": [ + " (37) The solution to this equation is p(t) = Z(t, to)q0 + ft Z(t, r)f(r) dT (38) IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS JULY 1974454 q, q2 q3 q4 Y = -q2 q1 -q3 {l3 -q4 q1 q2 -q4 q3 -q12 q Also introduce a related matrix Z, -q3 -q4 q4 -q3 qI q2 -q2 ql Denote the integral term in (38) by r(t). Then, comparing (36) and (38), we may write p(t) = q(t) + r(t) . By definition, lIq(t)ll= 1 (39) O A4 = LO(40) We assume 1r(t)IIU.I (41) A geometrical analog in two dimensions for the quaternion perturbation is shown in Fig. 3. The quaternion q is always confined to the circumference of a circle of radius 1. The perturbation r may be in any direction with equal likelihood. Given only the vector p, without being able to make reference to q, the only way we can tell that a perturbation has occurred will be from the fact that IIPII+1 . (42) Since there is no way we can estimate the angular deviation of p relative to q, the only realistic correction we can make is to rescale p back to the circumference of the unit circle in such a way that the angular deviation is equally likely to be positive or negative", + " (50), and (51) are actually substituted into (56), and that result is then entered into (57), one finds that where Y' and Z', respectively, denote the transposes of the matrixes Y and Z. One may verify directly that Y' and Z' are also, respectively, the inverses of Y and Z. Equation (54) is actually analogous to (5) of Part I. That is, let the perturbed version of A4 be called B4. Then (54) may be rewritten where 14 represents the 4 X 4 identity matrix and H4=Y Y+Z'Z . (56)4 r r S4 = 2(qlrl + q2r2 + q3r3 + q4r4)4 (59) Therefore, if the elements of 54 are positive, it means, referring back to Fig. 3, that the tip of r lies outside the unit circle. Similarly, if S4 has negative elements, it means that the tip of r lies within the unit circle. At the same time, the associated drift error could equally likely be in either direction. We can now readily see that our proposed correctional procedure, represented by (43), will have the effect of reducing S4 to zero. Furthermore, while this procedure will not drive U4 to zero, it will, in fact, almost always reduce the norm of U4. At worst, in a few situations (i" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003169_0369-5816(65)90020-7-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003169_0369-5816(65)90020-7-Figure1-1.png", + "caption": "Fig. 1. Vessel geometry.", + "texts": [ + " a = mean rad ius of nozzle , A = mean rad ius of shel l , A s = mean rad ius of shel l containing a pad r e i n - fo rced nozzle , Ap = mean rad ius of shel l plus pad containing a pad r e in fo r ced nozzle , t = nozzle wall th ickness , T = shel l wall th ickness , T s = shel l wall th ickness of shel l containing a pad r e in fo r ced nozzle , Tp = shel l plus pad wall th ickness of shel l containing a pad r e in fo r ced nozzle , p = l imi t p r e s s u r e , p* = l imi t p r e s s u r e of unpie rced shel l , P =p/p* , d = 2a, D = ~bi= ~b.= ~o = X O = 5 p = % = 2 A , mer id i an angle to nozzle in te rsec t ion , mer id ian angle to outer edge of r e in fo rce - ment pad, mer id i an angle to shell hinge c i rc le , dis tance f rom nozzle junct ion to nozzle hinge c i rc le , = nozzle thickening factor , = shell thickening factor , = Tp /Ts , ~ . - dPi, yield s t r e s s in uniaxial tension. 3. ANALYSIS The geometry under cons idera t ion is shown in fig. 1. The ma te r i a l is assumed to be perfect ly plast ic and t ime effects are not considered. The T r e s c a c r i t e r i on of yielding is a ssumed to gove rn the ma te r i a l together with the s implif ied yield surface suggested by Drucker [2] which is shown in fig. 2. With this yield surface, the hoop moment M~b is cons idered insignif icant which is a valid assumpt ion except for reg ions of the shell r e la t ive ly near the axis. The t r a n s v e r s e shear force does not affect the yield surface, but is important in the equi l ibr ium equations", + " In the following, a lower bound to the l imi t p r e s s u r e is found using the equi l ib r ium equations, the c i r c umsc r i be d yield surface and the lower bound theorem. The lower bound theorem may be stated as follows [8]: \"Any sys tem of forces and moments which sa t i s f ies the equi l ibr ium equations and has no components outside of the yield surface, cons t i - tutes a lower bound to the l imi t load\". The effect of geometry change on the equi l ib r ium condit ions is neglected. The equi l ib r ium equations for the ax i symmet - r ic shell of revolut ion (see fig. 1) are [9] d(N~br 0) dd) - N o r 1 cos ~ - Q s r o = 0 , (la) d(Mqsr 0) ddp - M ~ r 1 cos ~b - Q s r l r o = 0 , (lb) d(Qsro) N~br 0 + NOr I sin q5 + d ~ - PrOrl \" (Ic) Introducing the local radius, differentiating, and dropping (Ic) in favor of the equation of vertical equilibrium, eqs. (I) become N~b sin ~b + Qs cos dp = \u00bdPA sin q5 , (2a) d(NqS) d--~- sin 0 + (Nq5 -N O ) cos q5 - Qs sin q5 = 0 , (2b) d(M~b) dq~ + (M4) -MO) cos ~b - A Q s = 0 . (2c) It is r equ i red to find a solution to eqs. (2) valid f o r a s t a t e of i nc ip i en t p l a s t i c c o l l a p s e " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003112_2013.40500-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003112_2013.40500-Figure2-1.png", + "caption": "FIG. 2 Force system acting on a baked wheel.", + "texts": [ + " Equilibrium equations pertaining to forces acting on wheels can also be found in recent publications (9, 10, 11, 12); therefore they are omitted from this paper. However, it should be emphasized here that these equilibrium equations cannot be solved unless an 305 appropriate pressure distribution func tion is known: Braked Wheel If a moment (M) is applied to the wheel in an opposite sense to the direction of the motion, the wheel is braked. The sense of the frictional forces also will reverse. When slip or failure occurs, the resultant will be tangent to the friction circle at the left. Force system acting on a braked wheel is shown in Fig. 2. Towed W h e e l s T h e case of the towed wheel is very similar to that of the braked wheel. A towed wheel us ually moves with a certain magnitude of negative slip; therefore, a moment opposite since that of the direction of the motion must be present. In this work, slip (s) is denned as follows: S = 1 - da/dt where da and dt are actual and theo retical distance of locomotion, respec tively. TEST FACILITIES AND PROCEDURES To obtain actual pressure-distribution curves for rigid wheels under variable loading, slip and soil conditions, a spe cial apparatus was built (Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002978_pime_conf_1967_182_410_02-Figure11.4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002978_pime_conf_1967_182_410_02-Figure11.4-1.png", + "caption": "Fig. 11.4. Plan and elevation of conjunction zones", + "texts": [ + " Such parts of the surfaces will approach more closely, thus increasing the overall capaciProc lnstn Mech Engrs 1967-68 tance beyond that corresponding to the original undistorted contours. Such an effect will be more serious for high conformity geometries than for arrangements like the crossed cylinders machine. In view of this possibility, a more extended analysis was pursued, taking into account the specimen distortion outside the contact zone. Calculation for inter-specimen capacitance The deformed shapes of the disc and the ring and the distribution of the oil are assumed to be similar to those shown in Fig. 11.4. The inlet is assumed to be full of oil while the outlet has adhering films of thickness hJ2. The separation between the surfaces outside the parallel zone at a distance r from the centre of the contact is given by h,+l where 1 = -(tan y - y f y tan2 y ) This expression takes into account the Hertzian displacement of points near to the contact. The dielectric constant of the oil is assumed to be 2.4 in the zone of high pressure when r < a. The constant is taken to be 2.3 in the lowpressure zones where r > a" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003609_9780470929421.ch1-Figure1.1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003609_9780470929421.ch1-Figure1.1-1.png", + "caption": "FIGURE 1.1 Relation between adsorption energy of hydrogen atom and activation energy. (Plot adapted from Horiuti and Polanyi [8].)", + "texts": [ + " Published 2011 by John Wiley & Sons, Inc. 1 Br\u00f8nsted\u2019s \u03b1 and the transfer coefficient introduced by Erdey-Gruz and Volmer [7] to explain the slope of the Tafel plot obtained for electrochemical hydrogen evolution [7]. The meaning of Eq. (1.2) was explained by Horiuti and Polanyi [8] for a wide variety of proton transfer reactions when they represented the reaction path by a scheme of two approximately parabolic curves for the initial and final states, their intersection being the transition state (Fig. 1.1). The relative slopes of the two curves at this intersection gave the value of \u03b1 . They pointed out that this model could be applied to the proton transfer from a hydroxonium ion to a metal surface in the electrochemical process of hydrogen evolution. Although they discussed the effect of the metal\u2013hydrogen bond strength on this process, this did not lead them to derive a volcano curve because they did not consider the effect of the coverage of the surface by hydrogen atoms. Dogonadze, et al. [9] criticized the work of Horiuti and Polanyi because they used a quasi-classical approach" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003118_019-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003118_019-Figure1-1.png", + "caption": "Figure 1. Experimental device for the study of the spring\u2013mass system. Note that two plates hold the upper coil spring.", + "texts": [ + " The series consists of seven springs with different natural lengths l0 (see table 1), which have a constant diameter = 1.63\u00d710\u22122 m and their coils are in contact (that is, there is no separation h between the coil steps, h = 0). Different measurements were carried out on these springs in order to study the behaviour of the \u03c9, k and \u03b3 variables as a function of the natural length l0. The natural length of the springs was measured with a caliper and their masses were measured with a digital scale (OHAUS Adventurer AR0640). We used the experimental assembly shown in figure 1 for measuring the physical variables of the spring\u2013mass system (\u03c9, k and \u03b3 ). Two steel plates of 2 mm thickness were attached to a table, in the middle of which the upper coil of the spring was placed. This coil was fastened with screws to prevent external vibrations that could affect the measurements. In order to find the elastic constant k, we used a tape measure to determine the elongation x undergone by the spring when a mass m was suspended at its free end. Doing a graphical analysis of the applied force F = mg as a function of the spring elongation x, the elastic constant k was found" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003869_s00419-012-0608-6-Figure10-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003869_s00419-012-0608-6-Figure10-1.png", + "caption": "Fig. 10 The mode shapes corresponding to frequency \u03c921 (the first mode)", + "texts": [], + "surrounding_texts": [ + "As mentioned earlier, in the geometrical model of the gear, the geometry of the teeth is omitted. It allows us to reduce the system\u2019s FE model size. The simplified geometrical model of the system consists of five sectors (see Fig. 1) that have the cyclic symmetry feature. Each of these segments is meshed by using standard procedures of the ANSYS software. The 3-D solid mesh is elaborated and as mentioned earlier, the ten-node tetrahedral element (solid92) with three degrees of freedom in each node is used to realize each sector. During the mesh generation process, it is assumed that the maximum length of each element\u2019s side needs to be no more than 2.7 [mm]. The developed FE model is displayed in Fig. 2, and it consists of 19,620 elements and 36,188 nodes, respectively. The particular sectors are glued as a whole at the geometrical model preparing the stage by using standard procedure of the ANSYS program. The analysed gear is mounted in the roller bearings. Such bearings typically have slight load capacity under loads perpendicular to the primary supported direction. The gear shaft neck surfaces on which the bearings are assembled are denoted \u201cbearing\u201d (see Fig. 3a). The gear mates with the other devices by the splines. The splines is simplified down to a regular cylinder of the diameter assumed as equal to the splines pitch diameter. The surface denoted \u201cjoint\u201d (see Fig. 3a) is located on the pitch diameter of the splines. Parameters of the analysed system are shown in Table 1a\u2013b. The calculation results for natural flexural oscillations taking into account angular speed of the gear are shown in the paper. In the case of circular discs and annular plates, for each solution where nodal lines are nodal diameters, one obtains two identical arrangements of straight nodal lines, rotated by an angle of \u03b1 = \u03c0/(2n) one to another, where n is the number of nodal diameters. In accordance with the circular and annular plate vibration theory [5,6,12], the particular natural frequencies of vibration are denoted as \u03c9mn , where m refers to the number of nodal circles and n is the mentioned number of nodal diameters. As the shape of the gear model is fairy elaborate, the flexural modes of the system are subject to deformation (as compared to the system without any holes) to such extent that establishing which particular node it refers to becomes rather difficult. This problem is even worse if the angular speed of the gear is varying. The problem of influence of the angular speed on the flexural gear models deformation is analysed. For the purpose of identification of these modes, an algorithm of tagging oscillation modes, which determines the correspondence between vibration of the circular disc versus disc with holes, is used. For this purpose, an auxiliary model of annular plate in the form shown in Fig. 3b is used. The geometrical dimensions of the auxiliary model were taken from the gear geometry (shown in Fig. 1). They are as follows: addendum circle diameter dz , rim mounting diameter dp, root circle diameter dw2, and thickness h p and hz (see Table 1). Dynamic analysis is performed for the auxiliary model cases rotating at predetermined angular speed, where diameter of though holes d01 (see Fig. 3b) varies as seen in Table 2. Findings are compared to each other both quantitatively and qualitatively. This method makes it possible to investigate deformations of nodal lines associated with nodal diameters and circles due to through holes and then determine correspondence between oscillation modes of solid circular disc and a plate with holes. In the final step, solutions found for the auxiliary model are compared with the solution for the system whose FEM model is shown in Fig. 2 (the principal model). As for the principal model case, the 3-D solid mesh and the ten-node tetrahedral element (solid92) are used to discretize the auxiliary models. For all models subject to analysis, the boundary conditions were applied to the nodes. For each model, 1 d f associated with node radial displacement was subtracted from the nodes found on the surface identified as a bearing (see Fig. 3a,b). Furthermore, 1 d f associated with the displacement of nodes along the centreline of each model was subtracted from the nodes found on the surface, identified as a joint (see Fig. 3a,b). For the models obtained in this way, calculations were kept conducted as long as the natural frequency \u03c918 was determined. The calculations were performed assuming that the systems rotate as angular speed of \u03b8 , within the range of 0\u20131047 [ rad/s]. During the computing process, the angular speed values were gradually increased by 80[ rad/s], which made fourteen variants of the results (the natural frequencies and corresponding natural modes), which were subject to further interpretation. The rotation effect was taken into account by determining stress distribution due to rotation, for each model during the computational step associated with static analysis (the so called pre-stress effect). This stress distribution was then included in the computation step associated with modal analysis. The results of the numerical calculations related to the procedure of identifying deformed natural modes of flexural vibration of the gear under consideration are shown below. The results displayed here relate to the determination of the correspondence between the natural frequencies \u03c916 and \u03c925 at high angular speed (\u03b8 = 1047 [ rad/s]) as well as to the correspondence between oscillation modes and the natural frequency \u03c931 at lower angular speeds (\u03b8 = 80 [ rad/s]). The results as shown in Figs. 4, 5, 6, 7, 8, 9 allow for tracking deformations of nodal lines associated with nodal circles and diameters, due to varying diameter of the through holes. With respect to the natural frequency \u03c925, there is marked difference in shapes of natural modes. When one compares the results between each other, one can notice that in order to identify correctly deformed natural modes of the flexural oscillations in the gear under consideration at lower angular speeds, larger number of auxiliary models is required to be included during calculations, as compared to the higher angular speeds. It comes from the fact that additional stresses through the centrifugal effects appear. This effect causes the gear flexural stiffness to be an apparent function of rotational speed (stiffness grows for higher speed). In the next part, results of the numerical calculations associated with the extent of the influence of the angular speed to deformation of mode shapes of oscillations. For each discussed case, both mode solutions related to nodal diameters are shown. These analysed results are sorted by the order of their occurrence. For the frequencies \u03c923 and \u03c918, the results were obtained at angular speeds of \u03b8 = 0 and \u03b8 =1,047 [ rad/s] respectively. For the other cases, results were obtained at angular speeds \u03b8 of, 0, 320, 720, and 1,047 [ rad/s], respectively. Natural frequencies for these modes are included in Table 3. To determine this mode (see Figs. 10, 11), the procedure of tagging natural oscillation modes was required. Nodal lines associated with the circle and diameter are deformed. Minor influence of the angular speed to deformation of the nodal lines is noticeable. The task of determining modes in this case was not too difficult (see Figs. 12); no procedure of tagging natural oscillation modes was required. The slight impact of the gear angular velocity on the distortion of the nodal lines is observed. For these modes (see Figs. 13, 14), procedure of tagging natural oscillation modes was required. It is noticeable that angular speed affects markedly deformation of the nodal lines. Once the angular speed of 720 [ rad/s] is exceeded, the oscillation mode takes different shape. Major deformation of mode shape attributable to the shaft vibrations is evident at this speed. Moreover, additional problem associated with some similarity of the mode being tagged to the mode associated with frequency of \u03c931, emerged during mode identification. Establishing the correspondence between these modes was a complex task (see Figs. 15, 16) due to the shape of oscillation modes similarity to the case discussed earlier. The angular speed affects deformation of nodal lines markedly. Major shape mode variations emerge at \u03b8 = 400 [ rad/s]. The identification process in this mode was not easy (see Figs. 17, 18) . One can notice that angular speed affects the deformation of nodal lines. Major variation in mode shape emerges at \u03b8 = 720 [ rad/s]. Moreover, additional annular shaft vibration emerges at the highest considered angular speed. Finding correct correspondence between the modes in this case was fairly easy (see Figs. 19). High repeatability in deformations of nodal lines on circular plate at various angular speeds is noticeable. As a consequence of the conducted analysis (see Table 3), the Campbell diagram was plotted for the gear under consideration. This is a convenient method of displaying the relationship between gear natural frequencies and transmission system excitations [4]. Excited frequencies are plotted on a vertical axis, and the gear speed of rotation is plotted on the horizontal axis (see Fig. 20). Natural frequencies achieved from numerical analysis are plotted as near-horizontal curves. The forced frequency due to the meshing is determined by the following relation (as in Ref. [4]) f = n0 \u00b7 z 60 (4) where n0 [rpm] is the rotational speed and z is the number of teeth in the gear. For this system, the gear teeth number is z = 59. Vibration resonance phenomenon occurs when forcing frequency (4) matches as to its value with some natural oscillation frequency of the gear. The points where the near-horizontal \u03c9mn curves intersect the straight line (4) indicate the speeds at which the gear resonance will be excited (see Fig. 20). For instance, the rated excitation speed for the natural frequency of \u03c923 is 764 [rpm]. It may be inferred from both the Campbell diagram and Table 3 that the rotating movement makes flexural stiffness of the gear under consideration to increase. Moreover, at speed of 3,820 [rpm], one can notice major surge associated with the mentioned earlier changing of the shape of the natural mode frequency in the case of the frequency of \u03c931. The growth of the gear transversal stiffness observed during gyrate of the gear comes from the appearance of the additional stresses in the toothed gear through the centrifugal effects. The higher rotational speed generates higher centrifugal forces, higher stress level, thereby causing the transversal stiffness of the system to increase. Moreover, the growth of the gear flexural stiffness through the gyrate effect causes reduction of the needed numerical calculations connected with identifying the proper distorted mode shapes." + ] + }, + { + "image_filename": "designv11_7_0002381_j.electacta.2012.01.114-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002381_j.electacta.2012.01.114-Figure5-1.png", + "caption": "Fig. 5. Schematic representation of bioelectrocatalysis based on a whole bacterial cell. (1) Outer membrane; (2) cytoplasmic membrane; (3) cytoplasm; (4) porin; and (5) periplasmic space.", + "texts": [ + " Bacterial electrocatalysis In 1992, one of my students had trouble extracting an enzyme from bacterial cells, which led us to the unexpected observation that the whole bacterial cell itself produced a clear bioelectrocatalysis current [26]. After the observation I learned that many gram-negative bacteria have several kinds of redox enzymes in their periplasmic spaces located under the outer membranes, and that the substrates of the enzymes are able to approach the enzymes from the outside of the cells through the channel proteins (porin proteins) existing in the outer membranes. Then, I understood the bacterial bioelectrocatalysis as the scheme illustrated in Fig. 5, and in fact found that many kinds of gram-negative bacteria produced bioelectrocatalysis currents due to the catalytic action of the periplasmic enzymes for glucose, fructose, glycerol, nicotinic acid, and ethanol [16,27]. The magnitude of the catalytic currents was much larger than anticipated and was comparable to those of the currents obtained with the enzymes extracted from the bacterial cells. Acetobacter pasteurianus NP2503 (the strain lacking alcohol ica Acta 82 (2012) 158\u2013 164 161 p r i i b c a a a o p t k z e q o t c t b i o f T f 3 i a a a a s w l K e 6 o w 6 i ( c e a d d N t ( fi t t i c t i t o T" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003434_s2301385014500034-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003434_s2301385014500034-Figure5-1.png", + "caption": "Fig. 5. Schematic representation of the Qball-X4.", + "texts": [ + " The second part is the geometry that relates the generated thrusts to the applied lift and torques to the system. This geometry corresponds to the position and orientation of the propellers with respect to the center of mass of the Qball-X4. The third part is the dynamics that relate the applied lift and torques to the position (P), velocity (V) and acceleration (A) of the Qball-X4. The subsequent sections describe the corresponding mathematical model for each of the blocks in Fig. 4. 2.3. Geometry A schematic representation of the Qball-X4 is given in Fig. 5. The motors and propellers are configured in such a way that the back and front (1 and 2) motors spin clockwise (thus inducing two counterclockwise torques on the body) and the left and right (3 and 4) spin counterclockwise (thus inducing two clockwise torques on the body). Each motor is located at a distance L from the center of mass o (0.2m) and when spinning, a motor produces a torque i which is in the opposite direction of motion of the motor as shown in Fig. 5. The origin of the body-fixed frame is the system's center of mass o with the x-axis pointing from back to front and the y-axis pointing from right to left. The thrust Ti generated by the ith propeller is always pointing upward in the z-direction in parallel to the motor's rotation axis. The thrusts Ti and the torques i result in a lift in the z-direction (body-fixed frame) and torques about the x-, y- and z-axis. The relations between the lift/torques and the thrusts are uz \u00bc T1 \u00fe T2 \u00fe T3 \u00fe T4; u \u00bc L\u00f0T1 T2\u00de; u \u00bc L\u00f0T3 T4\u00de; u \u00bc 1 \u00fe 2 3 4: \u00f02\u00de Fig", + " The torque i produced by the ith motor is directly related to the thrust Ti via the relation of i \u00bc K Ti with K as a constant. In addition, by setting Ti \u00bc Kui from (1), the relations in (2) can be written in a compact matrix form as: uz u u u 2 664 3 775 \u00bc K K K K KL KL 0 0 0 0 KL KL KK KK KK KK 2 6664 3 7775 u1 u2 u3 u4 2 664 3 775; \u00f03\u00de where uz is the total lift generated by the four propellers and applied to the quadrotor UAV in the z-direction (bodyfixed frame). u , u , and u are respectively the applied torques in -, -, and -directions (see Fig. 5). L is the distance from the center of mass to each motor. 2.4. The payload releasing mechanism For the purpose of payload drop, a servo motor is used in a simple configuration and is installed under the quadrotor battery bay, as shown in Fig. 6. The PWM signal generated by Gumstix computer controls the servo motor to push/pull the metallic rod attached to servo horn. On the other hand the payload\u2014an empty battery weighing 300 g\u2014is hooked to the above mentioned metallic rod and can be dropped at the desired time" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000794_iros.2008.4650584-Figure9-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000794_iros.2008.4650584-Figure9-1.png", + "caption": "Fig. 9: Line Landmark Illustration", + "texts": [ + " Using not only the last scan data sk, but the last sk\u2212n latest scan data (7 second buffered data or 280 hundred scans) from the ring buffer explained on section IV.2, road edges were extracted. Then straight line segments were determined based on the small eigenvalue of the covariance matrix constructed with the set of edge points extracted from the road. If the computed small eigenvalue was lower than a threshold, then straight line was computed. Correspondence between extracted lines and the previously constructed map was made for position and orientation correction. Figure 9 shows the notation used for landmarks. Observation of the ith landmark is 2 dimensioned vector given by a range ri and a bearing \u03b8i: zr = ( r\u2212 xcos(\u03c6)+ ysin(\u03c6) \u03c6 \u2212\u03b8 ) The Jacobian of the observation model is given by \u2206Hr = ( \u2212cos(\u03c6) \u2212sin(\u03c6) 0 0 0 \u22121 ) and the covariance matrix considers independent errors between range and orientation and is given by the diagonal matrix Rr = ( \u03c32 zr 0 0 \u03c32 z\u03b8 ) . Landmark observations correct vehi- cle\u2019s position and orientation. The general scheme of vehicle localization is shown on figure 10" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001979_j.optlastec.2010.07.011-Figure8-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001979_j.optlastec.2010.07.011-Figure8-1.png", + "caption": "Fig. 8. Boundary conditions.", + "texts": [ + " The model is based on the finite element model approach [1\u20134]. The heat Eq. (3) is solved in a quasisteady state. Considering the symmetry of the problem, only one half of the part is modelled. A term of advection deriving from the relative speed Vs between the laser and the part is taken into account: r\u00f0T\u00decp\u00f0T\u00deVS @T @x \u00bcr\u00f0l\u00f0T\u00derT\u00de\u00feq \u00f03\u00de jimp \u00bc h\u00f0T T1\u00de\u00fees\u00f0T4 T4 1\u00de \u00f04\u00de jG8 \u00bcj\u00feh\u00f0T T1\u00de\u00fees\u00f0T4 T4 1\u00de \u00f05\u00de where q is the power per unit volume and j the power par unit surface. The boundary conditions are as follows (Fig. 8): nd ( Tab Pair P Sw Sw P Heat flux for boundaries 3, 6, and 7 (4); Thermal insulation (symmetry) for 5; Convective flux for 2; Ambient temperature for boundary 1; Global heat transfer between the system considered and the surrounding media and heat flux for boundaries 4 and 8 (5). A specific heat flux is selected to take into account the input energy of the part through the welding process. The equations governing this input are called equivalent heat source. The choice of an appropriate heat source and its associated parameters is essential for a correct prediction of the molten zone shape" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001065_09544062jmes1177-Figure6-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001065_09544062jmes1177-Figure6-1.png", + "caption": "Fig. 6 Finite-element model of laser welding", + "texts": [ + "comDownloaded from reaches the boiling point of the steel substrate [12]. The convection and radiation loads are simulated as surface loads on the element-free faces, specifying the film coefficient, ambient temperature, and emissivity of the material. Temperature-dependent material properties of AISI304 stainless steel are specified to conduct the non-linear transient thermal analysis. The whole solution domain is discretized into uniform eight-node hexahedrons consisting of 14 927 nodes and 18 362 elements as shown in Fig. 6. The accuracy of the finite-element method depends upon the density of the mesh used in the analysis. The temperature around the laser beam is higher than the boiling point of the material, and it drops sharply in regions away from the molten pool. Therefore, in order to obtain the correct temperature field in the laser irradiation region JMES1177 \u00a9 IMechE 2009 Proc. IMechE Vol. 223 Part C: J. Mechanical Engineering Science at Purdue University on May 21, 2015pic.sagepub.comDownloaded from it is necessary to have a more dense mesh close to the weld area while in regions located away from weld area a more coarse mesh is used" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000055_978-1-4684-1500-1-Figure5.2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000055_978-1-4684-1500-1-Figure5.2-1.png", + "caption": "Figure 5.2 A standard gripper mechanism can be customized through the addition of fingers. Properly designed attachments still retain the sensory capability of the basic gripper. (from IBM 7565 Specification Booklet)", + "texts": [ + " At present, there are two exceptions to this policy: the IBM 7565 and DEA's PRAGMA, both of which are supplied with grippers fitted with sophisticated sensing technology. Figure 5.1 shows the integral tactile and optical systems of the IBM 7565 gripper. The PRAGMA has a similar capability, which includes force sensing on its wrist. Currently, there are no industrial standards for the fixing holes of end effectors, so every gripper must have a different set of mounting holes to suit each robot. Although a gripper can be configured to a specific task, the mechanisms used to operate them are similar. The grippers are then customized through 'add on' fingers (Figure 5.2). It is usually assumed that a gripper has no independent degrees of freedom, as it is anticipated that all degrees of freedom are provided by other robot elements (eg the wrist and/or arm). It has been recognized, however, that certain devices (eg autoscrewdrivers) will, because of their inherent degrees of freedom, duplicate certain robotic capabilities. 54 Grippers whilst the force sensors can be used to detect presence, measure exerted pressure and for component detection. (from IBM 7565 Specification Booklet) Sophisticated gripper versus simple gripper The tasks performed during assembly often require precise movements of the objects being assembled" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000964_j.mechmat.2008.09.004-Figure8-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000964_j.mechmat.2008.09.004-Figure8-1.png", + "caption": "Fig. 8. Elementary volume of planes expressed in terms of angles ~a, ~b and k.", + "texts": [ + "29) holds because orientations of planes do not change during their displacements. If a plane in S3 is on the endpoint of vector ~S 2 S3, then hm \u00bc~S ~m. Therefore, Eq. (3.26), together with Eq. (3.28), takes the form ruN \u00bc~S ~m cos k ffiffiffi 2 p sS: \u00f03:30\u00de Plastic strain increments components and total strain components from Eqs. (3.24) and (3.25), for the case~S 2 S3, can be written as deS k \u00bc uNmk cos k; dV ; \u00f03:31\u00de eS k \u00bc Z ~a Z ~b Z k uNmk cos k cos ~bd~ad~bdk; k \u00bc 1;2;3 \u00f03:32\u00de The volume dV (see Fig. 8) contains an elementary set of planes on the surface cos ~bd~ad~b, and the thickness of dV, dh, is proportional to dk. It must be noted that Eq. (3.32) can be used only if ~S 2 S3 meaning that strain components can be calculated only for the case when three of the five components of stress-deviator-vector components are nonzero (Si \u2013 0 i = 1, . . .,3 and S4 = S5 = 0), i.e. the synthetic theory is inapplicable of modeling plastic straining when ~S 2 S5 (Si \u2013 i = 1, . . .,5). It is very important to note that, according to any flow plasticity theory, a strain is accumulated due to the change of a loading surface in five-dimensional deviatoric space independently of the quantity of nonzero stress deviator vector components" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003652_1.3581229-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003652_1.3581229-Figure1-1.png", + "caption": "FIG. 1. (Color online) Parallel-plate dielectric cell with Galinstan electrodes (a) schematic and (b) picture. Cell is mounted on an Agilent 16047E test fixture. Dimensions are in mm.", + "texts": [ + "10, 11 Here, we use Galinstan as an electrode for liquid impedance spectroscopy.14, 15 Polished American Society for Testing and Materials grade 304 stainless steel is used comparatively.16 Two 800 \u03bcl volume dielectric cells, one with stainless steel electrodes and one with Galinstan electrodes, were constructed to measure the impedance of various liquids. The construction of the stainless steel cell is published elsewhere.17 The Galinstan cell was built with a similar geometry to the stainless steel cell. The Galinstan cell schematic and picture are shown in Fig. 1. Four acrylic plates, measuring 20 mm by 35 mm, were cut out of 5.2 mm thick acrylic stock using a Rayjet laser engraver (Trotec). Holes for screws were cut into the outside plates. 9.5 mm wide channels and 9.5 mm diameter circles a)Electronic mail: brettmellor@byu.edu. were cut out of the two middle plates. An electrode spacing of 8 mm was attained by thinning the middle plates through a process of laser engraving and sanding. Steel zinc-plated 2\u201356 pan-slotted-head 1/2\u2032\u2032 screws were ground to a flat tip, then screwed into the end plates and left slightly recessed" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002519_bf01111855-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002519_bf01111855-Figure1-1.png", + "caption": "Fig. 1. Schematic membrane-electrode configuration.", + "texts": [ + " Thus for air electrode polarizations of about 350 mV at the low current densities encountered, the overall cell potential will be about 450 mV, which is a reasonable goal for a practical unit. For a 4.5 W fuel cell, a total current of 10 A will thus be required. Parametric calculations Model description The idealized physical model of the electrode used for the calculations is that of a membrane of thickness t, and pore size rn, backed by an electrode structure. The electrode structure is assumed to be made up of parallel pores of radius rp, and length,/ , arranged perpendicular to the membrane. The total thickness of the electrode is t + 1. This is illustrated in Fig. 1. The membrane-electrode structure is assumed to sit between two fluid reservoirs of constant glucose concentration. The reservoir on the membrane side contains venous blood with a glucose concentration of 0.50 x 10 -5 mol/cc. The reservoir behind the electrode contains plasma with a nominal glucose concentration 20 % that of the venous blood. Glucose diffuses through the membrane because of the concentration gradient, which is maintained by the reaction in the electrode. I f a pressure is applied across the structure, plasma is filtered through the membrane and the total glucose flux is then the sum of the diffusive flux and the convective flux" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000055_978-1-4684-1500-1-Figure7.2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000055_978-1-4684-1500-1-Figure7.2-1.png", + "caption": "Figure 7.2 Stacked construction refers to a group of items that are assembled along one axis. Often, but not exclusively, the components are symmetrical.", + "texts": [ + " The only additional considerations are incurred costs due to any changes to the design of components or processes (eg stocks of existing components being scrapped), and/or the need for compatibility with products that have or are being assembled manually because of servicing, stocking or approval reasons. 88 Product and process design for assembly Each product and subassembly can be described by one of four classifications: 1. Frame construction (Figure 7.1). Items such as television sets or computers are frame constructed as they need a frame onto which other items can be mounted. 2. Stacked construction (Figure 7.2). Designs that require the components to be assembled one on top of another (eg armatures). 3. Base component construction (Figure 7.3). Items that incorporate a base onto which all components are fitted and transported through the assembly process (eg printed circuit boards). 4. Modular (Figure 7.4), in which individual sub assemblies are combined to form different products (eg manufacture of automobiles in which different combinations of similar 'options' are used to produce a wide range of models)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001868_0278364910365093-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001868_0278364910365093-Figure4-1.png", + "caption": "Fig. 4. A differential-drive \u201cforwards\u2013right\u2013reverse\u201d trajectory and associated control line.", + "texts": [ + " A similar result can be obtained describing the angle a translation makes with the control line in terms of the value of H . Corollary 1. If the control corresponding to rotation center O and angular velocity is active at time t on an extremal trajectory of Hamiltonian value H, then at this time the signed distance from O to the control line is yO H . Corollary 2. If a translation control of velocity and forming angle with the horizontal axis is active at time t on an extremal trajectory of Hamiltonian value H, then at this time cos H , where is the orientation of the body frame with respect to the control line. Figure 4 gives an example of how these two corollaries may be applied. The vehicle has four controls: rotation at angular velocity l or r about the center of the body, forwards translation, and reverse. In the figure, the body starts slightly below the distance H l from the control line, and forward translation maximizes the quantity x y over all controls. The body drives until the rotation center hits the line H r , spins to the right until reaching a critical angle, reverses until the line at H l , spins to the left, and then repeats the process" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002763_j.sna.2011.09.037-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002763_j.sna.2011.09.037-Figure3-1.png", + "caption": "Fig. 3. Simplified electromagnetic actuator [5].", + "texts": [ + " The complex voltages are used together with the complex impedance to obtain estimates of the complex coil currents. The errors between the measured and modelled currents are fed to PI controllers, which yield estimates for the x and y rotor positions. In order to simplify the analysis of the parameter estimator, each pole pair (PP) is treated as an isolated actuator. In addition, the x and y position estimates are decoupled, implying that (i1, i3) are used to estimate y, and (i2, i4) are utilized to determine x (see Fig. 2(a) in Part I). The simplified AMB actuator can be represented as shown in Fig. 3. In the AMB, the rotor position information is embedded in the inductance of the electromagnetic transducer. The relationship between the voltage, current, and position is given by [5] v = 0N2a [ 1 2(g0 \u2212 x) + l/ r di dt + 2 i( 2(g0 \u2212 x) + l/ r )2 dx dt ] + iR (1) with N the number of coil turns, i the coil current, R the coil resistance, g0 the nominal air gap length, a the air gap area, l the effective magnetic material path length, r the magnetic material relative permeability, and x the position of the suspended body" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001948_20100915-3-de-3008.00018-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001948_20100915-3-de-3008.00018-Figure1-1.png", + "caption": "Fig. 1. The foundation of weather optimal positioning control is represented by the principle of a pendulum in a force field.", + "texts": [ + " Specific surge and yaw controllers are proposed to take into account maneuverability constraints of the vessel, and a geometrically inspired update law is designed to move the virtual suspension point relative to the desired vessel position. The scheme is applicable to both fully actuated and underactuated vessels, and is illustrated through a number of relevant simulation scenarios. In particular, it is shown that WOPC can provide significantly better energy efficiency than conventional DP. The principle of a pendulum in a force field is illustrated in Figure 1, where a point mass influenced by a uniform force field is connected to a suspension point through a wire. This pendulum system is equivalent to a marine system 978-3-902661-88-3/10/$20.00 \u00a9 2010 IFAC 114 10.3182/20100915-3-DE-3008.00018 involving waves, wind and current loads acting on a vessel tied to a pole. The weather constantly influences the vessel and moves it to a weather optimal position where the angle between the resultant environmental force and the wire is 180 degrees. The differential equation for a pendulum without damping can be stated as follows \u0308 + sin() = 0, (1) where 0 represents the point mass, 0 is the wire length, 0 is the force, and \u2208 [0 2i is the angle between the pendulum wire and the force direction" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003204_3.3019-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003204_3.3019-Figure3-1.png", + "caption": "Fig. 3b Critical closed loop gain at r2Y = -0.05.", + "texts": [ + " 2b that a large value of TL/T is desirable for the purpose of controlling a system with negative damping. However, a larger TL/r is accompanied by a smaller gain margin, which causes the human pilot difficulties in keeping the value of r*K within the narrow band. Consequently, although the theory predicts that the controllability limit attained for the present case is rX = \u20140.234 for TL/T = +\u00b0\u00b0, such a state of zero gain margin can never be realized by the human pilot. Figures 3a and 3b show a case of negative static stability, r2F = \u2014 0.05, It is seen from Fig. 3b that the lower boundary of the gain margin is limited by r*K = 0.05. A controllability limit can now be obtained theoretically. For the region of positive static stability, theoretical values of r*K and TL/T tend to zero and infinity, respectively, on the controllability limit. Consequently, the human pilot's transfer function on this limit reduces to = KP*[S/(l (13) Thus the limit is obtained by a condition that Eq. (11) at TL/T = \u00b0\u00b0 has double roots with respect to co2. Employing an approximation that tan (rco) = rco, which is equivalent to an approximation that e~TS ^ 1/(1 + r$) in Eq", + " 1 and with our experiments on one trial and on three trials, respectively, except for a region where the value of Y is nearly equal to zero. This may indicate that the human pilot controls the unstable element by taking notice of the unstable root only. However, in the region where the value of Y is nearly equal to zero, the damping of the mode corresponding to the negative root is small and the human pilot may be forced to take notice of both the stable and unstable roots. This may explain why the experimental results deviate from the corresponding straight lines in the vicinity of X axis. As Fig. 3 indicates, the human pilot must keep values of T2K and TL/r exactly constant at the theoretical controllability limit given by Eq. (19). This means that no margin is allowed for the two parameters at the limit. However, D ow nl oa de d by U N IV O F T E X A S A T S A N A N T O N IO o n Fe br ua ry 5 , 2 01 5 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /3 .3 01 9 946 K. WASHIZU AND K. MIYAJIMA AIAA JOURNAL Theory Y (,\\ v 1*TLS \u2022'\u2014\u2014\u2014 Ip^8;=K-p-\u2014\u2014\u2014\u2014e 1+0.Is Experiment e cenvergent & divergent - 4 - 2 0 2 4 x (rad/sec) Fig", + " Consequently, his controllability limit may be narrower than the theoretical prediction. When a set of X, Y is given, he may perhaps adjust the value of TL/T so that maximum gain margin can be realized. With this in mind, we analyzed the experimental results to obtain Table 4, which is constructed as follows: to begin with, we assume that r = 0.1 sec; take a set of values of 7, X, and co, such as \u20145, \u20141.68, and 3.14, from the controllability limit of the experiment (these correspond to r2F = \u20140.05 and rX = -0.168 in Fig. 3); read values of Xmax and -Kmin corresponding to rX = \u20140.168 from Fig. 3b, where Kmax is given by the envelope of the curves, and Kmin is obtained by the line rzK = \u2014 r2F; read the value of TL/r corresponding to Kmax; then, we can obtain the value of the critical circular frequency from the broken curve in Fig. 3a; finally, by using these values the first row of Table 4 can be completed, and the other three rows are completed in a similar manner. In order to compare the values of Kmax and Km-in thus obtained with the experiments, values of the closed loop gain K were analyzed from the test results. Since the records of the tests seem to show repetitions of divergent, neutral, and convergent behaviors, only the extremal values of the output -of the controlled element owtremai, and corresponding extremal values of the output of the control system \u00a3extremai> were read out from the figures, and the values of K were calculated approximately by \u2022K\" = ~\u00a3extremal/ttextremal" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001447_05698197508982750-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001447_05698197508982750-Figure4-1.png", + "caption": "Fig. 4-Coordinate system", + "texts": [ + " With these assumptions we have, corresponding to [2], the following approsimate relation in the plastic region b = ,/2crR (a > a,) The friction force in the contact region may be written as where TI is approximately equal to the shear stress in boundary lubrication theorv or it might be approximated by the product of coefficient of friction and hardness. The existence of a frictional force will change the relations between the vertical load and deformation of the asperities especially with plastic flow but, since the shear stresses are usually only of the order of 1/10 of the vertical load, this effect can be neglected. Outside the contact region, the flow of lubricant can be analyzed hydrodynamically. The bounding surface of the flow is that described by the dashed line in Fig. 4, where (r, 8 ) are polar coordinates. I t has been shown repeatedly (19) that, in general, the load carrying capacity in the classical lubrication is not very sensitive to the exact film shape, so long as the ratio of minimum to maximum film thickness is the same. Calculation also showed that one could replace the shape of the deformed asperity tip by a spherical surface that would yield the same maximum and minimum film thickness, as shown by the solid line in Fig. 4. The Reynolds equation in polar coordinates (r, 8) is i a ah - - (rlr3 'g) + ;f $ (h3 %) = 12vU cos 0 - r a r a r [61 where the film thickness h is a known function of r and the lubricant viscosity 7 and sliding speed U are both constant. The boundary condition for p is the value of pressure on the circular isobar, as shown in Fig. 2. The pressure on D ow nl oa de d by [ U ni ve rs ity o f T or on to L ib ra ri es ] at 1 8: 24 1 9 D ec em be r 20 14 A Model for AIixed Lubrication 93 this isobar is taken to be the macroscopic mean pressure in the region, p," + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001850_icmech.2009.4957202-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001850_icmech.2009.4957202-Figure3-1.png", + "caption": "Fig. 3. Planar, kinematically redundant mechanism", + "texts": [ + " The coordinates are chosen as follows q [81, 7j;1, 82, 7j;2, 83, 7j;3, XE, YE]T, Z == X = [XE' YE]T, 0= [81, 7j;1, 82, 7j;2, 83, 7j;3F and Oa = [81, 82, 83F. The six constraint equations of the robot have the following form (for i = 1,2,3): = { XAi + lilC!}i + li2 C!}i+'ljJi - XE }. YAi + lilS!}i + li2 S!}i+'ljJi - YE In addition, we have [ 10000000]T 8q = 0 0 1 0 0 0 0 0 80 a 0 0 0 0 1 0 0 0 It can be pointed out that the matrix K == E(8X8)' Further more, det(!}) = luh2l2ll22l3ll32S'ljJlS'ljJ2s'ljJ3 and JT is given by In this example, we exemplarily present the kinematically redundant parallel 3(\u00a3)RRR robot shown in Fig. 3 [22]. The robot has four DOFs and it is controlled by four actuators. In the following the inclination of the additional prismatic actuator is assumed to be a = 0\u00b0. The coordinates are chosen as follows q = [5, 81, 7j;1, 82, 7j;2, 83, 7j;3, xE, YE, \u00a2E]T, Z = [XE' YE, \u00a2E, 5]T, 0 = [81, 7j;1, 82, 7j;2, 83, 7j;3]T and Oa = [81, 82, 83, 5]T. It is important to note that in this case x = [XE' YE, \u00a2El T and we use the variable 5 (the prismatic actuator position) as an additional coordinate. The six constraint equations of the robot have the following form: <1>= XA l + lUC" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000199_iet-cta:20060105-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000199_iet-cta:20060105-Figure1-1.png", + "caption": "Fig. 1 Two-link robot arm", + "texts": [ + " ; p; i , j Remark 2 [5]: The control signal can be enforced to satisfy the constraint u(t)Tu(t) g2 if the following LMIs are added to Theorem 1. 1 e\u00f00\u00deT e\u00f00\u00de X \" # 0 and X NT i N i g2 I \" # 0; i \u00bc 1; 2; . . . ; p where g is a predefined positive scalar and e(0) is the initial state condition of the error system. By properly assigning the value of g, the values of feedback gains obtained by solving the GEVP with the additional LMIs in Remark 2 can be prevented to be too large to give large control signal. 4 Application example An MIMO two-link robot arm [16] shown in Fig. 1 is taken as the nonlinear plant. Refer to Fig. 1, ma1 is the centre of mass of link 1, ma2 is the centre of mass of link 2, ma3 is the mass of the load, l1 is the length of link 1, l2 is the length of link 2, lc1 is the length from the joint of link 1 to its centre of mass, lc2 is the length from the joint of link 2 to its centre of mass, I1 is the lengthwise centroidal inertia of link 1, I2 is the lengthwise centroidal inertia of link 2, u1 and u2 are the angles of the IET Control Theory Appl., Vol. 1, No. 1, January 2007 joints as shown in Fig. 1. The fuzzy controller of (8) will be employed to realise the tracking control. (1) The system dynamics of the two-link robot arm are governed by the following dynamic equation _x\u00f0t\u00de \u00bc \u00f0A\u00fe DA\u00f0x\u00f0t\u00de\u00de\u00dex\u00f0t\u00de \u00fe B\u00f0x\u00f0t\u00de\u00deu\u00f0t\u00de \u00fe E \u00f019\u00de where x\u00f0t\u00de \u00bc x1\u00f0t\u00de x2\u00f0t\u00de x3\u00f0t\u00de x4\u00f0t\u00de T \u00bc u1\u00f0t\u00de _u1\u00f0t\u00de u2\u00f0t\u00de _u2\u00f0t\u00de T x1\u00f0t\u00de [ x1min x1max \u00bc p p x2\u00f0t\u00de [ x2min x2max \u00bc 10 10 x3\u00f0t\u00de [ x3min x3max \u00bc p p x4\u00f0t\u00de [ x4min x4max \u00bc 10 10 A \u00bc 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 2 6664 3 7775 DA\u00f0x\u00f0t\u00de\u00de \u00bc 0 0 0 f2\u00f0x\u00f0t\u00de\u00dehx2\u00f0t\u00de 0 0 0 f3\u00f0x\u00f0t\u00de\u00dehx2\u00f0t\u00de 0 0 0 f1\u00f0x\u00f0t\u00de\u00deh\u00f02x2\u00f0t\u00de \u00fe x4\u00f0t\u00de\u00de 0 0 0 f2\u00f0x\u00f0t\u00de\u00deh\u00f02x2\u00f0t\u00de \u00fe x4\u00f0t\u00de\u00de 2 6664 3 7775 B\u00f0x\u00f0t\u00de\u00de \u00bc 0 0 f1\u00f0x\u00f0t\u00de\u00de f2\u00f0x\u00f0t\u00de\u00de 0 0 f2\u00f0x\u00f0t\u00de\u00de f3\u00f0x\u00f0t\u00de\u00de 2 6664 3 7775 E \u00bc 0 f1\u00f0x\u00f0t\u00de\u00deg1 \u00fe f2\u00f0x\u00f0t\u00de\u00deg2 0 f2\u00f0x\u00f0t\u00de\u00deg1 f3\u00f0x\u00f0t\u00de\u00deg2 2 6664 3 7775 f1\u00f0x\u00f0t\u00de\u00de \u00bc M22 M11M22 M12M21 f2\u00f0x\u00f0t\u00de\u00de \u00bc M12 M11M22 M12M21 f3\u00f0x\u00f0t\u00de\u00de \u00bc M11 M11M22 M12M21 M11 \u00bc I1 \u00fe I2 \u00fe ma1 l 2 c1 \u00fe ma2 \u00f0l 2 1 \u00fe l 2 c2 \u00fe 2l1lc2 cos\u00f0x3\u00f0t\u00de\u00de\u00de \u00fe ma3 \u00f0l 2 1 \u00fe l 2 2 \u00fe 2l1l2 cos\u00f0x3\u00f0t\u00de\u00de\u00de M12 \u00bc M21 \u00bc I2 \u00fe ma2 \u00f0l 2 c2 \u00fe l1lc2 cos\u00f0x3\u00f0t\u00de\u00de\u00de \u00fe ma3 \u00f0l 2 2 \u00fe l1l2 cos\u00f0x3\u00f0t\u00de\u00de\u00de M22 \u00bc I2 \u00fe ma2 l 2 c2 \u00fe ma3 l 2 2 h \u00bc ma2 l1lc2 sin\u00f0x3\u00f0t\u00de\u00de g1 \u00bc ma1 lc1 g cos\u00f0x1\u00f0t\u00de\u00de \u00fe ma2 g\u00f0lc2 cos\u00f0x1\u00f0t\u00de \u00fe x3\u00f0t\u00de\u00de \u00fe l1 cos\u00f0x1\u00f0t\u00de\u00de\u00de g2 \u00bc ma2 lc2 g cos\u00f0x1\u00f0t\u00de \u00fe x3\u00f0t\u00de\u00de ma1 \u00bc 3 kg, ma2 \u00bc 2 kg, ma3 [ 2 kg, I1 \u00bc 2" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000194_j.enconman.2006.08.002-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000194_j.enconman.2006.08.002-Figure2-1.png", + "caption": "Fig. 2. The location of thermocouples in the investigated induction cage machine FSg 100L-4B.", + "texts": [ + " In order to compare the differences, the author has conducted thermal tests for an induction cage machine with two ways of ventilation: one provided with a fan placed on the shaft and the other provided with a fan driven by an auxiliary motor. The measurement system consists of two induction cage machines with rated powers of 5.5 and 3 kW, supply and load systems. In different parts of the stators of both induction machines, there are built in thermocouples (J type): in the windings (11 in the 3 kW machine and nine in the 5.5 kW machine), in teeth, in stator cores, under bearings and on the casings. The locations of the thermocouples in the investigated 3 kW induction cage machine are presented in Fig. 2 and described in Table 2. The thermocouples are connected to temperature transmitters and are monitored by a computer system. The accuracy of the temperature measurement is about 2 K. The machines can be supplied with an inverter with independent voltage and frequency control, a programmable AC power source, an autotransformer and a synchronous generator. The motors are loaded with DC generators. The scheme of the measurement system is given in Fig. 3. All the presented results of the measurements were obtained for the 3 kW machine with two ways of ventilation: its own (motor TSg 100L-4B) and foreign (motor FSg 100L-4B)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002327_iccme.2012.6275613-Figure9-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002327_iccme.2012.6275613-Figure9-1.png", + "caption": "Fig. 9 Model of new type spiral jet motion", + "texts": [ + " CD is drag coefficient between fluid and robot. A is cross section of the outflow. We did experiment propulsive force of the robot. We did experiment 2 types to confirm spiral jet mechanism. One is the spiral jet motion which is covered with outer shell. The other is the spiral motion which isn't covered with outer shell. Experimental results are shown in Fig. 8. IV. NEW TYPE SPIRAL JET MOTION We developed improved new type spiral jet motion robot to implement small and light structure. The new type spiral jet microrobot is shown in Fig. 9. And, Specification of the robot is shown in Table III. In this robot, length is 23 mm, outer diameter is cjJ 14 mm and weight is 3.56g. We used polystyrene with robot to make neutral buoyancy and o-ring type neodymium magnet as actuator. We developed new type spiral jet type microrobot. It is shown in Fig. 10. Diameter of the spiral screw is 5mm. And we used o-ring type magnet as actuator. Residual magnetic flux density of the magnet is 1250mT and its size is tP 9.5x tP 5.1 X 1.5mm. This size is smaller than a commercial capsule We analyzed propulsive force of the new type spiral jet microrobot" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000037_811309-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000037_811309-Figure1-1.png", + "caption": "Fig. 1 \u2014 The effect of pre-load, frequency and vibration amplitude on the radial dynamic spring rate magnitude I k* (w) I of an automotive suspension bushing made of a carbon black-filled natural rubber.", + "texts": [ + " The measured static force deflection response and dynamic stiffness k*(=k,-Fjk,) of two automotive components used for vibration attenuation and isolation purposes is shown to be in good agreement with the theoretical predictions. THE BEHAVIOR OF ELASTOMERIC COMPONENTS derived from experimental testing is well known. It has been reported, for example, that the dynamic stiffness is sensitive to changes in pre-load, frequency, vibration amplitude and temperature in mounts made of elastomeric materials containing reinforcing fillers (I) * . An example of such sensitivity is illustrated in Fig. 1 for an automotive suspension bushing made of a carbon-black filled natural rubber. The sensitivity to vibration amplitude has been attributed to the presence of reinforcing fillers (2) which have been added to the basic gum vulcanizate to improve its strength and stiffness properties; unfilled material systems or gum vulcanizates do not exhibit this sensitivity. The present work presents a method of analyzing the isothermal steady-state dynamic response of components which have been subjected to an initial static pre-load" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003404_isma.2013.6547379-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003404_isma.2013.6547379-Figure4-1.png", + "caption": "Figure 4. Movement in Y direction", + "texts": [ + " For instance, the quadrotor can move in the vertical Z direction by varying the speed of all propellers at the same time and by the same amount as shown in Figure 2. To command the quadrotor to move in the X direction, the speed of the front and rear propellers should be changed by the same amount and in opposite directions as shown in Figure 3. Moving the quadrotor in the Y direction can be done by changing the speed of the right and left propellers by the same amount and in opposite directions as shown in Figure 4. 978-1-4673-5016-7/13/$31.00 \u00a92013 IEEE ISMA13-2 To control quadrotor heading, the speed of all propellers is commanded by the same amount but in different directions, front and rear propellers with the same direction and right and left the propellers with opposite direction, as shown in Figure 5. The quadrotor\u2019s model, mainly includes the nonlinear aero dynamical equations of the quadrotor along with the actuators dynamics and saturation limits [10-13]. The model is represented as follows: 1(sin sin cos sin cos ) U X m = \u03a8 \u03a6+ \u03a8 \u0398 \u03a6 (1) 1( cos sin sin sin cos ) U Y m = \u2212 \u03a8 \u03a6+ \u03a8 \u0398 \u03a6 (2) 1(cos cos ) U Z g m =\u2212 + \u0398 \u03a6 (3) 2yy zz xx xx I I U p qr I I \u2212 = \u2212 (4) 3zz xx yy yy I I U q pr I I \u2212 = \u2212 (5) 4xx yy zz zz I I U r pq I I \u2212 = \u2212 (6) where , ,X Y Z are the position of the center of mass WRT inertial frame, , ,\u03c6 \u03b8 \u03c8 are the Euler angles, , ,p q r are the body rates, m is the quadrotor\u2019s mass, , , xx yy zz I I I are the moments of inertia, 1 2 3 4 , , ,U U U U are the throttle, roll, pitch and yaw forces and moments respectively" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003268_j.ymssp.2012.10.005-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003268_j.ymssp.2012.10.005-Figure1-1.png", + "caption": "Fig. 1. The configuration of a multi-disc wet friction clutch, (a) cross-sectional and (b) exploded view.", + "texts": [ + " Technology Centre (FMTC), Celestijnenlaan 300D, 3001 Heverlee, Belgium. Tel.: \u00fe32 16 32 80 42. m (A.P. Ompusunggu). fluid (ATF) having a function as a cooling lubricant cleaning the contacting surfaces and giving smoother performance and longer life. However, the presence of the ATF in the clutch reduces the coefficient of friction (COF). In applications where high power is necessary, the clutch is therefore designed with multiple friction and separator discs. This configuration is known as a multi-disc wet friction clutch as can be seen in Fig. 1, in which the friction discs are mounted to the hub by splines, and the separator discs are mounted to the drum by lugs. In addition, the input shaft is commonly connected to the drum-side, while the output shaft is connected to the hub-side. The friction disc is made of a steel-core-disc with friction material bonded on both sides and the separator disc is made of plain steel. An electro-mechanical-hydraulic actuator is commonly used to engage or disengage wet friction clutches. This actuator consists of some main components, such as a piston, a returning spring which is always under compression and a hydraulic group consisting of a control valve, an oil pump, etc. As can be seen in Fig. 1, the piston and the returning spring are assembled in the interior of a wet friction clutch. To engage the clutch, pressurized ATF that is controlled by the valve is applied through the actuation line in order to generate a force acting on the piston. When the applied pressure exceeds a certain value to overcome the resisting force arising from both spring force and friction force occurring between the piston and the interior part of the drum, the piston starts moving and eventually pushes both friction and separator discs toward each other", + " It is worthwhile to emphasize here that the developed method only estimates the parameters of the dominant component of the post-lockup signal. Thus, the fitted signals or the estimated ones (black lines) as shown in the figures are referred to the dominant component. One may can see in Figs. 27\u201331 that the measured post-lockup torque signals (gray dashed lines) exhibit a deadzone-line effect which can be speculated due to the backlash present between the teeth of the separator discs and the lugs of the drum, see Fig. 1. Figs. 32\u201335 show the evolution of the dominant modal parameters fd and s (proposed features) and the normalized ones, which are extracted from the post-lockup velocity and torque signals. The upper and lower panels in the figures respectively depict the non- and normalized features. In similar way to the normalized mean COF (see Eq. (25)), the proposed features fd and s can be normalized which take the following forms: ^df d \u00bc f d f i d f i d , \u00f026\u00de d\u0302s \u00bc s si si , \u00f027\u00de where ^df d and d\u0302s respectively denote the normalized damped natural frequency and normalized decay factor, while f i d and si respectively denote the damped natural frequency and decay factor measured in the first cycle" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002040_bf00587838-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002040_bf00587838-Figure1-1.png", + "caption": "Fig. 1. Schematic diagram of tube used for ultrafiltration. The tube consists of an upper part made from Plexiglas tubing (R6hm u. I-Iass GmbH, Darmstadt, Germany) and a lower part made from a solid block of Plexiglas. The length and diameter in mm of the two parts, which have a cylindrical shape, are shown on the diagram. Before an experiment the two parts are screwed together, the O-ring (rubber) being inserted in the small grove of the lower part to form a tight seal. The porous teflon disk (Vyon 1.5 mm thick, Porvair Ltd., Norfolk, England) rests on the thread of the lower part and functions as a support of the cellophane bag.", + "texts": [ + "033 M phosphate buffer of the same pi t as that of the albumin solutions. Measurements of pit were done with a pH meter 25 (Radiometer, Copenhagen, Denmark), using a type G 202 C glass electrode. Ultrafiltration Procedure. The binding of phenol red to albumin was examined by comparing the ultrafiltrability of the indicator dye in the albumin and reference solutions. Albumin and reference solutions, having a volume of 4 ml, were enclosed in cellophane bags which were knotted carefully. The bags were placed in plastic tubes, the construction of which is depicted in Fig. 1. These tubes represent a modification of those described by Toribara, Terepka and Dewey [10]. Ultrafiltrate was formed by centrifuging the tubes in a Christ IV KS refrigerating centrifuge for 60 rain at 320 G and 25 ~ C. The concentration of phenol red in the ultrafiltrates was determined by measuring the extinction at 559 nm after dilution of ultrafiltrate with a suitable volume of water and alkalinizing the contents by addition of 0.2 ml 5 N NaOH. The fraction of phenol red bound to albumin (~) was calculated on the basis of the ratio between the optical density of the ultrafiltrates of the protein solution (Dup) and the corresponding reference solution (Dur), according to the following equation Dur -- Dup - Put (1) Spectrophotometric Measurements" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001093_09544062jmes923-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001093_09544062jmes923-Figure3-1.png", + "caption": "Fig. 3 Schematic of the z\u2013y\u2013x Euler angles", + "texts": [ + " Rotary inertia and gyroscopic effects are considered; (c) rotating shaft is simply supported; (d) supports O and O\u2019 of the shaft are fixed along the X -axis (Fig. 1); (e) the only dissipating mechanism in the system is the external viscous damping; and (f) amplitude is large, and stretching non-linearity due to extension of shaft centre-line is considered [1, 5]. The relation between the original frame X \u2013Y \u2013Z and the deformed frame x\u2013y\u2013z is described by three successive Euler angles \u03c8(x, t), \u03b8(x, t), and \u03b2(x, t) as shown in Fig. 3. First, the X \u2013Y \u2013Z system is rotated by an angle \u03c8 about the Z-axis to an intermediate coordinate system X1\u2013Y1\u2013Z . Then, the X1\u2013Y1\u2013Z system Proc. IMechE Vol. 222 Part C: J. Mechanical Engineering Science JMES923 \u00a9 IMechE 2008 at UNIV OF MICHIGAN on October 18, 2014pic.sagepub.comDownloaded from is rotated by an angle \u03b8 about the Y1-axis to a secondintermediate coordinate system x\u2013Y1\u2013Z2. Finally, the x\u2013Y1\u2013Z2 system is rotated by an angle \u03b2 (= t) about the x-axis to the system x\u2013y\u2013z. The kinetic energy for a balanced rotating shaft may be written as [17] T = 1 2 \u222b l 0 m(u\u03072 + v\u03072 + w\u03072)dx + 1 2 \u222b l 0 [I1\u03c9 2 1 + I2(\u03c9 2 2 + \u03c92 3)]dx (1) where mass per unit length, m, and polar and diametrical mass moment of inertia, I1 and I2, are m = \u222b A \u03c1 dA, I1 = \u222b A \u03c1(y2 + z2) d A, I2 = \u222b A \u03c1y2 dA = \u222b A \u03c1z2 d A (2) In equation (1), the first and the second terms represent the translational and rotational kinetic energy, respectively. Equation (1) is true when: (a) the shaft has circular cross-section; (b) the properties of the shaft are constant in a circumferential direction; (c) x\u2013y\u2013z are the principal axes of the shaft cross-section; and (d) the reference point coincides with the mass centroid of the shaft. Using Euler angles (Fig. 3), the angular velocities of the frame x\u2013y\u2013z with respect to the frame X \u2013Y \u2013Z are \u03c9 = \u03c91e1 + \u03c92e2 + \u03c93e3 = (\u03b2\u0307 \u2212 \u03c8\u0307 sin \u03b8)e1 + (\u03c8\u0307 sin \u03b2 cos \u03b8 + \u03b8\u0307 cos \u03b2)e2 + (\u03c8\u0307 cos \u03b2 cos \u03b8 \u2212 \u03b8\u0307 sin \u03b2)e3 (3) Substitution of equation (3) into equation (1) gives T = 1 2 \u222b l 0 {m(u\u03072 + v\u03072 + w\u03072) + I1[ 2 + \u03c8\u03072 sin2 \u03b8 \u2212 2( )(\u03c8\u0307 sin \u03b8)] + I2(\u03c8\u0307 2 cos2 \u03b8 + \u03b8\u03072)}dx (4) Also, the kinetic energy T e resulted from eccentricity can be computed as T e = \u2212 \u222b l 0 \u03c1A {v\u0307[e\u03be (x) sin t + e\u03c2 (x) cos t] + w\u0307[\u2212e\u03be (x) cos t + e\u03c2 (x) sin t]}dx + 1 2 \u222b l 0 \u03c1A 2[e2 \u03c2 (x) + e2 \u03be (x)]dx (5) where e\u03c2 (x) and e\u03be (x) are eccentricity distributions in two orthogonal planes", + " The strain along the centre-line of the shaft is e = \u221a (1 + u\u2032)2 + v\u20322 + w \u20322 \u2212 1 (6) Neglecting the shear deformation, the strain energy for a rotating shaft with the isotropic and linear material properties becomes [16] \u03b4\u03a0 = \u222b l 0 (A11e\u03b4e + D11\u03c11\u03b4\u03c11 + D22\u03c12\u03b4\u03c12 + D22\u03c13\u03b4\u03c13)dx (7) where (Fig. 2) A11 = \u222b A E dA, D11 = \u222b A G( y2 + z2)dA and D22 = \u222b A Ey2 dA = \u222b A Ez2 dA (8) In the above equation, E and G are the elasticity and shear modulus, respectively. Curvatures \u03c1i (i = 1, . . . , 3) are computed as \u03c1 = \u03c11e1 + \u03c12e2 + \u03c13e3 = (\u2212\u03c8 \u2032 sin \u03b8)e1 + (\u03b8 \u2032)e2 + (\u03c8 \u2032 cos \u03b8)e3 (9) If shear deformation is neglected, angles \u03c8 and \u03b8 can be related to the displacements (Fig. 3) \u03c8 = sin\u22121 v\u2032\u221a (1 + u\u2032)2 + v\u20322 \u03b8 = sin\u22121 \u2212w \u2032\u221a (1 + u\u2032)2 + v\u20322 + w \u20322 (10) Substituting equation (10) into equation (9), expanding outcomes in Taylor series, and retaining terms up to O(\u03b53), the curvatures are computed up to O(\u03b53). Substituting these curvatures into equation (7), and using equations (4), (5), and (10), the final form of kinetic and strain energies are obtained. Applying the Hamilton principle to these kinetic and strain energies, it is obtained \u2212mu\u0308 + A11(u\u2032\u2032 + w \u2032w \u2032\u2032 + v\u2032v\u2032\u2032) + D22(v\u2032v(IV) + w \u2032w(IV) + v\u2032\u2032v\u2032\u2032\u2032 + w \u2032\u2032w \u2032\u2032\u2032) = 0 (11) JMES923 \u00a9 IMechE 2008 Proc" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000069_841057-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000069_841057-Figure1-1.png", + "caption": "Fig. 1 - Liapunov stability results using the standard method for data set 1", + "texts": [ + " (19) is a quartic equation in n . Thfs quartic equation was solved repeatedly for different values of V to generate a curve in the V fi - plane thai: represents the boundary of The region in which V, < 0. The final step in determining the region of stability, or domain of attraction, is that of fitting the largest possible V, = constant curve inside the tf. < 0 region. The V, - 0 curve, the associated V, - constant curve, and the stability boundary obtained by digitally simulating Eqs. (5) and (6) are shown in Fig. 1 for Data Set 1 and in Fig. 3 for Data Set 2. Next, the modified kinetic energy function, V?s will be used for the nonlinear problem. STnce B,?>0 and B?1>0 for Data Sets 1 and 2, the funcTlon \\L of^q. (16) can be written as I. V2 = 2B. V 2B, al 12 J \"\"21 which is a positive definite function. equation for V2 can be written as , (B\u201eV.. + B,\u201e8- + B^V. The v2 = - 12 ii y '12\"z 16\\y 5 B17Vynz + B18Vyflz + B19az' B^ 0 such that (Z01 + \u03b51) \u22c2( N\u22c2 j=2 Z0j + \u03b51 ) = \u2205. Define\u21261 = Z01 + \u03b51 2 , then\u21261 \u22c2(\u22c2 j6=1 Z 0 j ) = \u2205. Using the same argument, we can find \u03b52 > 0 such that (Z02 + \u03b52) \u22c2( \u21261 \u22c2( N\u22c2 j=3 Z0j ) + \u03b52 ) = \u2205. Define \u21262 = Z02 + \u03b52 2 . Continuing this process, we have \u2126i = Z0i + \u03b5i 2 , i = 1, 2, . . . ,N and \u22c2N i=1\u2126i = \u2205. Define d = mini\u2208\u039b{\u03b5i}, thenOi = Z0i + d 2 are required.We refer to Fig. 2 for their geometric relations, where arc AB represents Oi, CE = yi, OE = zi, 6 COD is the cone Ci. Choosing L > 0 large enough such that \u03b8 = tan\u22121 ( 1 L ) < \u03c6 = d 2 , then Ci \u22c2 Sn\u22121 \u2282 Oi, \u2200 i \u2208 \u039b. (3.2) It follows from (3.2) that(\u22c2 i\u2208\u039b Ci )\u22c2 Sn\u22121 = \u2205. Since Ci(i \u2208 \u039b) are open cones with \u2018\u2018vertex\u2019\u2019 0, it is easy to see that\u22c2 i\u2208\u039b Ci = \u2205. (3.3) To simplify the discussion, we always assume P = In. The following discussion shows that this can be assumed without loss of generality. Definition 3.2. Assume P is a CJQLF for system (1" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002976_detc2013-12183-Figure7-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002976_detc2013-12183-Figure7-1.png", + "caption": "Figure 7. CURVE OF COORDINATE STRESSES AND RESULTING SHEAR STRESS INTO THE MATERIAL", + "texts": [ + " Hertzian Contact Stresses. The Hertzian contact load causes a three-axial, time-variant stress condition. It can be fully described by the coordinate stresses and the resulting principal normal and shear stresses in each volume element for a defined point in time during tooth contact. The main shear stress \u03c4H is often used to describe the Hertzian stress condition inside the material. Figure 6a exemplarily shows the distribution of this stress component in the material due to Hertzian contact. In Figure 7 the curve of the coordinate stresses \u03c3x and \u03c3y as well as the corresponding curve of \u03c4H for the central sectional plane are shown qualitatively. For each volume element in the material the stress condition changes with the rolling motion of the mating flank surfaces. Therefore, the rolling direction x can also be understood as the time axis. Consequently, all volume elements in the same material depth are subjected to equal stresses but at different times (Figure 8). In contrast, one single volume element is exposed to different stresses at different times" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000421_tii.2007.913064-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000421_tii.2007.913064-Figure1-1.png", + "caption": "Fig. 1. Definitions of aircraft body axes, angles, and control surfaces.", + "texts": [ + " Under the flat-Earth assumption, the standard six degrees of freedom (DOFs) equations used for conventional aircraft control design and flight simulation can be described in the following by a set of body-axes state equations: Force equation: (1) Kinematics equation: (2) Moment equation: (3) where Navigation equation: (4) where , , and are, respectively, the north, east, and vertical components of the aircraft velocity in the locally level geographic frame on the surface of the Earth. The forces and moments acting on the aircraft are defined in terms of dimensionless aerodynamic coefficients as follows: Drag force Lift force Side force Rolling moment Pitching moment Yawing moment (5) where , is wing reference area, is wing span, and is wing geometric chord. The angle-of-attack, side slip angle, and aircraft speed are determined by (6) where , , and are three variables determining the aerodynamic forces and moments. See Fig. 1 for the definitions of the aircraft body axes, angles, and all control surfaces. The force and moment components ( , , , , , ) in the 6-DOF equations are separated into aerodynamic and thrust contributions. The aerodynamic contributions are obtained from the set of (3). Also, a table of installed engine thrust versus altitude and Mach number is built, with throttle setting as a parameter. The coefficients of the aerodynamic forces and moments are dependent on the control surface deflections, i.e" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001528_gt2008-50806-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001528_gt2008-50806-Figure1-1.png", + "caption": "Figure 1. Gas Foil Bearing schematic.", + "texts": [ + " Regardless of the application, as gas foil bearings are considered for more turbomachinery applications, a better understanding of their system level characteristics is needed for successful design and integration into mainstream machinery. The system level characteristics not yet fully understood include thermal management schemes, alignment requirements, balance requirements, thrust load balancing, and others. This paper presents results of an experimental effort to characterize gas foil bearing misalignment capabilities in the context of how precisely gas foil bearing machinery would need to be manufactured. GFBs (Fig. 1) consist of an outer sleeve lined with a series of nickel-based superalloy sheet metal foils. The innermost sheet metal foil, or top foil, is smooth and constitutes the bearing inner surface against which the rotating shaft operates. The top foil is supported by a compliant structure, often made up of a layer of corrugated sheet metal foil referred to as bump foils, whose bumps behave like springs [3]. The bump foil layer gives the bearing flexibility that allows it to tolerate significant amounts of misalignment, and distortion that would otherwise cause a rigid bearing to fail" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000114_s0022112083001548-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000114_s0022112083001548-Figure1-1.png", + "caption": "FIGURE 1. Sketch defining the geometry of spheresj and k near a wall.", + "texts": [ + " Inclusion of the return Resistance and stability of a translating line of particles 187 flow would greatly complicate the stability calculation. It now appears unnecessary to include the return flow in the stability calculation. Consider first a single small sphere designated by the subscript k moving through a reservoir of otherwise stagnant fluid bounded by a no-slip surface a t z = 0. Let ak represent the radius of the sphere, (xk , y k , z k ) the instantaneous position of the sphere\u2019s centre, and (Uk, V,, Wk) the instantaneous translational velocity of the sphere (see figure 1 ) . Exact solutions to the creeping-flow equations for this geometry have been given by Brenner (1961), Maude (1961) and O\u2019Neill (1964) through use of spherical bipolar coordinates. However, if ak < zk the following relatively simple expressions can be established for the creeping flow induced at a remote point (q, y j , z j ) by the motion of the sphere centred a t (xk, y k , z k ) : ujk = f j k \u2018 k + g j k (xj - xk) (xj - x k ) Lrk + (Y j - Yk) v k + - zk) Wkl- hjk zj (xj - xk) w k > ( 1 4 ( 1 b ) + 5 k [(Zj - Xk) Zk Uk + (Yj - Y k ) Zk Vk - (zj\u201d + 2 3 Wkl, ( 1 c ) \u2018j\u2019k = f j k \u2018k + gjk (Y j - Yk) [ - %k) Uk + ( yj - yk) Vk + (zj - z k ) w k ] - hjk zj( yj - yk ) Wk, wj k = f j k wk + gjk (zj - z k ) - xk) Uk + ( yj - Y k ) Vk + (zj - zk) Wk] where 7 B L M 132 188 8" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000516_alife.2007.367817-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000516_alife.2007.367817-Figure4-1.png", + "caption": "Fig. 4. The meta-actions an ATRON meta-module is able to perform. Dark modules comprise the meta-module. The \u2217-marked modules in (a) and (b) are required to participate in the corresponding meta-actions.", + "texts": [ + " The goal-state is selected by a neural network (also evolved) based on characteristics such as proximity to attraction points. Finally, the meta-module will perform the first meta-action from the found sequence, and the action selection process can be repeated. c) Action execution: A meta-module performs a sequence of meta-actions to move. A meta-action is composed of a sequence of basic module actions (rotation, connection and disconnection), which are performed by the modules part of, or neighbor to, the meta-module. Meta-modules can perform four different types of metaactions (see Figure 4). Each type represents 2 or 4 different meta-actions, so in total a meta-module can perform 12 different meta-actions. However, in a given situation only a subset of these 12 meta-actions will be legal. The metaactions allow the meta-module to move quite freely on the surface of a structure of modules. Robustness is increased by handling meta-actions that fail. Usually this means that a rotation results in a collision, or that a failed module is connected to and therefore locks the module. Collisions are detected by the rotating modules using its encoders", + " The roll-back strategy is to reverse the rotation, mark the state (in the reachable space) as unreachable and select another action to perform (recalculate shortest path). IV. Experimental Setup A partial implementation of the meta-module-based controller has been transferred to the physical ATRON platform. The implementation builds on abilities of the modules, such as rotate, connect and disconnect. It corresponds to the lower level control of individual metamodules (refer to Figure 2). Each physical meta-module can: \u2022 On-line find a shortest-path of meta-actions from a reachable-space, which is known at compile-time. \u2022 Perform the meta-action types of Figure 4(c) or 4(d). \u2022 Detect and perform roll-back of failed actions. Module-to-module communication is currently unstable (due to reflections of IR-communication), this limitation Single meta-module following online-planned sequences of meta-actions. is the main reason for only demonstrating a partial transference, and the small number of experiments performed on the physical modules. We are working towards resolving this issue. In the physical experiments 24 passive modules are initially assembled as a horizontal sheet, on which the meta-modules can easily move" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003872_j.talanta.2012.07.040-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003872_j.talanta.2012.07.040-Figure1-1.png", + "caption": "Fig. 1. Schematic diagram of the proposed SI-LOV manifold in conjunction with voltammetry for hypoxanthine analysis. C: carrier (H2O); SP: syringe pump; HC: holding coil; W: waste; A: air; S: sample; PBS: phosphate buffer solution and EFC: electrochemical flow cell (internal volume: 200 mL).", + "texts": [ + " The Fe3O4/MWCNTs/b-CD/GCE was prepared by dropping this suspension on the glassy carbon electrode surface and the solvent was allowed to evaporate at room temperature in the air. Approximately 100 g of meat samples was triturated and homogenized. Then a portion of 3.0 g was mixed with 10 mL of 0.5 mol L 1 perchloric acid solution for about 1 h. After centrifugation, 1.0 mL of the supernatant extract was diluted to 10 mL with 0.1 mol L 1 PBS. A diagram of the SI-LOV system used in this study was illustrated in Fig. 1. The entire operating processes were summarized as follows: First, 500 mL of PBS was aspirated into the holding coil. After the flow reversal, the EFC and the connecting line were conditioned. Thereafter, 400 mL of carrier, 100 mL of air, 400 mL of sample solution, and 1600 mL of PBS were aspirated into the holding coil followed by transfer into EFC at a flow rate of 16 mL s 1, during which the analyte was accumulated onto the surface of modified electrode at a potential of 0.1 V for 120 s. Finally, the hypoxanthine was stripped with a potential range from 0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001403_gt2009-59226-Figure18-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001403_gt2009-59226-Figure18-1.png", + "caption": "Fig. 18 Experimental and simulation results with shroud U-shape drain, 135\u02da position, 15\u02da size, without back plate", + "texts": [], + "surrounding_texts": [ + "The calculation model is shown in Fig. 12. The revolutions of the gears were set to the same as the experiment. The bearings were modeled to cylindrical shape that filled the space between the rollers of the bearing. On the axial surface of the cylinder, the revolution of a bearing holder was assigned. The flow rate of the oil supply for the bearings was modeled to constant leakage from the surface of the cylinder that had the simplified shape of the bearing rollers. Figure 13 shows the calculation cells of the unshrouded gears. In these calculation cells, in order to simulate the oil supply in the into-mesh direction of the gears, the size of the cells around the meshing part was made small until the flow in the minimum space between the gears could be calculated. The bottom surface of cell block #4 was set on a constant pressure boundary and other surfaces of the block were set on a non-slip wall. In the calculation case with the shrouds, the velocity out of the shrouds is low and influence of the casing wall is nearly isolated. Therefore, with regard to the simulation with the nloaded From: http://proceedings.asmedigitalcollection.asme.org/pdfaccess.ashx shrouds, to reduce calculation time, cell block #4 was omitted and the outer surfaces of blocks #1, #2, #3 were set on constant pressure boundaries except for wall boundaries on the back of the gears. Other calculation conditions were set the same as Table 2. The CPU times with single CPU in 10 rotation of the input gear were 8.9 days in unshrouded case and 5.2 days in shrouded case." + ] + }, + { + "image_filename": "designv11_7_0000860_tsmcb.2007.910741-Figure8-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000860_tsmcb.2007.910741-Figure8-1.png", + "caption": "Fig. 8. (a) Outlook of the PIP device. (b) Profile of the PIP.", + "texts": [ + " 1\u20133, although the tracking is achieved, the control-input chattering with SMC is severe. When the ASMC is applied, the control input is much smooth, and the tracking performance is excellent, as shown in Figs. 4\u20136. The control input is much smaller, and the switching control part is small once the sliding layer is entered. The convergence of \u0393\u0302 is confirmed in Fig. 7. Notably, the knowledge of the upper bounds on the uncertainties is not required. A planetary gear-type inverted-pendulum (PIP) mechanism [16] is utilized to verify the effectiveness of the proposed ASMC. Fig. 8 shows the outlook of the PIP device. The angular acceleration of the star gear causes the pendulum to swing. An important advantage of the PIP mechanism is that the planet gear encircles the star gear, avoiding the winding wire problem. Define the state vector as x = [x1, x2] T, where x1 = \u03b80 and x2 = \u03b8\u03070 are the angle and the angular velocity of the pendulum, respectively. According to the Lagrange method, the state-space equation of the PIP control system can be represented as x\u03071 =x2 x\u03072 = p(x) + q\u03c4 (21) where p(x) = \u2212 ( \u03b52I1+I2 )( r1 \u03b5(r1+r2)I1 ) \u00d7 ( m0 ( l1 2 + l2 ) + m1(r1 + r2) + m3(l1 + l2) + m4l2 2 ) \u00b7g \u00b7sinx1 \u00b7 ( \u03b5 ( r1+r2 r1 ) I1\u2212 ( \u03b52I1+I2 )( r1 \u03b5(r1+r2)I1 ) \u00b7 ( 4I1 + m0(l1 + l2) 3 + m1(r1 + r2) 2 + m3(l1 + l2) 2+ m4l 2 2 3 \u2212 l32 3l1 ))\u22121 (22) q = ( \u03b5 ( r1+r2 r1 ) I1\u2212 ( \u03b52I1+I2 )( r1 \u03b5(r1+r2)I1 ) \u00b7 ( 4I1 + m0(l1 + l2) 3 + m1(r1 + r2) 2 + m3(l1 + l2) 2 + m4l 2 2 3 \u2212 l32 3l1 ))\u22121 (23) and \u03c4 is the control torque of the motor" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001521_s10514-008-9106-7-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001521_s10514-008-9106-7-Figure1-1.png", + "caption": "Fig. 1 Configuration of a biped robot model and its coordinate systems used for analysis and simulations. O\u2013XYZ: Absolute coordinates, H\u2013XH YH ZH : Body center coordinates fixed at the body of the robot, G\u2013XGYGZG: Mass center coordinates fixed at the mass center of the robot. The biped robot is equipped with a shock-absorbing elastic pad at its sole. The pad between the sole and the support surface is modeled as a nonlinear compliant contact model that consists of nonlinear springs with nonlinear damping. The reaction forces and moments generated at the foot in contact with the ground are computed by the amount of the pad deformation in computer simulations. When the pad is compressed, the stiffness and damping coefficient are 1.0 \u00d7 104 [N/m] and 80.0 [Ns/m], respectively. The pad has nonlinear stiffness and damping as it is compressed", + "texts": [ + " Sections 4 and 5 describe the asymmetric trajectory generation method and the impedance control strategy, respectively. The effectiveness and performance of the proposed running trajectory and impedance control through a series of computer simulations and experiments are shown in Sect. 6 and Sect. 7, followed by conclusions in Sect. 8. Running biped robots are different from typical robot manipulators in that they do not have fixed contact points with the ground and the constraints between both feet and the ground change repeatedly as they walk and run, as shown in Fig. 1. The motion equations of a running biped robot represented by the absolute coordinates, O\u2013XYZ, are described by the following equations (Walker and Orin 1982; Oh and Orin 1986; Fujimoto and Kawamura 1998; Park and Kim 1998): \u23a1 \u23a2\u23a2\u23a3 \u03c4r \u03c4l \u03c4b 0 \u23a4 \u23a5\u23a5\u23a6 = \u23a1 \u23a2\u23a2\u23a3 Hr 0 0 Kr 0 Hl 0 Kl 0 0 Hb Kb Qr Ql Qb R \u23a4 \u23a5\u23a5\u23a6 \u23a1 \u23a2\u23a2\u23a2\u23a2\u23a3 \u0308qr \u0308ql \u0308qb \u0308xh \u23a4 \u23a5\u23a5\u23a5\u23a5\u23a6 + \u23a1 \u23a2\u23a2\u23a3 Dr 0 0 Dl 0 0 Pr Pl \u23a4 \u23a5\u23a5\u23a6 [ fr fl ] + \u23a1 \u23a2\u23a2\u23a3 Lr Ll Lb S \u23a4 \u23a5\u23a5\u23a6 (1) where vectors \u0308qr , \u0308ql \u2208 \u03c1 , \u0308qb \u2208 and \u0308xh \u2208 6 are the joint acceleration of the right and left legs, the joint acceleration of the upper body, and the acceleration of the hip link, and vectors fr, fl \u2208 6 are the external force/moment applied at the right and left feet, respectively", + " Both conditions are discussed in detail in the next subsection. 3.1 Support phase The ZMP concept has been used to evaluate the dynamic walking stability (Vukobratovic and Juricic 1969). If the ZMP is inside the contact polygon of the foot on the ground, the biped robot is said to be stable. Similarly, in order for running biped robots to run stably, the ZMPs in Appendix A must be within the safety boundary area so that the biped robot should land on and then take off the ground. 3.2 Flight phase The dynamic equations of a biped robot shown in Fig. 1 can be written as follows: n\u2211 k=1 mk \u0308rk = n\u2211 k=1 mk g, (5) n\u2211 k=1 \u0307HOk = n\u2211 k=1 rk \u00d7 mk g = n\u2211 k=1 \u0307HGk + n\u2211 k=1 rk \u00d7 mk \u0308rk (6) where vectors \u0307HOk and \u0307HGk denote the rates of change in angular momentum of k-th link represented by the absolute coordinates and the mass center coordinates of the biped robot, respectively; vectors \u0308rk and g = [0 0 \u2212g]T denote the acceleration of the center of mass of k-th link represented by the absolute coordinates and the gravitational acceleration, respectively", + " For notational convenience, in the following sections the impedance control laws for the legs will be driven under the assumption that the right leg is supporting and the left leg is swinging in the support phase. In addition, the left leg is in front of the right leg in the flight phase. It is assumed that each foot is equipped with force sensors and the body contains a acceleration sensor, three Gyro sensors and absolute position sensors. 5.1 Impedance control for the support phase The impedance control of the swing left leg is obtained from the relationship between the joint velocity \u0307ql \u2208 6 of the left leg and the velocity vector \u0307xlf \u2208 6 of the left foot represented by the absolute coordinates in Fig. 1. \u0308xlf = \u0308xh + R0 \u0308xh lf + l (36) where \u0307xlf = [ \u0307x0 lf \u03c90 lf ] , \u0307xh = [ \u0307x0 h \u03c90 h ] , \u0307xh lf = [ \u0307xh lf \u03c9h lf ] = Jl \u0307ql, \u0308xh lf = Jl \u0308ql + J\u0307l \u0307ql, l = [ 2 \u03c90 h \u00d7 R0 h \u0307xh lf + \u0307\u03c90 h \u00d7 R0 h xh lf + \u03c90 h \u00d7 ( \u03c90 h \u00d7 R0 h xh lf ) \u03c90 h \u00d7 R0 h \u03c9h lf ] , R0 = [ R0 h 03\u00d73 03\u00d73 R0 h ] , and R0 h \u2208 3\u00d73 is the orientation matrix of the body center coordinates represented by the absolute coordinates. Vectors \u0307x0 lf \u2208 3 and \u03c90 lf \u2208 3 indicate the linear velocity and angular velocity of the left foot, respectively", + " Suppose the desired impedance of the rear right leg is MR \u00a8\u0303xrf + DR \u02d9\u0303xrf + ERx\u0303rf = \u2212 fr or (47) x\u0308rf = x\u0308rf,d + M\u22121 R (\u2212 fr \u2212 DR \u02d9\u0303xrf \u2212 ERx\u0303rf ) where \u02d9\u0303xrf = \u0307xrf \u2212 \u0307xrf,d . MR , DR and ER denote the desired mass, damping ratio and stiffness about the rear right leg, respectively. This equation implies that the swing right leg follows asymptotically the desired trajectory. Similarly, the inverse acceleration transformation is obtained from the relationship between the joint velocity \u0307qr \u2208 6 of the right leg and the Cartesian velocity vector \u0307xrf \u2208 6 of the right foot about O in Fig. 1. Thus, \u0308qr = (R0Jr) \u22121( \u0308xrf \u2212 \u0308xh \u2212 R0J\u0307r \u0307xrf \u2212 r) (48) where Jr \u2208 6\u00d76 is the Jacobian matrix of the right foot with respect to the hip. Finally, substituting (46), (47) and (48) into the torque equation related to the right leg in (1) leads to \u03c4r = (Hr \u2212 KrR\u0303 \u22121Qr)(R0Jr) \u22121( \u0308xrf,d + M\u22121 R (\u2212 fr \u2212 DR \u02d9\u0303xrf \u2212 ERx\u0303rf ) \u2212 \u0308xh \u2212 R0J\u0307r \u0307xrf \u2212 r) + Dr fr \u2212 KrR\u0303 \u22121S\u0303 + Lr. (49) Immediately on switching from a support phase to a flight phase, the supporting foot of the biped robot does not leave off the ground", + " Thus, Mh = diag(b0, b0, b0, b0, b0, b0), Dh = diag(d0, d0, d0, d0, d0, d0), Eh = diag(e0, e0, e0, e0, e0, e0) where b0 = 2mg [kg] or [kgm2], e0 = 2kleg [N/m] or [Nm], and d0 = 2 \u221a b0e0. And ML = MR = 1/2Mh, EL = ER = 1/2Eh, and DL = DR = diag(d0/2, d0/2, d0/2, d0/2, d0/2, d0/2). 6.1 Simulations without modeling error Running of a 19-DOF biped robot is simulated for the effectiveness and performance evaluation of the proposed asymmetric trajectory and impedance controller. The biped robot has a total of 19 degrees of freedom, as shown in Fig. 1. Each leg has 6 degrees of freedom, two joints at the ankle, one joint at the knee, and three joints at the hip and the upper body has 7 degrees of freedom. The specification of the biped robot model with two legs of mass 9.5 [kg] used in the simulations is listed in Table 1. The parameters used to generate the flight phase trajectories are shown in Table 2. The control period of the computer simulation is 0.002 [s]. During running, biped robots must interact iteratively with the external environment. In particular, when a foot of the freely swinging leg makes an initial contact with the ground, a large impact force may always be generated. To protect force sensors and joints from the touch-down impact force, many biped robots are equipped with some kinds of shock-absorbing elastic pads at their soles (Yamaguchi et al. 1995). The pads in the support surface are modeled as nonlinear springs and nonlinear dampers, as shown in Fig. 1. The stiffness and damping coefficient are chosen to reflect the nonlinear characteristics of the elastic pad. This nonlinear complaint model with Coulomb friction allows rotating of the foot on the ground (Marhefka and Orin 1999; Kwon and Park 2002). In the computer simulations performed without modeling error, the biped robot runs on a flat solid ground. Figure 9 shows a stick diagram from computer simulations of a 19-DOF biped robot when the average forward speed for running is about 0.774 [m/s] with Tf = 0", + " In order to meet these necessary conditions, asymmetric behavior of a biped robot including gait transition and change of speed is divided into trajectory segments, and then asymmetric trajectories are constructed using polynomial functions to concatenate these trajectory segments, as given in Sect. 4. Nomenclature The subscript \u2018f\u2019 corresponds to the flight phase and the subscript \u2018s\u2019 corresponds to the stance phase. And subscripts \u2018r\u2019, \u2018l\u2019, \u2018b\u2019, and \u2018h\u2019 denote the right leg of \u03c1-joints, left leg of \u03c1joints, and upper body of -joints, the hip link, respectively. Symbol Meaning Defined O\u2013XYZ Absolute coordinates Fig. 1 H \u2212 XH YH ZH Body center coordinates fixed at the body of the robot Fig. 1 G \u2212 XGYGZG Mass center coordinates fixed at the mass center of the robot Fig. 1 \u0308qr , \u0308ql \u2208 \u03c1 Joint acceleration of the right and left legs (1) \u0308qb \u2208 Joint acceleration of the upper body (1) \u0308xh \u2208 6 Actual acceleration of the hip link (1) \u0307xh,d Desired acceleration of the hip link (43) fr , fl \u2208 6 External force/moment applied at the right and left feet (1) Hr,Hl \u2208 \u03c1\u00d7\u03c1 Inertia matrices of the left and right legs (1) R \u2208 6\u00d76 Inertia matrix of the hip link (1) Kr,Kl \u2208 \u03c1\u00d76 Inertia matrices of the left and right legs (1) Qr,Ql \u2208 6\u00d7\u03c1 Inertia matrices of the hip (1) Hb \u2208 \u00d7 ,Kb \u2208 \u00d76 Inertia matrices of the upper body and the hip link (1) Qb \u2208 6\u00d7 Inertia matrices of the upper body and the hip (1) D,P \u2208 6\u00d76 Jacobians of the left and right feet (1) Lr,Ll \u2208 \u03c1,Lb \u2208 , S \u2208 6 Coriolis/centripetal and gravitational forces (1) \u03c4l, \u03c4r \u2208 \u03c1, \u03c4b \u2208 Joint torques of the left leg, right leg and upper body (1) Igk Inertia tensor of k-th link (2) \u03c9gk Angular velocity of k-th link with respect to the absolute coordinates (2) x0 h Linear velocity of the hip link with respect to the absolute coordinates (2) \u03c90 h Angular velocity of the hip link with respect to the absolute coordinates (2) P0 Linear momentum represented by the absolute coordinates (2) H0 Angular momentum represented by the absolute coordinates (2) PG = [( PG)x ( PG)y ( PG)z]T Linear momentum at the mass center of the robot (3) HG = [( HG)x ( HG)y ( HG)z]T Angular momentum at the mass center of the robot (4) rg = [Xg Yg Zg]T Position vector of the center of mass (4) rh = [X Y Z]T Position vector of the hip link (56) mg Total mass of a biped robot (4) mk Mass of k-th link (3) rk = [xk yk zk]T Position vector of k-th link represented by the absolute coordinates (3) Jkx , Jky , Jkz Inertia moments of k-th link about the mass center coordinates (4) \u03c6\u0307kx , \u03c6\u0307ky , \u03c6\u0307kz Angular velocities of k-th link about the mass center coordinates (4) \u0307HOk Rate of change in angular momentum of k-th link (6) \u0307HGk Rate of change in angular momentum of k-th link about the mass center (6) \u0308rk Acceleration of the center of mass of k-th link about the absolute coordinates (6) g = [0 0 \u2212g]T Gravitational acceleration (6) Xzmp, Yzmp x-component and y-component of the ZMP (10) lh Length from the center of the foot to the rear safety boundary (10) lt Length from the center of the foot to the fore safety boundary (10) ( HG)y,td+ Angular momentum at the moment t = ttd+ after touch-down (13) ( HG)y,td\u2212 Angular momentum at the moment t = ttd\u2212 before touch-down (13) \u03b10, \u03b11, \u03b12, \u03b13 Positive values which is determined by support phase trajectories (14) \u03b21, \u03b22 Positive values which is determined by support phase trajectories (17) Vxf , Vyf , Vzf Desired velocity of the hip link at lift-off Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003280_1.55923-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003280_1.55923-Figure1-1.png", + "caption": "Fig. 1 Model representation with reference frames and reference vectors.", + "texts": [ + " The system is modeled with a central body and two rigid wings. The wings are considered to be thin, flat plates with three degrees of freedom relative to the stroke plane. The stroke plane defines the mean motion of the wing and is defined relative to the longitudinal axis of the body. The three degrees of freedom for the wing are the flapping (sweep) angle ( ), the pitch angle relative to the stroke plane ( ), and the deviation (elevation) angle ( ). The coordinate frames and reference vectors are presented in Fig. 1. The wing angles and stroke-plane angle are presented in Fig. 2. D ow nl oa de d by M cG ill U ni ve rs ity o n N ov em be r 12 , 2 01 2 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /1 .5 59 23 The wings are considered to be holonomically constrained to the central body. The 12 generalized coordinates describing the position of the system qj are q j X Y Z R R R L L L (1) The associated quasi velocities of the system uj are u j u v w p q r pRW qRW rRW pLW qLW rLW (2) The multibody equations of motion can be placed into the following form: M _uj Faero Fg P 3 i 1 _ vi;red ci;red Maero Mg P 3 i 1 Ii " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000898_978-0-387-28732-4_4-Figure4-17-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000898_978-0-387-28732-4_4-Figure4-17-1.png", + "caption": "Figure 4-17. Flat interface nerve electrode (FINE).", + "texts": [ + " They combine the simplicity of extraneural electrodes with the selectivity of intra\u2013neural approaches. Both existing device types have been developed by D. Durand and coworkers at the Case Western Reserve University (Cleveland, OH, USA). One design variation is the flat interface nerve electrode (FINE) that reshapes peripheral nerves for selective stimulation [217]. By flattening the nerve into a more elliptical shape the fascicles were distributed next to each other and become more accessible to electrical stimulation in comparison with cylindrical cuffs (Fig. 4-17). Acute studies showed that different fascicles and populations of fibers within a fascicle can be selectively excited [217,218]. In chronic studies nerve damage occurred when a high reshaping force was necessary, whereas moderate reshaping forces did not cause any nerve damage. Moderately flattened nerves showed good selectivity in limb excitation throughout the implantation time up to three months [218,219]. The FINE seems to be an interesting approach for neural interfaces, although it has not yet proved its applicability in clinical use" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003975_s11044-011-9287-2-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003975_s11044-011-9287-2-Figure2-1.png", + "caption": "Fig. 2 A two-sled collision", + "texts": [ + " Identify vn2, In2 or En2, and stop the integration according to the chosen collision hypothesis; find In2, It2 and Is2 and then u1, . . . , up with (12a). 4. Evaluate the mechanical energy loss with both (23) (two versions) and (35a). Identical results validate of the entire procedure. These steps need modifications, discussed in Appendix C, when used to solve the 2D problem. With these modifications, all the results reported in Table 3 of [3] for the planar version of the two-sled problem are reproduced with a three-digit precision. Figure 2 shows two identical sleds A and B comprising rods of length 2l and mass m, supported by massless knife-edges with steering angles \u03b3 and \u03b4, touching planes A\u0304 and B\u0304 fixed in N at points As and Bs , a distance k from their mass centers A\u2217 and B\u2217; and supported by two back sliders moving in A\u0304 and B\u0304 , respectively. A\u0304 and B\u0304 are rotated with respect to one another about their intersection line L forming an angle \u03b8 < \u03c0/2 with a\u03041, a unit vector fixed in A\u0304, such that lines a and b lying in A\u0304 and B\u0304 normal to L form an angle \u03b7 < \u03c0/2; and b\u03041|\u03b7=0 = a\u03041. Let u1, . . . , u6 be generalized speeds, and let the velocities of A\u2217 and B\u2217, and the angular velocities of A and B in N , expressed as vA\u2217 = u1a1 + u2a2, \u03c9A = u3a3, vB\u2217 = u4b1 + u5b2, \u03c9B = u6b3, be subject to the constraints vAs \u00b7 a\u2032 2 = 0 and vBs \u00b7 b\u2032 2 = 0 imposed by the knife-edges. Here ai , bi , a\u2032 i and b\u2032 i (i = 1,2,3) are sets of three dextral, mutually perpendicular unit vectors fixed in A and B , with a3 and a\u2032 3, and b3 and b\u2032 3 normal to A\u0304 and B\u0304 , respectively, as shown in Fig. 2. The indicated constraint equations, when written explicitly and solved for u2 and u5, read u2 = t\u03b3 u1 \u2212 ku3, u5 = t\u03b4u4 \u2212 ku6, where t (.) = tan(.), and lead, with u1, u3, u4, and u6 regarded as independent generalized speeds, to the following equations, governing motions of A and B: \u2212u\u03071/c 2\u03b3 + kt\u03b3 u\u03073 \u2212 ku2 3 = 0, kt\u03b3 u\u03071 \u2212 (l2/3 + k2)u\u03073 + ku1u3 = 0, \u2212u\u03074/c 2\u03b4 + kt\u03b4u\u03076 \u2212 ku2 6 = 0, kt\u03b4u\u03074 \u2212 (l2/3 + k2)u\u03076 + ku4u6 = 0, where s(.) = sin(.) and c(.) = cos(.). Defining generalized coordinates q1, " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000429_j.trac.2006.11.015-Figure9-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000429_j.trac.2006.11.015-Figure9-1.png", + "caption": "Figure 9. Schematic diagrams of typical optical arrangements of mic E, excitation source; F, fluorescence; L, lens; O, optical fiber. Reprinted fr", + "texts": [ + " Xiao and co-workers [52] utilized a similar LED-IFMCE system with a violet or blue LED as the excitation source, and obtained LODs of 17\u201323 nM for DNA-tagged amino acids and 8\u201312 nM for FITC-labeled amino acids. http://www.elsevier.com/locate/trac 73 Despite its high sensitivity, the LOD of LED-IF is still lower than that of LIF. The LED source guided by an optical fiber also lacks proper focusing. Efforts have been made to achieve better detection (vide post). In LIF-MCE and LED-IF-MCE systems, the optical arrangement plays a very important role. There are typically two major types of arrangements in the MCE 74 http://www.elsevier.com/locate/trac system, as shown in Fig. 9 (a\u2013f) [53]. The confocal LIF system [45\u201349,54\u201356] (Fig. 9a) exhibited high sensitivity in microchip separation. As shown in Fig. 10, Harrison s group [54,55] used a confocal LIF system for the determination of fluorescein and cyanine-5 (Cy-5). The laser beam, which was generated by a 635-nm diode laser, was reflected onto the rofluidic chip laser-induced fluorescence (LIF) detection systems: om [53], with permission from ACS. Figure 10. Schematic diagram of the confocal laser-inducedfluorescence microchip capillary electrophoresis (LIF-MCE) system. Reprinted from [55], with permission from Elsevier", + " In spite of the low LOD achieved in the confocal LIF system, the application of the system in microchip CE is still limited because the whole system is complicated and hard to construct. Also, there is interference from scattering of the beam in these configurations. As a result, non-confocal optical arrangements, including bevelincident laser and orthogonal optical arrangements, are used; in these, the interference from the excitation light to emitted fluorescence was eliminated. In a bevel-incident laser system [57\u201362], as shown in Fig. 9 (b and c), the laser beam was positioned to minimize scatter while the fluorescence was detected perpendicular to the chip. Dandliker s group [60] used a non-focal LIF system (Fig. 11) in which the HeNe laser beam was at 45 to the chip surface, and the emitted fluorescence was then collected and focused perpendicular to the chip surface by a microlens into the photodetector. The LOD for Cy5 solution was 3.3 nM. As for the orthogonal optical arrangement [63\u201366] (Fig. 9 (d\u2013f)), the laser beam was guided by an optical fiber, inserted into the chip channel from a horizontal direction, and the emitted fluorescence was detected in the perpendicular direction with respect to the chip surface. Fang s group [53] developed an LIF system based on an orthogonal optical arrangement (Fig. 12). The laser beam was guided and focused into an optical fiber, which was inserted into a microchannel in the microchip, followed by the detection (by PMT) of the excited fluorescence, which was perpendicular to the chip surface" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000811_tmag.2008.2002379-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000811_tmag.2008.2002379-Figure2-1.png", + "caption": "Fig. 2. Coil ends in a phase belt and the cylindrical coordinate system with the positive directions indicated.", + "texts": [ + " In the nonconductive regions, no current density. Moreover, in the rotary parts, the tensor of conductivity was , where means slip, so only one frequency, , was assigned for the whole simulation. A weak form was used in the FEA. Using the shape function of edge-based elements as a weight function, i.e., Galerkin\u2019s method, deduced the weak form of (1) as (2) where is the corresponding domain; is the boundary of ; is the outward-directed normal unit vector on a boundary. In the cylindrical coordinate system shown in Fig. 2, a periodic condition was imposed in such a way that the components of the magnetic vector potential on two sides I and II, as pointed out in Fig. 2, that is, , , and on side I, and , , and on side II, fulfilled the condition: , , and , where is the number of poles to be simulated. Another condition was imposed on all the other sides. The first-order edge-based elements, tetrahedra and prisms, were used in the end region and active region, respectively. The number of degrees of freedom was 301654. The magnetic forces, exerted on end-windings, are a typical case of Lorentz forces. The Lorentz force density at a point in a current-carrying conductor is , where and are the current density and magnetic induction", + " From the above equation, the components of the force density at a point were (3) where , , and denote instantaneous values of the components of the force density; means taking the real part of a complex number; means taking a conjugate complex number; and is time. Obviously, in (3), each component is the sum of two components: a constant component and a sinusoidal component with a double-frequency, . Because the force density varied in the end-windings, the force on segment of a coil end was computed by integrating (3) on its volume as , where denotes the force on segment . Moreover, the force was assumed to be exerted on the centre of segment . The force was then expressed in the cylindrical coordinate system marked in Fig. 2. The -component of the force was the same as in the Cartesian coordinate system, whereas the - and -components, and , were obtained by (4) where is the four-quadrant inverse tangent function; and and are the - and -components of , respectively. belt: (a) the constant component, ; (b) the amplitude of the sinusoidal component, . Then the force was transformed into (5) where , , and , and , , and are the constant components and the amplitudes of the sinusoidal components of the -, -, and -components of the force, respectively; and , , and are the phase angles of the corresponding sinusoidal components. As the volume of each segment was not equal, for the sake of comparison, the average force density in segment , , was introduced and defined as . The components of the average force density, , , and , were written in (6) The phase belt in Fig. 2 was analyzed since the other phase belts would have similar situations. Here, the average force densities were studied but the results were fit for the forces. Three groups of coefficients in (6), i.e., and , and , and and in a phase belt: (a) the constant component, ; (b) the amplitude of the sinusoidal component, . , were computed at full load and are plotted in Figs. 3\u20135, respectively. In Fig. 3, from the values of , it is clear that in the four coil ends, except in segments 15\u201321 of the four coil ends, lies in positive -direction" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000312_s11071-005-9016-6-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000312_s11071-005-9016-6-Figure5-1.png", + "caption": "Figure 5. Tangent and normal vectors to the body surface at a contact point Pk .", + "texts": [ + " These surface parameters are independent variables that are treated in the system dynamics in the same manner as the system generalised coordinates. The difference between these surface parameters and the generalised coordinate is that there is no inertia or generalised forces associated with these surface parameters. Thus, the surface parameters are also referred to as the non-generalised coordinates. At the contact point, for each surface in contact a tangent plane is defined by two tangent vectors as shown in Figure 5. These tangent vectors are linearly independent and not necessarily orthogonal. The tangent vectors to the surfaces of bodies i and j are defined, respectively, in the body coordinate system as t\u0304ik l = \u2202u\u0304ik \u2202sik l , l = 1, 2 (21) t\u0304 jk l = \u2202u\u0304 jk \u2202s jk l , l = 1, 2 (22) Using these tangent vectors we can define the normal vectors to the surfaces in contact as n\u0304ik = t\u0304ik 1 \u00d7 t\u0304ik 2 (23) n\u0304 jk = t\u0304 jk 1 \u00d7 t\u0304 jk 2 (24) where n\u0304ik and n\u0304 jk are, respectively, the normal vectors to the surface of body i and j in the point of contact defined in the body coordinate system" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001950_10402000902913345-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001950_10402000902913345-Figure2-1.png", + "caption": "Fig. 2\u2014Construction of the compound sensor.", + "texts": [ + " Compound Information Diagnostic System The structure of a compound diagnostic system is shown in Fig. 1. As is apparent from the diagram in the figure, this system 725 D ow nl oa de d by [ U ni ve rs ity o f C al if or ni a, S an F ra nc is co ] at 0 7: 18 2 9 Ja nu ar y 20 15 consists of a compound sensor, a signal processor, and a signal processing software-loaded personal computer. By means of a compound sensor using the piezoelectric effect of the lead-zirconate-titanate (PZT) crystal, an input signal is transformed into the electrical signal. Figure 2 illustrates the construction of the compound sensor. The propagation of acceleration from a low-frequency vibration in the sensor develops a force on the damping material fixed to the crystal, and due to this force the whole crystal is strained, thus generating an electric charge in response to the magnitude of the acceleration. As a result of this action, the vibration acceleration is converted into the electrical signal. On the other hand, in case of high-frequency AE, as a result of the propagation process in the crystal, the crystal will be partially strained depending on the phase of AE, and accordingly a change in the electrical signal for the AE based on the generated electric charge is observed" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003823_icosc.2013.6750965-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003823_icosc.2013.6750965-Figure1-1.png", + "caption": "Figure 1. Mini Quadrotor Arducopter from diydrones.com.", + "texts": [ + " The results show that the overall system becomes stable and robust. Keywords-component; Mamdani-type fuzzy controller; PID classic controller Fuzzy control; UAV; Quadrotor; Non-linear systems I. INTRODUCTION This paper presents the design of hybrid intelligent approach, which combines fuzzy and PID classic regulation control to navigate an unmanned Quadrotor .The overall objective of our project is the design and implementation of, and experimentation on, a control system for a Arducopter mini-Quadrotor (Figure 1) . In these days the used of Fuzzy logic to the control of UAV Quadrotor has been increased because of her superior traits, which is resumed in practical, economical and intelligent. This long list, however, can only be realized in the existence of quality expert knowledge (pilot). Various types of control modes have already been tested for an unmanned Quadrotor [9, 10, and 11].Each control mode is named according to the states variables that are considered outputs. For example, to keep the Quadrotor at a specific location, the position and heading (x,y,z,y) control mode is used" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002529_1.4001812-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002529_1.4001812-Figure4-1.png", + "caption": "Fig. 4 Slider design \u201epico\u2026 with DP grooves on trailing pad", + "texts": [ + " This means that various ABS components make various contributions to the slider\u2019s damping, but the rear ABS is a prime contributor to the slider\u2019s damping characteristics. Those suggest that a specific rear ABS structure may achieve high damping at high frequencies, which requires achieving a stable head-disk interface. JULY 2010, Vol. 132 / 031702-3 ata/journals/jotre9/28775/ on 04/18/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use C g a h t v d g a F m F t 0 Downloaded Fr haracteristics. There is a slider design with three squared DP rooves distributed on its rear surface in Fig. 4. Its damping charcteristics were calculated and are shown in Fig. 5 b . Figure 5 a as the damping characteristics of the slider in Fig. 2. We can see hat the damping peak shifts to a higher frequency, and this is a ery important result in DP slider design Xu and Tsuchiyama 14 . However, how can we increase damping further and shift the amping peak to a much higher frequency? We found that a reater number of smaller DP grooves could increase the damping nd shift the damping peak to a much higher frequency", + " Grooves on the ABS can effectively enhance an air-bearing slider\u2019s damping characteristics, which may depend on the number of grooves, depth, location, width, length, distribution, orientation, and groove type. Therefore, we need to examine the relationship between the slider\u2019s damping ratios and design parameters and then to optimize the ABS design to obtain the highest damping ratio. In this study, a desktop slider for a 3.5 in. hard disk drive with a femto long Fig. 5 Damping characteristics in translation and pitch motions of \u201ea\u2026 slider in Fig. 2 and \u201eb\u2026 slider in Fig. 4 Transactions of the ASME ata/journals/jotre9/28775/ on 04/18/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use f a t i t g d b w s o d r i f a w fl g n w T F f F F J Downloaded Fr orm factor whose length is the same as that of pico and width, nd thickness is the same as that of femto used. The slider was of he subambient type with an 11 nm flying height, and it is outlined n Fig. 9. The speed of rotation of the disk rotation was 7200 rpm. 3.3.1 Number of Grooves Versus Damping Ratio" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000231_9781420005868.ch1-Figure1.6-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000231_9781420005868.ch1-Figure1.6-1.png", + "caption": "FIGURE 1.6 (a) Diagram of a potential waveform used in linear sweep (cyclic) voltammetry. (b) A cyclic voltammogram.", + "texts": [ + " DPV produces a peaked voltammogram, roughly corresponding to the derivative of the NPV voltammogram; this peaked voltammogram can improve both the qualitative and quantitative aspects of the technique. CYCLIC VOLTAMMETRY Chronoamperometry, NPV, and DPV are potential pulse techniques. Potential sweep methods are also available. Cyclic voltammetry (CV) is widely used in neuroscience applications. As the name implies, the potential is swept from an initial potential to a final potential and then returned to the initial potential, usually at the same sweep rate (Figure 1.6a). The current measured continuously during the sweep is reported against the applied potential (Figure 1.6b). Hence, the technique provides voltammetric information (current vs. potential) about the substance being detected. This is useful for the purposes of qualitative identification as the voltammogram of a substance q 2006 by Taylor & Francis Group, LLC D ow nl oa de d by [ Pu rd ue U ni ve rs ity L ib ra ri es ] at 0 5: 07 1 6 A ug us t 2 01 6 is generally unique in its position along the potential axis and its shape. For example, the cyclic voltammogram of dopamine is easily distinguished from the voltammogram of ascorbate" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003643_robio.2011.6181649-Figure6-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003643_robio.2011.6181649-Figure6-1.png", + "caption": "Fig. 6. The rebound of the ball on the racket.", + "texts": [ + "\ud835\udc63(\ud835\udc4e) := \u23a1 \u23a3 0 \ud835\udc4e\ud835\udc5f 0 \u2212\ud835\udc4e\ud835\udc5f 0 0 0 0 0 \u23a4 \u23a6 ?\u0304?\ud835\udf14(\ud835\udc4e) := \u23a1 \u23a3 0 \u2212 3\ud835\udc4e 2\ud835\udc5f 0 3\ud835\udc4e 2\ud835\udc5f 0 0 0 0 0 \u23a4 \u23a6, ?\u0304?\ud835\udf14(\ud835\udc4e) := \u23a1 \u23a31 \u2212 3\ud835\udc4e 2 0 0 0 1 \u2212 3\ud835\udc4e 2 0 0 0 1 \u23a4 \u23a6 . (4) The parameter \ud835\udc4e is switched as \ud835\udc4e = \ud835\udf07(1 + \ud835\udc52\ud835\udc5b) \u2223\ud835\udc63\ud835\udc4f\ud835\udc67\u2223 \u2225\ud835\udc97\ud835\udc4f\ud835\udc47 \u2225 (\ud835\udf08\ud835\udc60 > 0), 2 5 (\ud835\udf08\ud835\udc60 \u2264 0) \ud835\udf08\ud835\udc60 = 1 \u2212 2 5 \ud835\udf07(1 + \ud835\udc52\ud835\udc5b) \u2223\ud835\udc63\ud835\udc4f\ud835\udc67\u2223 \u2225\ud835\udc97\ud835\udc4f\ud835\udc47 \u2225 . \ud835\udf08\ud835\udc60 > 0 means the case of the sliding contact and \ud835\udf08\ud835\udc60 \u2264 0 means the case of the rolling contact. Note that the rebound model of the table is the piecewise linear equation with respect to \ud835\udc4e. The identified values are \ud835\udf07 = 0.25 and \ud835\udc52\ud835\udc5b = 0.93. As illustrated in Fig. 6 (a), the variables of the velocities are the same in the previous subsection. \u03a3\ud835\udc45 is the racket frame with the \ud835\udc67-axis normal to the racket surface. In the case of the rebound on the racket, there is the effect of the elastic as in Fig. 6 (b), where the tangent and rotational velocities are inversed after the rebound. The equations of the rebound model to express this phenomenon are given by the following coefficient matrices: \ud835\udc68\ud835\udc63 = \ud835\udc79\ud835\udc45?\u0304?\ud835\udc63(\ud835\udc4e)\ud835\udc79 T \ud835\udc45, \ud835\udc69\ud835\udc63 = \ud835\udc79\ud835\udc45?\u0304?\ud835\udc63(\ud835\udc4e)\ud835\udc79 T \ud835\udc45 \ud835\udc68\ud835\udf14 = \ud835\udc79\ud835\udc45?\u0304?\ud835\udf14(\ud835\udc4e)\ud835\udc79T \ud835\udc45, \ud835\udc69\ud835\udf14 = \ud835\udc79\ud835\udc45?\u0304?\ud835\udf14(\ud835\udc4e)\ud835\udc79T \ud835\udc45 (5) where the matrices with the bars are the same as those in (4) and \ud835\udc4e = \ud835\udc58\ud835\udc5d \ud835\udc5a (6) is the fixed value differently from the case of the table. \ud835\udc58\ud835\udc5d is the coefficient which relates the tangent velocity to the tangent impulse. \ud835\udc79\ud835\udc45(\ud835\udefd, \ud835\udefc) \u2208 \u211d 3\u00d73 is the rotation matrix of \u03a3\ud835\udc45 relative to \u03a3\ud835\udc35 and (\ud835\udefd, \ud835\udefc) is the \ud835\udc4c \ud835\udc4b-Euler angle parameterization" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002443_s12239-011-0023-y-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002443_s12239-011-0023-y-Figure4-1.png", + "caption": "Figure 4. Non-effective stroke in booster and master cylinder assembly.", + "texts": [ + " Also, the compression rate will change its transforming trend. Therefore, the expansion rate of brake pad compression is selected as a semi-empirical parameter. 4.2. Non-effective Stroke Non-effective stroke means that the vehicle has no reaction, even though the driver pushes the pedal and the pedal moves. Usually, there are two non-effective strokes in the brake system. The first one is located in the master cylinder and booster assembly. It is the gap between the booster push rod and the piston of the master cylinder. Figure 4 explains this non-effective stroke in the booster and master cylinder assembly. To increase the accuracy of the stroke model, the noneffective stroke must apply to equation (3). The value of the non-effective stroke (l0) is taken from booster test results as a semi-empirical parameter. Equation (7) is a modified equation showing the relationship between pedal stroke and brake fluid volume. (7) Another non-effective stroke is the pad clearance between the brake pad and the disc. Although the pad clearance has a small value, it exists in all wheels" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001354_0005-2736(75)90057-7-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001354_0005-2736(75)90057-7-Figure2-1.png", + "caption": "Fig. 2 (A) Transport of [14C]phenylalamne Comdlal transport of L-[l 'tC]phenylalamne was measured in pm-nbg 27 and compared to transport m pm-nb. Uptake was mmated by adding labeled amino acid to the mcubat ion medmm (1 \u00d7 Vogel's) with 0.1 mg/ml concentraUon of conl&a (B) Transport of [14C]argmme. Comdlal transport of L-[* 4C]arglmne m pm-nb and pm-nbg z7 was compared.", + "texts": [ + " However, following derepression of the general transport system by ammonium starvation (KNO3 Vogel's) pm-nb was found to be highly sensitive to p-fluoro-phenylalanlne In KNOs medium. The pm-n; pro-b; pm-g triple mutant can therefore be characterized as resistant to p-fluoro-phenylalanme under both conditions (KNO3 and NH4CI ) for growth. Amino acid transport experiments were performed to ascertain that the aboveobserved resistance of pro-n; pm-b; pm-g was due to deficiency in the transport of that particular amino acid and its analogs. Transport activity of neutral amino acids was measured using labeled phenylalanine (Fig. 2A). The triple mutant pm-nbo 27 exhibits an almost neghgible amount of transport of phenylalanine when compared to the parental strain pm-nb. Similarly labeled arginine was used to compare transport activity of basic amino acids, between pm-nb and pm-nbo 27 (Fig. 2B). Again pm-nbo 27 shows negligible transport of arginine compared to its pro-rib parent. 48 port activity following lncubatiort for 180 min in Vogers minimal medium (N) plus glucose as carbon source. A 10-fold amphfication of transport acuvlty was observed, due mainly to the actwlty of the general transport system. Transport experiments with 0 5 mg cells were incubated for 90 mm with 1 ~o glucose in Vogers medmm containing either [14C]phenylalanme or [14C]argmme or [14C]argmme with 10 times unlabeled phenylalamne" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002708_acc.2010.5530997-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002708_acc.2010.5530997-Figure3-1.png", + "caption": "Fig. 3. Waypoint via tangent path.", + "texts": [ + " The Dubins path can be easily obtained from the geometrical relations as can be seen in Ref. [13]. The DWP for the UAV guidance is determined as the end of the line segment in CLC Dubins path as shown in Fig. 2. 2) Waypoint based on a tangent to a circular path (TWP): The tangent to the circle is much simpler than the CLC Dubins path and therefore, is easily implementable onboard. The tangent point is set as the final turning waypoint and is determined as the tangent point of the nearest circle as shown in Fig. 3. C. Prediction of rendezvous point and time Time-to-rendezvous can be estimated using the current UAV position, velocity, and heading, and those of the future target information at rendezvous that is estimated from the current target position, heading, velocity, and turn rate. Assuming that these quantities are always available or estimated in each time step, the estimation of the time-to -rendezvous can be made by the following steps. 1) Set the time-to-rendezvous using the current relative distance between the UAV and the target aircraft as an initial value, as desRV VRt /= (14) where desV is a desired velocity, which is a pre-specified adjustable parameter" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001851_robot.2009.5152196-Figure7-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001851_robot.2009.5152196-Figure7-1.png", + "caption": "Fig. 7. Compressed Muscular Arrangements of 1-DOF Rotational System; (b) is h = 10, r = 30, d = 5. (a) is h = 10, r = 30, d = 0.", + "texts": [ + " COND1: \u2202P \u2202\u201e \u2223 \u2223 \u2223 \u201e=\u201ed = W (\u201e)v(\u201ed)|\u201e=\u201ed = 0 COND2: \u22022P \u2202\u201e 2 \u2223 \u2223 \u2223 \u201e=\u201ed > 0 If the system has plural local minimums, we should consider the additional condition; \u201dPotential P (\u03b8) has the unique local minimum at the stationary point \u03b8d in the supposed motion area.\u201d However, this paper takes account of only CONDs 1-2 as the local condition. From the perspective of potential minimization, we investigate the potential fields of the 1-DOF rotational systems, of which muscular arrangements are shown in Fig.7. The arrangement of Fig. 7-(a) is h = 10, r = 30, d = 5. On the other hand, that of Fig. 7-(b) is h = 10, r = 30, d = 0. These arrangements are similarly compressed by the muscular tension. Figure 8 presents the difference of the potential fields P , of which desired angles are \u03b8d = \u03c0/2, \u03c0/3 and \u03c0/4. The result of (a) is that each potential energy P is minimized at each desired angle. The system (a), in other words, is numerically satisfied with the above condition. On the contrary, the result of (b) is not. That is, the muscular arrangement shown in Fig. 7-(a) can quasi-statically achieve the feedforward positioning by inputting the internal force balancing at desired posture, even though both controlled links are compressed similarly. In the following, the muscular arrangement satisfied with the above conditions is defined as the \u201dstable\u201d arrangement. A. Decomposition of potential In this section, the above discussion is expanded into the two-link system with two joints (the shoulder and elbow joints) and six muscles (two biarticular muscles and four simple joint muscles), which is modeled after the human\u2019s upper limb as shown in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003156_robio.2013.6739739-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003156_robio.2013.6739739-Figure3-1.png", + "caption": "Fig. 3. The radius of grasp circle", + "texts": [ + " (5) where hr is the installation height of the manipulator, l1, l2 and l3 are the lengths of the connecting rods, \u03b81 [0, \u03c0], \u03b82 [-\u03c0/2, \u03c0/2] and \u03b83 [-\u03c0/2, \u03c0/2] are the wrist joint, the elbow joint and the shoulder joint of the manipulator, respectively. Suppose that the height of grasp point to the ground is he, all possible angle combinations are scanned to obtain the maximum and minimum length of the manipulator, that is, lm=max(l)|h=he, ln=min(l)|h=he. A proper radius of the grasp circle le=(lm+ln)/2 is chosen, which is shown in Fig. 3. Thus, the position of end point i is represented as cos sin i e t e i i e t e i x x l y y l \u03c6 \u03c6 \u23a7 = +\u23aa \u23a8 = +\u23aa\u23a9 ( , 1, , )i e e ek k n\u03c6 \u03d1= \u0394 = \u2026 (6) where 2 / en\u03d1 \u03c0\u0394 = is the angle interval between the adjacent end points. In addition, t3 is given based on the straight-line distance and the initial velocity v0 of the mobile manipulator. 2 2 3 0( ) ( )s t s tt x x y y v= \u2212 + \u2212 (7) According to the feature of tangent vector of Bezier curve, it is obvious that the second/third control point is on the direction of velocity of the first/fourth control point" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002099_j.cad.2010.08.007-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002099_j.cad.2010.08.007-Figure3-1.png", + "caption": "Fig. 3. Coordinate systems.", + "texts": [ + " (rd)d = R [id, \u2212 (90\u00b0 \u2212 \u03b2)] (ra)a \u2212 a0id = xdid + ydjd + zdkd, (3) xd = xa \u2212 a0, yd = ya sin\u03b2 + za cos\u03b2, zd = \u2212ya cos\u03b2 + za sin\u03b2; (n)d = R [id, \u2212 (90\u00b0 \u2212 \u03b2)] (n)a = nxid + nyjd + nzkd, (4) nx = sin\u03c6 cos \u03b8, ny = sin\u03b2 sin\u03c6 sin \u03b8 + cos\u03b2 cos\u03c6, nz = \u2212 cos\u03b2 sin\u03c6 sin \u03b8 + sin\u03b2 cos\u03c6; (gm)d = R [id, \u2212 (90\u00b0 \u2212 \u03b2)] (gm)a = gmxid + gmyjd + gmzkd, m = 1, 2; (5) g1x = cos\u03c6 cos \u03b8, g1y = sin\u03b2 cos\u03c6 sin \u03b8 \u2212 cos\u03b2 sin\u03c6, g1z = \u2212 cos\u03b2 cos\u03c6 sin \u03b8 \u2212 sin\u03b2 sin\u03c6; g2x = \u2212 sin \u03b8, g2y = sin\u03b2 cos \u03b8, g2z = \u2212 cos\u03b2 cos \u03b8; where a0 = a \u2212 rf1 \u2212 rd and R [id, \u2212 (90\u00b0 \u2212 \u03b2)] = 1 0 0 0 sin\u03b2 cos\u03b2 0 \u2212 cos\u03b2 sin\u03b2 . All the coordinate systems needed in the first envelope are shown in Fig. 3. The fixed coordinate system, \u03c3o1(o1; io1, jo1, ko1), indicates the initial position of the worm blank. Unit vector ko1 lies along the center line of the worm blank. The fixed coordinate system, \u03c3o2(o2; io2, jo2, ko2), herein indicates the initial axial position of the tool post; and unit vector ko2 is along its axis. Unit vectors io2 and jo2 are in the axial section of the worm blank. The two unit vectors, ko1 and ko2, are mutually perpendicular since the discussion is limited to the worm pair with orthogonal axes", + " (9) shows a relationship among \u03c6, \u03b8 and \u03d5. Consequently, only two variables among the three are independent of each other, and they are the two parameters of helicoid \u03a31. The threedimensional graphics of the helicoid \u03a31, in Example B in Section 6, is illustrated in Fig. 4. The meshing course of a height-modified DTT worm pair is called the second envelope. In the second envelope, the two stationary systems, \u03c3o1 and \u03c3o2, indicate the initial positions of a height-modifiedDTTwormand its mating worm wheel, also as depicted in Fig. 3, respectively. Unit vector ko1 is along the worm axis while unit vector ko2 is along the worm gear centerline. The two movable systems, \u03c31 and \u03c32, are rigidly connected to the modified worm and its mating worm gear, respectively. When the rotation angle of the worm about its axis is \u03d51, the corresponding rotation angle of the worm wheel is \u03d52; and \u03d51 = i12\u03d52. When a height-modified worm rotates around its axis, its helicoid \u03a31 forms a one-parameter family of surfaces {\u03a31} in \u03c3o1. By coordinate transformation, the vector equation of {\u03a31} and its unit normal vector can be represented in \u03c3o1 as: r\u2217 1 o1 = R [ko1, \u03d51] (r1)1 = R [ko1, \u03d51 \u2212 \u03d5] (r1)o1 = x\u2217 o1io1 + y\u2217 o1jo1 + yodko1, \u03a6d(\u03b8, \u03c6, \u03d5) = 0, (11) x\u2217 o1 = (xod + a) cos (\u03d51 \u2212 \u03d5) + (zd \u2212 1b) sin (\u03d51 \u2212 \u03d5) , y\u2217 o1 = (xod + a) sin (\u03d51 \u2212 \u03d5) \u2212 (zd \u2212 1b) cos (\u03d51 \u2212 \u03d5) ; n\u2217 o1 = R [ko1, \u03d51 \u2212 \u03d5] R [io1, 90\u00b0] (n)od ; (12) where R [ko1, \u03d51 \u2212 \u03d5] = cos (\u03d51 \u2212 \u03d5) \u2212 sin (\u03d51 \u2212 \u03d5) 0 sin (\u03d51 \u2212 \u03d5) cos (\u03d51 \u2212 \u03d5) 0 0 0 1 " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002745_robio.2010.5723320-Figure16-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002745_robio.2010.5723320-Figure16-1.png", + "caption": "Fig. 16 Coordinate system of the camera", + "texts": [ + " In this environment, we conduct an experiment in which the robot avoids these obstacles. Fig. 13 shows the experiment environment in task 3. Fig. 13 Avoiding multiple objects Fig. 14 shows the developed mobile robot. This robot has two active wheels. We employ Logicool Qcam Pro 9000 as the CCD camera. Fig. 14 Mobile robot In this paper, we employ tau-margin for avoiding the mobile robot. We model the mobile robot as shown Fig. 15. The robot has two wheels and impellent force of each wheel is controlled independently. Fig. 16 shows the coordinate system of the camera. Equation (6)-(9) shows the controller. [Task1 and Task3] C ob L T x kkT + \u2212 \u2212 \u2212= 11 21 \u03c4 (6) C ob R T x kkT + \u2212 \u2212 \u2212 \u2212= 11 21 \u03c4 (7) 21 , kk : Proportional gain [Task2] ( ) CT ob L Txk x kkT +\u2212\u2212 \u2212 \u2212 \u2212= 321 11 \u03c4 (8) CT ob R Txk x kkT +\u2212 \u2212 \u2212 \u2212 \u2212= 321 11 \u03c4 (9) 321 ,, kkk : Proportional gain RL TT , denote impellent force of each wheel, CT denotes the constant torque, obx denotes the center of the detected object on the coordinate of the camera. \u03c4 denotes tau-margin of the detected object" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003211_j.compstruc.2011.05.015-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003211_j.compstruc.2011.05.015-Figure2-1.png", + "caption": "Fig. 2. ZPST shell element.", + "texts": [ + " For example, an order of 8 and 10 is sufficient to interpolate the real and imaginary part of the material C elastic modulus, while an order of 14 is necessary for the material B on two frequency bands. An order of 14 is also used for the material A on a single frequency band. The forced vibration problem is described by the classical variational formulation: Z V fdegt frg \u00fe q duf g @2u @t2 ( ) dV \u00bc Z V Fe du dV ; \u00f09\u00de where e and r are the strain and stress tensors, u the displacement, q the density, and Fe the excitation force assumed to be harmonic in the following. The finite element ZPST used in this paper is depicted in Fig. 2. The formulation presented in details by Sulmoni et al. [20] is reminded here briefly, and solved by FEM. The displacement approximation employed in the ZPST element is depicted in Fig. 3 with the p-order approximation and the zigzag function. The zigzag function is added in order to enhance the convergence of the solution at the interfaces. The same approximation is used for the in-plane displacements along n1 and n2, and for the normal displacement along n3. The displacement vector eu over the element e is hence described with a p-order polynom and a first-order zigzag function such as: eu\u00f0n\u00de \u00bc Xn i\u00bc1 Hi\u00f0n1; n2\u00de eq\u00f00\u00dei \u00f0t\u00de \u00fe n3 eq\u00f01\u00dei \u00f0t\u00de \u00fe \u00f0 1\u00deKfeq\u00f0Z\u00dei \u00f0t\u00de h \u00fe n2 3 eq\u00f02\u00dei \u00f0t\u00de 2" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001237_19346182.2008.9648483-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001237_19346182.2008.9648483-Figure2-1.png", + "caption": "Figure 2. Measurement setup of the rowing simulator: instrumented single scull placed inside the Cave.", + "texts": [ + " 6, 257\u2013266258 Research Article J. von Zitzewitz et al. D ow nl oa de d by [ R M IT U ni ve rs ity L ib ra ry ] at 0 1: 28 2 0 Ju ne 2 01 6 actual length (lR) of the unwound rope can be measured for a given winch diameter (dW). Furthermore, three incremental wire potentiometers (4 cts/mm) lead from the ground and from the sculling rigger to the oar. With this sensor configuration, the spatial orientation of the oar, as well as the oar displacement in the direction of its longitudinal axis, can be measured (Figure 2). The position of the boat seat (xS) is measured by a further incremental wire potentiometer (4 cts/mm). In general, a model for virtual rowing is driven by measured variables, which reflect the rower\u2019s performance. The model output controls the displays presented to the user. In our setup, a haptic, visual, and acoustic display are integrated. Our model inputs are the three oar angles y (in the horizontal plane), d (in the vertical plane), and f (around the longitudinal oar axes), and the seat position xS (Figure 3) summarized in the vector k" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002992_s10846-013-9962-z-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002992_s10846-013-9962-z-Figure1-1.png", + "caption": "Fig. 1 Quadrotor vehicle", + "texts": [ + " Section 3 is devoted to describe the hardware setup and the procedure to identify the parameters of the aerodynamic actuators. In Section 4 we present the hard real-time programming strategy and the tuning procedure for the gains of the nonlinear controller. Section 5 is devoted to the experimental results. Finally, Section 6 concludes this work with remarks and possibilities for further research. 2 The Quadrotor Model and the Nonlinear Controller 2.1 Quadrotor Model The kinematic and dynamic models of the rotary wing vehicle expressed in mixed inertial and body coordinates, as shown in Fig. 1, are given by [30]) X\u0307 = R( ) Vb m V\u0307b = \u2212m \u00d7 Vb + Fb (1) \u0307 = W( )\u22121 where m is the vehicle mass, J is the vehicle inertia matrix,1 X = [x y z], = [\u03c6 \u03b8 \u03c8] denote the translational position and the attitude parameterized by Euler angles respectively. Vb = [u v w] and = [p q r] denote the translational and 1The quadrotor has two axes of symmetry, then J = diag{Jxx, Jyy, Jzz}. angular velocities in body coordinates respectively. From a zyx rotation sequence we have R( ) = \u23a1 \u23a3 c\u03b8c\u03c8 c\u03b8s\u03c8 \u2212s\u03b8 c\u03c8s\u03b8 s\u03c6 \u2212 s\u03c8c\u03c6 s\u03c8 s\u03b8 s\u03c6 + c\u03c8c\u03c6 c\u03b8 s\u03c6 c\u03c8s\u03b8c\u03c6 + s\u03c8 s\u03c6 s\u03c8 s\u03b8c\u03c6 \u2212 c\u03c8s\u03c6 c\u03b8c\u03c6 \u23a4 \u23a6 W( )\u22121 = \u23a1 \u23a2\u23a3 1 t\u03b8 s\u03c6 t\u03b8c\u03c6 0 c\u03c6 \u2212s\u03c6 0 s\u03c6 c\u03b8 c\u03c6 c\u03b8 \u23a4 \u23a5\u23a6 (3) with cx = cos(x), sx = sin(x) and tx = tan(x)", + " The external forces are the vehicle weight and the total thrust which in body coordinates are described by Fb = \u23a1 \u23a3 \u2212m g s\u03b8 m g c\u03b8s\u03c6 m g c\u03b8 c\u03c6 \u23a4 \u23a6 + \u23a1 \u23a3 0 0 \u2212TT \u23a4 \u23a6 (4) with TT = \u22114 i=1 Ti and Ti the thrust of rotor i. Angular motion around the xb axis is consequence of the moment generated by a differential thrust between rotor 3 and rotor 1, while angular motion around the yb axis is due to the moment generated by a differential thrust between rotor 4 and rotor 2. Finally, yaw motion is an outcome of the algebraic sum of each rotor\u2019s reactive moment, this means that two rotors turn in clockwise direction while the other two turn in counterclockwise direction. For the rotors configuration shown in Fig. 1, viewing the quadrotor from the \u2212zb axis, the rotors 2 and 4 rotate in clockwise direction, while rotors 1 and 3 rotate in the opposite direction. As a result, we have Mb = \u23a1 \u23a3 (T3 \u2212 T1) (T2 \u2212 T4) Q1 \u2212 Q2 + Q3 \u2212 Q4 \u23a4 \u23a6 (5) where is the distance between the rotors axis of rotation and the vehicle\u2019s center of gravity and Qi, i = 1, \u00b7 \u00b7 \u00b7 , 4 the reactive moment of rotor i. Remark 1 All attitude parameterizations based on coordinates fail to represent, globally and uniquely, the set of attitude configurations" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001991_1.3451641-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001991_1.3451641-Figure1-1.png", + "caption": "Fig. 1 Control volume", + "texts": [ + " 2 Location of control volume relative to the finite difference mesh that the intervals between grooves are sufficiently small for the microscopic groove and ridge pressure gradients to remain con stant within a groove ridge pair. If indeed the distance between grooves is this small, it is reasonable to restate this assumption as an approximation that the microscopic pressure gradients re main constant within small intervals rA6 and As, where these small intervals are not necessarily tied to the distances between grooves. In this way A\\ps and bipo can be considered simply as the fluxes crossing small intervals r Ad and As, respectively, and will be treated as such in the subsequent analysis. Fig. 1 shows a rectangular control volume, bounded above and below by the bearing surfaces, whose sides are oriented perpen dicular and parallel to the direction of surface motion. A flux balance for this control volume may be stated as follows: (A^6 (AiAe)e + ( A ^ , ) , + A . - (A*. ) . + T7 (pV) = 0 (5) ot where V is the total volume enclosed by the control volume boundaries. If the control volume covers a normal grooved (or smooth) surface, V is given by V = KJirrA6As (6) which is simply the mean film height multiplied by the surface area" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003499_s11771-013-1495-x-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003499_s11771-013-1495-x-Figure2-1.png", + "caption": "Fig. 2 Contact force at a meshing point", + "texts": [ + " (8) can be defined as 2 2 0 2 1/2 2 2 2 1 2 1 2 ( / ) ( ) ( ) ( ) ( ) 2 \u03c0 3 (1 ) 1 11 B a b E e K e A K e E e P p ab b e a v v E EE (9) In order to obtain the value of e, we can use the numerical method to solve the first formula of Eq. (9). The results of solution are 1/3 2 2 1/2 0 1.5 ( ) ( ) [ ] \u03c0 (1 ) 1.5 \u03c0 P K e E e a E e A b a e P p ab (10) 2.1.2 Contact force of face gear drive under torque Usually, the torque of transmission upon pinion is known. But the values of normal contact force should be calculated, when computing the contact stress of tooth flank. The face gear meshes with pinion at point M, and the torque on the pinion is T (N\u00b7m) (see Fig. 2). It is easily known that, the action line of force P is tangent with base circle Rb1 (m), so force P can be obtained as P=T/Rb1 (11) 2.1.3 Calculation of contact path and principal curvatures of meshing points Considering that tooth number of pinion is less than the ones of shaper, the contact point of face-gear drive is presented, in which the contact path shifts as a result of assembly error [13]. Before carrying out LTCA based on \u201cHertz theory on normal contact of elastic solids\u201d, it is necessary to obtain the contact points and their principal curvatures" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003276_tasc.2013.2283238-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003276_tasc.2013.2283238-Figure5-1.png", + "caption": "Fig. 5. Photograph of fabricated HTS rotor. (a) Gd-system shield bulk. (b) Completed rotor.", + "texts": [ + " This shows one of the evidences for the saturation mode reluctance torque. In other words, the reluctance torque is autonomously generated with the aid of the magnetic condition of the rotor core. Fig. 4 shows the schematic diagram of the magnet torque, the reluctance torque, and the total torque waveforms. Unfortunately, the torque value cannot be quantitatively obtained based on the present analysis, and be our future work. Based on the analysis results, we try to fabricate the HTSISM with an HTS shield body. Fig. 5(a) shows a photograph of the Gd-system shield bulk, and the completed HTS rotor is shown in Fig. 5(b). The HTS squirrel-cage windings are made of DI-BSCCO tapes (critical currents at 77 K are 72 A for rotor bars and 166 A for end rings). Five pieces of the DI-BSCCO tapes are stacked together for one rotor bar (total critical current for one rotor bar: 360 A), and then, such rotor bars are installed in a total of 44 slots of the rotor core. After that, DI-BSCCO end rings are wound by means of the solder. Then, infinitesimal contact resistance is included in the cage windings, even such windings are in the superconducting state" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002132_cdc.2010.5718000-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002132_cdc.2010.5718000-Figure3-1.png", + "caption": "Fig. 3. 2D SpiderCrane pulley-cable schematic", + "texts": [ + " The form of the total energy of the system is given as H\u0304 (q, p) = 1 2 p\u22a4M\u0304\u22121 (q)p + V\u0304 (q), (2) with M\u0304 = M\u0304\u22a4 > 0 the mass matrix, given by M\u0304(q3) = mr +m 0 mL3 cos(q3) 0 0 0 mr +m mL3 sin(q3) 0 0 mL3 cos q3 mL3 sin(q3) mL2 3 0 0 0 0 0 I1 0 0 0 0 0 I2 where mr is the ring mass, m the mass of the load and L3 the (fixed) length of the cable attached to the load. The potential energy is given by V\u0304 (q2, q3) = (mr +m)gq2 \u2212mgL3 cos(q3) , and the input matrix is G\u0304 = 1 0 0 1 0 0 0 0 0 0 . We refer to [8] for a detailed description of the modeling issues. We can see that the gantry part is decoupled from the pulley mechanism, as shown in Figure 2 and Figure 3. Hence, we can concentrate on the gantry part and our objective is to position the payload, which is suspended by a cable from the ring mass mr on which two actuated forces u = col(u1, u2) act. The (reduced) inertia matrix is then M\u0303(q3) = mr +m 0 mL3 cos q3 0 mr +m mL3 sin(q3) mL3 cos(q3) mL3 sin(q3) mL2 3 with the (reduced) input force matrix G\u0303 = 1 0 0 1 0 0 . In order to simplify the dynamic equations we apply a partial linearization that transforms the system into Spong\u2019s Normal Form, see [17] for details" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001668_j.jsv.2010.11.010-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001668_j.jsv.2010.11.010-Figure4-1.png", + "caption": "Fig. 4. Root locus plot of Eq. (78) for: (a) x\u00bc 0, (b) x\u00bc 1=50, (c) x\u00bc 1=9, and x\u00bc 1=6.", + "texts": [], + "surrounding_texts": [ + "To investigate the roots of the characteristic equation (62) p2\u00feg\u00fet ge p2\u00feCo2 1pg\u00feCo2 0t g e \u00bc 0 (78) at Ca1 and C=1, let us rewrite it in the form p2\u00feo2 1C neo2 1C\u00bd1\u00fe\u00f0pte\u00deg 1 \u00bc 0, (79) where ne \u00bc \u00f0o2 1 o2 0\u00deo 2 1 . Note that when C=1 characteristic equation (78) coincides with that for the fractional oscillator based on the fractional derivative standard linear solid model [1]. Putting p\u00bc reic in Eq. (79) and separating the real and imaginary parts, we obtain r2cos2c\u00feCo2 1\u00f01 neR 1 e cosFe\u00de \u00bc 0, r2sin2c\u00feCo2 1neR 1 e sinFe \u00bc 0, (80) where Re \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1\u00fe2rgtgecosgc\u00fer2gt2g e q , Fe \u00bc rgtgesingc 1\u00fergtgecosgc : Tending parameter tge to 0, we obtain that Fe-0, Re-1, and c-p=2, r2-Co2 0. Tending parameter tge to 1 results in Fe-gc, R 1 e -0, and c-p=2, r2-Co2 1. In order to calculate the roots of the characteristic equation based on the set of Eqs. (80), we introduce the notation X \u00bc \u00f0rte\u00deg, multiply the first and second equations of this system by ( sin2c) and cos2c, respectively, and then add them. As a result we obtain sin2c\u00bc neR 1 e sin\u00f0Fe\u00fe2c\u00de: (81) At each fixed magnitude p=2o jcjop (since two complex conjugate roots of the characteristic equation locate only within this domain), from Eq. (81) we obtain the equation for determining the real part of the positive value of X, which impacts the values of Re and Fe. Substituting the found magnitude X, for example, in the second equation in (80) at the same fixed magnitude of the anglec, we obtain the magnitude of the value r, and then, knowing the magnitudes of the values \u00e6 and r, we determine the parameter tge via the formula: tge \u00bc Xr g. The magnitudes of three values, namely: c, r, and tge , completely define the characteristic equation roots at the fixed magnitudes of o2 0, o2 1 and g. The behaviour of the characteristic equation roots as function of the parameter tge at x\u00bco2 0o 2 1 \u00bc 0, 1/50, 1/9, and 1/6 is shown in Figs. 4a\u2013d, respectively, when Co2 1 \u00bc 1. The magnitudes of the fractional parameter g are denoted by figures near the corresponding curves. It is seen that the curves for the complex conjugate roots of the characteristic equation at fractional magnitudes of g depend essentially on the magnitude of the parameter x and remain inside the curves for the three roots of the characteristic equation with g\u00bc 1 (the ordinary standard linear solid model). Two limiting points on each curve located on the imaginary axis correspond to the elastic cases." + ] + }, + { + "image_filename": "designv11_7_0003869_s00419-012-0608-6-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003869_s00419-012-0608-6-Figure3-1.png", + "caption": "Fig. 3 The boundary conditions (a) and the auxiliary model (b)", + "texts": [ + " The developed FE model is displayed in Fig. 2, and it consists of 19,620 elements and 36,188 nodes, respectively. The particular sectors are glued as a whole at the geometrical model preparing the stage by using standard procedure of the ANSYS program. The analysed gear is mounted in the roller bearings. Such bearings typically have slight load capacity under loads perpendicular to the primary supported direction. The gear shaft neck surfaces on which the bearings are assembled are denoted \u201cbearing\u201d (see Fig. 3a). The gear mates with the other devices by the splines. The splines is simplified down to a regular cylinder of the diameter assumed as equal to the splines pitch diameter. The surface denoted \u201cjoint\u201d (see Fig. 3a) is located on the pitch diameter of the splines. Parameters of the analysed system are shown in Table 1a\u2013b. The calculation results for natural flexural oscillations taking into account angular speed of the gear are shown in the paper. In the case of circular discs and annular plates, for each solution where nodal lines are nodal diameters, one obtains two identical arrangements of straight nodal lines, rotated by an angle of \u03b1 = \u03c0/(2n) one to another, where n is the number of nodal diameters. In accordance with the circular and annular plate vibration theory [5,6,12], the particular natural frequencies of vibration are denoted as \u03c9mn , where m refers to the number of nodal circles and n is the mentioned number of nodal diameters", + " As the shape of the gear model is fairy elaborate, the flexural modes of the system are subject to deformation (as compared to the system without any holes) to such extent that establishing which particular node it refers to becomes rather difficult. This problem is even worse if the angular speed of the gear is varying. The problem of influence of the angular speed on the flexural gear models deformation is analysed. For the purpose of identification of these modes, an algorithm of tagging oscillation modes, which determines the correspondence between vibration of the circular disc versus disc with holes, is used. For this purpose, an auxiliary model of annular plate in the form shown in Fig. 3b is used. The geometrical dimensions of the auxiliary model were taken from the gear geometry (shown in Fig. 1). They are as follows: addendum circle diameter dz , rim mounting diameter dp, root circle diameter dw2, and thickness h p and hz (see Table 1). Dynamic analysis is performed for the auxiliary model cases rotating at predetermined angular speed, where diameter of though holes d01 (see Fig. 3b) varies as seen in Table 2. Findings are compared to each other both quantitatively and qualitatively. This method makes it possible to investigate deformations of nodal lines associated with nodal diameters and circles due to through holes and then determine correspondence between oscillation modes of solid circular disc and a plate with holes. In the final step, solutions found for the auxiliary model are compared with the solution for the system whose FEM model is shown in Fig. 2 (the principal model). As for the principal model case, the 3-D solid mesh and the ten-node tetrahedral element (solid92) are used to discretize the auxiliary models. For all models subject to analysis, the boundary conditions were applied to the nodes. For each model, 1 d f associated with node radial displacement was subtracted from the nodes found on the surface identified as a bearing (see Fig. 3a,b). Furthermore, 1 d f associated with the displacement of nodes along the centreline of each model was subtracted from the nodes found on the surface, identified as a joint (see Fig. 3a,b). For the models obtained in this way, calculations were kept conducted as long as the natural frequency \u03c918 was determined. The calculations were performed assuming that the systems rotate as angular speed of \u03b8 , within the range of 0\u20131047 [ rad/s]. During the computing process, the angular speed values were gradually increased by 80[ rad/s], which made fourteen variants of the results (the natural frequencies and corresponding natural modes), which were subject to further interpretation. The rotation effect was taken into account by determining stress distribution due to rotation, for each model during the computational step associated with static analysis (the so called pre-stress effect)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001163_00368790810902241-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001163_00368790810902241-Figure1-1.png", + "caption": "Figure 1 Experimental system (schematic)", + "texts": [ + " For example, zinc dialkyl dithiophosphate is acting as a combined anti-wear, anti-oxidant and corrosion inhibitor additive, sulphonate dispersants are acting to neutralize acids, prevent varnish formation as well as preventing the agglomeration of particles and deposition of carbon in engines, organo-molybdenum friction modifier compounds also behave as anti-wear and anti-oxidant additives (Kaleli and Berthier, 2001; Product Review, 1997). In the paper was studied the effect of polytetrafluoroethylene (PTFE) based additive on the friction coefficient in the journal bearing under different loads and rotating rotational speeds. Also, the obtained experimental data such as friction coefficient variations are employed as training and testing data for a neural network. An experimental procedure shown schematically in Figure 1 was used to investigate the variation of the friction force according to different rotational speeds and loads in journal bearings. The test rig was described in detail in the references (Kaleli and Durak, 2003; Durak, 1998, 2004). A ZnAl alloys bearing was used for the test bearing. The test bearing has a central circumferential groove where oil supply holes were placed. The journal (shaft) was manufactured from SAE W1 hardened steel which has 800HV. The journal was ground to N4 surface finish with an average height of asperity Ra \u00bc 4mm and the journal bearing was ground to N4 surface finish with an average height of asperity Ra \u00bc 7mm" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003470_j.ymssp.2012.08.014-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003470_j.ymssp.2012.08.014-Figure1-1.png", + "caption": "Fig. 1. Photograph of operational test rig.", + "texts": [ + " The test rig is also used to validate the identification by two methods. The first validation method tests the identified model\u2019s ability to predict (or mimic) measured SFD force data when the rig is excited by forces entirely different from those used to generate the training data. The second validation method uses the identified bearing model within a rotordynamic analysis in order to assess the ability of the network to predict the measured vibration response of the rig subjected to arbitrary excitation and modification to its configuration. Fig. 1 shows a photograph of the commissioned test rig with significant items labelled. With reference to the schematic diagram of Fig. 2, the rig is composed of a shaft mounted on a self-aligning bearing at one end and an SFD bearing at the other. The SFD housing (10) is flexibly mounted onto a rigid frame (3) via suspension (6) comprising four flexible bars. The frame is rigidly bolted to a cast iron bedplate which is itself rigidly bonded to a massive concrete block that rests on the ground at basement level of the building" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002301_mesa.2010.5551993-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002301_mesa.2010.5551993-Figure4-1.png", + "caption": "Fig. 4. Current solution to the FDA of the 2-DOF RR-RRR-RRR SPM (02 = 30\u00b0 and 03 = 30\u00b0).", + "texts": [ + " These formulas have been used to solve the FDA of the 2-DOF SPM for a number of sets of inputs within the input-space, and the obtained results have been verified using a CAD software. Equation (32) derived in this paper is the key equation which makes it possible for one to identify the unique current solution [Eqs. (39) and (40)] from the four solutions ([Eqs. (37) and (38)]) to the FDA of the 2-DOF RR-RRR-RRR SPM. For the RR-RRR-RRR 2-DOF SPM (Fig. 1), a set of inputs is B2 = 30\u00b0 and B3 = 30\u00b0. Using Eqs. (39) and (40), we obtain its current solution as \u00a23 = 30\u00b0 and \u00a22 = 30.69\u00b0. The configuration of the 2-DOF SPM is shown in Fig. 4. A formula that produces the current solution - a unique solution - to the FDA of the 2-DOF RR-RRR-RRR SPM has been derived. The current solution is in the same working mode and assembly mode as the reference configuration. This simplifies the FDA of the 2-DOF SPM. In addition, the Type II singularity conditions have been derived for the 2-DOF SPM. The input space of the 2-DOF SPM has also been identified. The 2-DOF RR-RRR-RRR SPM proposed in this paper has the same workspace as the 2-DOF SR SPM" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001511_204103-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001511_204103-Figure3-1.png", + "caption": "Figure 3. Scallop-like swimmer consisting of two circular cylinders of radius a and length L connected by a hinge at P.", + "texts": [ + "74, while the larger sphere advances in front for \u03b2 > (3 + \u221a 5)/2 \u2248 2.62. For 1.74 < \u03b2 < 2.62, the direction of rotation depends on the value of \u03b80. In dimensional form, the net angular velocity is \u3008 \u3009 = \u03c9\u03b5Rep\u3008\u03031\u3009 + O(\u03b54 Rep, Re2 p). (18) Note that the rotator reduces to the previous example of two unequal spheres moving along their line of centres for R\u0303 \u2192 \u221e with constant \u03b5 = 1/(2R\u0303 sin \u03b80). In this limit, sin \u03b80 \u2192 0, \u03b31 \u2192 8R\u03032, and the net linear velocities predicted by (11) and (18) agree. We study the scallop-like swimmer schematized in figure 3. The swimmer consists of two circular cylinders of radius a and length L a connected by a hinge. The angle between the two cylinders, 2\u03b8(t), is a prescribed periodic function of time with radian frequency \u03c9. The swimmer undergoes an unknown translational velocity, W (t), whose time average we want to determine. By neglecting hydrodynamic interactions between the cylinders, the hydrodynamic forces exerted on each cylinder are related to the velocities of the cylinder by the resistance coefficients" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002821_9781119970422-Figure6.3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002821_9781119970422-Figure6.3-1.png", + "caption": "Figure 6.3 Scenario classification (All sensor nodes (x) are covered with the transmission ranges that depicted as (o) for some examples). (a) Structured scenario with a known spatial deployment of nodes and a controllable assist node. (b) Unstructured scenario with unknown node positions and unpredictable movement node.", + "texts": [ + " For scenarios with controllable node mobility we design an integrated path planning algorithm. For all scenarios we design appropriate algorithms to collect energy information. Scenario Classification In the gMAP approach, we focus on three important types of scenarios that provide basic features to build more detailed realistic scenarios. 1. In a structured scenario we assume that the spatial deployment of sensor nodes is known a priori and that the mobility of the assist node is controllable (Figure 6.3(a)). 2. In a semi-structured scenario with an a priori known (or reliably estimated) spatial deployment of sensor nodes we assume that the mobility of the assist node to be controllable (Figure 6.3(a)). 3. In an unstructured scenario the topology is unknown (e.g. random spatial deployment) and the mobility of the assist node is assumed to be unpredictable and uncontrollable (Figure 6.3(b)). 82 Pervasive Computing and Networking Our main driver for the scenario selection is the proof of the concept in extreme scenarios. Furthermore, in a realistic scenario, the spatial deployment of sensor nodes can be structured or known only partially. The mobility of the assist node can be either controllable or uncontrollable and may follow varied patterns. Path Planning of Assist Nodes Path planning is required for structured and semi-structured scenarios. The assist node plans its movement according to the positions of sensor nodes" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003257_1.3617043-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003257_1.3617043-Figure3-1.png", + "caption": "Fig. 3 Shoe coordinate system", + "texts": [ + "/2 X, Y, Z = x/c, y/c, z/L wxi wy \u2014 external loads Xi ' ,X i ' ,X j ' \u2014 \u2014, \u2014, \u2014 shoe coordinates c c c T = y,L/c A = SR/c e = shoe-shaft coordinate (ec- centricity ratio) a,, a'2 \u2014 angular coordinates of shaft axis y = shoe roll angular coordinate Po = distance from shoe pivot point to shoe mass center p\u201e = distance from x-y plane to m, c? = e \u201e - e 9 = shaft speed 0 = shoe pitch angular coordi- \"1, co3 = ih i2, is components of shaft nate angular velocity \u00a3 = shoe-shaft coordinate (lead to/, co2'| _ AV, AV, AV components of angle) co3' J shoe angular velocity 464 / O C T O B E R 1 9 6 7 Transactions of the A S M E Downloaded From: http://tribology.asmedigitalcollection.asme.org/ on 01/29/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use Pad Dynamics Referring to Fig. 3 the dynamic equations for the motion of each pad are written, relative to the pivotal point 0 ' F' = m' ii* cir(R + 9o) oG X m' d*R dl\"+ djV dt (15) (16) The first terms of equations (15) and (16) are equal to zero if the pivot is fixed. Since the pivot points can only move in the A V - direction, the use of equation (15) is restricted only to a single component. Expressing the angular velocity of the pad by \u00ab ' the third component of equation (15) becomes <2-If T ' ' fd2RA (12 = \u00ab|7 i i ' + oil-hi 2', ' = Cii'ht \u2014 Wi'oh'ln TJ = u/In' + 0),V>'(/22 ' - In') ( IS ) (19) The first two equations are used to compute the shaft motion while the third produces the value of the torque necessary to eliminate yaw motion" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001965_tpas.1971.293004-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001965_tpas.1971.293004-Figure1-1.png", + "caption": "Fig. 1. Thyristor-controlled series motor.", + "texts": [ + " The prediction of transient behavior will be confined to the determination of the temporal variation of the average values, rather than the instantaneous values, of current and speed, for any given disturbance. The current being unidirectional, the average voltage across the self-inductance of the motor will be zero over a cycle. Thus (1) may be written in terms of average values as Eav(f) = RIav + RBNavIaV (2) where EaEv(0)= E-(1 + Cos 0) IT (3) I. CIRCUIT The series motor is assumed to be controlled by means of a full-wave rectifying circuit employing thyristors as shown in Fig. 1. The free-wheeling diode Dp avoids current chopping during voltage reversals. The thyristors T, and T2 are fired alternately at 180-degree intervals and the circuit is supplied from single-phase ac mains. II. DIFFERENTIAL EQUATIONS AND ASSUMPTIONS The differential equations governing the performance of the series motor are nonlinear; therefore it is not possible to derive analytically a transfer function that will be valid under all conditions. However, transfer functions that will be valid for Paper 69 TP 719-PWR, recommended and approved by the Rotating Machinery Committee of the IEEE Power Group for presentation at the IEEE Winter Power Meeting, New York, N" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000193_13506501jet89-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000193_13506501jet89-Figure1-1.png", + "caption": "Fig. 1 Analytical model of an aerostatic porous journal bearing", + "texts": [ + " In addition, to our knowledge, no article has been published comparing the theoretical whirling instability of aerostatic porous bearings with a surface-restricted layer with experimental results. Therefore, the objectives of this article are to theoretically clarify the whirling instability of a rotor supported by aerostatic porous journal bearings with a surface-restricted layer by considering the radial and axial air flows in the porous material and to make a comparison between theoretical and experimental results to verify the theoretical predictions. An aerostatic porous journal bearing with a surfacerestricted layer, as treated in this article, is shown in Fig. 1. Pressurized air is fed into the porous material through a feed groove. A surface-restricted layer is formed on the bearing surface that has a smaller permeability than that of the bulk of the porous material. In the theoretical calculations, it is assumed that air flows in the bulk of the porous material and the surface-restricted layer are subject to Darcy\u2019s law. From Darcy\u2019s law, the mass flowrates of the porous material in the r, u, and z directions are given, respectively, as follows u \u00bc kr m @p @r (1) v \u00bc ku m 1 r @p @u (2) w \u00bc kz m @p @z (3) In the above equations, kr, ku, and kz indicate the permeability of the porous material in the r, u, and z directions, which are experimentally determined in practice", + "comDownloaded from Considering the continuity of mass flowrate in a surface-restricted layer, the following equation is obtained Dmt \u00femr jout \u00fe (mujout \u00fem0 ujout)\u00fe (mzjout \u00fem0 zjout) m0 r jin (mujin \u00fem0 ujin) (mzjin \u00fem0 zjin) \u00bc h @r @t r dudz dr 2 \u00fe h @r @t r dudz drs 2 r kr m @p @r out r \u00fe dr 2 dudz r k0 u m @p r@u out dz drs 2 \u00fe r ku m @p r @u out dz dr 2 r k0 z m @p @z out rdudrs 2 \u00fe r kz m @p @z out r dudr 2 \u00fe r k0 r m @p @r in r drs 2 dudz \u00fe r k0 u m @p r @u in dz drs 2 \u00fe r ku m @p r@u in dz dr 2 \u00fe r k0 z m @p @z in r dudrs 2 \u00fe r kz m @p @z in r dudr 2 \u00bc 0 (5) In the bearing clearance, the following continuity equation is obtained Dmt \u00femujout \u00femzjout mujin mzjin \u00fem0 r jout \u00bc @rh @t r0 dudz rh3 12m @p r0 @u out dz \u00fe rhr0v 2 out dz rh3 12m @p @z out r0 du\u00fe rh3 12m @p r0@u in dz rhr0v 2 in dz \u00fe rh3 12m @p @z in r0 du r k0 r m @p @r r0 dudz \u00bc 0 (6) Next, to normalize equations (4) to (6), the following dimensionless variables are introduced R \u00bc r r0 , Z \u00bc z r0 , H \u00bc h h0 , dR \u00bc dr r0 , dZ \u00bc dz r0 , dRs \u00bc drs r0 \u00f07\u00de In addition, by assuming isothermal air flow, the density of air, r, is expressed in terms of pressure, p, as follows r \u00bc p RaT (8) Furthermore, assuming that the coordinate system is rotated with the whirling angular velocity of a rotor vp, when a rotor rotates at the angular velocity v and is whirling around the bearing centre with vp as shown in Fig. 1(b), the following coordinate conversions are obtained u \u00bc u vpt (9) @ @u \u00bc @ @u (10) @ @t \u00bc @ @u @u @t \u00bc vp @ @u (11) Therefore, the dimensionless governing equations of an aerostatic porous journal bearing are expressed as follows. 1. For the bulk of the porous material kr @P2 @R out R\u00fe dR 2 du dZ \u00fe ku @P2 R @u out dRdZ \u00fe kz @P2 @Z out Rdu dR JET89 # IMechE 2006 Proc. IMechE Vol. 220 Part J: J. Engineering Tribology at University of Birmingham on May 30, 2015pij.sagepub.comDownloaded from kr @P2 @R in R dR 2 du dZ ku @P2 R@u in dRdZ kz @P2 @Z in Rdu dR \u00bc 2mhvpr 2 0 pa @P @u Rdu dRdZ (12) 2" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002449_03093247v014313-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002449_03093247v014313-Figure3-1.png", + "caption": "Fig. 3. Pure shear with principal strains inclined to the co-ordinate axes", + "texts": [ + " 2, where the unit square (solid line) is understood to be the undeformed body and the dotted rectangle the deformed body. Obviously, the matrix for this deformation is where E and -r are the natural strains in the most severely stretched and most severely compressed fibres, respectively. The axes O X , and OX2 in Fig. 2 are the principal axes, because a line in the undeformed body does not rotate as a result of the deformation if, and only if, it is in the direction of either O X 1 or OX2. The deformation in Fig. 3 is the same as that in Fig. 2 except that the body is stretched along a line at an angle 4 from the xl-axis and compressed along a line at an angle + from the x2-axis, as shown. The matrix for the deformation in Fig. 3 is the product cos+ sin -sin41.(e\u2019 cos+ 0 0 e-\u2018 ~ * ~ c o s + -sin+ C O S ~ sin41 (10) In other words, this deformation is equivalent to three operations, a clockwise rotation of the body through +, then stretching it along xl-axis and compressing it along x2-axis, and rotating it anti-clockwise through +, The product of the matrices in equation (10) is in fact co-ordinate axes 314 J O U R N A L OF S T R A I N A N A L Y S I S VOL I N O 4 1966 at University of Bath - The Library on June 20, 2015sdj.sagepub.comDownloaded from all a12 a21 a12az1+1 0 1 1 Matrix (9), representing Fig. 2, is of course a particular case of matrix in equation (1 1) representing Fig. 3, namely, when + = 0. Matrix (1 1) is a symmetrical matrix and it satisfies the condition of incompressibility in equation (7). It can be shown that any symmetrical two-by-two matrix satisfying equation (7) may be reduced to the form of matrix (1 1). Thus, let lull 1 Ico$~inhr.cos26 I sinh E . sin 24 . . - (14) cosh E lal2 -1 = lsinh \u20ac.sin 24 -sinh E . cos 24 . . * (12) Solving equation (12), a112+a122+ 1 cosh t = sin 24 = sin w cos w cosh t +sinh E . cos 24 sinh E .sin 24 sinh E .sin 24 cosh e-sinh E", + " (19) 10 cost1 In the language of matrix algebra, a matrix of the general two-dimensional deformation may be factored either into a pure shear and a rotation, or a simple shear and a rotation, or in some other way, all the different ways of factoring being equally valid. In the discussion of large two-dimensional deformations, however, it is desirable to have a basis of comparison to which all deformations can be referred. The choice of this basis is necessarily arbitrary. However, it has been shown (I) that the pure shear represented by matrix (11) and Fig. 3 is the only type of two-dimensional deformation which occurs along a coaxial strain path, that is, a strain path in which all the incremental strains have the same principal axes with respect to the material, all other types of deformation being results of non-coaxial strain paths. It is, therefore, reasonable to adopt the pure shear as standard and, for convenience, to express all other types of deformation in terms of pure shear. To find the relations between pure and simple shear, the matrix (1 1) is equated to the left-hand side of equation (18) post-multiplied by a rotation matrix, thus cosh a + sinh a " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002873_978-88-470-2427-4_22-Figure7-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002873_978-88-470-2427-4_22-Figure7-1.png", + "caption": "Fig. 7 The singular set which defines a 3-dimensional origami. The angle condition is satisfied on every edge (the rings highlight the measures of the alternating angles)", + "texts": [ + " Thus u satisfies the Dirichlet problem{ Du \u2208 O(2), a.e. x \u2208 \u03a9 u(x) = \u03d5(x), x \u2208 \u2202\u03a9 for some given boundary values \u03d5 (see [5]). From the scalar picture (see Fig. 6) we can also read the boundary value of the vectorial map u. We end by giving a picture with a 3\u2212dimensional flat origami. It is a mathematical origami, being a rigid application from R3 \u2192 R3. Theorem 2 (3D Dirichlet Problem). On the cube \u03a9 = [0,1]3 it is possible to define a piecewise C1 rigid map u : \u03a9 \u2192R3 such that u = 0 on the boundary. The singular set \u03a3u is represented in Fig. 7. This result was first obtained by Cellina and Perrotta [3] and extended in [6] to general n-dimensional origami. 1. R.C. Alperin, A mathematical theory of origami constructions and numbers. J. Math. 6, 119\u2013 133, 2000. 2. M. Bern, B. Hayes, The complexity of flat origami. Proceedings of the 7th Annual ACMSIAM Symposium on Discrete Algorithms, 175\u2013183, 1996. 3. A. Cellina, S. Perrotta, On a problem of potential wells. J. Convex Analysis 2, 103\u2013115, 1995. 4. B. Dacorogna, P. Marcellini, Implicit partial differential equations" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001992_ipec.2010.5543157-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001992_ipec.2010.5543157-Figure1-1.png", + "caption": "Fig. 1. Inverter switching states and resulting voltage vectors", + "texts": [], + "surrounding_texts": [ + "As the aim of this paper is to show a very basic idea, the PMSM is modeled linear and with a saliency of 2nd order. The stator voltage equation (6) is known. us s = Rsi s s + \u03c8\u0307 s s (6) The flux linkage \u03c8s s is composed of the permanent magnet flux linkage and the flux linkage caused by the inductance of the stator windings. \u03c8s s = L s si s s +\u03c8s pm (7) The PM flux linkage can be transformed from its constant rotor fixed value \u03c8r pm. \u03c8s pm = T\u03c8r pm = T \ufffd \u03a8pm 0 \ufffd (8) The rotor fixed saliency is modeled by the inductance tensor Ls s that is constant in the rotor fixed frame. L r s = \ufffd Ld 0 0 Lq \ufffd (9) L s s = TL r sT \u22121 (10) = \ufffd Ld cos 2 \u03b8 + Lq sin 2 \u03b8 (Ld \u2212 Lq) sin \u03b8 cos \u03b8 (Ld \u2212 Lq) sin \u03b8 cos \u03b8 Ld sin 2 \u03b8 + Lq cos 2 \u03b8 \ufffd (11) Since L s s is time variant in the stator fixed frame it has to be considered when deriving the stator flux (7). \u03c8\u0307 s s = L\u0307 s si s s + L s si\u0307 s s + \u03c8\u0307 s pm (12) = L s s \u2032\u03c9iss + L s si\u0307 s s + J\u03c9\u03c8s pm (13) Using (13) the voltage equation (6) can be transposed to calculate the derivative of the stator current iss. i\u0307ss = L s s \u22121 \ufffd us s \u2212Rsi s s \u2212 L s s \u2032\u03c9iss \u2212 J\u03c9\u03c8s pm \ufffd (14) The torque equals the vector product of stator currents and flux linkage. M = is T s J \u03c8s s (15) The rotor speed and angle are obtained by integrations of the torque. \u03c9 = 1 \u0398 \ufffd M \u2212ML dt (16) \u03b8 = \ufffd \u03c9 dt (17)" + ] + }, + { + "image_filename": "designv11_7_0001403_gt2009-59226-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001403_gt2009-59226-Figure1-1.png", + "caption": "Fig. 1 Accessory gearbox of aeroengine[1]", + "texts": [ + " Some methods that improve engine efficiency are to increase by-pass ratio, use higher efficiency compressors and turbines, reduce weight, decrease frictional losses and so on. The technologies for decreasing frictional losses, such as the hydrodynamic loss around rotating parts mentioned in this paper, have wide application potential not only for aeroengines but also for industrial gas turbines and automobile engines, because the technologies could be adopted without major changes in engine design. : http://proceedings.asmedigitalcollection.asme.org/pdfaccess.ashx? The aeroengine has an accessory gearbox (AGB) to drive accessories such as generators and pumps (Fig. 1). The power losses in the gearbox are classified into oil churning loss, windage loss, and frictional losses of meshings, bearings, seals, and so on. The total of oil churning loss and windage loss (hydrodynamic loss) might exceed 50% of the gearbox loss. This is because the hydrodynamic loss is proportional to the peripheral velocity of the gears to the third power [2,3,4] and the velocity often exceeds 100m/s. Hence, a reduction in hydrodynamic loss is important towards decreasing power loss in AGB and that translates as an improvement in engine efficiency as a result" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000831_med.2008.4602258-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000831_med.2008.4602258-Figure2-1.png", + "caption": "Fig. 2. Quadrotor mini-aircraft configuration", + "texts": [ + " Section 3 is devoted to the presentation of the proposed technique i.e., the backstepping based robust nonlinear PI for the attitude stabilization of the quadrotor. Simulation results and their discussions are given in section 4. Finally, conclusions are made in section 5. II. DYNAMIC MODEL OF THE QUADROTOR Where The Breguet-Richet quadrotor is built in 1907, the quadrotor principle so has been for a long time. The quadrotor has four rotors (each rotor have a motor, propeller and a gearbox) in the end of two frames in cross configuration Figure 2, and 6DOF, three for the orientation (roll, pitch, yaw) and three for the position. Noting that the front and rear motors rotate clockwise and the right and left motors rotate counter clockwise to obtain a zero-yaw motion when the motors rotate at the same speed. The roll motion is ensured by increasing (decreasing) the thrust generated by front rotor while decreasing (increasing) the thrust of the rear rotor. Using the right and left rotors similarly, the pitch motion is produced. The yaw motion is produced by increasing (decreasing) the thrust of the front and rear rotor while increasing (decreasing) the thrust of the right and left rotor", + " By increasing the front or rear rotor thrust and decreasing the rear or front rotor thrust in the objective to maintain the total thrust, the forward and backward motion is achieved. The sideways motion is achieved similarly using the right (left) rotor thrust. II.1. Position and orientation dynamics of the quadrotor Let us consider the inertial fixed frame { }321 ,, eeeE attached to earth and a body fixed frame { }zyx eeeB ,, rigidly attached to the quadrotor and assumed to be at its center of mass as seen in Figure 2. Using the Euler angles parameterization, the attitude of the quadrotor is given by the orthogonal rotation matrix 3SOR\u2208 . The model that will be derived based on the following assumptions: - Earth is supposed flat and stationary in inertial space. - The mini-aircraft is seen as a single rigid body. - The effect of the body moments on the translational dynamics is neglected. - The center of mass and the body fixed frame origin are assumed to coincide. - The ground effect is neglected. - The structure is supposed rigid and symmetric (diagonal inertia matrix)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000791_e2007-00358-1-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000791_e2007-00358-1-Figure3-1.png", + "caption": "Fig. 3. Local parameterization of the torus.", + "texts": [ + " For a torus rotating with angular velocity \u03c9 and translating with velocity Ux the boundary conditions are u\u0303x = \u03c9(a \u2212 r\u0303) + U\u0303x and u\u0303r = \u03c9x\u0303 at the surface of the torus. The non-dimensional boundary conditions thus become ux = (1 \u2212 r) + Ux and ur = x. In the special case of an immobile torus, we set Ux = 0. We further consider here the case of a slender torus (the ratio of the two radii of the torus, \u03b5 = b/a is small), and the surface is locally parameterized by an angle \u03c8, such that x = \u03b5 cos\u03c8 and r = 1 + \u03b5 sin\u03c8 (Fig. 3). This implies the expansion k2 = 1\u2212 \u03b52 4 +O(\u03b53) in the slender torus limit. The asymptotic expressions for the elliptic integrals in the k = 1 limit (Appendix A) can therefore be used to simplify the expressions. The boundary conditions demand a scaling , m = m0 \u03b5 2, dpx = \u03b54dpx0 and fx = \u03b52fx0. The boundary conditions for the x and r directional no slip velocity conditions read as follows: Ux\u2212 \u03b5 sin\u03c8 = \u22122\u03b5mo sin\u03c8 \u2212 \u03b52(mo+4dpxo\u22122fxo) 2 cos 2\u03c8 + \u03b52 2 ( 2mo(log 8 \u03b5 \u2212 1 2 ) + 4fxo(log 8 \u03b5 + 1 2 ) ) (25) \u03b5 cos\u03c8 = 2 \u03b5mo cos\u03c8 \u2212 \u03b52(mo + 4dpxo \u2212 2fxo) 2 sin 2\u03c8" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002392_j.matdes.2012.02.002-Figure9-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002392_j.matdes.2012.02.002-Figure9-1.png", + "caption": "Fig. 9. The schematic diagram on the clamp of the diameter changing 1-diameter regulating stem; 2-roller wheel spacing gutter; 3-adjusting skewback; 4-adjusting roller wheel; 5-fixture internal stay.", + "texts": [ + " 8; secondly, the fixture should be able to complete the laser butt welding of the cylinder structure; thirdly, the parts can be loaded and unloaded smoothly on the fixture in the welding process. The variable diameter fixture will be designed to meet the assembly requirement. Through the fitting-in of the variable diameter and the external clamp, the gaps between the cylinders are reduced and eliminated. Taking the problem of loading and unloading of parts in laser welding process into account, the adjustment range of the fixture diameter is between 218 mm and 228 mm. The key diagram of the fixture diameter variation is shown in Fig. 9. The principle of operation is as follows: when the adjustable bar forces the adjustable oblique block move axially, the adjustable oblique drives the adjuster roller to move radially due to the axial motion of the roller forbidden in the slot limit. Therefore, the changes in diameter can be achieved. The geometry relations and the number of laser welding joint on the cylinder structure are shown in Fig. 10. So as to make superplastic forming of multi-sheet cylinder sandwich structure successful, the core cylinder can not be welded together with the inner cylinder during the welding preparation for outer cylinder and core one" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002301_mesa.2010.5551993-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002301_mesa.2010.5551993-Figure5-1.png", + "caption": "Fig. 5. Redundantly actuated 2-DOF RR-RRR-RRR SPM.", + "texts": [], + "surrounding_texts": [ + "For the RR-RRR-RRR 2-DOF SPM (Fig. 1), a set of inputs is B2 = 30\u00b0 and B3 = 30\u00b0. Using Eqs. (39) and (40), we obtain its current solution as \u00a23 = 30\u00b0 and \u00a22 = 30.69\u00b0. The configuration of the 2-DOF SPM is shown in Fig. 4." + ] + }, + { + "image_filename": "designv11_7_0000823_s11044-008-9122-6-Figure14-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000823_s11044-008-9122-6-Figure14-1.png", + "caption": "Fig. 14 Definition of DH parameters", + "texts": [ + " The Denavit and Hartenberg (DH) parameters [16] are a systematic method to define the relative position and orientation of the consecutive links in a multibody robotic system and can be assigned differently for the same system, as in [31, 36]. The DH parameters that are used in this paper are explained here. Referring to Fig. 1, the serial robot manipulator under study consists of (n + 1) bodies or links, namely, the fixed base and the bodies numbered as #1, . . . ,#n. All the bodies are coupled by n joints, numbered as 1, . . . , n. The ith joint couples the (i \u2212 1)st link; for the (i + 1)st frame, i.e., Xi+1, Yi+1, Zi+1. Now referring to the Fig. 14 for the first n frames, the DH parameters are defined according to the following rules: 1. Zi is the axis of the ith joint. Its positive direction can be chosen arbitrarily. 2. Xi is defined as the common perpendicular to Zi\u22121 and Zi , directed from the former to latter. The origin of the ith frame, Oi , is the point where Xi intersects Zi . If these two axes intersect, the positive direction of Xi is chosen arbitrarily. And the origin, Oi , coincides with the origin of the (i \u2212 1)st frame, i.e., Oi\u22121. 3. The distance between Zi and Zi+1 is defined as ai , which is a nonnegative number. 4. The Zi coordinate of the intersection of the Xi+1 axis with Zi , which is shown in Fig. 14 as the distance between Oi and O \u2032 i is defined as bi . This can be either positive or negative. For a prismatic joint, bi is a variable. 5. The angle between Zi and Zi+1 is defined as \u03b1i , and is measured about the positive direction of Xi+1. 6. The angle between Xi and Xi+1 is defined as \u03b8i , and is measured about the positive direction of Zi . For a revolute joint, \u03b8i is a variable. Since no (n + 1)st link exists, the above definitions do not apply to the (n + 1)st frame and its axes can be chosen at will" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001544_6.2008-4506-Figure7-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001544_6.2008-4506-Figure7-1.png", + "caption": "Figure 7. Leakage flow paths included in non-contacting finger seal flow model.", + "texts": [ + " A single cycle leakage performance test was conducted at room temperature. Then a second spin test was conducted in the same manner as the first except the pressure was increased up to 241 kPa. The time of rotational operation in this second spin test was 68 minutes. A total of 93 minutes of rotational testing were accumulated in the first and second spin tests combined. V. Leakage Flow Model A simple leakage flow model was used to predict the seal leakage rate. There are three flow paths for air to leak through the seal as illustrated in Fig. 7. The first flow path goes from high pressure through the slots in the spacers and holes in the finger elements into the pressure balance cavity and then exits through the finger slots at the seal dam. The second flow path goes through the pinholes created by the high pressure finger element id, the rotor od, and the circumferential gaps between the lift pads. The third flow path goes under the lift pads. The sum of the areas for each of these three flow paths equals the seal leakage area. The leakage rate through the seal is predicted using the isentropic flow equation as shown in Eq" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001524_tmag.2008.2001341-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001524_tmag.2008.2001341-Figure5-1.png", + "caption": "Fig. 5. Scheme of the simplified 2-D structure employed for the validation of the nonlinear homogenization procedure. The instantaneous magnetic flux lines are reported when both coils are excited.", + "texts": [ + " VALIDATION OF THE HOMOGENIZATION PROCESS The homogenized procedure shall be verified comparing the field distributions in the homogenized equivalent material with those provided by FEM computation on the entire heterogeneous structure. This analysis can be reasonably performed under simplifying conditions, due to the extremely high increase of the computational burden with the number of elementary cells. To this aim, the approach for validating the results on the nonlinear equivalent \u2013 curve is similar to the one adopted in [4]. A 2-D structure ( plane) constituted of a heterogeneous material with a limited number of cells (10 10) is supplied by two orthogonal coils, to produce rotating magnetic fields (see Fig. 5). The results of the analysis, performed with two cells having different grain size (50 m and 100 m), are presented in Fig. 6, which shows the distribution of the magnetic flux density components along the -axis approximately at the middle of the domain. The agreement is more than satisfactory, even if, obviously, the homogenized solution cannot take into account the local effects produced by the cell nonmagnetic walls. A good m and m. The results of the heterogeneous model and the homogenized one are compared" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000473_s11071-007-9293-3-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000473_s11071-007-9293-3-Figure3-1.png", + "caption": "Fig. 3 Jeffcott rotor-bearing-seal system and the coordinate system", + "texts": [ + "06 \u00d7 1011 Pa Density of the rotor 7800 kg/m3 Parameters of the bearing Length of the bearing 0.1 m Diameter of the bearing 0.1 m Clearance of the bearing 2.0 \u00d7 10\u22124 m Ellipticity of the bearing 0.5774 Type of the lubricant oil 32# Turbine Oil Temperature of the oil 40\u00b0C Parameters of the labyrinth seal Height of the tooth 2.3 \u00d7 10\u22123 m Pitch of the seal 7.0 \u00d7 10\u22123 m Width of the tooth 3.0 \u00d7 10\u22123 m Clearance between tooth tip and rotor 7.0 \u00d7 10\u22124 m or stator disk and two journals at the bearings. The model of the rotor\u2013bearing\u2013seal system is shown in Fig. 3. O is the geometric center of the bearing, O1 is the geometric center of the disk, and O2 is the geometric center of the journal. M1 is the mass of the disk and M2 is the mass of the journal at the bearing. (X1, Y1) is the dis- placement of the geometric center of the disk O1 and (X2, Y2) is the displacement of the geometric center of the journal O2. 3.1 Nonlinear oil\u2013film forces of the journal bearing Considering the nonlinear oil\u2013film force model under the short bearing theory [12], a dynamic model of the nonlinear oil\u2013film force is established, for the model has better accuracy and convergence" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000904_j.mechmachtheory.2008.08.005-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000904_j.mechmachtheory.2008.08.005-Figure5-1.png", + "caption": "Fig. 5. Fault tolerant operation.", + "texts": [ + " 3a indicate that the manipulator can continue the desired circle motion when the joint 4 is locked at t = 0.225 s. And, the JVJ of remaining joints does occur during the fault tolerant operation by locking failed joint as shown in Fig. 3b The simulation results of the reduced manipulator with least-norm joint velocity are shown in Figs. 4 and 5. Due to the limited space, only the simulation with K = 100 is presented here. When t = 0.275 s, the JVJ of the joint 3 reaches the maximum 2.46 rad/s shown in Fig. 4, which is larger than 1.78 rad/s for the optimal case shown in Fig. 1b. Fig. 5 indicates that when the joint 4 is locked, although the manipulator can continue the desired task, its motion stability decreases, the larger the K is, the more obvious the decrease is. It is worth explaining that the joint velocity of the reduced manipulator does not affect the reduced manipulability, so it is the same as the optimal joint velocity case. Combining the method proposed here with the optimization of initial posture [10] will lead to further reduction in the JVJ of the manipulators at the moment of locking joint" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003560_978-1-4613-4560-2_2-Figure8.19-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003560_978-1-4613-4560-2_2-Figure8.19-1.png", + "caption": "Fig. 8.19. The consequences of an electron-transfer reaction are numerous; the charging of the interface and the establishing of a potential drop are the most direct ones.", + "texts": [ + " This first description of the state of affairs at the instant of immersing a metal in a solution can be summarized. The metal and solution sides of the interface are at first uncharged. There is no potential difference and no electrical field across the interface. Nevertheless, the metal-solution interface may not be at equilibrium, in which case thermodynamics indicates that an electron-transfer reaction will occur. The rate of the electron-transfer reaction under zero field is given by purely chemical-kinetic considerations. Once the electron-transfer reaction occurs, a train of consequences ensues (Fig. 8.19). The emigration of the electron from the electrode to the electron ac ceptor A + leaves the metal poorer by one negative charge. The metal has become charged positive. Its electroneutrality has been upset. A similar argument can be applied to the solution side of the interface. Prior to the electronation reaction, this solution side was electro neutral. The electronation reaction involving the transfer of a positive ion toward the metal has the effect of reducing the positive charge on the solution side of the interface which thus acquires a net negative charge" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000312_s11071-005-9016-6-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000312_s11071-005-9016-6-Figure1-1.png", + "caption": "Figure 1. Forces at a braked wheel.", + "texts": [ + " During braking, forces (or torques) are applied to the wheels in order to decelerate the wagon, which produces reaction forces in couplers and pitch torque to the wagon body and the bogies. These forces affect the dynamics of wagons, both the running stability and curving performance. The braking performance is usually measured through the stopping distance and also from skidding or wheel slide. With the reduction of the wheel load, the chance of the skid occurrence increases. Braking involves friction. During the process of braking, friction occurs between the brake shoe and the wheel and between the wheel and the rail (Figure 1). When the wheel moves with a speed v and angular velocity \u03c9, at the contact point a longitudinal force Fx and a vertical force FZ arise as a reaction due to the brake torque (TB = \u03bcb FBr0, where r0 is the radius of the wheel) and the static force mg. From basic statics, we obtain the following three system equations of a braked wheel: mv\u0307 = \u2212FX FZ = mg Jy\u03c9\u0307 = FXr0 \u2212 TB (2) where m is the mass, Jy , r0 and TB denote the polar moment of inertia, wheel radius and brake torque respectively. Over dots denote differentiation with respect to time" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003989_j.mseb.2012.03.001-Figure9-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003989_j.mseb.2012.03.001-Figure9-1.png", + "caption": "Fig. 9. Evidence of temperature rise on the", + "texts": [ + " Cage noise can be generated in any type of bearing, nd its magnitude is usually not very high. Characteristics of the oise are shown as follows: [17] 1) Occurs with pressed steel cages, machined cages and plastic cages. 2) Occurs with grease and oil lubrication. lues during the shaft test. (3) Tends to occur if a moment load is applied to the outer ring of a bearing. (4) Tends to occur more often with greater radial clearance. To understand the reason for the FTF, the supporting bearing was disassembled, and evidence of temperature rise was discovered, as shown in Fig. 9. The FTF and harmonics (62 Hz) of the FTF in Fig. 8(c)\u2013(e) was caused by friction between the cage and outer race. In addition, the harmonics decreased from 18 min in Fig. 8(e); therefore, this phenomenon proved run-in stage in Fig. 7. Moreover, it was shown that crack growth was related to the FTF because the FTF in Fig. 8(d) was dominantly detected after 30 min. To clarify the crack growth further, the energy value was observed. Through acoustic emission technology, energy is a 2- byte parameter derived from the integral of the rectified voltage signal over the duration of the AE hit (or waveform), hence the voltage-time units" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002527_revet.2012.6195318-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002527_revet.2012.6195318-Figure2-1.png", + "caption": "Figure 2. Snapshot of the resulting 'IM' flux distribution for 20A stator current and 25rd/s rotor speed.", + "texts": [ + " In this work, 3D effects were computed and included in electrical circuit, Geometrical dimensions and physical material properties were defined, rotating air gap is considered, boundary conditions were set up with geometrical model, and mesh generation was executed for 'FEM' analysis pre-processing step Mesh generation of the studied three phase squirrel cage 'IM' is shown in Fig.1. The two dimensional flux calculations are performed to study and analyse the variation the IM mutual inductance as well as stator and rotor inductances for different rotor speeds and stator currents. Fig.2 shows a snapshot of the resulting induction machine flux distribution for 20A stator current and 25rd/s rotor speed. The flux equations can be written as follows [MRM2] : s s s r r r r s L I +M I L I +M I \u23a7\u03a6 =\u23aa \u23a8 \u03a6 =\u23aa\u23a9 (11) Where Ls : stator inductance per phase; Lr : rotor inductance per phase; Lm : mutual inductance between stator and rotor phase; M = m 3 L 2 ; Thus Stator and rotor inductances can be expressed by: s r s s r s r r \u03a6 -M IL = I \u03a6 -M IL = I \u23a7 \u23aa\u23aa \u23a8 \u23aa \u23aa\u23a9 (12) The rotor time constant is given by: r r r LT = R (13) The magnetic dispersion coefficient can be written as follows: 2 m s r L\u03c3=1L L \u239b \u239e \u239c \u239f \u239d \u23a0 (14) The mutual inductance is deduced from zero current rotor and different stator currents simulations" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003411_isvri.2011.5759599-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003411_isvri.2011.5759599-Figure2-1.png", + "caption": "Figure 2: Example of the \u201dSweep and Prune\u201d algorithm with a nonoverlapping condition (left) and an overlapping one (right).", + "texts": [ + " In I-COLLIDE [5] used \u201dSweep and Prune\u201d, a pseudo-dynamic object collision pruning method that reduced 3D collision detection between AABBs into three separate 1D problems. It is one of the most used methods in the broad-phase algorithms because it provides an efficient pairs removal and it does not depend on the objects complexity. The sequential algorithm of \u201dSweep and Prune\u201d takes in input the overall objects of the environment and feeds in output a collided object pairs list. AABBs appear, in general, as perfect candidates for the algorithm because of their alignment on the environment axis (cf. Figure 2). The algorithm is in charge of the detection of overlaps between objects. A projection of higher and upper bounds of each AABB is made on the three environment axis. Three lists with overlapping pairs on each axis (x, y and z) are then obtained. We can notice in related work two related but different concepts on the way the \u201dSweep and Prune\u201d operates internally: by starting from scratch each time or by updating internal structures. The first type is called brute-force and the second type persistent" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002222_9783527627646-Figure10.6-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002222_9783527627646-Figure10.6-1.png", + "caption": "Figure 10.6 Pore size estimation by bubble point measurement.", + "texts": [ + " The disk is then flooded with a liquid, so that a pool of liquid is left on top. Air is then slowly introduced from 162 | 10 Sterilization below, and the pressure increased in stepwise manner. When the first steady stream of bubbles to emerge from the membrane is observed, that pressure is termed the \u2018\u2018bubble point.\u2019\u2019 The membrane pore size can be calculated from the measured bubble point Pb by using the following, dimensionally consistent Equation 10.9. This is based on a simplistic model (see Figure 10.6) which equates the air pressure in the cylindrical pore to the cosine vector of the surface tension force along the pore surface [7]: Pb \u00bc K2prscosy=\u00f0pr2\u00de \u00bc K\u00f02s\u00decosy=r \u00f010:9\u00de where K is the adjustment factor, r is the maximum pore radius (m), s is the surface tension (Nm 1), and y the contact angle. The higher the bubble point, the smaller the pore size. The real pore sizes at the membrane surface can be measured using electron microscopy, although in practice the bubble point measurement is much simpler" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000208_robot.2005.1570615-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000208_robot.2005.1570615-Figure4-1.png", + "caption": "Fig. 4 Tentacle system parameters.", + "texts": [ + " We will assume that the backbone never bends past the \"smallstrain region\" where an applied stress produces a strain that is recoverable and obeys an approximately linear stress-strain relationship. Each element of the arm has two types of deformations: bending and axial tension/compression. Thus, we will use an extensible model that closely matches the characteristics of the prototype arm. Also, the system is frictionless and any other damping and frictions are neglected. The essence of the tentacle model is a 3-dimensional backbone curve C that is parametrically described by a vector ( ) 3R\u2208sr and an associated frame ( ) 33\u00d7\u2208\u03c6 Rs whose columns create the frame bases (Fig. 4). The independent parameter s is related to the arclength from the origin of the curve C, a variable parameter, where (Fig. 3b) ( )\u2211 = \u2206+= N i ii lll 1 0 (1) or ull += 0 (2) where 0l represents the length of the N elements of the arm in the initial position and \u2211 = \u2206= N i ilu 1 (3) determines the control variable of the arm length. position vector, ( )srr = (4) when [ ].l,s 0\u2208 For a dynamic motion, the time variable will be introduced, ( )t,srr = . The position vector on curve C is given by ( ) ( ) ( ) ( )[ ]Tt,szt,syt,sxt,sr = (5) where ( ) ( ) ( )\u222b \u2032\u2032\u2032\u03b8= s 0 sdt,sqcost,ssint,sx (6) ( ) ( ) ( )\u222b \u2032\u2032\u2032\u03b8= s 0 sdt,sqcost,scost,sy (7) ( ) ( )\u222b \u2032\u2032= s 0 sdt,sqsint,sz (8) with [ ]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001296_j.jsv.2008.05.022-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001296_j.jsv.2008.05.022-Figure1-1.png", + "caption": "Fig. 1. Sketch for a uniform Timoshenko beam supported by r intermediate pins, carrying u spring\u2013mass systems and v various concentrated elements.", + "texts": [ + " Lin and Tsai determined the exact values of natural frequencies and associated mode shapes of a \u2018\u2018multispan\u2019\u2019 uniform beam carrying multiple spring\u2013mass systems [15] and those of a multiple-step beam carrying a number of intermediate lumped masses and rotary inertias [16] with the NAM. From the foregoing literature review, one finds that the literature regarding determination of exact natural frequencies and mode shapes of a \u2018\u2018multispan\u2019\u2019 Timoshenko beam carrying multiple various concentrated elements is little. Therefore, the objective of this paper is to extend the theory of NAM to investigate the free vibration characteristics of a multispan Timoshenko beam carrying multiple point masses, rotary inertias, linear springs, rotational springs and spring\u2013mass systems. Fig. 1 shows the sketch of a uniform beam supported by r pins, carrying u spring\u2013mass systems and v various concentrated elements. If each of the points that the r intermediate pinned supports, the u spring\u2013mass ARTICLE IN PRESS H.-Y. Lin / Journal of Sound and Vibration 319 (2009) 593\u2013605 595 systems or the v concentrated elements located is called a \u2018\u2018station,\u2019\u2019 then the total number of intermediate stations is n. Considering the effects of shear deformation and rotary inertia, the equation of motion for a uniform beam is given by [17] EI q2j\u00f0x; t\u00de qx2 \u00fe k0GA qy\u00f0x; t\u00de qx j\u00f0x; t\u00de R2 gm q2j\u00f0x; t\u00de q2t \u00bc 0 (1) m q2y\u00f0x; t\u00de qt2 k0AG q2y\u00f0x; t\u00de qx2 qj\u00f0x; t\u00de qx \u00bc 0 (2) where E is Young\u2019s modulus, A is the cross-sectional area, I is the moment of inertia of the cross-sectional area A about the axis of bending, k0 is the shear coefficient, G is the shear modulus and r is the mass density of the beam material, m \u00bc rA is mass per unit length of the beam, Rg \u00bc ffiffiffiffiffiffiffiffi I=A p is radius of gyration of crosssectional area A, y(x, t) is the transverse deflection of the beam at position x and time t and j(x, t) is the bending slope", + " (7) and (8) take the forms Y \u00f0x\u00de \u00bc C1 sin\u00f0l1x\u00de \u00fe C2 cos\u00f0l1x\u00de \u00fe C3 sinh\u00f0l2x\u00de \u00fe C4 cosh\u00f0l2x\u00de (10) C\u00f0x\u00de \u00bc C01 sin\u00f0l1x\u00de \u00fe C02 cos\u00f0l1x\u00de \u00fe C03 sinh\u00f0l2x\u00de \u00fe C04 cosh\u00f0l2x\u00de (11) where Cp and C0p (p \u00bc 1, 2, 3, 4) are the integration constants, and l1 \u00bc 1 2 \u00bd4c\u00fe \u00f0a b\u00de2 1=2 \u00fe 1 2 \u00f0a\u00fe b\u00de n o1=2 (12a) l2 \u00bc 1 2\u00bd4c\u00fe \u00f0a b\u00de2 1=2 1 2\u00f0a\u00fe b\u00de n o1=2 (12b) The substitution of Eqs. (5), (6), (10) and (11) into Eq. (1) gives 1 rIo2 k0AG \u00bdC01 sin\u00f0l1x\u00de \u00fe C02 cos\u00f0l1x\u00de \u00fe C03 sinh\u00f0l2x\u00de \u00fe C04 cosh\u00f0l2x\u00de EI k0AG \u00bd C01l 2 1 sin\u00f0l1x\u00de C02l 2 1 cos\u00f0l1x\u00de \u00fe C03l 2 2 sinh\u00f0l2x\u00de \u00fe C04l 2 2 cosh\u00f0l2x\u00de \u00bc C1l1 cos\u00f0l1x\u00de C2l1 sin\u00f0l1x\u00de \u00fe C3l2 cosh\u00f0l2x\u00de \u00fe C4l2 sinh\u00f0l2x\u00de (13) C01 \u00bc a1C2; C02 \u00bc a1C1; C03 \u00bc a2C4; C04 \u00bc a2C3 (14a2d) where a1 \u00bc l1 \u00bd1 \u00f0rIo2=k0AG\u00de \u00fe \u00f0EI=k0AG\u00del21 ; a2 \u00bc l2 \u00bd1 \u00f0rIo2=k0AG\u00de \u00f0EI=k0AG\u00del22 (15a,b) For an arbitrary station located at xs (cf. Fig. 1), from Eqs. (10) and (11) one obtains Y s\u00f0xs\u00de \u00bc Cs;1 sin\u00f0l1xs\u00de \u00fe Cs;2 cos\u00f0l1xs\u00de \u00fe Cs;3 sinh\u00f0l2xs\u00de \u00fe Cs;4 cosh\u00f0l2xs\u00de (16) Cs\u00f0xs\u00de \u00bc Cs;1a1 cos\u00f0l1xs\u00de Cs;2a1 sin\u00f0l1xs\u00de \u00fe Cs;3a2 cosh \u00f0l2xs\u00de \u00fe Cs;4a2 sinh\u00f0l2xs\u00de (17) Y 0s\u00f0xs\u00de \u00bc Cs;1l1 cos\u00f0l1xs\u00de Cs;2l1 sin\u00f0l1xs\u00de \u00fe Cs;3l2 cosh\u00f0l2xs\u00de \u00fe Cs;4l2 sinh\u00f0l2xs\u00de (18) C 0 s\u00f0xs\u00de \u00bc Cs;1a1l1 sin\u00f0l1xs\u00de Cs;2a1l1 cos\u00f0l1xs\u00de \u00fe Cs;3a2l2 sinh\u00f0l2xs\u00de \u00fe Cs;4a2l2 cosh\u00f0l1xs\u00de (19) where the primes refer to differentiation with respect to the coordinate x. If the station numbering corresponding to the intermediate spring\u2013mass system is represented by u, then the continuity of deformations and equilibrium of moments and forces require that Y L u \u00f0xu\u00de \u00bc Y R u \u00f0xu\u00de (20) ARTICLE IN PRESS H", + " (46)\u2013(49), respectively, one obtains Cr;1 sin\u00f0l1xr\u00de \u00fe Cr;2 cos\u00f0l1xr\u00de \u00fe Cr;3 sinh\u00f0l2xr\u00de \u00fe Cr;4 cosh\u00f0l2xr\u00de \u00bc 0 (50) Cr\u00fe1;1 sin\u00f0l1xr\u00de \u00fe Cr\u00fe1;2 cos\u00f0l1xr\u00de \u00fe Cr\u00fe1;3 sinh\u00f0l2xr\u00de \u00fe Cr\u00fe1;4 cosh\u00f0l2xr\u00de \u00bc 0 (51) Cr;1a1 cos\u00f0l1xr\u00de Cr;2a1 sin\u00f0l1xr\u00de \u00fe Cr;3a2 cosh\u00f0l2xr\u00de \u00fe Cr;4a2 sinh\u00f0l2xr\u00de Cr\u00fe1;1a1 cos\u00f0l1xr\u00de \u00fe Cr\u00fe1;2a1 sin\u00f0l1xr\u00de Cr\u00fe1;3a2 cosh\u00f0l2xr\u00de Cr\u00fe1;4a2 sinh\u00f0l2xr\u00de \u00bc 0 (52) Cr;1a1l1 sin\u00f0l1xr\u00de Cr;2a1l1 cos\u00f0l1xr\u00de \u00fe Cr;3a2l2 sinh\u00f0l2xr\u00de \u00fe Cr;4a2l2 cosh\u00f0l2xr\u00de \u00fe Cr\u00fe1;1a1l1 sin\u00f0l1xr\u00de \u00fe Cr\u00fe1;2a1l1 cos\u00f0l1xr\u00de Cr\u00fe1;3a2l2 sinh\u00f0l2xr\u00de Cr\u00fe1;4a2l2 cosh\u00f0l2xr\u00de \u00bc 0 (53) Writing Eqs. (50)\u2013(53) in matrix form, one obtains Br\u00bd Crf g \u00bc 0 (54) where Crf g \u00bc Cr;1 Cr;2 Cr;3 Cr;4 Cr\u00fe1;1 Cr\u00fe1;2 Cr\u00fe1;3 Cr\u00fe1;4 n o (55) and the coefficient matrix [Br] is given by Eq. (A.5) in Appendix A at the end of this paper. If the left-end support of the beam is pinned as shown in Fig. 1, then the boundary conditions are Y 0\u00f00\u00de \u00bc C00\u00f00\u00de \u00bc 0 (56,57) From Eqs. (16), (19) and (56), (57) one obtains C0;2 \u00fe C0;4 \u00bc 0 (58) C0;2a1l1 \u00fe C0;4a2l2 \u00bc 0 (59) or in matrix form B0\u00bd C0f g \u00bc 0 (60) where 1 2 3 4 B0\u00bd \u00bc 0 1 0 1 0 a1l1 0 a2l2 \" # 1 2 (61) C0f g \u00bc C0;1 C0;2 C0;3 C0;4 n o (62) If the right-end support of the beam is pinned as shown in Fig. 1, then the boundary conditions are Y N \u00f0L\u00de \u00bc C0N\u00f0L\u00de \u00bc 0 (63,64) N \u00bc n\u00fe 1 (65) From Eqs. (16), (19), (63) and (64), one obtains CN ;1 sin\u00f0l1L\u00de \u00fe CN ;2 cos\u00f0l1L\u00de \u00fe CN;3 sinh\u00f0l2L\u00de \u00fe CN ;4 cosh\u00f0l2L\u00de \u00bc 0 (66) CN ;1a1l1 sin\u00f0l1L\u00de CN;2a1l1 cos\u00f0l1L\u00de \u00fe CN ;3a2l2 sinh\u00f0l2L\u00de \u00fe CN ;4a2l2 cosh\u00f0l2L\u00de \u00bc 0 (67) or in matrix form BN\u00bd CNf g \u00bc 0 (68) ARTICLE IN PRESS H.-Y. Lin / Journal of Sound and Vibration 319 (2009) 593\u2013605600 where 4N 3 4N 2 4N 1 4N BN\u00bd \u00bc sin\u00f0l1L\u00de cos\u00f0l1L\u00de sinh\u00f0l2L\u00de cosh\u00f0l2L\u00de a1l1 sin\u00f0l1L\u00de a1l1 cos\u00f0l1L\u00de a2l2 sinh\u00f0l2L\u00de a2l2 cosh\u00f0l2L\u00de \" # q 1 q (69) CNf g \u00bc CN;1 CN;2 CN ;3 CN ;4 n o (70) where q denotes the total number of equations for the integration constants given by q \u00bc 4\u00f0v\u00fe r\u00de \u00fe 5u\u00fe 4 (71) From the next Eq", + " Before the free vibration analysis of a multispan Timoshenko beam carrying multiple concentrated elements is performed, the reliability of the theory and the computer program developed for this paper are confirmed by comparing the present results with those obtained from the conventional FEM. In FEM, the two-node beam elements are used and the entire beam is subdivided into 80 beam elements. Since each node has two degrees of freedom (dofs), the total dof for the entire unconstrained beam is 162. The dimensions of the Timoshenko beam studied in this paper are (cf. Fig. 1): the total length is L \u00bc 1.0m; the mass density is ARTICLE IN PRESS H.-Y. Lin / Journal of Sound and Vibration 319 (2009) 593\u2013605 601 r \u00bc 7.835 103 kg/m3 and Young\u2019s modulus is E \u00bc 2.069 1011N/m2, the shear coefficient is k0 \u00bc 5/6, the Poisson ratio is v \u00bc 0.3, the shear modulus is G \u00bc 7.9577 1010N/m2. 5.1. A single-span Timoshenko beam carrying multiple concentrated elements The first example is a pinned\u2013pinned (P\u2013P) beam as shown in Fig. 2 carrying three point masses, two rotary inertias, two linear springs, one rotational spring and one mass\u2013spring system" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003151_0954406212468407-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003151_0954406212468407-Figure2-1.png", + "caption": "Figure 2. The planetary gearbox test rig.", + "texts": [ + " Please note that a higher ranking number actually indicates a lower ranking. In equation (16), 1 and 2 are two adjustable parameters to balance the effectiveness term and the correlation term. A relatively larger parameter 1 emphasizes the effectiveness term more. A relatively larger parameter 2 weights the correlation term more heavily and thus could produce a feature subset with less redundancy. The proposed multi-criterion algorithm for feature selection is summarized in Table 1. The planetary gearbox test rig shown in Figure 2 was designed to investigate diagnostic systems for gear faults. The test rig has a 15 kW (20 hp) drive motor, a one-stage bevel gearbox, a two-stage planetary gearbox, two speed-up gearboxes, and a 30 kW (40 hp) load motor. We study only the second stage planetary gearbox shown in Figure 3. We created two types of gear faults including crack and tooth missing using electro discharge machining (EDM). Crack may develop due to repetitive loading and impurity within the gear material. The tooth missing damage mode is very close and sometimes is equal to gearbox failure" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002182_robio.2009.4913121-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002182_robio.2009.4913121-Figure5-1.png", + "caption": "Fig. 5 Stability margin calculation", + "texts": [ + " Then, stair climb initializing motion is performed. We used Normalized Energy Stability Margin proposed by Hirose [14] to confirm the stability when the robot raises its legs on non-horizontal plane. As the robot movement is only in one direction, applying standard stability margin by checking if the center of gravity is within supporting area or not before Normalized Energy Stability Margin can reduce a number of consideration cases and number of calculations. The procedure of our stability checking algorithm is as follow, Fig.5: 1) Calculate the position of center of gravity. 2) Check if the position of center of gravity projection is within area of supporting leg or not. If not, regard as unstable and additional movement will be added in order to increase the stability of robot. 3) If within the supporting leg area, locate the pivot point existing on the straight line connecting the supporting legs when the robot may fall down. 4) Calculate the highest height (hmax) on the path of COG rotation about supporting line. In our case, \u210e = \ud451 +\u210e 5) Compare the calculated highest height with current height of COG (h0)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003204_3.3019-Figure9-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003204_3.3019-Figure9-1.png", + "caption": "Fig. 9 Controllability limit for negative static stability.", + "texts": [ + " These curves show that the reduction of the value of T may be one of the important factors when the value of Y is considerably large. Figures 8 and 9 show representation of the theoretical and experimental results for negative static stability, where the damping X is an abscissa, and the critical values of the circular frequency co and static stability Y are ordinates, respectively, and the marks have the same meaning as those in Fig. 6. We have seen that at the theoretical controllability limit the critical circular frequency vanishes, and the relation between X and Y is given by Eq. (19). Thus the solid curve in Fig. 9 is plotted by solving Eq. (19) for r = 0.1 sec. It is observed that the theoretical results are not in good agreement with the experimental results. Some consideration will be given to this subject in the following paragraphs. When the value of Y is negative, the controlled element has two real characteristic roots: one is positive and the other is negative. The instability of the element is mainly determined by the positive root, and the time to double amplitude, denoted by T2, of the unstable root is related to the static stability Y and damping X as follows: Y = - (22) These are a family of straight lines, as shown in Fig. 9, with T% as a parameter. It is observed from Fig. 9 that Eq. (22), when values of T2 are taken equal to 0.240, 0.195, and 0.173 sec, is in good agreement with the experimental results obtained by Ref. 1 and with our experiments on one trial and on three trials, respectively, except for a region where the value of Y is nearly equal to zero. This may indicate that the human pilot controls the unstable element by taking notice of the unstable root only. However, in the region where the value of Y is nearly equal to zero, the damping of the mode corresponding to the negative root is small and the human pilot may be forced to take notice of both the stable and unstable roots", + " It is interesting to observe from Table 4 that the ratio Kma^/Km-m seems to take nearly constant value for each trial test. This might suggest that the ratio of Kmax/Km-in may be one of the decisive factors as the criterion of gain margin for the human pilot on the threshold of instability, although a more general criterion may be expressed such that n, TL/T, rX} r2F) = 0 (24) To emphasize this circumstance, values of Xmax/Kmin are calculated for several sets of (X, Y) on the straight lines with the constant times to double amplitude shown in Fig. 9. The calculations have been made for the straight lines indicating T2 = 0.195 and 0.173 sec, respectively, and the results are shown in Table 5. It is seen that the condition that the time to double amplitude is constant seems roughly to correspond to the condition that Km^/Kmin is constant. Final Remarks T It may be mentioned from the analysis and experiments that the proposal of representing the transfer function of a human pilot by Eq. (1), and of employing the characteristic equation of the closed system, Eq" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003812_20110828-6-it-1002.00031-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003812_20110828-6-it-1002.00031-Figure1-1.png", + "caption": "Fig. 1. Target platform and spacecraft. Non disk-shaped target platforms can be handled by a disk shaped overbound.", + "texts": [ + " This approach has several practical advantages: The MPC optimization problem can be solved by conventional Quadratic Programming (QP) solvers and, furthermore, an explicit solution of the MPC optimization problem (A. Bemporad et. al. (2002)) can be generated off-line and deployed on-line thereby avoiding the need to embed an optimization solver within the spacecraft software. We consider an autonomous rendezvous between a spacecraft and a target platform of radius rp with a docking port on its surface (see Figure 1). The target platform is in a circular orbit around the Earth and the spacecraft motion relative to the platform in the x-y orbital plane is considered. The Clohessy-Wiltshire equations of motion (see the book by Fehse (2003)) have the following form \u03b4x\u0308\u2212 3n2\u03b4x\u2212 2n\u03b4y\u0307 = ux, \u03b4y\u0308 + 2n\u03b4x\u0307 = uy, (1) where n = \u221a \u00b5 R3 0 is the orbital rate, R0 is the orbital radius, \u00b5 is the gravitational parameter of the Earth and ux and uy are spacecraft accelerations in x (radial) and y (along the orbital track) directions that are treated as control signals realized by thrust forces" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000735_j.talanta.2008.03.026-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000735_j.talanta.2008.03.026-Figure2-1.png", + "caption": "Fig. 2. Schematic diagram of the microchip and its surrounding equipment.", + "texts": [ + " Three ends of the micro-channels accessed the eservoirs, R1\u2013R3, which were holes of 2 mm in diameter. R1\u2013R3 ere located 10 mm from the intersection. The other end of the icro-channels was combined with a micro-flow line, i.e., reagent ow line (100 m in depth and 380 m in width) as shown in Fig. 1. he detection window (2 mm \u00d7 2 mm) was made at the connecting oint to the reagent line with black tape. The distance from the ntersection to the detection window was 55 mm. .3. Analytical conditions and procedures The microchip was set in a microchip-holder as shown in Fig. 2; he microchip was pinched between the upper and lower holders ightly through the four screws in order not to release solutions rom connecting points between micro-channels and PEEK tubes. e have reported many papers concerning CE with CL detection ystems including microchip CE with CL detection systems, more han ca. 50 papers. Analytical conditions in the present study were ecided with reference to those reported in our previous papers 1,2,4,6,7,10,17], together with the results obtained in preliminary xperiment of Section 3" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000914_i2007-10215-3-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000914_i2007-10215-3-Figure4-1.png", + "caption": "Fig. 4. Growth of the slip zone: (a) early stage; (b) late stage.", + "texts": [ + " However, if we impose a local sliding velocity v,very soon the bridges are torn out; then the slippage stress \u03c3(v) can be a decreasing function of v (at moderate v) (Fig. 3). This generates a mechanical instability: stick-slip. Stick-slip has been studied on many gels [2]. The most detailed study in gelatin gels was performed by Baumberger et al. [3]. With a drive velocity U above a certain velocity v\u2217 (\u223c 100\u00b5m/s) they found stable slipping (v = U). For U below v\u2217 they (mainly) found a periodic stick-slip regime. In the present paper we are mainly concerned with the decohesion process, where a part of the contact is slipping, and a part is still stuck (Fig. 4). We must distinguish carefully the velocity of rubber with respect to glass v(x) and the velocity VTIP of the crack tip (the line separating stuck regions from sliding regions). Inspired by recent experiments [4] we propose a rough, but simple picture of the tip motion. In Section 2 we follow a classical picture [3] based on bridges between (for instance) a rubber and the solid wall a e-mail: francoise.brochard@curie.fr \u2020 Deceased. (Fig. 2). We characterise these bridges by a minimal set of parameters: a) their number per unit area \u03bd, which can vary via rupture and healing; b) their maximum extension at rupture l (a few nanometers) and the corresponding force f ; c) the \u201chealing time \u03c4ON\u201d (required for rebuilding a broken bridge in static conditions)", + " The sphere is sheared, and behaves like an elastic spring of rigidity k (Eq. (8)). The overall force F (t) required to maintain the velocity U is thus increasing linearly with time, F = kUt, Optical observations suggest that the size and shape of the contact area do not change much during this stage [4]. Thus the stress on the junction is proportional to F : \u03c3 = F/\u03c0a2. At a certain moment (t = t1) we reach the threshold stress (\u03c3 = \u03c30). Here we assume (in agreement with current observations [3,4]) that a decohesion zone appears at the rear end of the contact (Fig. 4a). The growth velocity VTIP of this zone will be discussed below. Ultimately, at a time t2 = t1 + \u03c4 , we have complete decohesion, with \u03c4 \u223c= 2a VTIP . (9) After this, the sphere is elastically relaxed, and slows down under the action of the \u201cbare friction\u201d \u03b6, reaching a velocity comparable to U in a time again comparable to \u03c4 . Since U is smaller than the velocity v\u2217, healing can occur, and the sphere stops: a new cycle begins. Our starting point is Figure (4a) where most of the rubber is still in a stressed state, with a deformation \u03b50 = \u03c30/E and a stored energy per unit volume 1 2 E\u03b52 0 = 1 2 \u03c32 0 E ", + " We derive v from the following argument: relaxation has allowed for a displacement \u03b4 of the rubber \u03b4 \u223c \u03b50x (13) Thus, the velocity is v = d\u03b4 dt = \u03b50VTIP . (14) Inserting equation (14) into equation (12) we arrive at the basic scaling law VTIP \u223c= E \u03b6 . (15) Here most of the sphere is relaxed, except for a small region of linear dimensions y = 2a \u2212 x near the forward end (volume y3). Repeating a similar argument, we arrive again at equation (15). We conclude that the velocity VTIP is not singular near the end of the decohesion process: at the level of scaling laws VTIP is a constant. Let us focus on the late stage (Fig. 4b). The local stress \u03c3L in the region (of volume y3) which has not relaxed yet has a displacement \u03b4 \u223c \u03b50a at the top and a deformation \u03b4/y. Thus, \u03c3L \u223c E\u03b50 a y (16) and the overall force FD during decohesion is FD \u223c= \u03c3Ly 2 = E\u03b50ay = E\u03b50a(2a\u2212 VTIP t), (17) where t is measured from the onset of decohesion. The net result of equation (17) is that we expect a force dropping linearly during the decohesion stage (Fig. 5). Equation (16) has another interesting consequence. The slip velocity v is not given any more by equation (14), but is estimated from \u03b6v = \u03c3loc = E\u03b50 a y " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001168_s0263574708004566-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001168_s0263574708004566-Figure1-1.png", + "caption": "Fig. 1. Body fixed and earth fixed reference frames.", + "texts": [ + " It is convenient to define the underwater vehicle state vectors according to the Society of Naval Architects and Marine Engineers (SNAME) notation.1 Two common vectors that are being used in defining the underwater vehicle state vector are \u03b7 and v. The vector \u03b7 is defined as \u03b7 = [\u03b7T 1 \u03b7T 2 ]T , where \u03b71 = [x y z]T is the vehicle position vector in the earth fixed frame and \u03b72 = [\u03c6 \u03b8 \u03c8]T is the vehicle Euler angle in the earth fixed frame. And the vector v is defined as v = [vT 1 vT 2 ]T , where v1 = [u v w]T is the body fixed linear velocity vector and v2 = [p q r]T is the body fixed angular velocity vector. In Fig. 1, the defined coordinate frames are illustrated. Besides the Euler angle representation, Euler parameters or unit quaternions1,12 can also be used. The vehicle\u2019s motion path relative to the earth fixed frame coordinate system is given by the kinematics equation1 as follows: \u03b7\u0307 = J (\u03b7)v = [ J1(\u03b7) 0 0 J2(\u03b7) ] v, (1) where J (\u03b7) is a 6 \u00d7 6 kinematics transformation matrix or a Jacobian matrix. The dynamics behavior of an underwater vehicle is described through Newton\u2019s laws of linear and angular momentum" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001704_s0894-9166(10)60036-5-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001704_s0894-9166(10)60036-5-Figure3-1.png", + "caption": "Fig. 3. Geometrical relationship between half of the folding wavelength (H) and the axial displacement (\u03b4).", + "texts": [ + " Wierzbicki and Abramowicz introduced the BFM, as shown in Fig.2, and calculated the dissipated energy rate by this mechanism[4]. At the start time, \u03b1 = 0 and \u03b3 = 90\u25e6. At commence of the folding, \u03b1 increases and \u03b3 decreases, continuously. When the folding is initiated, \u03b3 and \u03b2 vary with \u03b1 and \u03c80 according to the following formulas[4]: tan\u03b3 = tan\u03c80 sin\u03b1 , tan\u03b2 = tan \u03b3 sin\u03c80 (1) The instantaneous folding distance designated by \u03b4 denotes the decreasing axial distance between the upper and lower edges of the BFM. As shown in Fig.3, this quantity is calculated as \u03b4 = 2H(1\u2212 cos\u03b1) (2) where the initial height of the BFM is defined by 2H . Differentiating the above relation yields \u03b4\u0307 = 2H sin\u03b1 \u00b7 \u03b1\u0307 (3) In the folding process, the dissipated energy rate, E\u0307int, results from the continuous and discontinuous velocity fields as[4] E\u0307int = \u222b S ( M\u03b1\u03b2 \u03ba\u0307\u03b1\u03b2 +N\u03b1\u03b2 \u03bb\u0307\u03b1\u03b2 ) dS + \u222b L M0\u03b8\u0307d (4) where N\u03b1\u03b2 ,M\u03b1\u03b2 , \u03ba\u0307\u03b1\u03b2 and \u03bb\u0307\u03b1\u03b2 are stress resultants, stress couples, the rate of curvature and the rate of extension in the continuous deformation field, respectively[4]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000055_978-1-4684-1500-1-Figure9.3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000055_978-1-4684-1500-1-Figure9.3-1.png", + "caption": "Figure 9.3 (a) Components used in the construction oj the compressor valve; (b) the assembled unit. (from a DEA PRAGMA catalogue)", + "texts": [ + " Finally, a suction cup leaf is collected from one of the two righthand stacks on the table and placed on top' of the now complete assembly sandwich. The entire four element assembly is transferred by the sec ond robot to the autoscrewdriver station, at which four screws are issued by the bowl feeder and used to clamp the entire com pressor valve together. When the assembly is complete, it is removed from the autoscrewdriver cell by the same robot and transferred to an exit conveyor. The compressor valve is shown 'exploded' in Figure 9.3(a) and assembled in Figure 9.3(b). Feeding delicate items Vibratory bowl feeders and gravity feeders have one fault in common, ie the components can bump into one another, and/ or are moved relatively across or along fixed frictional sur- 121 Assembly with Robots faces. In extreme cases, this can cause functional damage or a cosmetic surface to be marred or scuffed which, if not noticed, could result in the waste of all the added value work. There are three alternative methods by which delicate com- 122 Material feeders ponents and materials can be presented to the robot without risk of damage: 1" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002189_ijrapidm.2010.036116-Figure16-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002189_ijrapidm.2010.036116-Figure16-1.png", + "caption": "Figure 16 Component manufacture using three-axis HLM after blinding the undercuts (a) actual part; (b) modified CAD model for deposition (see online version for colours)", + "texts": [ + " In the similar manner, it will be possible to build curved features such as cylinders, torus etc.; however, adaptive layers shall be used to build these features so as to keep the overhang within the limit of 0.7 mm. This means that it may be possible to build components with smooth variations such as the ones shown in Figure 15. This pertains to manufacture of complex components through blinding the undercuts for deposition. The undercut features will be suppressed in the CAD model. An example is shown in Figure 16. The near-net shape of its CAD model suppressed for undercuts can be built using the 3-axis HLM. Depending on the complexity of the undercut features, finish-machining may require 3\u2013/5-axis kinematics. Note that this approach is very similar to that of LAM (Griffith et al., 1998). This approach is suitable for the component geometries in which the volume of undercut is substantially smaller than the volume of the final component, say, 10%. Manufacture of extremely complex components like geometries with substantial undercuts would require 5-axis deposition" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000067_2006-01-0647-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000067_2006-01-0647-Figure3-1.png", + "caption": "Figure 3: Appropriate rough surface patch size for flow factor analysis", + "texts": [ + " In this manner, flow and stress factors can be calculated. It is important to choose dimensions of the rough surface patch carefully. The patch must be large enough to include a large number of asperities. The patch must still be small relative to the total contact area between the ring and liner so that large scale effects, such as surface geometry, do not affect the results. A diagram displaying some key parameters pertinent to selecting the patch size between the ring and liner is shown in Figure 3. In Figure 3, Lx and Ly are the patch lengths in the axial and circumferential directions, respectively, g is the characteristic perpendicular distance between honing marks, and is the honing cross hatch angle. For the ring-to-liner interaction being considered, the axial patch length was chosen as one fortieth of a typical ring width in the axial direction of the cylinder bore, , 40 )1( B xnLx (13) where n is the number of nodes in the x-direction and B is the ring axial width. This is the same nodal distance used when solving the Reynolds equation between the ring and liner within MIT\u2019s ring pack program" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000351_1.2185661-Figure9-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000351_1.2185661-Figure9-1.png", + "caption": "FIG. 9. The fluid potential energy changes due to two effects. First, when the body is displaced, fluid enters the region labeled EF1. Second, when the fluid profile is shifted, fluid moves into an area equivalent in size to the region indicated by EF2.", + "texts": [ + " 18 There is an immediate difficulty in applying an energy minimizing principle to the unbounded configuration we are considering, as the total surface energy is infinite. The energy of the disturbance from the rest configuration with the same fluid level at infinity is, however, finite, and we apply the principle to that difference. Referring to Fig. 8, it is clear that since the fluid profile becomes asymptotically horizontal the difference in arc length is the horizontal distance x. Thus, lim A\u2192 E = \u2212 2 x = \u2212 2 r cos 0 0. 19 We first introduce some terminology see Fig. 9 . Let bi x , defined on 0 x x0, represents the height of the submerged part of the cylinder prior to displacement; bf x , defined on 0 x x0+ x, represents the corresponding height after displacement. Likewise, f i x , defined on x x0, represents the fluid profile height before displacement, and f f x , defined on x x0+ x, represents the same height after displacement. Outside of their defined intervals, these four quantities are defined to be identically zero. The change in fluid potential energy is then EF = g 0 bf 2 x + f f 2 x \u2212 bi 2 x \u2212 f i 2 x dx = g 0 x0 bf 2 x \u2212 bi 2 x dx + x0 x0\u2212 x f f 2 x \u2212 bi 2 x dx + x0\u2212 x f f 2 x \u2212 f i 2 x dx = g 0 x0 bf 2 x \u2212 bi 2 x dx + x0 f f 2 x dx \u2212 x0 x0\u2212 x bi 2 x dx \u2212 x0\u2212 x f i 2 x dx , 20 but the integrals of f f 2 x and f i 2 x must be equal as they represent identical profiles horizontally shifted" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000583_j.cma.2008.11.014-Figure6-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000583_j.cma.2008.11.014-Figure6-1.png", + "caption": "Fig. 6. Fictitious flat surface, wrinkled su", + "texts": [ + " In the fictitious flat surface (abc0d0), the modified Green\u2013Lagrange strain based on the contravariant basis Gi can be written as eE \u00bc 1 2 \u00f0eF T eF I\u00de \u00bc 1 2 \u00bd\u00f0F \u00fe bw wF\u00deT\u00f0F \u00fe bw wF\u00de I \u00bc E \u00fe 1 2 b\u00f02\u00fe b\u00dew0 w0; \u00f05\u00de where w \u00bc waga; w0 \u00bc wF \u00bc FT w \u00bc Ga ga wbgb \u00bc waGa. In the current configuration the wrinkling direction vector w is orthogonal to the uniaxial tension direction t, both vectors form the wrinkling axes (t,w). The pull-back of the wrinkling direction vector w is w0. An orthogonal vector pair t0, w0 constitutes an orthonormal wrinkling basis in the undeformed configuration whereas t0 is not the result from an inverse mapping of t. To prevent confusion, the notation used in subsequent section should be mentioned: As illustrated in Fig. 6, any variable without any mark ( ) is a nominal variable on the material axes (A1,A2) and a variable with hat \u00f0\u0302 \u00de is a nominal variable on the wrinkling axes (t0, w0). A variable with tilde\u2013hat \u00f0b~ \u00de is a variable on the wrinkling axes (t0, w0) that is modified by the wrinkling model whereas a variable with tilde \u00f0~ \u00de is a variable on the material axes (A1,A2) which is modified by the wrinkling model. One remark is that on the Cartesian coordinate the covariant and contravariant basis are invariant (Aa = Aa). With respect to the material basis (A1,A2), the modified Green\u2013 Lagrange strain tensor eE in Eq. (5) and its energetic conjugate which are based on the reference configuration can be described by feEg \u00bc fEg \u00fe 1 2 b\u00f02\u00fe b\u00dejjw0jj2 s2 c2 2cs T \u00bc fEg \u00fe lU2; feSg \u00bc \u00bdC feEg; \u00f06\u00de where U2 is the transformation vector of stress towards the wrinkling direction w0 as mentioned in Eq. (2) and Fig. 5 as well as Fig. 6. Obviously, l represents the amount of wrinkling, while c and s stand for cosh and sinh, respectively. The angle h is an angle of rotation that is measured counter-clockwise from the local Cartesian basis in the reference configuration (A1,A2) to an orthogonal basis formed by the wrinkling axes(t0,w0). The wrinkling direction vector in the reference configuration is given by w0 = kw0ksinhA1 + kw0kcoshA2 = w0aAa. By stretching edge cd to edge c0d0 to form the fictitious flat surface in Fig. 6, the corresponding wrinkling direction vector on this surface is w ^ , and the corresponding uniaxial tension vector on the same surface is t ^ . During a strain free movement to remove wrinkles from the surface, a uniaxial tension state of the Cauchy stress is invariant. Consequently, after wrinkles have vanished, the fictitious flat surface is still under uni- rface and their coordinate systems. axial tension. On the wrinkling axes of the fictitious flat surface \u00f0t ^ ;w ^ \u00de, the push-forward of the modified PK2 stress tensoreS \u00bc ~SabGa Gb is described with respect to the curvilinear coordinate by ~r \u00bc \u00f0det eF \u00de 1eF eS eF T ; t ^ 0 \u00bc eF T t ^ \u00bc t ^ eF ; w0 \u00bc eF T w ^ \u00bc w ^ eF ; \u00f07\u00de and the pull-back t ^ 0 of t ^ is given in Eq", + ", a membrane. In this figure, one observes that a constraint on the condition of no-compressive stress can be fulfilled by two different approaches, either the Lagrange multiplier or the penalty method (see [2]). Obviously, these figures exhibit a resemblance between wrinkling in membranes and the perfect plastic process. (iii) With a known wrinkling direction, the corresponding modified stress field is determined in such a way that the plastic flow direction r and the wrinkling direction w0 (see Fig. 6) are identical (r fS = w0) where fS is the gradient of the yield function in a stress space. Details for the elasto-plastic adopted wrinkling model is summarized in Box 1 in the Appendix B (see [2,11]). Because objectivity requirements are not relevant for the small-strain setting, the material time derivative is the relevant stress rate _S and strain rate _E replaces the rate-of-deformation (for more details, see [2]). g With this similitude, wrinkling can be deemed as an analogue to the perfect plastic process", + " (13) and the continuum elasto-plastic adopted wrinkling constitutive tensor Cepw in Eq. (17). In reality, the compressive stiffness of a real membrane is not absolute zero. As a consequence, it is reasonable to prescribe an allowable compressive stress Salw in the membrane. Thus, Eq. (10) can be modified toebS2 \u00bc UT 2feSg \u00bc Salw; ebS3 \u00bc UT 3feSg \u00bc 0: \u00f018\u00de Eq. (18)2 can be interpreted as a projection of the modified PK2 stress with the help of the transformation vector U2 towards the wrinkling direction w0 (see Fig. 6). For isotropic material, this argument is valid as well for the projection of the nominal stress tensor onto the wrinkling direction. By decomposing fictitious stress into an elastic part and a prestress as described in Eq. (1), Eqs. (11) and (12) can be rewritten as l \u00bc Salw UT 2\u00f0\u00bdC fEg \u00fe fSpreg\u00de UT 2\u00bdC U2 ; \u00f019\u00de UT 2\u00bdC U2\u00f0UT 3\u00f0\u00bdC fEg \u00fe fSpreg\u00de\u00de \u00fe UT 3\u00bdC U2\u00f0Salw UT 2\u00f0\u00bdC fEg \u00fe fSpreg\u00de\u00de \u00bc 0: \u00f020\u00de In case that Salw vanishes, Eq. (12) is recovered. Alternatively, when the allowable compressive stress concept is used, a small amount of compressive stiffness can be allowed via a penalty parameter q", + " This modified strain includes both influences of the prescribed allowable compressive stress with factor q and the reduction factor c, which accounts for the effects of prestress, on the wrinkling direction. The second term N stands for a modified constitutive tensor which maps a nominal Green\u2013Lagrange strain tensor E onto a modified PK2 stress field regarding to the occurrence of wrinkles. In the Appendix, the symmetry and positive semi definiteness properties of N are investigated. Before proceeding further, geometrical explanations of Eq. (2) should be discussed. According to Fig. 6, the PK2 stress on the wrinkling axes (t0,w0) in the reference configuration can be described by fSg \u00bc T 1fbSg \u00bc bS1n1 \u00fe bS2n2 \u00fe bS3n3|ffl{zffl} 0 ; \u00f027\u00de where n1,n2 are the transformation vectors mentioned in Eq. (2) which map the strain {E} in an arbitrary Cartesian basis to the component bE1 and bE2 of the strain fbEg in the rotated basis, i.e., the wrinkling axes (t0,w0), respectively. Obviously, on the wrinkling axes (t0,w0) the shear stress bS3 in Eq. (27) vanishes. Furthermore, the cross product of these two vectors is a bi-orthogonal vector, which points out of the plane of the undeformed configuration in Fig. 6. This vector is interpreted as the transformation vector towards the shear stress of the wrinkling axis (t0,w0) U3 \u00bc n1 n2: \u00f028\u00de From Eq. (2), the rate from of U2 is described by _U2 \u00bc oU2 oh _h \u00bc 2U3 _h: \u00f029\u00de For further investigation, a close look shows that Eq. (18)2 is automatically satisfied in the wrinkling direction. This argument can be proven readily by the convergence of the wrinkling direction search algorithm of Eqs. (10)\u2013(12) which can be interpreted as the vanishing of the projected modified stress in Eq" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003414_s207510871304007x-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003414_s207510871304007x-Figure1-1.png", + "caption": "Fig. 1. Autonomous robot, path S, and task based coordi nates (s, e).", + "texts": [ + " Differentially geometric methods of nonlinear control theory [1, 5, 8\u201310, 13\u201314] are used in the pro posed analysis method for these systems and synthesis of control algorithms solving the path following prob lem as a stabilization problem with respect to typical segments such as a straight line or a circle creating the desired path set by the way points. This article focuses directly on the synthesis of con trollers without restricting the path planning method. The main requirement is that the path should be com posed of straight lines and circles. All physical limita tions on the circle radius should be taken into consid eration at the planning stage based on the object maneuverability, speed, and available control resources. ROBOT MOTION MODEL AND STATEMENT OF CONTROL PROBLEM The position of robot body as a solid body on a plane (Fig. 1) is characterized by the Cartesian posi tion vector of center of mass C (x, y) and \u03b1 (angle of C fixed frame with respect to the base frame XOY) [11]. DOI: 10.1134/S207510871304007X GYROSCOPY AND NAVIGATION Vol. 4 No. 4 2013 CONTROL OF MOBILE ROBOT FOLLOWING A PIECEWISE SMOOTH PATH 199 Dynamic model of robot motion can be presented as (1) where is the robot longitudinal velocity in C fixed frame, is the transverse velocity, \u03c9 is the angular velocity, m is the robot weight, J is the robot moment of inertia, Fx is the longitudinal control force, Fy is the lateral control force, M is the control moment", + " Also, historically the majority of studies in this field deal with kinematic models generating the desired velocities for the lower level controllers. Specific envi ronment is also neglected in these cases. As to the practice, up till now nearly all path fol lowing modes are the functions of autopilots and self steering gears, i.e., only heading is regulated without account for longitudinal and lateral dynamics. It makes our approach rather universal. The desired path is a smooth segment of curve S (see Fig. 1) implicitly described as (4) and relevant local coordinate s (path length) is defined as 1 , 1 , 1 , x y x y x y F m F m M J \u23a7 = \u03c9 + \u23aa \u23aa\u23aa = \u2212 \u03c9 +\u23a8 \u23aa \u23aa\u03c9 = \u23aa\u23a9 v v v v xv yv ( ) ,xT y x T y \u23a1 \u23a4\u23a1 \u23a4 = \u03b1 \u23a2 \u23a5\u23a2 \u23a5\u23a3 \u23a6 \u23a3 \u23a6 v v cos sin sin cos \u03b1 \u03b1 \u2212 \u03b1 \u03b1 1 ( ) .xT y Fx T Fy m \u23a1 \u23a4\u23a1 \u23a4 = \u03b1 \u23a2 \u23a5\u23a2 \u23a5\u23a3 \u23a6 \u23a3 \u23a6 ( , ) 0,x y\u03d5 = (5) It should be noted the description of a curve as a smooth geometrical object is not the only one possi ble, and the selection of functions (4) and (5) is ambig uous. Selection of functions \u03d5(x, y) and \u03c8(x, y) is mostly limited by regularity condition [7] implying that Jacobian matrix (6) is not degenerate for any (x, y) belonging to curve S, i" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000183_bf00147425-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000183_bf00147425-Figure3-1.png", + "caption": "Figure 3", + "texts": [ + " Choose points B and C on either side of line AO such t h a t / _ BOA = ~ AOC = n/kn, and choose a point D on segment AO such that the line perpendicular to AO at D intersects BO at E and CO at F, w h e r e / k A E F is equilateral (see Figure 2). Then segment EF is one side of a regular kn-gon with the same center as the n-gon. For each side Y Z of this kn-gon, construct a ray from O which bisects that side, and let X be the point where this ray intersects the n-gon. Let the dissection include all kn (possibly degenerate) triangles X YZ, as well as the kn triangles lying between the isoceles triangles (Figure 3). If we hold k constant, and hold one side of the n-gon constant, while letting n ~ ~ , then the k + 1 sides of the kn-gon adjacent to that side of the n-gon approach a line segment parallel to that side, and the angles of all 2k + 1 triangles on that side of the n-gon approach n/3 uniformly. But all triangles in the dissection are congruent to one of those 2k + 1 triangles; so all angles are eventually less than 0. Proof Use the same construction as in Lemma 3, but let point D lie on line AO on the other side of A from O" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002325_amm.86.374-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002325_amm.86.374-Figure2-1.png", + "caption": "Fig. 2 Planet position errors (radial: xj e , tangential : yj e ; j\u03a6 : planet distribution angle)", + "texts": [ + " The mesh parametric excitations are controlled by the evolutions in the relative positioning of the mating parts which include: a) the pinion rotations leading to contact length variations (even for errorless rigid gears), and b) the variations in centre-distance, pressure angle, etc. caused by deflections. Moreover, the unilateral contact conditions between the tooth flanks can also generate strong non-linearity with momentary contact losses and shocks (backlash). All these effects are incorporated in the state equations as explained below. Initial Separations and Rigid - Body Motions. As illustrated in Fig. 2, planet position errors (radial and tangential pin-hole errors) are considered and it is assumed that their amplitudes are small compared with the radii of the PTG members. Because of the redundant paths for motion transfer from the input (sun-gear in this paper) to the output (carrier or ring-gear), contacts in rigidbody conditions can be lost between parts normally in contact for errorless gears. In the model, every planet is attributed an additional rigid-body angle about its pin axis in order to satisfy the following functional requirements: a) all the planets are in contact with the sun-gear and b) there is at least one contact between a planet and the ring-gear in order to close the kinematic chain" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001175_ijista.2008.016364-Figure9-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001175_ijista.2008.016364-Figure9-1.png", + "caption": "Figure 9 Industrial trial \u2013 injection moulding dies of a massager (a) massager and its dies; (b) both dies arranged in hybrid RP; (c) near-net shape of the die pair and", + "texts": [ + "75 kg, costing Rs. 3120.00 for both dies. The first activity in CNC machining is NC programming and the equivalent activity in HLM is data processing using HLMSoft. For a valid STL file, HLMSoft can process data in about 10\u201315 min whereas the NC programming activity using CAM software such as Unigraphics may take several hours. The near-net shape in CNC route is obtained by rough machining the block and the same is obtained by depositing layers in HLM. The finish machining is almost same in both cases. Figure 9(a) shows the cavity and punch inserts of these moulds in exploded view. Both of them were small enough for building together along Y axis as shown in Figure 9(b). This pair was built using HLM over a MS substrate of 275 \u00d7 150 \u00d7 30 mm. It weighed 9.66 kg and cost Rs. 47 per kg. Therefore, the cost of the substrate was Rs. 453.67. The near-net shape of these moulds is shown in Figure 9(c) and its finished version in Figure 9(d). Each layer was 1.5 mm thick. The total die height was about 75 mm. Since more than 30 mm at the bottom has no variation in section, the thickness of the substrate was chosen as 30 mm. The remaining height was built in 30 layers. The time taken for building each layer is presented in Table 4. The volume of the deposited portion of both the moulds is 0.00059075461 m3. Assuming an average yield o f 60%, the weight of the wire consumed in building these moulds is 7.68 kg. As the wire costs Rs. 68 per kg, the cost of the welding wire consumed is Rs" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002907_1077546311435349-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002907_1077546311435349-Figure2-1.png", + "caption": "Figure 2. Rolling element ball bearing geometry.", + "texts": [ + " These bearing faults change machine dynamics and generate a certain vibration pattern that depends upon bearing characteristics frequencies. The vibration characteristic frequencies (Benbouzid, 2000) for inner race (fID), outer race (fOD) and ball (fBD) defects can be represented by equations (1) to (3): fID \u00bc n 2 frm 1\u00fe dball dpitch cos , \u00f01\u00de fOD \u00bc n 2 frm 1 dball dpitch cos , \u00f02\u00de fBD \u00bc dpich 2dball frm 1 dball dpitch 2 cos2 ! , \u00f03\u00de where frm, dpich, dball, and represent speed of rotation, pitch diameter, ball diameter, number of balls and the contact angle respectively, as highlighted in Figure 2. Vibration signal is non-stationary in nature, i.e., its spectral contents vary with respect to time. Wavelet transform (WT) is effectively used in order to extract the time-frequency domain contents of the vibration signal (Peng and Chu, 2004). In particular, wavelet packet transform (WPT) (Bao Liu et al., 1997; Yen and Kuo-Chung, 1999; Eren and Devaney, 2004; Peng and Chu, 2004; Teotrakool et al., 2009; Zhao et al., 2009; Eren et al., 2010; Jianhua et al., 2010; Lau and Ngan, 2010; Rodriguez-Donate et al" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003305_1.4026080-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003305_1.4026080-Figure5-1.png", + "caption": "Fig. 5 Test cell: friction torque device", + "texts": [ + " The same running conditions are then established during a period of 15 to 20 min, again before any acquisition of data. This operation is repeated until the average initialization correction of the probes is less than 1 lm. An evaluation of the feasibility of using eddy current sensors to measure the oil film thickness was undertaken previously by Glavatskih et al. [10]. A force sensor was employed for the determination of the friction torque during operation. The rotation of the thrust bearing around its axis was prevented by the friction torque measurement device fixed to the frame (Fig. 5). This experimental device allows a wide range of operating conditions of the thrust bearing to be investigated. The experimental results presented here were established for steady state conditions, but it is possible to study the behavior during a transient regime. The test rig is controlled by a National Instrument Data Acquisition System driven by a Labview interface, which also permits data in the data files to be saved. A series of a hundred values of each probe\u2019s signal is acquired at a 10 Hz frequency, this being 021703-2 / Vol" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003052_10402004.2012.727531-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003052_10402004.2012.727531-Figure3-1.png", + "caption": "Fig. 3\u2014Rotation angles of the equilateral triangle: (a) apex leading; (b) apex to oil; (c) apex lagging; and (d) apex to air (color figure available online).", + "texts": [ + " This assumption resulted in a geometry simplification because the orientation of the equilateral triangle had only 12 variations because the triangle rotated 10\u25e6 each time, which D ow nl oa de d by [ U O V U ni ve rs ity o f O vi ed o] a t 0 5: 30 3 1 O ct ob er 2 01 4 benefited the angle rotation test in this study. Four orientations, to the air side, to the oil side, leading, and lagging were tested in the experiment, as shown in Fig. 2. These four orientations are of the rotation angles 90, 30, 0, and 60\u25e6, as shown in Fig. 3. The center-to-center spacing of the triangles was 150\u03bcm in the circumferential direction and 114 \u03bcm in the axial direction, as shown in Fig. 4. The depth of the surface cavity and the step height of the asperity were 5\u03bcm. In the model, the sharp (vertical) edges of the triangle were sloped as shown in Fig. 5 to accommodate the discretization of the solution domain. The grid spacing for the fluid calculation was about 2 \u03bcm. This selection resulted from balancing the need for computational speed and a high-density grid to increase accuracy", + " After the oil pressure and the oil density ratio were obtained, the dimensional axial flow rate over the computational domain was calculated using Eq. [14]. The pumping rate over the entire circumference of the lip seal was calculated using Eq. [15]. The total load-carrying capacity over the computational domain was calculated using Eq. [16]. Figure 12 shows the gauged pressure distribution over the computational domain for the lip seal running against the triangular surface cavity oriented at 90\u25e6 (see Fig. 3). The operating speed was 1,000 rpm. The fluid pressure was converted into the nodal force using Gaussian integration. The obtained nodal force was then involved in the off-line FE analysis to relax the oil film. Qy = \u222b Lx 0 \u2212 h3 12 \u03bc \u2202P \u2202y dx [14] Qtotal y = Qy\u03c0D Ly [15] W = \u222b A 0 Pgdxdy [16] In this article, the sign convention used is that reverse pumping is negative and forward pumping (leakage) is positive. The load capacity was calculated over the computational domain and the pumping rate was calculated over the entire circumference of the lip seal", + " 19b of this study, the elastomer roughness minimized the area in contact and provided small pumping paths among the asperities in contact; and (3) the composite surface roughness measured from these seals in Kanakasabai (22) was approximately 1 \u03bcm. The critical point was that selection of the equivalent film thickness in the contact region was not arbitrary but based on measured data and a physically motivated approach. Figure 13 shows the load capacity vs. speed and the pumping rate vs. speed curve for the seal against the triangular surface cavity with a rotation angle of 90\u25e6 (see Fig. 3). Figure 14 shows the speed testing result for the asperity with the same rotation angle of 90\u25e6. By comparison, it was found that the cavity and the asperity with the same orientation pumped oil in the opposite direction. The triangular cavity pointing to the air side pumped oil to the oil side. It was also shown that the asperity provided more load capacity and a greater pumping effect than the cavity especially at high speeds. Interestingly, the model predicted that without the elastomer roughness and the squeeze effect, neither the cavity nor the asperity pattern could generate enough hydrodynamic lifting force to completely separate the seal from 0 0", + " Figure 16 shows the angle rotation test result for the asperity. The operating speed was 750 rpm. The negative load capacity in Fig. 15 was caused by the excessive presence of the cavitation in which the gauged oil pressure was \u2212101, 325 Pa. It can be seen more clearly that the asperity tended to pump oil toward its apex as the maximum forward pumping occurred at a rotation angle of 90\u25e6 (pointing to the air side) and the maximum reverse pumping occurred at a rotation angle of 30\u25e6 (pointing to the oil side; see Fig. 3). For the cavity, the maximum forward pumping rate and the maximum reverse pumping rate were obtained at 50 and 80\u25e6, which deviates from the best pumping angles of 30 and 90\u25e6. The deviation was caused by the single load peak between the angles of 60 and 70\u25e6 shown in Fig. 15. In general, the cavity pumped oil toward its base. A general explanation for the directional pumping ability of the surface triangles was related to the cavitation. As shown in Fig. 12, the cavitation broke the anti-symmetry of the pressure distribution over the triangles by truncating the negative pressure", + " 16\u2014Angle rotation result for the surface asperity (model) (color figure available online). D ow nl oa de d by [ U O V U ni ve rs ity o f O vi ed o] a t 0 5: 30 3 1 O ct ob er 2 01 4 Fig. 17\u2014Pumping rate for the cavity and smooth shaft (experiment) (color figure available online). oil film thickness in the asperity area was smaller, which means that the asperity impeded the flow to be pumped toward its base. It was also found that when the orientation of the triangle was leading (0\u25e6) or lagging (60\u25e6; see Fig. 3), there was no significant pumping effect for either the cavity or the asperity. This was because in the leading and the lagging cases, the triangle was symmetrical about the circumferential direction (fluid incoming direction); thus, there was no significant pumping preference (again, this assumed no elastomer surface roughness). Though the pumping rate at angles of 0 and 60\u25e6 was insignificant compared to the values at other orientations, there existed a small pumping rate because the uneven axial sealing force slightly undermined the symmetry of the axial oil film distribution", + " (3) The viscoelasticity of the material was absent from the model. In the real system, the elastomer should be hardened at a high operating speed due to the viscoelasticity. The impact of the viscoelasticity is just like the impact of the harder material. Fig. 19\u2014Rough seal surface (a) and the zero speed contact status with the cavity (b) (color figure available online). The second discrepancy is that in the model, the cavity leading (0\u25e6) and the cavity lagging (60\u25e6) pumped very little oil (see Fig. 3), whereas in the experiment they reverse pumped significantly more oil than the smooth shaft did, as shown in Fig. 17. Warren and Stephens (21) determined this experimentally and attributed this phenomenon to the uneven sealing force across the sealing zone as well as the elastomer roughness. In this section, the model is modified to include elastomer roughness. It was assumed that the elastomer roughness had a sinusoidal pattern as shown in Fig. 19 and described in Eq. [17]. This roughness was a little higher than the actual surface roughness to make the influence more obvious" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002530_tbcas.2012.2195661-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002530_tbcas.2012.2195661-Figure1-1.png", + "caption": "Fig. 1. Protein-based electrochemical biosensor array microsystem concept with fluid delivery to an electrode array on the top of a silicon integrated circuit.", + "texts": [ + " In continuation of previous work [10], [11], this research on microsystem integration fills the gap between heterogeneous protein-based biosensors and CMOS electrochemical instrumentation circuitry by identifying suitable processes for post-CMOS electrode fabrication, bio-interface formation and sensor interrogation. By replacing the protein bio-recognition elements, this model platform can be expanded to tackle a wide range of detection challenges in fundamental biomedical research, medical diagnostics and drug discovery. Combining CMOS electrochemical instrumentation circuitry with IC-compatible electrode arrays introduces the opportunity to realize an electrochemical analysis microsystem with fluid handling structures to facilitate bio-interface formation and test sample delivery, as illustrated in Fig. 1. The electrode array enables a biology-to-silicon interface provided it can simultaneously meet requirements set by 1) IC process compatibility, 2) biointerface self assembly, and 3) electrochemical analysis techniques. This section analyzes the limitations imposed by 1932-4545/$31.00 \u00a9 2012 IEEE these overlapping requirements and highlights solutions that can be adapted to many electrochemical microsystems. Instrumentation circuitry supporting many electrochemical methods can be implemented in a low cost integrated circuit (IC) using complementary metal-oxide-semiconductor (CMOS) technology" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001089_elps.200600603-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001089_elps.200600603-Figure2-1.png", + "caption": "Figure 2. Microfluidic chip integrated with CFNE. (A) Layout of the chip. (B) Configuration of electrophoresis system with an integrated electrochemical detector: (1) sample reservoir; (2) buffer reservoir; (3) sample waste reservoir; (4) separation channel; (5) detection cell; (6) working electrode; (7) reference electrode; and (8) epoxy. (C) Enlarged view of the outlet of separation channel.", + "texts": [ + " The CFME was obtained by cutting the protruding carbon fiber to the desired length (in this experiment ,200 mm), and the CFNE was achieved by etching the protruding carbon on the flame to form a nanometer-scale tip. The tip of CFNE can be controlled within the range from 100 to 300 nm. The SEM images of the general views of a CFNE, CFME, the tips of a CFNE and a CFME are shown in Figs. 1A\u2013D, respectively. The schematic illustration of the microchip CE system mainly composing of microchip for separation and the detection cell is shown in Fig. 2. The glass microchip, fabricated by Alberta Microelectronic (AMC-mChip-T180, Canada) has a 76 mm long separation channel and a 250 mm long offset double-T injection channel, and the distances from the sample reservoir, buffer reservoir, and sample waste reservoir to the double-T injection channel are all 5 mm. The cross-section of the channels is approximately semicircular with a width of 50 mm at the top and a maximum depth of 20 mm. The original outlet of the buffer waste reservoir was cut to expose the channel outlet and then the edge of the channel outlet was polished with an abrasive. The resulting chip was washed extensively with deionized water and sonicated for 30 min to remove any alumina particles which may adhere to the separation or sample channel (Fig. 2A). Subsequently, the detection cell was formed by adhering a glass slide to the bottom of the chip and another concave-shaped organic glass (poly(methyl methacrylate), 3 mm thickness) on the top of the chip, respectively (Fig. 2B). Finally, an optical microscope and a five-dimensional micromanipulator were employed to insert the electrode into the separation \u00a9 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.electrophoresis-journal.com Electrophoresis 2007, 28, 1579\u20131586 Miniaturization 1581 channel, and then the electrode was fixed on the glass plate by epoxy resin (volume ratio of epoxy resin/ethylenediamine ,8:1) (Fig. 2C), after the epoxy resin was solidified, an Ag/ AgCl reference electrode was positioned sufficiently close to the working electrode and adhered to the detection cell. Pipette tips (200 mL) were cut flat and adhered to the drilled holes (diameter 2 mm) on the chip to form the buffer, sample, and sample waste reservoirs. A platinum wire (diameter 0.5 mm) was inserted into each reservoir as the electrodes of high voltage supply. A fast replacement of passivated electrode can be performed by ablating the epoxy with a heated scalpel and refixing a new electrode on the chip" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003534_978-1-4419-6022-1-Figure3.24-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003534_978-1-4419-6022-1-Figure3.24-1.png", + "caption": "Fig. 3.24 Circuit diagram for Task 3", + "texts": [ + " Then plot an I V curve for a Zener diode, which should be shown in the third quadrant (Fig. 3.23). You can clearly identify the Zener voltage of around 5.1 V. Question 3.3 Plot VZener (y-axis) against IZener (x-axis) for the above data. Did you notice the voltage is almost constant for a certain window of current? 54 3 Diodes and Transistors \u2022 A breadboard, wires, wire cutter/stripper, a power supply and a DMM. \u2022 1 MO and 10 kO pots, and a screw driver. \u2022 Bipolar transistor 2N4401 (NPN-type). \u2022 100 and 1 kO resistors. Figure 3.24 shows the circuit layout. Transistors come in several different packages, but the TO-92 plastic package is the most common (Fig. 3.25). The circuit layout indicates a larger pot and resistor are used on the base side of a transistor, while smaller ones are used on the collector side. Why? A transistor is basically a current amplifier; a small current to the base produces a much larger current flow from the collector to the emitter. Like a water faucet, the amount of current applied to the base controls the collector-emitter current" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002222_9783527627646-Figure7.12-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002222_9783527627646-Figure7.12-1.png", + "caption": "Figure 7.12 Schematic diagrams of two types of microreactorheat exchanger; (a) parallel flow, (b) cross flow.", + "texts": [ + "26a, respectively. . As a result of the first two points, microreactor systems are much more compact than conventional systems of equal production capacity. . There are no scaling-up problems with microreactor systems. The production capacity can be increased simply by increasing the number of microreactor units used in parallel. Microreactor systems usually consist of a fluid mixer, a reactor, and a heat exchanger, which is often combined with the reactor. Several types of system are available. Figure 7.12, for example, shows (in schematic form) two types of combined microreactor-heat exchanger. The cross-section of a parallel flow-type microreactor-heat exchanger is shown in Figure 7.12a. For this, microchannels (0.06mm wide and 0.9mm deep) are fabricated on both sides of a thin (1.2mm) 128 | 7 Bioreactors metal plate. The channels on one side are for the reaction fluid, while those on the other side are for the heat-transfer fluid, which flows countercurrently to the reaction fluid. The sketch in Figure 7.12b shows a crossflow-type microreactor-heat exchanger with microchannels that are 0.1 0.08mm in cross-section and 10mm long, fabricated on a metal plate. The material thickness between the two fluids is 0.02\u20130.025mm. The reaction plates and heat-transfer plates are stacked alternately, such that both fluids flow crosscurrently to each other. These microreactor systems are normally fabricated from silicon, glass, metals, and other materials, using mechanical, chemical, or physical (e.g., laser) technologies" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003819_elan.201200393-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003819_elan.201200393-Figure1-1.png", + "caption": "Fig. 1. Fully automated injection device for EAI-CE-MS experiments. Main components: Fixed separation capillary (A), screen-printed electrode with drop of sample (B) and CE buffer reservoir with high voltage electrode (C).", + "texts": [ + " W. Thielmann & Cie KG, Germany) according to Hummers method [20] with slight modifications published by Chen et al. [21]. Finally, chemical reduction with hydrazine resulted in reduced graphene oxide (rGO) and was used for the drop coating process in a concentration of 0.25 mg mL 1 [22]. For EAI-CE-MS experiments a fully automated EAI cell was used. The cell arrangement was a further development of a previously reported semi-automated injection device [4]. The new injection device is shown in Figure 1. The schematic representation (left part in Figure 1) illustrates the electrochemical analyte conversion during hydrodynamic injection. The fully automated cell configuration allows a microprocessor-controlled vertical and horizontal positioning of the capillary with the help of high-precision servo motors. The cell can either be operated via a computer program or by a manual controller unit. A power supply HCN 7E-35000 obtained from F. u. G. Elektronik (Germany) served as high voltage source. The HV source was capable of providing separation voltages up to 35 kV" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003762_robio.2012.6491146-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003762_robio.2012.6491146-Figure5-1.png", + "caption": "Fig. 5. Foot of biped robot", + "texts": [ + " Moreover, the PDW of our biped robot is much more energy-efficient than the active walking of the conventional biped robots. We can thus expect that our biped robot achieves more high-speed and energy-efficient active walking than the conventional biped robots by mimicking this PDW on level ground. Fig. 4 shows a front view of our biped robot. This robot has mechanical parameters as shown in Table I. To measure each joint angle and leg\u2019s angular velocity, this robot has rotary encoders and a gyroscope. This robot also has motors and timing belts for active walking on level ground. Fig. 5 shows the foot of our biped robot. This foot has a spring, joint damping and a rotary inerter at the ankle. Moreover, it has a toe-switch and heel-switch to detect contact conditions of the robot. Fig. 6 shows the rotary inerter at the ankle. Since the rotary inerter consists of two pinions, gears and a flywheel, we can easily modify the ankle inertia of the robot by changing the gear ratio and flywheel [10]. The inner legs are then synchronized by a mechanism of the robot, and the outer legs are also synchronized by a mechanism of the robot" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002348_j.tsf.2011.06.011-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002348_j.tsf.2011.06.011-Figure1-1.png", + "caption": "Fig. 1. Schematic drawing of platinum electrode chips.", + "texts": [ + " Ag/AgCl during the experiment at a rotation speed of 2000 rpm. The solutions were bubbled with high purity nitrogen, and a nitrogen flow was maintained over the solution during the measurements. The working electrode used for deposition of the composite coatings was elaborated using microsystem technologies, and in particular a lift-off process that consists in photolithography followed by platinum sputtering on a SiO2 wafer. This technique made it possible to fabricate a flat platinum electrode (Fig. 1) which was very useful for characterization of composites using surface analysis methods such as AFM, SEM or profilometry. The first step of the fabrication process consisted in drawing the required pattern with a commercial mask design software Cadence. A Cr/Glass mask, on which the shape of the pattern was drawn, was then made with an electromask optical pattern generator. The process startedwith a 100- oriented standard 3\u2033 silicon wafer, thermally wet-oxidized, at 1200 \u00b0C inwater vapor, in order to produce a 1" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003490_03093247v043208-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003490_03093247v043208-Figure2-1.png", + "caption": "Fig. 2. Dissection of disc specimen", + "texts": [ + " During the dissection, especially boring out, care was taken to ensure that the method of holding the workpiece did not introduce further plastic deformation. Strain gauges attached to the surface of the rolling track in the axial and circumferential directions were used to deduce the stress changes caused by dissecting the disc. T o measure the change in curvature due to layer removal, the strain gauges having been removed, metallic-foil grids were attached with Araldite to the ring specimen as shown in Fig. 2b. The J O U R N A L O F S T R A I N A N A L Y S I S VOL 4 NO 3 1969 21 1 at Auburn University on March 13, 2015sdj.sagepub.comDownloaded from R. J. POMEROY AND K. L. JOHNSON dimension g was measured with a Zeiss Universal measuring machine. Thus, by simple bending theory, Ag ( A K ) ~ = -- 27rR' ' . . In the strip the bending deflections are unavoidably much smaller than in the ring. To increase the sensitivity, light alloy arms carrying the metal-foil grids were attached to the strip as shown in Fig. 2c. The dimension d was measured in the measuring machine, whence All measurements were made in a constant-temperature environment. Layers were removed from the stressed surfaces by electropolishing. The thickness of the layers varied between 0.0002 in and 0.005 in, depending upon the stress gradient and the detail required. Further details of the technique are given in (11). Experimental results Aluminium-alloy discs First the background residual stresses in an unrolled disc were measured by the same method as for the rolled discs" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000084_s00170-005-0312-6-Figure14-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000084_s00170-005-0312-6-Figure14-1.png", + "caption": "Fig. 14 Illustration of the first and second detecting coordinates", + "texts": [ + " Therefore, carrying over the collision-free included angle in the previous section as the foundation, we can find out the yaw angle of the cutter to determine the collision-free cutter orientation. From the previous section, it is known that the collisionfree zone detected initially is as shown in Fig. 12. However, it is limited to plane detection, and actually, no collision of cutter can be created in 3-dimensional space. Therefore, in the collision-free detection at the second stage, the collisionfree angle range will be taken as the foundation to encircle a cone angle, and a detection of adjacent surfaces will be made for the second time. Its method is as follows. As shown in Fig. 14, the extreme values of the collisionfree zone acquired from first detecting coordinate system and the included angle of \u2013YL1 axis are (\u03b8cf )max and (\u03b8cf )min, respectively. Hence, the mean value of two extreme values is: \u00f0\u03b8cf \u00demid \u00bc \u00f0\u03b8cf \u00demax\u00fe\u00f0\u03b8cf \u00demin 2 . That is, the second detecting coordinate system L2 is formed by the rotation of \u03b1L12 angle (\u03b1L12 = 90\u00b0\u2013(\u03b8cf ) mid) along the XL1 axis, and the original point of this coordinate is at the center of the cutter. Half of the included angle of two extreme values is \u00f0\u03b8cf \u00dedif \u00bc \u00f0\u03b8cf \u00demax \u00f0\u03b8cf \u00demin 2 " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001478_j.1600-0838.2009.01043.x-Figure8-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001478_j.1600-0838.2009.01043.x-Figure8-1.png", + "caption": "Fig. 8. Sketch of the variables involved in the calculation of leaning angle of the body during running in a circle (see Appendix).", + "texts": [ + " It can be demonstrated that the relationship between leaning angle (a, deg.), circle radius (rf, m) and tangential speed along the path (vf, m/s) is tan a \u00bc r2f g \u00f0rf l cos a\u00dev2f where (m) is the average height of the BCOM. We used an equation graphing software (Grapher, Apple Inc., Cupertino, California, USA) to calculate that at the measured vf range (1.64\u20132.49m/s), as measured, and for an rf of 1m, as expected in the transition between stair ramps, a ranged from 781 to 681. Then, the speed of the BCOM (vcm, m/s) vcm \u00bc vf rcm rf where rcm \u00bc rf l cos a (Fig. 8), was in the range from 1.37 to 1.79m/s. Finally, the cost of running in circles with a 1m radius was found to be almost speed independent, and equal to 283.1 64.1mlO2/ (kg km). The mechanical equivalent work [J/(kgm)] was obtained by multiplying the metabolic cost by the muscle efficiency (0.25), and expressed as J/(kg floor) by assuming that two half-circles are normally expected to be travelled for each floor of the building." + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002494_j.conengprac.2010.05.009-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002494_j.conengprac.2010.05.009-Figure1-1.png", + "caption": "Fig. 1. Reference coordinate system of the prototype UH.", + "texts": [ + " Vertical control includes takeoff and landing decision and vertical velocity control is based on height tracking. The autonomous takeoff and landing flight control strategy is successfully applied on a prototype UH with coaxial rotor and ducted fan configuration. Real time flight test results presented indicate the effectiveness of the designed control strategy. The prototype unmanned helicopter (UH), with a net weight 160 kg and height of 1.9 m, is a vertical takeoff and landing aircraft that includes a fuselage with toroidal portion and coaxial rotors, as shown in Fig. 1. A duct is formed through the fuselage and extends from the top to the bottom of the fuselage. A propeller assembly is mounted to the top portion of the fuselage with a main rotor of diameter 4.4 m. A ducted rotor assembly is installed in fuselage compensating the propeller antitorque besides providing some fraction of lift. The coaxial rotors, main and ducted, rotate at 800 revolutions per minute in opposite directions. The main rotor provides about 80% of lift, drag, pitch and roll movements of UH and the ducted rotor provides about 20% of lift and yaw movements", + " In order to ensure takeoff and landing safety, UH uses inertial-radio device to measure the altitude making full use of the radio altimeter\u2019s high precision at low altitudes. In comparison with conventional main and tail rotor configuration, the coaxial rotors with ducted fan configuration provide more lift and move easily in any direction, during takeoff and landing. These design features not only increase the maneuverability of UH but also increase its stability making it easier to fly especially in narrow takeoff and landing site. The reference coordinate system of UH is shown in Fig. 1. X-axis is roll axis, pointing forwards along the symmetry axis; Y-axis is pitch axis, pointing outwards and Z-axis is yaw axis, pointing upwards. Consider 6-degree of freedom (DOF) equations of motion of the UH in nonlinear form, given by _X \u00bc f \u00f0X,U,t\u00de \u00f01\u00de where motion states and controls are, X\u00bc[Vx, Vy, Vz, ox, oy, oz, g, y, c]T, U\u00bc[d7, da, de, dT]T and vx, vy, vz are forward, lateral and vertical velocities; ox, oy and oz are roll, pitch and yaw rates; g, y and c are roll, pitch and heading; d7, da, de and dT are main rotor collective, lateral cyclic, longitudinal cyclic and fan collective pitches" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002707_elan.200970007-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002707_elan.200970007-Figure1-1.png", + "caption": "Fig. 1. Schematic diagram of the BIA cell.", + "texts": [ + " Nafion (5% w/v solution in a mixture of water and lower alcohols) was purchased from Aldrich (St. Louis, Missouri). A 1% w/v Nafion working solution was prepared after dilution with absolute ethanol. A solution containing 1000 mg L 1 of Triton X-100 (BDH, Poole, England) was prepared in doubly-distilled water. The electrochemical BIA wall-jet cell was designed and constructed in-house and allowed separation between the solution inlet and the working electrode. A schematic diagram of the BIA cell is illustrated in Figure 1 with the inlet-electrode separation set to 3 mm and the dead-volume of the cell was 20 mL. Injections of solutions were made with HPLC syringes (Hamilton, Switzerland) with nominal capacities of 25, 50, 100 and 250 mL. The working electrode was a glassy carbon disk (2 mm in diameter), the reference electrode was a gel-based Ag/AgCl and the counter electrode was a stainless steel rod. The electrodes were connected to an adder-type home-made potentiostat with provision for external potential input and current output connections" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001677_1.4000517-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001677_1.4000517-Figure5-1.png", + "caption": "Fig. 5 A geared five-bar linkage", + "texts": [ + " In a cyclic motion, the motion is in the order f D, P1, C, P2, P3, and D continuously through both subranches. Let 8C and 8D be the input values at C and D, respecively, in Fig. 4. To have the one-to-one correspondence property, he input domains of sub-branches DP1C and CP2P3D are dened in 8C , 8D and 8C , 8D+2 , respectively, and the point t P3 in a continuous motion should correspond to the input value t 8P3 +2 , where 8P3 is the 8 value of point P3 in Fig. 4. 2.2 Geared Five-Bar Linkages. In Fig. 5, the four-bar loop f a Stephenson six-bar linkage is replaced by a gear train and a eared five-bar linkage is formed. The geared train provides a inear I/O curve relating 5 and 4 Fig. 6 , which intersects the ve-bar JRS boundaries at the branch points 1, 2, 3, and 4. Segents 1\u20132 and 3\u20134 within the five-bar JRS represent two branches f the five-bar linkage. The branch identification can be carried ut in the way similar to that of Stephenson six-bar linkages 1,8 . 2.3 Remark. One may note that the reference links in Figs", + " ournal of Mechanisms and Robotics om: http://mechanismsrobotics.asmedigitalcollection.asme.org/ on 04/21/2 One may note later that sub-branch and full rotatability are input related, and the choice of the reference link will affect the input parameter. Hence, if the sub-branch or full rotatability is also a concern, the input reference may be taken into consideration to avoid excessive derivation. Since the input parameter is usually the angle between adjacent links, relative angles are used in Fig. 5. On the other hand, in a Stephenson type linkage, subbranch or full rotatability condition is complicated with the input given through a joint, i.e., C0, C, or D, not in the four-bar loop. Resolving the full rotatability problem under this input condition is the focus of this paper. This may explain why A0C0 and C0C are used as the reference links in Figs. 1 and 7, respectively. Figure 1 highlights the feature of having 2 or 8 as the input joint parameter. Figure 7 highlights the feature of having 8 or 7 as the input joint parameter", + "org/ on 04/21/2 listed in Tables 2 and 3, respectively, and their corresponding points on the 3 versus 2 curve are shown in Fig. 8. One must note the corresponding angular transform relationship between these two inversions of Stephenson linkages, which are indicated in Tables 1\u20133. The superscripts 1 and 7 on the angular displacements represent the corresponding values in Figs. 1 and 7, respectively with the same dimensions. 3.2 Singularity of Geared Five-Bar Linkages. A geared five-bar linkage Fig. 5 can also be considered as a multiloop linkage consisting of a five-bar loop and a gear loop. With an imposed gear train or a linear constraint, the five-bar linkage becomes a single degree of freedom mechanism. The following general gearing relationship 31 can be used to express the gear constrain: 4 + 5 \u2212 40 = 1 \u2212 n 5 \u2212 50 12 where 4 and 5 are the joint variables at joints D and E, 40 and 50 are the joint displacements of the reference gear position, and n is the gear ratio. With the angle definition in Fig. 5, the gear ratio is negative if both terminal gears rotate in the same direction with respect to link DE. Equation 12 can be expressed as 4 = \u2212 n 5 + 13 where = 40 if 50=0. The calculation of dead center singularity of geared five-bar linkages can be carried out in the way similar to that of Stephenson linkages. In the first category, the input is given through the of Stephenson linkage of Fig. 1 with input of Output deg 8 8 7 = \u2212 \u2212 8 7 7 = 7\u2212 8 64.64 159.03 0.01 104.02 119.65 180.00 79.75 303.42 180", + "37 FEBRUARY 2010, Vol. 2 / 011011-5 015 Terms of Use: http://asme.org/terms g b I t 3 s c t s t p T s d b E c e T P 0 Downloaded Fr eared train joint A or E . The dead center positions are the ranch points, which are the intersection points between the linear /O curve, i.e., Eq. 13 and the JRS boundary. This case was well reated 2,8 and shown in Fig. 6, in which the branch points 1, 2, , and 4 are also the dead center positions. In the other two categories, the input is given through a joint uch as A or C and B Fig. 5 , not in the geared train. Since the hoice of the output joint does not affect the dead center positions, o offer a unified treatment for having 4 or 5 as the input, conider the relationship between 4 and 5. The loop closure equaion of the five-bar loop ABCDEA of this linkage can be exressed as a1 + a5ei 5 + a4ei 4+ 5 + a3ei 3+ 4+ 5 = a2ei \u2212 1 14 he relationship among all angles can be written as 1 + 2 + 3 + 4 + 5 = 2 15 For the input given through joints A, B, and C, let 5 be conidered as the output, which does not affect the generality of the iscussion on the existence of the dead center positions \u2022 1 5 Let 1 be the input angle and 5 the output", + "42 304.43 34 2.12 238.98 21 4.93 242.56 96 11.72 279.49 ons 8 26. 16. 77. 19. ons 7 50. 31. 89. 06. Transactions of the ASME 015 Terms of Use: http://asme.org/terms T P a a t c 5 o 4 b s c t f r l l fi l d J Downloaded Fr 3 = P35 3 Q35 3 = 0 24 hus, the dead center positions can be obtained by solving 35 3 =0 and Q35 3 0. It should be noted that, for ease of calculation, Eqs. 17 , 21 , nd 23 must be rewritten in the half-tangent-angle formula. Example 2: The dimensions of a geared five-bar linkage Fig. 5 re given as a1 = 2.345, a2 = 0.665, a3 = 1.810, a4 = 1.235 a5 = 1.661, n = \u2212 1/2, = \u2212 17.325 deg The branch points or dead center positions with the input given hrough 5 are listed in Table 4 and shown in Fig. 6. The dead enter positions with the input given through 3 are listed in Table and shown in Fig. 10. There is no dead center position when 1 r 2 is the input Figs. 11 and 12 . Full Rotatability Identification The full rotatability of a linkage is input related while the ranch is irrelevant to the input", + " The folowing discussion on full rotatability takes the effect of using ifferent input joints into consideration. Table 4 Branch points of geare Position Input deg 1 1 107.23 109.65 2 133.45 267.64 3 178.34 75.79 4 211.39 232.50 Table 5 Dead center positions of g Position Input deg 3 1 1 80.75 42.33 2 111.39 207.59 3 190.15 135.65 4 215.24 294.92 ournal of Mechanisms and Robotics om: http://mechanismsrobotics.asmedigitalcollection.asme.org/ on 04/21/2 4.1 Input Given to a Link of the Four-Bar Loop or Geared Train. The full rotatability of geared five-bar linkages Fig. 5 with the input given to the geared train was discussed by Ting 2 . The linear input-output I/O constraint must lie within the JRS of the five-bar loop and a unit geared ratio is required 2 unless the host five-bar contains no uncertainty singularity or dead center positions . For a branch of a Stephenson linkage Fig. 1 to have full rotatability, the following conditions must be satisfied. 1. The four-bar loop is a Class I chain and the input joint must connect the short link of the four-bar loop" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001003_1.31865-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001003_1.31865-Figure1-1.png", + "caption": "Fig. 1 Three-body system model.", + "texts": [ + " In particular, the study focuses on how the viscosity of the liquid and the location of the center of the tank influence the attitude acquisition of the spacecraft. As an equivalent model representing the slosh motion of a liquid, a spherical pendulum is adopted [10,11]. Also, equations of motion for the system composed of three bodies are derived. Results from a digital simulation based on the equations of motion are presented. The spacecraft is assumed to be initially spin stabilized about the axis of the maximummoment of inertia and the wheel spin axis is parallel to the axis of the spacecraft\u2019s intermediate moment of inertia. Figure 1 shows a typical momentum biased satellite system consisting of themain bodyBof a spacecraft, amomentumwheelW, and a liquid fuel tank F. The main body has mass mb and inertia dyadic Ib about the x, y, and z axes. The momentum wheel has mass mw and inertia dyadic Iw about the x, y, and z axes. The wheel spin axis is fixed in the body frame and aligned with the z axis. The integrated body BI (not shown in the figure) consisting of the main bodyB and themomentumwheelW hasmassm1 and center of mass C1, wherem1 is the sum ofmb andmw" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000382_j.triboint.2005.11.011-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000382_j.triboint.2005.11.011-Figure1-1.png", + "caption": "Fig. 1. Schematic of lip seal.", + "texts": [ + " The bulk deformation of the lip is computed using influence coefficients, while the junctions between the asperities and the shaft are modeled as Hertzian contacts. Since the shaft is rough, the flow is unsteady and an unsteady analysis is required. The model shows how the shaft roughness affects such seal characteristics as load support, contact load ratio, contact area ratio, cavitation area ratio, reverse pumping rate and average film thickness. r 2005 Elsevier Ltd. All rights reserved. Keywords: Elastohydrodynamic lubrication; Lip seals; Rotary seals A schematic diagram of a lip seal is shown in Fig. 1. As is well-known, a successful lip seal operates with a thin lubricating film between the rotating shaft and the lip surface [1], and this film prevents damage to the lip surface. It is also known that the load support and sealing mechanism are associated with the micro-asperities on the lip surface in the sealing zone [2]. Those microscopic asperities act as mini-slider bearings and provide the load support necessary to lift the lip off the shaft by generating elevated pressures within the film [2]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002287_iros.2012.6385948-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002287_iros.2012.6385948-Figure5-1.png", + "caption": "Fig. 5. Equivalent Global Model explicitation", + "texts": [ + " 3, by writing Fvel = \u2212MeJ\u0307eJ \u2020 e(x\u0307 \u2212 x\u0307cmd) which encapsulates operationnal effects of the task execution error resulting from the external disturbance, and Fimp = Ke(x des \u2212 x) + Ce(x\u0307 des \u2212 x\u0307) + Mex\u0308 des standing for virtual effector impedance describing the control law. External disturbances can now be accounted for at the CoM level of consideration and henceforth the formulation of Sec. II-B can be used in a more generic way. The manipulation model is concatenated with the inverted pendulum one to build the complete model composed of the manipulation and balance models shown in Figs. 3 and 4, respectively, which relies on the decoupling hypothesis described in Fig. 5. The transmission of external disturbance through the main mechanical chain involved in the manipulation task is described and the application of the resulting effort (that applies thoroughly to the rest of the body) is considered to occur at the center of mass of the robot (which is, of course, a non-physical point). The validity of this approximation decreases with high CoM accelerations, and a specific attention needs to hover the choice of the manipulation chain and of the dynamic parameters (mass, notably) involved in each description (upper/lower behavior)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002687_21573698-1303444-Figure6-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002687_21573698-1303444-Figure6-1.png", + "caption": "Fig. 6 Effect of spine length on the period of rotation of the model diatom compared with the minimal-volume inscribing spheroid model.", + "texts": [ + " Note that since only the number of spines was varied, the modeled diatoms have the same minimal inscribing spheroid whose period of rotation is 1.27 s. [17] To examine whether spine length affects the period of rotation, we fixed the number of spines at 24 (i.e., 12 spines each on top and bottom) and the spine angle at 608 and varied spine length. We used the minimal inscribing spheroids to compare their Jeffery orbits Tsph with the computed periods of the diatoms Tsim. In this case, the minimal inscribing spheroid also minimized the difference in periods of rotation in comparison with larger inscribing spheroids (Fig. 6). The addition of short spines resulted in a decrease in the period of rotation, compared with a spineless cell, until a critical spine length was reached. A further increase in spine length slowed the rotation, but the period of rotation was still shorter than that of the cell without spines. For the given fixed spine angle and spine number, the period of rotation of the cell can be approximated by an effective spheroid (Fig. 6). [18] Based on the formula used to compute the period of rotation T \u00bc 2p g ar \u00fe 1 ar ; \u00f06\u00de it is clear that a sphere with ar \u00bc 1 has the shortest period. When the minimal inscribing spheroid is a sphere or nearly spherical, the period of the corresponding plankter is also smallest (Fig. 6, Table 4). Note that the axis ratio of the minimal inscribing spheroid depends on four factors: height of the cell body, diameter of the cell body, spine length, and spine angle. For a diatom with short spines relative to the body dimensions, the spheroid axis ratio will depend more heavily on the ratio of body height to diameter (the spines will have less influence over the shape of the spheroid). If the spines are long relative to the body, then spine angle becomes more important in governing the axis ratio of the spheroid" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002812_s11771-012-1220-1-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002812_s11771-012-1220-1-Figure1-1.png", + "caption": "Fig. 1 Typical motions of vectored thruster AUV: (a) Cruising forward; (b) Vertical descend; (c) Transverse turning; (d) Wheeled moving or transverse pushing; (e) Landing sea-bottom or vertical ascending; (f) Pivot steering or crawling on sea-bottom", + "texts": [ + " The multi-moving state AUV in this work makes use of the flexible transmission shaft based on spherical gear as the kinetic source equipment [1], on the end of which a new wheel propeller is installed. The whole equipment can achieve four functions such as wheels, legs, thrusters and course control based on the characteristics of spatial deflexion and continual circumgyratetion of the flexible transmission shaft. The rudders and vectored thrusters are used to control the course at high speed and low speed, respectively. The typical motions of the AUV are shown in Fig. 1 [2]. As AUVs are subjected to the larger interference effect from underwater environment, in order to ensure the stability of the new AUV, it needs a good control system with strong robustness and anti-jamming capability. However, the new AUV is a highly non-linear, time-varying and strong coupling system. Taking into account the uncertainty of environmental interference, it is difficult to establish an accurate motion model. Therefore, the control method used by the new AUV should get rid of the dependence on the precise mathematical model" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000805_tmag.2007.893297-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000805_tmag.2007.893297-Figure4-1.png", + "caption": "Fig. 4. Proposed model (top view from z axis).", + "texts": [ + " Moreover, we made a half model using the general purpose electromagnetic field analysis software and performed 3-D numerical analysis using the FEM. The number of elements is 60 900, and the number of nodes is 70 032. The air region of the whole model (including an air\u2013gap region) employs an automatic element generator which automatically adds mesh and generates elements every time the mover moves. The amount of movement per step is an interval of 2 mm. The proposed model that deforms the shape of the outlet edge at the armature side to decrease the cogging force is shown in Fig. 4. The basic model is arranged in the armature coil as a short-pitch winding, so the (A) and (B) slots of the basic model in Fig. 3 become a single layer. We deformed the shape of the armature side\u2019s outlet edge by dividing the 30-mm armature width of the single layer into three equal parts and cutting one-third of the armature width. We examined the cogging force at the outlet edge using the basic model and the five proposed models with adjusted the armature\u2019s widths of each tooth. In this paper, only the shape of the armature side\u2019s outlet edge at the ejection interval is changed" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000475_tfuzz.2006.876728-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000475_tfuzz.2006.876728-Figure1-1.png", + "caption": "Fig. 1. Exact representation of (x) by (x)d + (x)d .", + "texts": [ + ", satisfying and . To represent exactly, we must suitably assign and . Accordingly, we have the following form: (9) Let , and substitute it into (9), it yields . Then, we obtain , for , . However, care must be taken to determine the value of such that for all . To this end, it is essential to choose satisfying and let . For clarity, an example for the rule base containing only two rules, i.e., , is with and . This case has a nice geometric illustration when we consider the nonlinearity sketched in Fig. 1. We can see that the first step of modeling is simply to choose and to be a upper bound and a lower bound of the nonlinearity , respectively, as shown in Fig. 1. Then and are obtained by normalizing and , i.e., and . For the system dynamics including uncertainty, we can still keep and constants and allow and to be uncertain functions. It means that the membership functions will vary in a certain region as shown in Fig. 2(a) and 2(b) for and , respectively. Therefore, we can use fixed and known subsystems integrated with uncertain membership functions to model uncertainty systems. This modeling approach can be extended to deal with general nonlinear systems" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001453_jp803577d-Figure8-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001453_jp803577d-Figure8-1.png", + "caption": "Figure 8. Histogram of the absorbance changes of the two porphyrin films when exposed to each of the six amine vapors.", + "texts": [ + " Figure 7 shows the absorbance values at these four wavelengths plotted as a function of time. Upon exposure to the amine vapor, dramatic changes in absorbance are observed. At the Soret band (435 nm) a small increase in absorbance is detected, but at either side of the Soret band (424 or 443 nm), absorbance changes of around 20-30% are observed. It is clear from Figure 7 that the exposure- recovery cycle is reproducible and that, over the four complete cycles shown, little or no degradation in response is observed. The plot in Figure 8 represents an example of the data collected by measuring the response of 20 layer LB films of each porphyrin to six different organic amines, namely, pro- pylamine, dipropylamine, tripropylamine, butylamine, dibutylamine, and tributylamine. These amines have been chosen since there are two examples of primary, secondary, and tertiary amines, and they are all volatile liquids at 0 \u00b0C, the temperature at which they are maintained prior to vapor delivery into the sample chamber. Figure 8 depicts the average absorbance change (over four response-recovery cycles) at 443 nm for the exposure of each porphyrin to each of the six amines. The response of the 20 layer LB film of 4 is greater than that of film 1 for each corresponding amine. This is because the smaller area per molecule (Figure 5) of 4 compared to 1 means that the LB film of 4 possesses a higher molecular density and therefore a greater density of available active sites for interaction with amine molecules. The two secondary amines, dipropylamine and dibutylamine, induce a larger response, in both of the porphyrins, compared to the primary or tertiary amines", + "11 It was anticipated that primary amines would produce the greatest sensing response due to their larger solution binding constants with these porphyrins compared to secondary and tertiary amines. In this work, it was found that, for tert-butylamine, K ) 4100 ( 100 M-1; for diethylamine, K ) 810 ( 100 M-1; and for triethylamine, K ) 9.3 ( 1.0 M-1. However, the association constant is indicative of the fraction of binding pairs (porphyrin-amine) rather than the strength of the effect each bound amine has on the absorption spectrum. Our research data presented in Figure 4 and Figure 8 show that the secondary amines produce a larger absorbance change than primary or tertiary amines. We hypothesize that the binding of secondary amines by these porphyrins results in a strongly asymmetric porphyrin ring distortion compared to that resulting from the binding of tertiary amines. Primary amines are expected also to induce an asymmetric ring distortion, but this will be less pronounced than for secondary amines as a result of the presence of only one alkyl group (primary) rather than two in secondary amines" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000047_mhs.2004.1421268-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000047_mhs.2004.1421268-Figure5-1.png", + "caption": "Figure 5 Magnetic micro actuator for moving in a liver.", + "texts": [ + " The arrow in this graph was the step-out frequency at kinematic viscosity of 100 mm2/s. At the step-out frequency, the rotation of the machine could not be synchronized to the rotational magnetic field. The micro actuator swam at the speed of 0.2 ~ 1.6 mm/s. The Reynolds numbers on this condition were 2\u00d710\u20133 ~ 1.6. This result shows that the spiral shape is suitable for miniature swimming machine. 3. MICRO ACTUATOR MOVING IN A LIVER On the basis of swimming actuator, a magnetic micro actuator moving in a liver was fabricated (figure 5). The actuator composed cylindrical magnet, spiral structure and two cutting blades. A motion test of the actuator was examined in a liver excised from a pig. In this experiment, the strength of the external rotational magnetic field was 150 Oe and the frequency of the field was 10 Hz. Figure 6 shows experimental result. The actuator could move a distance of 40 mm in the liver. The actuator has possibility of carrying a hyperthermia (heating) device[5] for liver cancer. Colonoscopy (colon endoscopy) is widely carried out to find a disease such as colon cancer at the early stage" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000898_978-0-387-28732-4_4-Figure4-29-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000898_978-0-387-28732-4_4-Figure4-29-1.png", + "caption": "Figure 4-29. Polyimide based electrode array for CNS applications with capability to store bioactive substances [300].", + "texts": [ + " With respect to a patient oriented therapy some research groups have already started to investigate sensing and actuating principles other than recording and electrical stimulation in neuro science applications. Electro-active substances in the brain, such as dopamine, were monitored with tetrode arrangements of electrodes on ceramic based substrates [299]. Bioactive substances for attracting nerve fibres were integrated into flexible multi-channel shaft electrodes [300] for neural recording (Fig. 4-29). The combination of micro-fluidics channels and electrode sites for recording [301] and stimulation opens new opportunities for detecting pathophysiological neural excitation patterns and deliver specific pharmaceutical agents in small doses directly near the sites of the incidents. The combination of these measurement and actuation modalities to multimodal neural implants paves the way towards patient specific diagnosis and therapy and therapy control and hopefully helps to cure diseases and alleviate symptoms where currently no reliable methods and adequate therapies are present" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003616_j.1460-2695.2012.01686.x-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003616_j.1460-2695.2012.01686.x-Figure2-1.png", + "caption": "Fig. 2 Coordinate system implemented in the current rolling contact simulations.", + "texts": [ + "18 It should be noted that the determination of the material constant sets c(i) and r(i) describe the plastic deformation due to proportional loading was based on the assumption that the parameters \u03c7 (i) associated with the non-proportional loading were large enough, such that the plastic modulus function could be treated as a step function in terms of plastic strain.18 Furthermore, previous experimental and computational results on similar yet different materials support the success of this approach in predicting ratchetting behaviour under cyclic loading,12,13 including a comparison of the current approach with other available models.17 The wheel\u2013rail contact profile is modelled as a Hertzian contact. Shear loading is assumed to be proportional to the normal pressure at every point in the distribution (Fig. 2) as dictated by the Q/P ratio, where Q is the shear force and P the normal force. It is proposed that the stress in the body throughout the loading cycle is equal to the elastic stress field. The elastic stress data are computed using Smith and Liu\u2019s equations for line loading contact throughout the loading cycle.19 Following the passage of the load, stress and strain components are different than zero based on the elastic stress cycle. However, the geometrical constraints require these stresses and strains are zero after the passage of the load" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003560_978-1-4613-4560-2_2-Figure8.35-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003560_978-1-4613-4560-2_2-Figure8.35-1.png", + "caption": "Fig. 8.35. At low io values, the interface has high resistance or polarizability.", + "texts": [ + "6 The Influence of io upon the Current Density Required to Attain a Given Overpotential acjl - acjle 13 = 0.5 and T = 25\u00b0C io , Current density [A em-'] required for the following overpotentials [V] Aem-' 0.001 0.010 0.100 0.200 10-6 4 x 10-8 3.9 X 10-7 6.9 X 10-6 4.9 x 10-5 10-3 4 x 10-5 3.9 X 10-' 6.9 X 10-3 4.9 X 10-' 4 X 10-' 0.39 6.9 49.4 of potential from the equilibrium value iJ1>e characteristic of the given reac tion. Similarly, one can conceive of the other extreme, the case of io -+ 0 (Fig. 8.35). Here, drJldi, the polarizability, and the reaction resistance e.l1/S become infinite. The potential departs from the equilibrium values even with a very small current density leaking across the interface. This, however, is precisely what could be expected for a highly polarizable inter face; its potential is easily changeable, it can be varied at will by an external power source without passing significant currents. Thus, the concepts of polarizable and non polarizable interfaces are quantified" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000964_j.mechmat.2008.09.004-Figure12-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000964_j.mechmat.2008.09.004-Figure12-1.png", + "caption": "Fig. 12. Negative Bauschinger effect.", + "texts": [ + " 11) consists of three parts: the cone constituted by boundary planes (b = b1) located on the endpoint of the vector ~S, the initial sphere (3.23), and the sphere determined by Eq. (6.5). The subsequent yield stress, SS, in opposite direction to the vector ~S can be calculated from Eq. (6.3) as SS = h m(b = p/2): SS \u00bc S0 2 ffiffiffi 2 p sS; \u00f06:6\u00de where S0 P ffiffiffi 2 p sS. Eq. (6.6) gives the positive value of SS for S0 P 2 ffiffiffi 2 p sS, which corresponds to the so-called Bauschinger negative effect when a plastic deformation occurs even during unloading (Fig. 12). Consider the following loading path: an element of a body is first loaded in tension by a vector ~S ffiffiffiffiffiffiffiffi 2=3 p rx; 0;0\u00de and then, holding the tensile stress constant, is subjected to an additional torsion, D~S\u00f00;0; ffiffiffi 2 p Dsxz\u00de, D~S ?~S. Eqs. (2.2), (3.8), (3.28) and (3.30) give the following distances to planes and irreversible deformation intensity for tension (taking into account that rS \u00bc ffiffiffi 3 p sS): HN \u00bc ffiffiffiffiffiffiffiffi 2=3 p rx cos a cos b cos k; ruN \u00bc ffiffiffiffiffiffiffiffi 2=3 p rx cos a cos b cos k rS\u00f0 \u00de: \u00f07:1\u00de The boundary value of k is determined from the condition uN = 0: cos k1 \u00bc rS=\u00f0rx cos a cos b\u00de; 0 6 k 6 k1: \u00f07:2\u00de Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002993_icelmach.2012.6350093-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002993_icelmach.2012.6350093-Figure2-1.png", + "caption": "Fig. 2. Mechanical assembly dynamic test rig (mounted horizontally)", + "texts": [ + " Related to the simulation model, there is only little danger of the appearance of EDM currents at operating points with thin film thicknesses. The results shown above were generated in a test rig with two deep grove ball bearings, which were loaded with constant axial load. The question is whether bearing vibrations influence the lubricating film. Vibrations in electric motors can be excited by a driven machine. It is known that bearing vibrations can have a positive effect on the reflow of lubricant into the contact zone. In order to investigate this effect, a new test rig was designed. Fig. 2 shows the mechanical assembly of the test rig for dynamic axial loads. The shaft is supported in the housing by two hybrid spindle bearings. As hybrid bearings are equipped with ceramic rolling elements, there is no current path over these bearings. The test bearing is mounted at the end of the shaft. Thus, the inner ring of the 6008-type test bearing is fixed in radial and axial direction. The outer ring is movable within the limits of the bearing clearance. To load the bearing in the axial direction, the outer ring is preloaded using disc springs in one direction" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001334_j.oceaneng.2008.09.011-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001334_j.oceaneng.2008.09.011-Figure1-1.png", + "caption": "Fig. 1. Submersible with bow and stern hydroplanes.", + "texts": [ + " However, for this design, one needs to know the sign of the two minors of the input matrix, but no other knowledge of the submarine parameters is required. In the closed-loop system, it is shown that the depth and pitch angle trajectories asymptotically track the reference trajectories. The organization of the paper is as follows. Section 2 presents the mathematical model and the control problem. The SDU decomposition and the adaptive control law are presented in Section 3. Finally, Section 4 presents simulation results. We consider here the dive-plane dynamics of the submarine (see Fig. 1). Readers can refer to Dumlu and Istefanopulos (1995) and Babaoglu (1988) for more details. The equations of motion along the z-axis and y-axis are given by _w\u00f0t\u00de \u00bc Z0wU Lm03 w\u00f0t\u00de \u00fe 1 m03 \u00f0Z0_y \u00fem0\u00deU _y\u00f0t\u00de \u00fe Z0\u20acyL m03 \u20acy\u00f0t\u00de \u00fe Z0dBU2 m03L dB\u00f0t\u00de \u00fe Z0dSU2 m03L dS\u00f0t\u00de \u00fe 2 rL3m03 Zd\u00f0t\u00de (1) \u20acy\u00f0t\u00de \u00bc M0_w LI02 _w\u00f0t\u00de \u00fe M0wU LI02 w\u00f0t\u00de \u00fe M0_yU LI02 _y\u00f0t\u00de \u00fe M0dBU2 LI02 dB\u00f0t\u00de \u00fe M0dSU2 LI02 dS\u00f0t\u00de \u00fe 2mg\u00f0zG zB\u00de rL5I02 y\u00f0t\u00de \u00fe Md\u00f0t\u00de rL5I02 (2) where w is the heave velocity, h is the depth error, y is the pitch angle, and dB and dS are the hydroplane deflections in the bow and stern planes, respectively, and Zd and Md denote the disturbance inputs" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003088_j.jmatprotec.2011.09.010-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003088_j.jmatprotec.2011.09.010-Figure5-1.png", + "caption": "Fig. 5. The linear velocity field in a rectangular zone.", + "texts": [ + " However, in general, this goal can be achieved by decreasing the size of rectangular zones. But, since the calculation should be done numerically, decreasing the size of zones will lead to more numerical error, and therefore, less accurate results. For each zone, parameter \u0131 is introduced as the distance between the center of volume of the axial velocity prism and the centroid of the rectangle. The more the value of the \u0131, the more is the curvature of the exit profile. For a zone with constant velocity the value of \u0131 is zero which leads to a straight final product. Fig. 5 illustrates the linear velocity distribution in a rectangular zone. a is the length of the zone and V1 and V2 are the maximum 254 A.K. Meybodi et al. / Journal of Materials Processing Technology 212 (2012) 249\u2013 261 a e o s a nd minimum axial velocities, respectively. Rc is the radius of the xit profile curvature. The curvature of the exit profile has been btained as the following: = 1 Rc = 12 \u00d7 \u0131 a2 (9) To calculate the exit profile curvature for the given die, the exit ection has been divided into rectangular zones as shown in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003300_j.wear.2011.02.017-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003300_j.wear.2011.02.017-Figure5-1.png", + "caption": "Fig. 5. A typical hysteretic friction loop [48].", + "texts": [ + " Hence, nly the results obtained with a typical sphere diameter of 2 mm nd a 2% kinematic hardening are used in the following to present he effect of other parameters such as the ratio E/Y0 and dimenionless normal load P* on the constant dissipated energy at plastic hake-down. We shall start by examining the regime of fretting that coresponds to the present model of cyclic tangential loading in re-sliding under full stick contact condition. Varenberg et al. 47,48] offered the concept of the slip index \u0131 as a mean to charcterize regimes of friction\u2013displacement loops obtained during retting experiments (see also Refs. [49,50]). Fig. 5 shows schemat- ically a hysteretic friction\u2013displacement loop where Ad and As are the relative displacement amplitude and the resulting slip amplitude, respectively. Note that F* and Ad in Fig. 5 correspond to the maximum tangential load Qmax and displacement amplitude ua of the present model, respectively. The slip ratio s = As/Ad was related in Ref. [47] to the slip index \u0131 = AdSc/N (where N and Sc correspond to the normal load P and initial tangential stiffness (KT)i of the present model, respectively) by the empirical expression: s = 1 \u2212 0.5 \u0131 (1a) Eq. (1a) represents best fit of experimental results that were obtained from both macro and nano-scale fretting tests. According 892 V. Zolotarevskiy et al", + " The uniqueness of the slip index approach was justified in Ref. 48] from an energetic point of view. A modification of Eq. (1a) was ound analytically in Ref. [48] in the form: = 1 \u2212 \u0131 (1b) 0.0 0.1 0.2 0.3 0.4 0.5 0.4 0.6 0.8 1 Numerical Simulations Poly. (Ref. [47])Eq 1(a) Sl ip R at io , s Slip Index, d ig. 6. The present numerical results for the slip ratio versus slip index in comparson with the empirical expression of Ref. [47]. where the friction coefficient is the ratio Qmax/P. Referring again to Fig. 5, it was shown in Ref. [48] that the slip ratio s = As/Ad is in fact an energy ratio in the form s = Ea/Em. Hence, by assuming Ed \u2248 Ea (see corresponding marked areas in Fig. 5 and more details in Ref. [48]), Eq. (1b) can be approximated as: Ed Em = 1 \u2212 \u0131 (2) Using the analogy between the parameters in Fig. 5 and the present model to describe Em and \u0131, we have: Em = 4F\u2217Ad = 4Qmaxua = 2 Pk\u03c90 (3) \u0131 = ua(KT)i P = 0.5kK\u0304i (4) where k is the dimensionless displacement peak-to-peak amplitude in the form k = 2ua \u03c90 (5) and K\u0304i is the dimensionless initial tangential stiffness in the form (see also [37]) K\u0304i = (KT)i ( \u03c90 P ) (6) Normalizing energies by P\u03c90, and using Eqs. (3) and (4), Eq. (2) becomes: E\u0304d = 2 k ( 1 \u2212 2 kK\u0304i ) (7) The effect of the ratio E/Y0 on the dimensionless constant dissipated energy E\u0304d is shown in Fig", + " Since in our model the value of Qmax and, hence at any given P* is uniquely determined by the dimensionless displacement peak-to-peak amplitude k, it is clear from Eq. (7) that, with a fixed k and resulting , a higher K\u0304i increases the dimensionless dissipated energy. Also as K\u0304i becomes very large its effect on E\u0304d diminishes. A higher K\u0304i may correspond to higher sphere stiffness, or higher E/Y0, which explains the effect, shown in Fig. 7, of this parameter on the dimensionless dissipated energy. A similar but more physical approach to explain this effect is by the relation between Ed and Em shown in Fig. 5. It is clear from that figure that for a given relative displacement Ad and resulting tangential force F* (see Fig. 5), the dissipated energy Ed increases with increasing initial tangential stiffness Sc and eventually approaches a constant value of Em. V. Zolotarevskiy et al. / Wear 270 (2011) 888\u2013894 893 s E r o c f o c t s e n ( i c F w \u2202 F P The effect of the normal load, P*, on the dimensionless contant dissipated energy E\u0304d is presented in Fig. 8 for a typical ratio /Y0 = 1000. As can be seen from the figure, initially E\u0304d increases apidly with increasing P* up to about P* = 20. Thereafter, the rate f increase \u2202E\u0304d/\u2202P\u2217 tapers off and above P* = 50 it becomes almost onstant" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003742_s0263574711000397-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003742_s0263574711000397-Figure2-1.png", + "caption": "Fig. 2. Ankle joint with torsional spring. The torque generated by the spring is proportional to the deviation of the angle between links from the equilibrium position.", + "texts": [ + " Similar to Wisse et al.,12 a kinematic coupling has been used in the model to keep the body midway between the two legs. In addition, our model adds compliance to the knee joints and ankle joints. Specifically, knee joints and ankle joints are modeled as passive joints that are constrained by torsional springs. The springs are mounted at the joints in the torsional way, which means that the torque generated by the spring is proportional to the deviation of the angle between links from the equilibrium position (see Fig. 2). To simplify the motion, we have several assumptions, including (1) shanks and thighs suffering no flexible deformation; (2) hip joint and knee joints with no damping or friction; (3) the friction between the walker and the ground is enough. Thus, the flat feet do not deform or slip; (4) strike is modeled as an instantaneous, fully inelastic impact where no slip and no bounce occurs. The bipedal walker travels forward on level ground with hip torque and ankle actuation. The stance leg keeps contact with ground while the swing leg pivots about the constraint hip" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001779_j.memsci.2009.01.013-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001779_j.memsci.2009.01.013-Figure1-1.png", + "caption": "Fig. 1. The assembly of the prepared enzyme-membrane with a glassy carbon electrode for pesticide biosensor.", + "texts": [], + "surrounding_texts": [ + "repared single-layered BPPO-PVA film could act as both external nd internal membranes. Since the upper part of the film was not ully pore-filled with the cross-linked PVA, the transport of large olecular pollutants through the membrane is avoided due to the mall pores. While the bottom part was filled well with the crossinked PVA containing TYR due to the large sized pores induced rom the asymmetric structure and used as an enzyme layer as ell as an inner membrane. In addition, the leakage of the enzyme ontaining PVA could be prevented by the small pores, and the echanical stability of the enzyme-membrane would be enhanced y the robustness of BPPO film. Further it was thought that a longerm stability was obtained not only by the use of membrane but lso by the hydrogel characteristic of PVA which provides a proper nvironment to enzyme. . Experimental .1. Materials Bromomethylated poly(2,6-dimethyl-1,4-phenylene oxide) BPPO) was kindly donated by Laboratory of Fundamental embranes in University of Science and Technology of China USTC). Tyrosinase (EC 1.14.18.1, from mushroom, 50,000 U mg\u22121), oly(vinyl) alcohol, ferrocenecarboxylic acid (FcA), HEPES, gluaraldehyde (GA), and 1-methyl-2-pyrrolidine (NMP), carbaryl, and arathion was purchased from Sigma\u2013Aldrich (USA). Ammonia 28%) was supplied by Junsei (Japan). Other chemical used in his study were analytical reagent grade. All the solutions were repared with Milli-Q water (18 M cm\u22121) as needed. .2. Preparation of enzyme-membrane A pBPPO film was prepared by a wet phase inversion method. ne gram of BPPO was dissolved in 7.5 mL of NMP to make a castng solution and it was spread on a glass plate to form a membrane. he film was immediately immersed in a mixture of NMP and ater (6:4, v/v) for 12 h and then subsequently stored in water or 6 h. To enhance the mechanical properties, the membrane was ross-linked by soaking in 28% of ammonia solution for 5 h at oom temperature. After soaking in 98% of sulfuric acid for 1 h o form sulfate groups on the pBPPO, the membrane was washed ith distilled water and dried at room temperature. PVA was disolved in distilled water (10 wt.%) by heating while it was stirred. hen it was transparent, the heating was stopped and cooled own to room temperature. Then, 100 L of FcA (mg/mL 0.05 M EPES buffer), 30 L of 0.5 M sulfuric acid, 15 L of GA (25 wt.%), nd 200 L of TYR (50 kU/mL 0.1 M PBS, pH 7) was added to 1 mL f PVA solution in order. After mixing well, the casting solution as spread on a glass plate and then the pBPPO base membrane as covered on the spread PVA mixture. After detaching with a teel knife, the enzyme-membrane was dried and stored at 4 \u25e6C ithout any storage solution but in a fully sealed container. The repared enzyme-membrane (thickness \u224850 m) was assembled ith a polished glassy carbon (GC) electrode (dia. = 3 mm, BAS F-2070, USA) for electrochemical measurements as shown in ig. 1. .3. Characterization of enzyme-membrane Membrane surfaces were characterized by scanning electron icroscopy (SEM) and atomic force microscopy (AFM). SEM analsis of the pBPPO film and the enzyme-membrane was carried out sing a FE-SEM (S-4700, Hitachi, Japan) at an acceleration voltage f 15\u201320 kV and a working distance of 4\u20135 mm. Surface topograhy of the membranes was also studied in contact mode by AFM (XE-100, PSIA, Korea) equipped with a cantilever (ACTA-10, Applied NanoStructures, USA) using a pyramidal silicon tip. The change of moisture in the membrane was observed to estimate a stability of the enzyme electrode since an enzyme needs a certain amount of water to maintain activity. The membrane samples were stored at 4 \u25e6C and weighed before and after drying for 2 h at 110 \u25e6C. The tensile strengths and strains of the wet membranes using the Instron model 5567 universal testing machine according to the ASTM method D882-79. In the measurement, 2 cm \u00d7 5 cm dumbbells were tested in a flat-faced grip initially spaced 2 cm apart with a crosshead speed of 10 mm min\u22121. The membrane area was measured in water, and the change in membrane area ratio between the swollen and the dried states, Sa (%) in term of dimensional stability was evaluated [13]" + ] + }, + { + "image_filename": "designv11_7_0003499_s11771-013-1495-x-Figure6-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003499_s11771-013-1495-x-Figure6-1.png", + "caption": "Fig. 6 Contact stress of meshing point 1", + "texts": [ + " The output of CPRESS is the contact stress that we need, because there is no friction in the model [14]. Figures 5\u20136 are the cloud pictures of meshing point 6 and meshing point 1, respectively, and it states that the edge contact happens at meshing point 1. The results of two methods are described, and compared in detail as listed in Table 4. For the meshing points close to the addendum, their semi-major axes are longer, while their contact stresses are less. The meshing points 1 and 2 are close to the addendum, so the results are slightly unreliable. As shown in Fig. 6 and Table 4, the edge contact appears at meshing point 1. Due to the existence of edge contact, J. Cent. South Univ. (2013) 20: 354\u2013362 358 the analytical method fails, and the error in contrast is vast. The stress concentration happens in ABAQUS at point 1. At every meshing point except points 1 and 2, the errors of contact stresses are all below 10%, and the contact forces of two methods have identical value. It is proved that the two methods of contact stress calculation are verified by each other" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003305_1.4026080-Figure7-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003305_1.4026080-Figure7-1.png", + "caption": "Fig. 7 Thrust bearing geometry and the locations of the thermocouples and static pressure sensors on the active surface", + "texts": [ + " For the temperature measurements, thin thermocouples were used (0.25 mm in diameter) in order to avoid disturbing the thrust bearing behavior. The 32 type-K thermocouples were inserted through 0.3 mm holes, flush to the film/pad interface and, thus, being in direct contact with the fluid film. A silicone adhesive kept the thermocouple on position. The temperature at the halfthickness and at the backs of the two pads was also measured. The location of the measuring instrument was similar for each pad (see Fig. 7), while the experimental temperature and pressure fields were built by using 12 points located at 7, 40, 70, and 85% along the length of the pad and at 15, 50, and 85% along the width of the pad. Moreover, a temperature measurement was performed at 75% along the pad length and at 75% along each pad\u2019s radius, corresponding to the \u201cclassical\u201d location of the monitoring thermocouple, as used in industry. The pressure was also measured at 70% along the pad length and at 50% along the pad radius on each pad, except in the case of two pads which were fully equipped with thermocouples", + " [10] found, in an experimental study on tilting pad thrust bearings, that the variation in pressure between the pads was caused by unequal pad heights. For a better understanding, two additional tests were performed in order to measure the temperature and pressure fields on the same pad by shifting the thrust bearing on its support. The results on the TBGS for pad number 8 are presented in Fig. 16. The temperature and pressure fields are generated from the experimental data with the implantation of the sensors, as depicted in Fig. 7. The temperature fields were built with shades of gray for a better reading. However, the linear interpolation between the experimental values is misleading and it is not representative of the real evolution between them. In the graphs shown in Fig. 16 the flow direction of the fluid through the pad occurs from the right to the left of the picture. These charts were plotted for nominal supply conditions (40 C supply temperature and 0.1 MPa supply pressure) at 2,000 rpm, 2,000 N, 2,000 rpm, 8,000 N, and 10,000 rpm, 8,000 N", + "1 MPa, the rotational speed at 6,000 rpm, and the applied load at 8,000 N. The fluid film is passing through the pad from right to left in the picture. The 021703-8 / Vol. 136, APRIL 2014 Transactions of the ASME Downloaded From: http://tribology.asmedigitalcollection.asme.org/ on 01/28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use pressure and temperature measurements are presented on two pads which were located at 90 deg to each other. The temperature and pressure fields are established using the sensors depicted in Fig. 7. The pressure field (see Figs. 23(a), 23(c), and 23(e)) indicates that the maximum pressures are located at the center of the pad near the inner radius. It can also be noted that the maximum pressure shifts weakly to the trailing edge and the inner radius when the supply temperature rises. This is probably due to the thermal distortion of the active surface of the pad, which depends on the supply temperature. Indeed, as can be observed from the temperature field (see Figs. 23(b), 23(d), and 23(f)), the variations in the supply temperature result in changes of the temperature gradient along the pad" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002189_ijrapidm.2010.036116-Figure19-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002189_ijrapidm.2010.036116-Figure19-1.png", + "caption": "Figure 19 The generic HLM facility (hybrid flexible manufacturing system) (see online version for colours)", + "texts": [ + " More complex contours such as the one shown in Figure 18 will require simultaneous 5-axis deposition as the slice will no longer be planar. In addition to the existing 3-axis HLM, a 5-axis HLM machine is being built by integrating a Hermle C30U 5-axis CNC machining centre and a Fronius TPS 2700 CMT. CMT stands for cold metal transfer, an improved version of pulsed synergic welding with considerably low power consumption and hence the heat input. A generic HLM facility by integrating both these 3-axis and 5-axis HLM machines through a pallet system is shown in Figure 19. This is a hybrid flexible manufacturing system (Hybrid FMS) to demonstrate the various applications of HLM. Note that a typical user may have to configure only a subset with the necessary sub-systems to meet this specific application(s). RP is evolving into RM. In order to cater to a number of combinations of materials, quality specifications, production volume, sensitivity to cost etc., a unique strategy like slicing is not sufficient for RM; it will require multi-faceted and hybrid approaches" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000475_tfuzz.2006.876728-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000475_tfuzz.2006.876728-Figure5-1.png", + "caption": "Fig. 5. Structure of a ball-and-beam system.", + "texts": [ + " The neuron of the output layer is labelled as , for and is with the following form: (20) After substituting (19) into (20), it yields (21) The control objective is to design the control law (3) such that the state can be stabilized at an equilibrium point. In light of this, we define the performance index function as follows: We obtain the weight and threshold value through learning cycle of the BP algorithm defined as follows: (22) (23) where is turned by the following law: (24) where is a learning rate and is a momentum term. The tuning law for the weight between the hidden layer and the output layer is obtained by using chain rule for [7] Consider a ball-and-beam system [13] depicted in Fig. 5. The feedback equivalent system of the dynamic system can be written as (26) where is the position of the ball; is the velocity of the ball; is the angle of the beam with respect to the horizontal axis; is the angular velocity of the beam with respect to the horizontal axis; is the acceleration of gravity; and the system parameter which may be unknown. Here, is the moment of inertia of the ball; is the mass of the ball; and R is the radius of the ball. Equation (26) can be written as (27) where " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002210_9781782420545.178-Figure6.7-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002210_9781782420545.178-Figure6.7-1.png", + "caption": "Fig. 6.7 - Normalised cyclic voltammograms. Parameters as Fig. 6.6.", + "texts": [ + " 6 transport increases and becomes comparable to the rate of electron transfer. The most noticeable effect of this is to increase the peak separation. Whilst not normally done, a useful way of studying data such as that of Fig. 6.6 is to normalise the currents for the change in the rate of diffusion, i.e. to replot the data as I/vll2 as a function of E. For reversible systems such normalised voltammograms should superimpose at all sweep rates ((provided double layer charging effects can be ignored (see later)). Fig. 6.7 shows normalised cyclic voltammograms for a system such as that used to obtain the date for Fig. 6.6. It can immediately be seen that in addition to the increasing peak separation with increasing sweep rate, the peak height is slightly reduced from that for a rever sible system. In the limit for a totally irreversible process the shape of the cyclic voltammogram can again be obtained mathematically by solution of the differential equations described by Equations (6.2) and (6.3), though in this case, whilst the initial and first boundary conditions remain the same as for the reversible case, the boundary condition for t > 0, x = 0 becomes" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003534_978-1-4419-6022-1-Figure7.2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003534_978-1-4419-6022-1-Figure7.2-1.png", + "caption": "Fig. 7.2 A photoresistor", + "texts": [ + " A photoresistor (also known as photoconductive cell, but we will not use this term to avoid confusion with the photoconductive mode of a photodiode) is a resistor that changes its resistance when it is exposed to light (i.e., photons). Any resistors can be used to sense light, but there are special types of semiconductor Type Wavelength l Frequency n materials that change resistance upon light irradiation more significantly than the others. These include cadmium sulfide (CdS), lead sulfide (PbS), and cadmium selenide (CdSe). Figure 7.2 shows a working principle of a photoresistor. The resistor is S-shaped, to increase the area of light exposure and its length. This is initially a big resistor, with typical resistance in the MO scale, which behaves almost like an insulator. The electrons and holes are firmly bound together.When light (i.e., photons) hits this material, however, things change. Remember the photons are packets of energy, thus they provide extra energy that can strip valence electrons off a molecule. This process creates extra electrons and leaves the atom positively charged (extra holes), i" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003992_s00422-014-0625-3-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003992_s00422-014-0625-3-Figure4-1.png", + "caption": "Fig. 4 The schematic diagram of the coupled neural oscillators. The neurons marked with \u201ce\u201d is for equilibrium position control, while the neurons marked with \u201cs\u201d for joint stiffness control. The outputs of the coupled neural oscillators to the mechanical system are the equilibrium angle and stiffness (thus the torque and stiffness) of each joint as shown in the figure", + "texts": [ + " In order to study the respective effects of joint torque and stiffness, the interaction terms of the unit oscillators for equilibrium control do not include coupling with the unit oscillators for stiffness control, and vice versa. Inter-limb coordination between the two legs is established between the hip unit oscillators on the contralateral side. Inhibitory connection of equilibrium positions results in phase difference between hip angles and thus form periodic motions. Intra-limb coordination makes the stiffnesses of ipsilateral joints increase or decrease proportionally. The structure of the coupled neural oscillators is shown in Fig. 4. The equations of the unit oscillator model are adapted from the work of Taga et al. (1991). A unit oscillator controlling the joint equilibrium position can be mathematically represented by the following equations: u\u0307i = 1 \u03c4i ( ci \u00b7 u\u0303e i \u2212 ui + \u2211 j, j =i wi j (\u02dc\u03b8 j + di j \u00b7 \u02dc\u03b8i ) \u2212 \u03b2vi + Feed,i (q, q\u0307) ) v\u0307i = 1 \u03c4 \u2032 i (\u2212vi + \u02dc\u03b8i ) \u02dc\u03b8i = \u23a7 \u23a8 \u23a9 \u03c0/2, ui > \u03c0/2 ui , \u2212\u03c0/2 \u2264 ui \u2264 \u03c0/2, i = 1, 2 \u00b7 \u00b7 \u00b7 12 \u2212\u03c0/2, ui < \u2212\u03c0/2 (7) where i is the index of the joints (see Fig. 4); ui and vi are state variables; \u02dc\u03b8i is the output of the unit oscillator, i.e., the equilibrium position; u\u0303e i is the input signal, which is equal to ue or \u2212ue or a constant, depending on the specific joint and the walking phase; \u03c4i and \u03c4 \u2032 i are time constants for equilibrium position control; \u03b2 is the coefficient of adaptation effect for equilibrium position control; ci is a signal coefficient; di j is a coefficient to adjust the coordination among different joints; wi j is the connection weights; and Feed,i is the feedback from the motion states of the walker to the unit oscillator for equilibrium position of joint i " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002301_mesa.2010.5551993-FigureI-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002301_mesa.2010.5551993-FigureI-1.png", + "caption": "Fig. I. A 2-DOF RR-RRR-RRR spherical parallel manipulator.", + "texts": [ + " To facilitate the analysis, two coordinate systems, 0 -XY Z and 0 - Xp YpZ p are set up. The Y - and Z-axes are along the axes of the two actuated R joints on the base. The Xp-, Yp- and Zp-axes are along the axes of the three R joints on the moving platform. The unit vectors along the joint axes of joints in leg i (i =1, 2 and 3) starting from the base are denoted by WI and VI and ui, Wi and Vi (i=2 and 3). We have w, \ufffd UJ u, \ufffd n ODd U3 \ufffd [n In 0 - moving plalfonn \"'\" v; \ufffd [\ufffdI]. v; \ufffd [\ufffd ood v; \ufffd [\ufffd]. In the reference configuretion (Fig. I). 0 - XpYpZp coincides with 0 - XY Z. The unit vectors along the three intennelliate R jomffi are w\" \ufffd m ood w\" \ufffd [ \ufffd11 Let O2 and 03 denote the joint variable of the two actuated joints and (-\u00a23) and (-\u00a22) denote the joint variables of the two passive joints in leg 1. In the reference configuration, we have \u00a23 = 0 and \u00a22 = O. From leg 1, the rotation matrix of the moving platform is (1) where R_y and R-z denote the rotation matrix about the negative Z- and negative Y-axes respectively. Let Rx, Ry and Rz denote the rotation matrix about X -, Y - and Z-axes respectively" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000893_s0076-6879(78)48020-6-Figure11-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000893_s0076-6879(78)48020-6-Figure11-1.png", + "caption": "FIG. 11. Manual f luorescence polarometer. This ins t rument is designed to provide a direct analog readout of both fluorescence intensity and polarization. Helipots operated manual ly serve to null an indicating meter: the balance points provide the separate readout for intensity and polarization. An image of the source (S~) is focused by lens (L,) onto aperture (A,) which acts as a secondary source of controllable size and shape. An image of A~ is then focused into the cuvet te (C~) by lens L2. The temperature of C~ is controlled by a s t ream of air passing through the cuvet te compar tment . The temperature is sensed by a thermistor in the compar tment and can be read externally. Heat filter (F~) protects the interference bandpass filter F2 from overheating, and polarizer (P~) polarizes the beam in an azimuth perpendicular to the plane of the paper. Standard source ($2) in conjunction with opal glass diffusor (F:~) and polarizer (P2) supplies a polarized beam of constant hut adjustable intensity to act both as a s tandard source for intensity measurements and as a completely polarized beam for polarization standardization. When the light from Se is being used for standardization the cuvet te is removed and the beam from $1 is cut off by a shutter between A~ and F2. When measu remen t s on solutions are being made S.2 is automatically shut off by", + "texts": [], + "surrounding_texts": [ + "This instrument represents a compromise between the ultimate in precision and the speed and ease of operation. Both intensity and polarization R36 D8 P6 iR38 I ~ R39 UNDER 4( LED 3 ~4 \u00a9 ( - I 5 V K +15V OVER LED2 ZR33 Flo. 8. \"Over -Under ' \" indicating circuit (Module C-II). This circuit indicates whether or not the variable t ransformer feeding the lamp power supply (cf. legend of Fig. 6) is set at a point where control will ensue. For this condition, both LED2 and LED3 must be \"off. '\" The parts list includes: D5-D8--si l icon diode, IN914: LED2, LED3--1ight-emitt ing diode. Monsanto MV2050: P6- -2 -K[ t Bourns Trimpot 3006P-1-202; R 3 3 ~ 7 0 - 1 L 10cA, Ohmite RC20: R34- -4 .7 -KlL 10%, Ohmite RC20: R35--91-fL 5%, Ohmite RC20: R36, R37--2.2KfL 10%, Ohmite RC20: R38--510-,Q. 5% Ohmite RC20; R39--220-tL 5%, Ohmite RC20: Xl I -XI5- -1 inea r t ransistor array, RCA CA3046: and Z3- -Zener diode, 9-V. Motorola IN4739. are read out directly and blank subtraction is automatic. It is very well adapted to making rapid equilibrium measurements and also kinetic measurements with a time resolution of about 1 sec. A photograph of the instrument is shown in Fig. 10, and the details of construction and operation are shown in Figs. 11-13. Measurements of the polarization of a glass standard with an intensity equivalent to 6 x 10 ~ M fluorescein were made over two successive l-hr periods. The means and standard errors for about thirty readings in each group were 0.3914_+ 0.0052 and 0.3919 + 0.0031, respectively. Intensity measurements with this instrument are subject to erratic fluctuations due to wandering of the arc. A tungsten source eliminates this problem, but lowers the sensitivity of the instrument. Experimental data on a number of systems have been obtained with this polarometer (see Dandliker and Levison,\" Levison et a l . , '~ Levison and Dandliker, :: Levison e l al. , ,a Dandliker ~, Levison el al. , \"; Portmann el al., ,r Levison e l a l . , TM Portmann e t al. . TM Levison e t al.\"-~'). f* S. A. l,evison, A. N. Jancsi, and W. B. Dandliker, Biochem. Bh~phys. Res. Comm,n. 33, 942 (1968). 'a S. A. Levison, F. Kierszenbaum, and W. B. Dandliker, Bk~chemistJ3' 9, 322 (1970). \"; S. A. Levison, A. J. Portmann, F. Kierszenbaum, and W. B. Dandliker, Biochem. Biol~hys. Res. Comm,n. 43, 258(1971). ,r A. J. Portmann, S. A. Levison, and W. B. Dandliker. Biochem. Biophys. Res. Comm,n. 43, 207 (1971). '~ S. A. Levison, A. N. Hicks, A. J. Portmann. and W. B. Dandliker, Biochemistp3' 114, 3778 (1975). ':~ A. J. Portmann, S. A. Levison, and W. B. Dandliker, lmm,nochemistrv 12,461 (1975). eo S. A. Levison, W. B. Dandliker, R. J. Brawn, and W. P. VanderLaan, Endocrinolo&v 99, 1129 (1976). [18] MEASURING REACTION EQUILIBRIA AND KINETICS 405" + ] + }, + { + "image_filename": "designv11_7_0002699_tac.2011.2126630-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002699_tac.2011.2126630-Figure2-1.png", + "caption": "Fig. 2. Nonlinear (state-space) symmetry: relations between , , and .", + "texts": [ + " Taking into account the definition of and as in Proposition 5, one gets equivalence between (36) and (37). Remark 12: In the case of linear symmetric systems we have , and (36) becomes which gives for all . This means that the controllability Gramian of the equivalent system is the observability Gramian of . Furthermore, (as in Theorem 1). Using Definition 5 for symmetry of the nonlinear system and the property in Proposition 3, we have a set of relations described by the diagram presented in Fig. 2. Since the system is assumed symmetric, according to Proposition 5 we have . Then, defines a coordinate transformation between the state-space realizations of and , respectively. Also, Proposition 3 establishes a coordinate transformation between the realization of and the one of the operator , , defined as . Then we can define (38) as a coordinate transformation between and , i.e., , or equivalently in coordinates . This further yields (39) Remark 13: In the linear case, , where is the cross Gramian described by Definition 1 or equivalently by Theorem 1, or (7)", + " Proposition 8: If a nonlinear system is symmetric then the cross operator satisfies (40) where is described by (38). Proof: If the system is symmetric, then (36) holds. Using Proposition 6 we write and so (36) becomes (41) Multiplying with , and using (15) we get where we also made use of the definition of from (38). From Proposition 3 we have that the state-space realization of is obtained from the state space realization of , via the coordinate transformation and , and thus, we obtain (40) (see also Fig. 2). The converse statement requires an extra assumption made upon the input vectorfield and the output. Proposition 9: Assume that for the nonlinear system (10) there exists satisfying (40) and described by (38) such that holds. Then the system is symmetric in the sense of Definition 5. Proof: Substituting from (38) in (40), we have Since the system is assumed asymptotically reachable, satisfies the Hamilton-Jacobi (14). Then we obtain that and according to Proposition 7 the system is symmetric. Remark 15: In the linear case, if the system is symmetric, then the cross Gramian satisfies , where " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002529_1.4001812-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002529_1.4001812-Figure1-1.png", + "caption": "Fig. 1 Schematic of flying motion of slider on disk", + "texts": [ + " Finally, the dynamic characteristics of the femto slider we designed with distributed DP grooves on a trailing pad were evaluated in the experiment, and some issues on air-bearing stiffness reduction and negative damping at low frequency and contamination and lube pickup on the DP grooves were also clarified. We did not find that the DP slider had any degradation in performance. JULY 2010, Vol. 132 / 031702-110 by ASME ata/journals/jotre9/28775/ on 04/18/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use 2 fl s s s w s a c t i H p g w a t r w f a h W fi w 0 Downloaded Fr Descriptions of Modeling Procedures 2.1 Governing Equations. Figure 1 shows a schematic of the ying mode of an air-bearing slider on a disk. Assuming that the lider is a rigid body and vibrates in a range near its steady flying tate, we can express the governing equations of the motion of the lider as m d2z dt2 + cz dz dt + kzz = \u2212 F0 + fz t + A p \u2212 ps dA 1 I d2 dt2 + c d dt + k = f t + A p \u2212 ps xg \u2212 x dA 2 I d2 dt2 + c d dt + k = f t + A p \u2212 ps yg \u2212 y dA 3 here z, , and are the slider\u2019s vertical displacement from the teady flying condition at the slider\u2019s center of gravity, its pitch, nd roll angles" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001403_gt2009-59226-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001403_gt2009-59226-Figure2-1.png", + "caption": "Fig. 2 Prototype bevel gearbox", + "texts": [ + " Therefore, the flow rate of oil supply was set dozens times higher than the actual flow rate, in order that oil would spread through the gearbox in fewer gear rotations. Although the power loss from the simulation with the larger oil flow rate could be higher than the actual loss, a relative comparison of the shroud was thought possible with regard to loss reduction rate. For the purpose of validating the CFD simulation, experimental results are presented in this section for a prototype bevel gearbox for the engine of a 100-seater aircraft. The gearbox is shown in Fig. 2. The test conditions are shown in Table 1. Input gear Output gear Pitch diameter [mm] 100 150 Revolution [rpm] 20,000 15,000 Load condition No load Oil MIL-PRF-23699, 80deg.C 2 Copyright \u00a9 2009 by ASME ?url=/data/conferences/gt2009/70580/ on 02/28/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use Dow In the gearbox, there are two bevel gears with meshing and four bearings. Lubrication oil is supplied to the gear meshing and the bearings, and the inner spline of the input gear shaft" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003259_j.cja.2013.04.006-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003259_j.cja.2013.04.006-Figure3-1.png", + "caption": "Fig. 3 Coordinate systems for the processing of the arc tooth face-gear.", + "texts": [ + " M0a \u00bcM0eMedMdcMcbMba \u00f03\u00de The matrixMba describes the translation from Sa to Sb; The matrix Mcb describes rotation about z-axis from Sa to Sb, forming cutting angle c; The matrix Mdc describes rotation about x-axis from Sc to Sd, forming cutting major movement; The matrix Med describes translation from Sd to Se, which is the middle section of the tooth width on the pitch circle; The matrix M0e describes translation from Se to S0, which is the center of the cutter-gear rotation. Under the transformation of the coordinates of the center C of the top edge curvature of the cutter into the imaginary gear coordinate system S0, the position vector is r00 \u00bcM0arc1 \u00f04\u00de As shown in Fig. 3, the fabrication method is adopted to process an arc tooth face-gear. S0 is fixed to the fabricated gear; Sh is the auxiliary coordinate system, which is fixed to the frame and provides the installation position of the fabricated gear; S2 is fixed to the arc tooth face-gear to be processed; and Si is another auxiliary coordinate system which is fixed to the frame and represents the installation position of the arc tooth facegear to be machined. To obtain good meshing transmission with the arc cylinder-gear, the center of the cutter is placed at rp2, on the pitch circle of the arc tooth face-gear", + " By directly transforming the position vector and normal vector of the tooth surface of the fabricated gear into the coordinate system of the arc tooth face-gear, the position vector and normal vector of the tooth surface of the arc tooth facegear are obtained as rc2 \u00bcM20rc0 nc2 \u00bc L20nc0 \u00f05\u00de where M20 is a 4 \u00b7 4 matrix representing the transformation of the radius vector from the fabricated gear surface to the tooth surface of the arc tooth face-gear. L20 is the matrix obtained by removing the last column and last row of the matrix. M20 \u00bcM2iMihMh0 \u00f06\u00de In Fig. 3, Matrix M2i describes rotation /2 about x-axis from Si to S2, matrix Mih describes along the x-axis translation rp0 and z-axis translation rp2 from Sa to Sb, and rp2 is the radius of the arc tooth face-gear; matrix Mh0 describes rotation /0 about z-axis from S0 to Sh.A meshing equation can be written for the processing of the arc tooth face-gear: nc2v 20 2 \u00bc f20\u00f0lf; hf;/2\u00de \u00bc 0 \u00f07\u00de where v202 is the relative velocity of the contact point between the cutting face of the cutter and the processed arc tooth face-gear in coordinate system S2" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001914_12_2010_103-Figure10-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001914_12_2010_103-Figure10-1.png", + "caption": "Fig. 10 Typical LCE sample geometry and the preparation of the sandwich sample for angular-dependent 2H-NMR measurements", + "texts": [ + " The outermost part of the spectral lines corresponds to the molecules aligned parallel to the magnetic field [the largest value of P2(cosy)], whereas the inner part represents the most misaligned molecules. Therefore, the value of the order parameter is given by the maximum frequency shift nmax. The width of the spectral line is a measure of the average misalignment angle dy, which for most LCE monodomains typically lies between 10 and 15 . An analysis of the domain-director misalignment in LCEs is most easily conducted with spectra that are recorded deep in the nematic phase at various relative orientations of the LCE\u2019s principal aligning direction with respect to the external magnetic field. Figure 10 shows a typical setup for the 2H-NMR of LCEs allowing this. An LCE strip with the average director orientation (denoted by) along the strip\u2019s long dimension is carefully cut into smaller, identically sized rectangular pieces. These are stacked together into a block, while great care is taken to ensure that the principal aligning orientation of the LCE perfectly matches for all the stacked pieces. Such a specimen is fitted into the coil of the NMRprobehead equippedwith a goniometer that makes it possible to set up an arbitrary orientation of the sample with respect to the external magnetic field B0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000723_j.ijfatigue.2008.01.003-Figure16-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000723_j.ijfatigue.2008.01.003-Figure16-1.png", + "caption": "Fig. 16. Fluid trapped inside a crack (adapted from [17]).", + "texts": [ + " SIFs in this case are calculated using the edge Green functions (presented graphically by Rooke et al. [8]) and are given by: KPH N Hertzian load \u00bc 1ffiffiffiffiffi pa p Z l1 l2 P \u00f0x\u00deGP left N \u00f0x\u00dedx \u00fe Z l4 l3 P \u00f0x\u00deGP right N \u00f0x\u00dedx ; \u00f04\u00de where N = (I, II), H = (left, right), a is the crack length, x is a general position on the surface, P(x) is the Hertzian pressure distribution (see for instance Johnson [13]), GP N are the edge Green functions, and l1, l2, l3 and l4 are the limits of integration. The mechanism that conduces to the fluid entrapment inside the crack is described in Fig. 16. To model the fluid pressure inside the crack, the fluid is considered to be incompressible and the pressure at the crack mouth is equal to the Hertzian pressure when it moves on the crack and zero when it does not move on it. It is also considered that the fluid volume inside the crack does not change when the Hertzian pressure is moving on it. It is assumed that the fluid inside the crack transmits stress normally to the crack faces, with a magnitude decreasing linearly from the crack mouth to its tip (linear distribution), defined by: P crack\u00f0g\u00de \u00bc P mouth 1 g a \u00f05\u00de where Pmouth is the magnitude of the Hertzian contact pressure acting at the crack mouth, which is dependent on contact patch position e" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000336_s11340-006-9018-4-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000336_s11340-006-9018-4-Figure1-1.png", + "caption": "Fig. 1 Schematic diagram of the experimental apparatus", + "texts": [ + " High-speed video images were recorded from the backside of the target and used to determine the contact time, contact area, and the ball center, contact center, and initial contact point displacements. The average tangential and angular ball velocities along the target were then calculated. An oiled PMMA target was used to study the effect of reduced friction between the ball and target. The results were correlated with earlier data for a steel target having a relatively rough surface [16], and we discuss the findings in this report. The experiment was performed using the apparatus illustrated in Fig. 1. A golf ball was launched using an air gun so that it obliquely struck a PMMA target clamped to a rigid steel frame. The target, which had smooth transparent surfaces, was 130\u00d7170 mm2 and 20 mm thick; its surface had been degreased with alcohol. An oiled PMMA target was also used to reduce the friction between the ball and target. The distance from the gun muzzle to the target was 450 mm and the inbound ball velocity was varied between 15 and 60 m/s. The velocity was determined by measuring the time interval between two laser beams intercepted by the inbound ball. The ball struck the target at a nominal angle of 30\u00b0 to the normal and rebounded in the same vertical plane. The dynamic contact behavior was recorded using a high-speed video camera (HPV-1; Shimadzu Co.) [17]. The camera was triggered using a piezoelectric sensor when the inbound ball hit the target. The high-speed images were recorded from the backside of the PMMA target using a mirror (see Fig. 1). The images were recorded using a framing interval of 10 \u03bcs and saved as a bitmap having 312\u00d7260 pixels. Two-piece golf balls (Pinnacle; Acushnet, Brockton, MA, USA) were used in this study. The diameter and mass of the balls were 42.6 mm and 46 g, respectively. All of the experiments were conducted using new 90- compression balls and new targets in order to avoid changes in surface roughness due to impact. High-speed video images during impact Figure 2 shows nine images combined to illustrate the dynamic contact behavior of the ball, where (a) is an image recorded before impact, (b) shows the initial contact with the target, (c)\u2013(g) show the compression and restitution phases, (h) indicates the final contact prior to rebounding, and (i) shows the ball after the impact", + " Also, a larger impedance mismatch between the ball and the steel target could result in the same effect, since the energy loss due to the elastic wave propagation from the ball into the target could decrease. It should be noted that the differences between the contact times measured for the steel and PMMA targets were much larger than that of the maximum measurement error (20 \u03bcs) due to the framing interval (10 \u03bcs). Ball center, contact center, and initial contact point displacements To study the tangential and angular ball velocities, we measured the deformation of the ball on the target with the assumption that it was much smaller than the distance between the target and camera (see Fig. 1). The initial contact point was determined as follows: First, the image where contact initiated between ball and the target was selected [see Fig. 2(b)]. Second, that image was enlarged and the center of the contact area was determined as shown in Fig. 3. Finally, the center of the contact area was used as the initial contact point and the displacement of that point was measured as a function of time during impact. A similar procedure was used to determine the ball center and the contact center displacements" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002071_s0091-0279(71)50004-1-Figure16-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002071_s0091-0279(71)50004-1-Figure16-1.png", + "caption": "Figure 16.", + "texts": [], + "surrounding_texts": [ + "It should be carried out in a systematic fashion, for the animal's compensatory adjustments usually involve more than one structure. For example, the lowering of the head is always accompanied by the extension of the neck, so that a 10 per cent body weight shift can be made to the foreleg support, thus making the forelegs support 70 per cent of the entire weight. The extension of the head and neck, when seen without further compensating changes, usually is observed when only minor pathologic lesio~s involve one or both hindlimbs. For ex ample, a ruptured anterior cruciate ligament necessitates this compen sation to remove weight from the unstable affected joint. When lesions of the posterior part of the body require substantial weight shift, we see not only an extension of the head and neck, but also a dropping back of the forelimb to a more posterior position. The more severe the condition, the more weight is shifted by the reposition ing of the forelimbs in this manner. In the severe spinal disk syndrome, in hip dysplasia, and in arthritic dogs. I have observed compensations that allow at least 90 per cent of the weight to be carried on the fore limbs. In one case of a small Terrier whose hindleg had been ampu tated by a mowing machine, a 100 per cent weight bearing by the fore legs was possible. Clinicians should also be aware that in these exaggerated compensa tory cases a learning period of three to six months is required. If a foreleg lesion should appear, and the forelegs can no longer support extra weight, a complete and sudden paralysis occurs that simulates many other, more serious conditions. The straightness of the back in the lateral stance phase is also of great importance, for the only way for a foreleg pathologic lesion to be relieved of weight is to shift it to the hindquarters. This cannot be strictly accomplished by repositioning the hindlimb farther forward, but necessitates an arching of the back. An example of this compensation is always observed in the heavier dog when one forelimb has been ampu tated. Also in the lateral view the degree of slope of the pelvis should be carefully noted- not necessarily for its functional qualities, but because a deviation from its 30\u00b0 to 45\u00b0 slope can be considered a congenital de fect. Like all congenital defects, this one rarely appears alone. In more severe hip dysplastic cases, it is not uncommon to find a 15\u00b0 to 20\u00b0 pelvic slope. Examination of the Posterior Stance In the posterior view of the normal dog, the hindlimbs extend from the lateral edges of the pelvis perpendicular to the ground. In the dog with gross weakness in the hindquarters, the hindlegs are spread farther apart in the stance position; in motion, this straddle-legged appear ance becomes even more exaggerated owing to instability. EXAMINATION OF THE CANINE LOCOMOTOR SYSTEM Figure 14. The posterior stance, showing normal and pathologic, un stable positions. Normal 67 Noting this abnormal stance and movement is important in the evaluation of hip dysplasia cases. In my experience radiographic find ipgs do not always parallel the performance in locomotion. The \"cowhock\" condition observed in the posterior view is a con genital defect often associated with other pathologic lesions. In the St. Bernard, for example, a \"cowhock\" condition commonly is associated with hip dysplasia. Chronic Luxating Patellas In chronic luxating patellas, seen more frequently in the smaller breeds, the dog tends to rotate the femur slightly laterally and the tibia medially. With this compensating body arrangement, the patella is pulled medially to the trochlea at the beginning of its motion. This alleviates the discomfort caused when the patellas transverse a portion of the rim of the trochlea. These dogs have a fairly characteristic stance and gait. The stance is \"toed-in\" and bowlegged. The animal walks with a shuffling gait becau~e of an inability fully to extend the knee joint. Clinicians examining these dogs for frequency of luxation and bony joint changes tend to remove the weight from the leg by lifting it from ground contact, then making their evaluation by extreme extension and flexion. I believe this to be a great mistake. To evaluate the patho logic changes correctly, one must examine the leg in normal weight bearing and muscle pull. This can easily be accomplished by placing one 68 WILLIAM E. Rov hand over the affected knee and the other on the dorsal pelvis area; then gently rock the dog's own weight on and off the affected limb. This examination allows the animal to align the bony structures in their compensated positions, and the patella moves in its pathologic course. A much more accurate evaluation of the accompanying lesions can be made by this procedure. ABNORMALITIES IN MOTION Osteochondritis Dissecans In the motion phase of our examination, we can observe definite pattern changes when we compare them to a calculated normal stride. One of the often described pattern changes takes place as a result of a lesion of the head of the humerus known as osteochondritis dis secans. This gait pattern is usually described as short and choppy. Most clinicians are well aware that in the examination for osteochondritis dissecans the anterior and posterior extension of the foreleg causes severe pain. The dog compensates for these painful areas, which are at the extreme ends of the stride arc, by shortening his contact point and by a premature lift point. Thus we see the short, choppy stride observed in the slower gaits of affected dogs. Un-united Anconeal Process The un-united anconeal process leads to a pattern similar to the short, choppy foreleg stride. However, in this condition the pain is elicited only when the elbow joint is in its fully extended position. This causes the dog to compensate by keeping the joint in a slightly flexed position at all times. In motion, the dog with this condition has an ap- EXAMINATION OF THE CANINE LoCOMOTOR SYSTEM 69 pearance something like that of a cat stalking a prey. This is especially observable when the condition exists bilaterally. Shifting the Weight Forward in Rear Leg Abnormalities The most common and unique ability of the dog is his capability of shifting his weight to the forelegs when posterior pathologic lesions exist. In such cases as the spinal disk syndrome, hip dysplasia, and spondylosis this ability is utilized to its fullest extent. In the stance phase the forelegs are placed more posterior, closer to the center of gravity, to support most of the body's weight. This abnormal stance and weight shift influence a greatly diflerent stride pattern. In motion, the foreleg is advanced to a shortened contact point in order to continue to bear the increased load. To keep the majority of the body's weight balanced on this supporting member while its oppo site member is being advanced, it must be extended far beyond the nor mal lift point at the posterior end of the stride arc. The hindlimbs, so as not to interfere with the foreleg motion, adopt a very shortened stride. 70 WILLIAM E. RoY In extreme cases of anterior weight shift, the affected animal has a \"seallike\" waddle. Hip Dysplasia These dogs provide the ultimate examples of the compensating changes of which the dog is capable. The severe dysplastic dog has very unstable, weak hip joints, which produce pain if called upon for any extra effort. In the lateral stance view, these animals have the maximum posterior forelimb placement, whereas the hindlimbs will be in a nor mal lateral stance position. A decrease in pelvic slope also is often observed. In the posterior view, the hindlimbs will spread abnormally far apart to compensate for the lateral instability. If these dogs are prone and wish to rise, they must literally pick themselves up by the forelimbs, because the hindlimbs are incapable of the extra propelling force. In motion the dog will walk or run with the typical stride of maxi mum anterior weight shift: a shortened contact point; a greatly in creased lift point; and a short, shuffied hindleg stride. The posterior view, in motion, is a straddle-legged, swaying, unstable movement with very little propulsive power- so weak, in fact, that if the dog is forced into a fast gait he may have to resort to using both hindlimbs together for power, producing a \"hopping\" gait." + ] + }, + { + "image_filename": "designv11_7_0003013_s11340-012-9600-x-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003013_s11340-012-9600-x-Figure3-1.png", + "caption": "Fig. 3 Machining flat slot and 45\u00b0 slope profile on piston crown and location of the mounted triaxial accelerometer", + "texts": [ + " In order to capture the different piston secondary motion, two laser spots, L1 and L2, are directed toward the surface of a 24-mm-long flat slot located on the right side of the piston head surface to capture the piston rotational motion, while the other laser spot, L3, is directed toward the 45\u00b0 slope profile located on the left side of the piston head surface, which has a slope height h1 of 2 mm, to capture the piston lateral motion. The arrangement of the laser spots on the piston head is shown in Fig. 3. In order to limit the signal to the one related to the piston secondary motion, a lowpass filter with a cutoff frequency of 300 Hz is used. Verification of the Measurement System A miniature triaxial accelerometer (Dytran 3023 M20) is mounted at the center of the piston crown, as shown in Fig. 3, to capture the lateral acceleration component of the piston. The z-axis of the accelerometer is positioned in the direction lateral to the piston travel. The frequency spectrum of the lateral acceleration signal will be used to verify the frequency component of the piston lateral motion measured by the laser displacement sensors. FFT of Piston Motion Fast Fourier transform (FFT) analysis is used here to identify the different modes of the piston motion. The time series data of the reciprocating motion, rotational motion, and impact acceleration captured by the triaxial accelerometer are analyzed online and transformed into the frequency domain by the IMC data acquisition system [19]", + "4 Hz, and the acceleration level of the steel base plate in the z direction, which corresponds to the lateral motion direction, is 0.3\u00d710\u22123 m/s2. These results show that the effect of the vibration of the experimental rig components induced by the AC motor on the piston motion is insignificant at operating speeds below 500 rpm. The first two laser spots (L1 and L2) are aimed at the flat slot on the piston crown to capture the piston tilt angle, and the third laser spot (L3) is aimed at the sloped surface to determine the piston lateral motion, as shown in Fig. 3. The piston secondary motion can be further classified into four different components, which are pure translational motion, pure lateral motion, pure rotational motion, and a combination of lateral motion and rotational motion, as shown in Fig. 5. For the first mode, which represents pure translational motion of the piston inside the cylinder bore, as shown in Fig. 5(a), the difference between L1 and L2 is 0, as there is no relative horizontal displacement between the two laser spots. This condition is represented by the equation below: L1 L2 \u00bc 0 \u00f01\u00de In order to confirm that the motion is purely translational, an additional condition is set that requires the difference between L3 and the piston crown center displacement xc to be equal to 0, as shown in equation (2), because during purely translation motion the laser spot of L3 remains stationary on the slope surface, and thus there is no relative horizontal displacement between these two points" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002189_ijrapidm.2010.036116-Figure11-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002189_ijrapidm.2010.036116-Figure11-1.png", + "caption": "Figure 11 A simple component suitable for three-axis HLM (a) original orientation; (b) preferred build orientation (see online version for colours)", + "texts": [ + " While most applications use planar deposition, repair of forging dies and fresh manufacture of some complex components require non-planar deposition. While the planar deposition requires only 2.5 axis kinematics, the non-planar deposition requires three to five-axes. These applications are briefly described in the following paragraphs. Manufacture of monolithic tools for injection moulding and die casting (with and without conformal cooling ducts), forging dies and simple components that become free from undercuts through an appropriate choice of the build orientation (as illustrated in Figure 11) can be made using the 3-axis HLM machine through planar deposition and face milling alternately. Most of the finish machining also can be done in the 3-axis machine. However, some features including the portions of the conformal cooling ducts can be finish-machined faster in the 5-axis machine. Composite dies with a hard case and soft core as shown in Figure 12 will have long life as well as very good fatigue strength. The surface can be built with a hard material of about 55-60 HRC while the interior with the soft MS wire giving a hardness of about 19\u201321HRC" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002835_s10798-010-9138-0-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002835_s10798-010-9138-0-Figure3-1.png", + "caption": "Fig. 3 a HexWalker insect robot and b LCD timer screen", + "texts": [ + " They developed practical skills in constructing (such as soldering skills) and programming the microchip that was part of the UniBoard. They were exposed to some advanced and reasonably high cost devices to broaden their horizons about the capability of the Picaxe system. The exposure was designed to underline the Picaxe microcontroller as a device capable of connecting with cutting-edge, state-of-the-art electronics. Examples of these devices are an ultrasonic sensor, the HexWalker insect robot (Fig. 3a), the LCD timer screen (Fig. 3b), a temperature sensor and a light seeking buggy. The second 2 days were led by Education academics from the university where the project was coordinated. These days focused on planning and curriculum development with the twin foci of mechatronics itself as a curriculum area and the integration of mechatronics into the wider curriculum, an element that satisfies the local curriculum framework for government schools in the first 11 years of schooling. Following the professional development days there was about 8 weeks of the first school term available for program preparation" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000516_alife.2007.367817-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000516_alife.2007.367817-Figure1-1.png", + "caption": "Fig. 1. (a) A single ATRON module: on the top hemisphere the two male connectors are extended, on the bottom hemisphere they are contracted. (b) A meta-module is composed of three modules, one center module and two legs.", + "texts": [ + " Alternatively, as in this work, self-repair can emerge as a side effect of the self-reconfiguration, without having a specialized self-repairing part of the controller [20]. The ATRON self-reconfigurable robotic system is our experimental platform. ATRON is a simple, one degree of freedom, homogeneous, lattice-based module, which is able to self-reconfigure in 3D (described in Section II). To control self-reconfiguration between shapes we use a strategy which is based on distributed control of metamodules. A meta-module consists of three modules and is able to move around quite freely, on top of other modules (see Figure 1(b)). The control strategy is described in [2] and summarized in Section III. As in preceding work [12], [16], [18], [23] meta-modules are used to reduce the motion constraints of the base modules, in order to simplify the process of self-reconfiguration at a higher hierarchical level. This paper explores fault tolerance to action failure, module failure and robot failure, especially applicable in the context of self-reconfigurable robots consisting of large number of modules (>50). First, Sections V-A to V-C present real world experiments with up to nine active and up to 24 passive modules both to illustrate the basic capabilities of a meta-module, and to verify tolerance to action failures", + " Modules can be assembled into a variety of robots: Robots for locomotion (like snakes, cars, and walkers), robots for manipulation (like small robot arms) or robots that achieve some functionality from their physical shape, such as structural support. By self-reconfiguring, modules can change the shape of the robot, for example from a car to a snake and then to a walker. An ATRON module has a spherical appearance composed of two hemispheres, which can actively be rotated relative to each other. On each hemisphere a module has two actuated male connectors and two passive female connectors. In the HYDRA project [14] we have manufactured 100 ATRON modules, a single module is shown in Figure 1(a). Rotation around the center axes is, for selfreconfiguration, always done in 90 degree steps. This moves a module, connected to the rotating module, from one lattice position to another. One full 360 degree rotation takes about 6 seconds, without the load from other modules. Encoders are used to control the rotation of the center axes. Male connectors are actuated and shaped like three hooks, which grasp on to passive female connector bars. A connection or a disconnection takes about two seconds" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002978_pime_conf_1967_182_410_02-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002978_pime_conf_1967_182_410_02-Figure1-1.png", + "caption": "Fig. 1 I .I. Large-radius disc and ring machine", + "texts": [], + "surrounding_texts": [ + "A GREAT DEAL of both theoretical and practical information has now been published concerning the nature of the contact between rotating discs which are lubricated and loaded together at their peripheries. In configurations of this sort, the disc-to-disc contact takes place, nominally, along a line. However, the actual contact is broadened by displacements of the material near to the periphery of the discs to form a narrow band. A very satisfactory measure of agreement has been obtained in many cases between the theoretical elastohydrodynamic predictions and the experimental observations of the oil film thickness. Various techniques have been employed for the purpose of measuring the thickness of the extremely thin oil films which persist between such heavily loaded rotating discs. These include measurements of the capacitance between the two discs, the measurement of the discharge voltage through the oil film, and the use of X-rays to measure the dimensions of the oil-filled gap. In many ways, the problem of the contact between discs or cylinders having parallel axes is less complex than that of the contact between, for example, a sphere and a plane (or, for that matter, two spheres). Where the contact is The MS. of this paper was first received at the Institution on 24th Seatember 1967 and in its revised form. as acceoted bv the Council -~ fo; publication, on 14th Deccmber\"l967. 4 * Rolls-Royce Ltd, Derby. -f Department of Mechanical Engineering, The University of Lecds. Proc Insrn iMech Engrs 1967-68 similar to that of a sphere resting upon a plane, side leakage of the oil assumes significant proportions and must be taken into account in any realistic assessment. This complication has delayed the development of those theories which deal with the nominal point contact situation. Nevertheless, Archard and Cowking have derived, from theoretical considerations, the following expression: h, = 2-04$0.74(a7~) 0.74 ($)0-074R0.41 (ll.l) Measurements of the oil film thickness taken from a crossed cylinders machine indicate reasonable agreement with this formula; over the full range of experimental conditions the discrepancy was never greater than a factor of 2. The machine used in the work being reported employs a disc of diameter 6.14 in, crowned to a radius of 25 in. The disc is loaded against the inner surface of a cylinder of diameter 7 in. This high conformity configuration is geometrically equivalent to that of a 50-in diameter sphere resting upon a plane. Measurement of the disc-tocylinder capacitance for various loads and speeds has emphasized the inherent difficulties of employing this technique for a configuration of high conformity. Analysis shows that those surface areas of the two components in the vicinity of but outside the area of high pressure may contribute a substantial part of the total disc-to-cylinder capacitance. This complexity raises Vol I82 Pt 3N at WEST VIRGINA UNIV on June 5, 2016pcp.sagepub.comDownloaded from difficulties when an attempt is made to interpret the discto-cylinder capacitance in terms of the minimum oil film thickness. A simple approach, based upon the assumption of a constant oil film thickness with varying load (in accordance with elastohydrodynamic principles) yields film thicknesses which are consistently and substantially smaller than those to be expected from equation (1 1.1). A more exact treatment of the disc-to-cylinder capacitance is seen to resolve much of the discrepancy. Notation Area of parallel plate capacitor. Radius of Hertzian contact zone. Total inter-specimen capacitance. Inter-specimen capacitance of areas outside the Capacitance of inlet region. Capacitance of outlet region. Capacitance of parallel region. Young's modulus of components 1 and 2. parallel zone. 1 1-fJ12 1-u22 { = z [-K-+-]:). E, Minimum oil film thickness computed from the inter-specimen capacitance. Minimum oil film thickness computed from the inter-specimen capacitance difference method. Theoretical minimum oil film thickness. Thickness of the dielectric in a parallel plate caDacitor. Additional separation of the specimen surfaces beyond that due to the thickness of the ail film. Relative radius of curvature - = - +- Radius of curvature of components 1 and 2. Relative radius of curvature in x and y directions. Distance measured from the centre of the contact. Mean surface speed. Load. Pressure coefficient of viscosity. Cosine- air. Dielectric constant. Dielectric constants of the oil in the inlet and outlet regions. Dielectric constant of the oil in the parallel zone. Viscosity of the oil a t the mean disc temperature. (; $, 1,) Side leakage factor 1 +- - ( :RR:)-l Poisson's ratio for compone&s 1 and 2. was designed and built by Associated Electrical Industries and is now on loan to the Department of Mechanical Engineering in the University of Leeds. The machine is capable of simulating some of the contact conditions which may be found in conforming tooth gears, for example those of the Novikov type. Nominally, the contact occurs at a point as in the case of a sphere or ellipsoid resting upon a plane. Under practical conditions, where elastic displacements take place due to the applied load, the contact takes the shape of a circle or an ellipse. A further characteristic of conforming tooth gears is that the relative sliding velocity between the components may take place in a plane inclined to that of the rolling velocity (I)\" These features may be obtained a t the inter-specimen contact in the large-radius crowned disc machine. In Fig. 11.1 the crowned dsc, B, is used as one of the specimens under test. The disc runs against the inner cylindrical surface of the outer specimen A. When the specimen axes are parallel the resulting inter-specimen contact is circular in shape, but by skewing the axes an elliptical contact may be produced. This configuration is achieved by traversing the inner specimen loading arm supported on slideways in the machine base-plate. This arrangement also introduces angularity between the directions of rolling and sliding. The outer specimen, of 7-in inside diameter, is mounted in roller bearings in the housing E, and is belt driven by a motor M through an infinitely variable gear. The inner specimen, of dameter 6.14 in, is crowned to a radius of 25 in, and is mounted on angular contact bearings at one end of the loading arm. The dimensions given for the * References are given in Appendix II.1. (2) (3). APPARATUS A diagram of the large-radius crowned disc machine is shown in Fig. 11.1. The machine, along with the circuits for the measurement of the inter-specimen capacitance, Proc Instn Mech Engrs 1967-68 Yo1 182 Pt 3N at WEST VIRGINA UNIV on June 5, 2016pcp.sagepub.comDownloaded from components are geometrically similar to that of a 50-in diameter sphere resting on a plane. The disc may be driven by friction through the oil film at the contact or, alternatively, by a flexible coupling from the outer specimen drive. The loading arm is mounted in a gimbal bearing, C , which permits rotation in the vertical and horizontal planes. The specimens are insulated from each other by a glass plate positioned between the gimbal mounting and its support, thus permitting the measurement of interspecimen resistance or capacitance. Surface traction on the surface of the inner specimen tends to rotate the loading arm in the horizontal plane. This action is resisted by a slender vertical pillar, the horizontal displacement of which is measured by a 0-0001-in dial gauge, D. The friction-force measuring system may be calibrated by applying horizontal loads to the end of the loading arm. Oil is supplied from a tank containing thermostatically controlled heaters. The oil is passed through a full flow Nter to the inner and outer specimen bearings and also, through a magnetic filter, to the contact in a jet. Valves permit the control of the oil flow to each feed point. A spill flow passes through a centrifugal filter and returns to the tank. Throughout the experimental project, the oil used was Shell Turbo 33. Both the disc and the ring were machined to form thermocouple pockets extending from the sides of the components to within 0.1 in from the working surfaces. The components were made from hardened En 31 steel. The surfaces of both components were polished to yield a surface finish reading of less than 1 pin c.1.a. For the measurement of the inter-specimen capacitance a modified Wien bridge is used fed with the output from a 1000 Hz oscillator as shown in Fig. 11.2. A number of switched capacitors are incorporated in the bridge in order to extend the range of measurement. Under running conditions, the bridge output has, generally, a high content Proc Imtn Mech Engrs 1967-68 of spurious signals as a result of fortuitous and irregular variations in conditions within the contact zone. For this reason, the bridge output is passed to an amplifier tuned to a frequency of 1000 Hz which serves to increase the sensitivity of the circuit besides filtering out unwanted signals. The amplifier output, in the form of a 1000-Hz waveform of greater or lesser amplitude, is displayed on an oscilloscope. When the bridge is balanced, the amplitude of the trace diminishes to zero. Switched resistances are also incorporated in the bridge in order to balance any resistive component in the machine-oil film circuit. All the connections and components of the circuit are screened. The capacitance of the leads from the bridge to the machine was observed to be 520 pF, and this value was subtracted from subsequent capacitance measurements taken when the machine was under test. The speeds of the outer and inner components were measured with a tachometer and a stroboscope respectively." + ] + }, + { + "image_filename": "designv11_7_0001917_2009-01-2868-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001917_2009-01-2868-Figure4-1.png", + "caption": "Figure 4: Principle of Torque Control", + "texts": [ + " Power is transmitted from the two outer discs through the six rollers to the two inner discs by shearing an extremely thin, elasto-hydrodynamic fluid film (traction fluid [12]) and not through metal-to-metal friction. Hence the name 'traction drive', which is defined in [13] as: \u201ca power transmission device which utilizes hardened, metallic, rolling bodies for transmission of power through an elasto-hydrodynamic fluid film\u201d. The Torotrak variator is torque controlled in that the required system torque is set by applying hydraulic pressure to the pistons of the variator and the variator follows the ratio automatically [10]. Figure 4 explains this approach using a simplified model of the driveline with the variator represented by two discs and a single roller and the driveline and flywheel represented by two inertias. Applying a reaction force F to the roller causes a reaction torque (Ta and Tb) at the variator discs and consequently an acceleration of the two inertias (driveline side inertia A and flywheel side inertia B). This may change the speed of the driveline and/or flywheel inertia resulting in a change of variator ratio" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002182_robio.2009.4913121-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002182_robio.2009.4913121-Figure3-1.png", + "caption": "Fig. 3 URG-04LX laser range finder attached with motor", + "texts": [ + " From its features and torque provided, we chose smart actuator module Dynamixel DX-117 by ROBOTIS as joint actuators. This module contains a servo motor, a reduction gear, a control unit, and a communication interface in a compact package. We improved the first joint module using harmonic drive system in order to enlarge the range of motor angle and to increase torque. Then the modules can generate enough motor torque to support the robots using three legs. As laser range finder is a low-cost, easy to use sensor with high accuracy, we chose URG-04LX laser range finder of Hokuyo Electric Co., Ltd, shown in Fig.3, as a ranging sensor for stair position and posture detection in this experiment. We implemented 3D scanning by using 2D laser range finder, which its range scan is from -120 degree to 120 degree with detection range of 20 mm to 4000 mm, vertically attached to the motor. Therefore, not only 360 degree scanning could be easily done by 180 degree Z-rotation of motor, but the scan resolution also could be easily adjusted. Its scanning space was obtained from the scanned data, Fig.4. This scanning space is depending partially on the robot posture" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003862_ijsi-08-2013-0017-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003862_ijsi-08-2013-0017-Figure3-1.png", + "caption": "Figure 3. (a) Geometrical model and (b) close-up of the meshed model consisting of two helical gears and two shafts, used in the present work", + "texts": [ + ", 2011, 2012a, d) dealing with the friction stir welding (FSW) process model. In the remainder of this section, a brief overview is provided of the key aspects of the employed FEA, such as: . geometrical model; . meshed model; . mesh sensitivity; . computational algorithm; . initial conditions; . boundary conditions; . contact interactions; . material model; and . computational tool. Geometrical model. The geometrical model/computational domain of the problem analyzed in this portion of the work is depicted in Figure 3(a). The model comprises two mating helical gears and their two associated shafts. The basic geometrical parameters of the two gears and their shafts are summarized in Table I. Under ideal gear-meshing conditions (i.e. in the absence of gear misalignment), the axes of the two shafts are parallel and aligned in the global Cartesian y-direction, as indicated in Figure 3(a). On the other hand, under abnormal loading conditions involving gear misalignment, the axes of the two shafts are assumed not to be parallel. Meshed model. Each of the four components (i.e. two helical gears and two shafts) are meshed using four-node, first-order, reduced-integration, tetrahedral continuum elements. After conducting a mesh sensitivity analysis to ensure that further refinement in the mesh size does not significantly affect the results (not shown for Computer-aided engineering analysis 67 brevity), a meshed model containing ca. 460,000 tetrahedron elements (of comparable size and shape) was adopted for the analysis. A close-up of the meshed model used in this portion of the work is depicted in Figure 3(b). Mesh sensitivity. In order to ensure that the key results and conclusions yielded by the present work are not affected by the choice of the computational mesh, a mesh sensitivity analysis was carried out within which progressively finer finite element meshes are used. The selected finite element mesh(es) represents a compromise obtained between the numerical accuracy and computational efficiency. Computational algorithm. All the calculations carried out in this portion of the work are based on a transient, displacement-based, purely-Lagrangian, conditionally-stable, explicit finite-element algorithm, of the type used in our recent work (Grujicic et al" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001825_icma.2009.5246308-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001825_icma.2009.5246308-Figure1-1.png", + "caption": "Fig. 1 A proposed biomimetic microrobot", + "texts": [ + " And, because the gravity center and rotating center are not the same point, it can't be positioned precisely and consume more energy while rotating. Also, the 6-legged one can't realize the diving/surfacing locomotion. Aimed to a compact structure with efficient and precise locomotion, we proposed a biomimetic underwater microrobot with 8 pieces of IPMC actuators as legs, which is used to resolve problems for previous developed 6-legged one. This paper consists of four parts. Firstly, we proposed the biomimetic underwater microrobot with 8 pieces of IPMC actuators as legs, as shown in Fig.1, and evaluated the walking, rotating and floating mechanisms of the proposed robot. Secondly, we evaluated the Mechanical behavior of the IPMC actuator, analyzed the forces applied to the four drivers and simulated the walking and rotating speeds. Thirdly, we developed the biomimetic microrobot, carried out experiments and measured their walking speeds and angular velocities with and without payloads. Then the diving/surfacing experiments were realized by the characteristic of electrolysing water around the IPMC surface", + " With different frequencies and voltages, the tip displacements of the IPMC are recorded from the experiment , as shown in the Fig.8. From the results, we can see that when the frequency increases, the tip displacement decreases. So, there is a top speed for the microrobot based on equation (2) and (4). B. Equivalent beam modeling The IPMC beam actuator can be modelled as a supported cantilever beam as shown in Fig.9. When the microrobot crawling, the forces applied to the four drivers are shown in Fig.1a, where q is the surface tension of the IPMC actuator and F is the resultant force of friction and water resistance to one driver. According to the cantilever beam theory, the relationship between the deformation curvature 1/p(x) and mechanical moment M is shown in the equation (5), where E is the elastic modulus for IPMC in hydrated conditions and I is the moment of inertia for the equivalent cantilever beam. Mechanical moment M, produced duo to IPMC bending is a function of applied forces. D. Mechanism ofthefloatting Motions Decreasing the frequency of the applied voltage to a" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002010_1.4002342-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002010_1.4002342-Figure5-1.png", + "caption": "Fig. 5 Two-point contact", + "texts": [ + "org/about-asme/terms-of-use I a a F d c d c t fl p 4 a p a s i p p b b r a r D s t a r B fi l J Downloaded Fr C i qw,swr1,swr2,swr3 = Cwr1 qw,swr1 Cwr2 qw,swr2 Cwr3 qw,swr3 RX w \u2212 X i w \u2212 i w = 0 9 n the preceding equation, the wheelset longitudinal position X i nd the yaw angle i are incremented every step and the pitch ngle w is assumed to be zero in the contact geometry analysis. or given longitudinal position of the wheelset, the rail profile ata are also updated and used for determining the location of ontact point at this location. It is important to note that the lateral isplacement of the wheelset is determined as a result of the hange in the yaw displacement when the wheelset is subjected to wo-point contact. Also, note that the location of the lead/lag ange contact or the back of flange contact can be accurately redicted using Eq. 9 , as shown in Fig. 5. Numerical Examples 4.1 Wheel/Rail Profiles. In this section, numerical examples re presented in order to demonstrate the use of the numerical rocedure presented in this investigation and the effect of wheel nd tongue rail profiles on the location of contact point in turnout ection is discussed. Three different wheel profiles are considered n this example, as shown in Fig. 6. That is i conical wheel rofile, ii arc wheel profile, and iii severely worn arc wheel rofile obtained by measurement. The track gauge is assumed to e 1067 mm narrow gauge " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002156_robot.2009.5152525-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002156_robot.2009.5152525-Figure1-1.png", + "caption": "Fig. 1. Ball Pitching Motion", + "texts": [ + " [4], [5] are remarkable in showing the various manipulations of a rectangular object, such as throwing and rotation on a link that can be realized by a robot having relatively low degrees of freedom (DOF). In these works, the nonholonomic property of the dynamics plays an important role in achieving tasks even though the systems are underactuated. This paper discusses a ball-throwing motion by a roboticlink mechanism. Several groups have studied ball-throwing robots [6], [7], [8]. However, the main aim was the control of the trajectory of a ball, i.e., the velocity and direction. Consider the ball-throwing motion of humans. As illustrated in Fig. 1, for example, pitching a ball in baseball is considered complex since not only the velocity of the ball needs to be controlled appropriately, but also the direction and angular velocity. In biomechanics, a more accurate investigation including the motion of fingers has been conducted, e.g., [9]. The goal of this work is to independently control three kinematic variables of a ball released from a robot link: velocity, angular velocity, and direction, starting from a common initial condition. All three kinematic variables are determined by the physical interaction between the ball and Wataru Mori and Tsukasa Ogasawara are with the Graduate School of Information Science, Nara Institute of Science and technology, Nara 630- 0192, Japan" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001424_0094-114x(75)90076-2-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001424_0094-114x(75)90076-2-Figure2-1.png", + "caption": "Figure 2.", + "texts": [ + " However, the number of such equations will be less than six, which simplifies determining a position function as opposed to the method based on the use of the matrix closure equation (1). Imagine that a link k including two turning pairs M and N is to be mentally removed from a contour. These pairs connect the link k to links m and n. Consider the motions of both of the unclosed chains and find in the stationary coordinate system S connected to the frame: (a) the radius vectors R ~M~ and R ~M\u00b0~ of the points M,~ and M, of links m and n; (b) the unit vectors a,. ~u~ and a, (N) of the turning pair axes M and N of links m and n (Fig. 2). II (M) X a (N) Rim\")- R t i n ' = hla-7~ ~ (5) a(')a (r~) = cos & (6) a (M) \u00d7 a (m) la (M) \u00d7 a(N) I is directed along the line of the shortest distance between turning pairs M and N from the point Mm to the point M, (Fig. 2). Equations (5) and (6), with projections considered, yield four equations of correlation between the link motion parameters. Here and below the subscript of a vector gives the number of the coordinate system in which the vector's projections are described. For example, the subscript m in the symbol a~ (m~ shows that the vector projections are described in the coordinate system S,~. The subscript of a vector is omitted only when the vector is described in the stationary coordinate system S. Should the link k, including the turning pair M and spherical pair N, be removed from a contour, the equations IR ( ' ~ - R(\") I = h (7) (R (u') - R(U~))a (m) = 0 (8) must be used to coordinate the motions of the two halves of the contour" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000077_2006-01-0358-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000077_2006-01-0358-Figure2-1.png", + "caption": "Figure 2: Circumferential damped springs representing the cage pocket circumferential flexibility. (N is the number of cage pockets)", + "texts": [ + " A two-dimensional flexible cage model was developed to investigate the effects of cage flexibility on bearing performance. A three-dimensional, six degree-offreedom Dynamic Bearing Model (DBM) for deep groove and angular contact ball bearings was modified to include the Flexible Cage Model (FCM). Figure 1 illustrates the ribbon style ball-guided cage used in this investigation. To include cage flexibility in the DBM, the cage pockets are represented by lumped masses and connected in the circumferential direction by a series of springs, kc, and dampers, ccd, as shown in Figure 2. Changes in the cage pocket geometry are neglected for ease in detecting contact between the balls and cage pockets, although the deflection of the spring-damper systems between cage pockets is considered to be representative of the deflection of a cage pocket during ball-to-cage pocket contact. A torsional spring with stiffness, kt, as shown in Figure 3, is used to model the cage bending stiffness. A change in the angle formed between three consecutive pockets causes a restoring moment to be generated within the torsion spring" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002238_978-3-642-25489-5_25-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002238_978-3-642-25489-5_25-Figure2-1.png", + "caption": "Fig. 2. Applied forces and torques", + "texts": [ + " X \u2208 \u211c3\u00d71: Linear acceleration of the link Ci. \u0393 and \u0393 \u2208 \u211c3\u00d71: Holonom forces applied respectively to the proximal and distal articulation of the link Ci expressed in the inertial coordinate system. f \u2208 \u211c3\u00d71: Intrinsic torque of the link Ci expressed in the body coordinates system (x , y , z and relating angular velocity to the link inertia. It is described by: f f W I W W . (4) Human body\u2019s balance of forces and torques reveals that humanoid limbs are subject to three kinds of forces: holonom, non holonom and muscular forces. Fig.2 shows the applied forces and torques to the humanoid lower body. Holonom forces and torques result of the interaction between limbs. They are described by: F K A T\u0393 . (5) F L A T\u0393 . (6) A limb is also subject to a certain effort in order to remain aligned with the previous limb. This effort is resulting from non-holonom torques described by: G ATA R \u039b . (7) G R \u039b . (8) where: \u039b \u2208 \u211c2\u00d71: Non-holonom torque applied to the proximal articulation of the link Ci expressed in the body coordinate system of the previous link Ci-1" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002993_icelmach.2012.6350093-Figure11-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002993_icelmach.2012.6350093-Figure11-1.png", + "caption": "Fig. 11. Capacitances at constant loads at 80\u00b0C (for four bearings)", + "texts": [], + "surrounding_texts": [ + "The electric properties of a motor bearing are essential for assessing the risk of EDM currents. In [3] and [5], a simulation model is developed to predict EDM currents. To get precise results from this model, input quantities such as lubricating film thickness and bearing capacity are required. To examine bearing capacitances and lubricating film thicknesses, different test rigs have been designed and extensive bearing tests have been conducted. When carefully evaluating the charging curves it became clear that the parallel resistance RP of a bearing is not invariable. Up to a threshold value, the lubricating film seems to insulate the bearing. However, when a current starts to flow, the bearing voltage is limited. This fact is taken into account by the probability of a fully charged capacitor for each operating point of the motor in the simulation model, which is described in [3] and [5]. When calculating the capacitance, only the gradient of the curve beneath this threshold value is considered. With this improved evaluation process, tests with vibrating loads were conducted. In the next step, the influence of static loads at different speeds and temperatures was determined. The mechanical load has only a low influence on the maximum bearing test voltage. A similar behaviour was measured for the capacitance and the lubricant film thickness for loads higher than 50 N. In this case, speed, temperature and starvation are the main influencing parameters. Results shown above will be used as input quantities for the simulation model in [3] and [5]." + ] + }, + { + "image_filename": "designv11_7_0001042_3.50437-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001042_3.50437-Figure3-1.png", + "caption": "Fig. 3 The flexible Earthpointing satellite.", + "texts": [ + " One approach consists of the introduction of new timedependent coordinates representing certain integrals involving elastic displacements. This approach may require the use of the Schwarz inequality for functions. Another discretization technique is, of course, modal analysis in conjunction with series truncation. Stability of Motion of Earth-Pointing Satellites with Flexible Appendages A. Method of Testing Density Functions We shall be concerned with the stability of an Earth-pointing satellite consisting of a main rigid body with three pairs of rods (see Fig. 3), where the rods can undergo flexural motion. The rods coincide with the satellite principal axes when in undeformed state. Since in this special case axes xiyizi (i = 1,2,..., 6) and xyz coincide, it follows that [/.] = [1] (i = 1,2,3) and [/.] = \u2014 [1] (i = 4,5,6), where [1] is the unit matrix. In view of this, K can be written as \\,{lt} +tr [J],- 7 /7 \\Tr n / / u_io2 V n (U \\JlV LJ-\\r\\Lai) 211 Zj Ui(\\lc> i = l U)+i I. PI i= 1 (20) The domains Dt (i = 1,2,...,6) in Eq. (20) are defined by ht < xt< fc" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000783_sice.2008.4654707-Figure7-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000783_sice.2008.4654707-Figure7-1.png", + "caption": "Fig. 7 Shake-motion model", + "texts": [ + " In this model, human shakes hands mainly, and a robot generates a handshake motion passively as the generated motion concerts with human handshake motion. In a shake-motion between humans, the vibration of the hand motion is generated at a constant cycle and amplitude. Furthermore, it is known that human\u2019s joint is modeled by the spring and damper system. From these, in this research, the second order lag element is used for a shake-motion model to generate shake-motions. The shake-motion model is shown in Fig.7 and equation (2). F = m d2x dy2 + c dx dy + kx (2) The parameter c is the viscous coefficient of the human\u2019s joint [5], m is the weight of arm. The viscous coefficient of the joint and the weight of the arm were set based on the mean value of humans [6]. The spring constant (k) is determined to become the average cycle of human shake motions. The amplitude can be adjusted when the spring constant is made constant. However, the cycle cannot be adjusted. Therefore, it is difficult for a shake-motion that the robot cooperated with a human" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000419_1.2735636-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000419_1.2735636-Figure2-1.png", + "caption": "Fig. 2 The general 6R serial robot", + "texts": [ + " The displacement analysis of this mechanism can be stated as follows: given input angle 7, and structural parameters, determine six rotary angles i i=1\u20136 . Given input angle 7, we can convert the 7R serial robot problem to the 6R serial robot problem. Accordingly, the forward kinematics problem of the general 7R single-loop mechanism is coincident with the inverse kinematics problem of the general 6R serial robot in nature, so its computing method and steps are omitted here. Numerical Examples Example 1. The general 6R serial robot is shown in Fig. 2. The position and orientation of the end effector, p ,z7 ,x7 , are given as follows Transactions of the ASME 3 Terms of Use: http://asme.org/terms w a s d N 1 2 3 4 N 1 2 3 4 5 6 7 8 9 1 1 1 J Downloaded Fr z7 = 0.471671858,\u2212 0.861908796,0.186115248 x7 = \u2212 0.653179277,\u2212 0.483313013,\u2212 0.582893956 , p = 2.244466453,\u2212 1.364396051,1.537440730 Structural parameters are shown below l1 = 0 l2 = 0.56 l3 = 0.61 l4 = 0.32 l5 = 0.43 l6 = 0.35 l7 = 0.23 a1 = 0.76 a2 = 1.36 a3 = 0.81 a4 = 1.31 a5 = 1.43 a6 = 1" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002195_2010-01-0515-Figure24-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002195_2010-01-0515-Figure24-1.png", + "caption": "Figure 24. Polar plot of the left B-pillar resultant displacement (in body coordinates) versus roll angle.", + "texts": [ + " In terms of magnitude, the largest accelerations were not the three roof-to-ground impacts but left side body/tire impacts between the 2 and 3 o'clock positions during rolls 2 and 4. Furthermore, the polar plot graphically illustrates the magnitude and direction of the variable for a series of discrete impacts that occurred in the rollover test.
The dynamic pillar displacement on the driver and passenger upper A and B-pillar junctions were analyzed in the bodyfixed coordinate system. The driver (far) side A-pillar displacement is depicted in Figure 23 and the driver side Bpillar displacement is shown in Figure 24. In the first roll, the left A-pillar is shifted during near side contact to the right roof rail and then immediately displaced again from direct contact between the ground and left roof rail. After being displaced nearly 4 inches (10 cm) due to these ground impacts, the left A-pillar returned to a residual state near the as-designed position. This dynamic deformation in the first roll demonstrates two characteristics; 1) vehicle impacts with a lateral orientation can result in elastic deformation to the roof structure and 2) displacement of the non-contact side of the roof structure occurs because the roof structure behaves as an integrated assembly" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000299_bf02844114-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000299_bf02844114-Figure3-1.png", + "caption": "Figure 3 Conceptual drawing of test apparatus", + "texts": [], + "surrounding_texts": [ + "Physical models of male hands were constructed using skin-like latex shells used in intravenous needle insertion trainers. The pliable latex shells were filled with liquid wax and allowed to solidify with the desired finger spread. An aluminum rod was set in the cooling wax to serve as an attachment point between the model and the drive system creating the stroke motion. Two hand positions were tested in this experiment, one with 10\u00b0 between each finger and one with 0\u00b0 (fingers flat against each other). A second model for the 10\u00b0 configuration was built and tested in order to assess error due to construction irregularities. For this study, \u2018pitch\u2019 was defined as the angle formed between the plane of the hand and the direction of forward progress of the swimmer. A pitching motion is caused by actuation of the wrist along the axis of the forearm, as shown in Fig. 1. \u2018Roll\u2019 was defined as the angle formed between a swimmer\u2019s forearm and vertical, as shown in Fig. 2. Rolling motion is created by a rotation of the forearm about the elbow. A two-axis motor drove the model hands in a rolling and pitching motion. The two-axis motor was then fixed to a railmounted carriage, which pulled the assembly through the water in the opposite direction to that of a swimmer\u2019s progress. The longitudinal motion of the carriage combined with the transverse pitching and rolling motion of the two-axis motor were designed to produce a stroke pattern similar to the pull-down phase of freestyle swimming as determined by Sato & Hino (2002). The two-axis motor was attached to the carriage with a hinge that supported the motor while allowing it to swing freely in the direction of stroke force generated by the hand. The swinging motion was then constrained using a uniaxial load cell. The load cell measured the moment about the hinge, and this data was used to calculate the combined lift and drag resultant force on the hand that produced forward swimmer motion." + ] + }, + { + "image_filename": "designv11_7_0001395_bf00045793-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001395_bf00045793-Figure2-1.png", + "caption": "Figure 2. (x < 0).", + "texts": [ + "16) Since 6'(x \u00b0) = 6(x \u00b0) and 6'(x) > 6(x) for every x ~ S~(x\u00b0), and because f ' > 0 o n [0, Po], there follows u(x) < u'(x), u'(x \u00b0) = u(x\u00b0). (3.17) Accordingly, M(u, x \u00b0, 2)--u(x \u00b0) < M(u' , x \u00b0, 2)--u(x\u00b0). Hence, by (3.2), (3.16), and Part (C) of Lemma 3.1, Au(x \u00b0) < Au'(x\u00b0). (3.18) By introducing polar coordinates centered at z, one may show that Au,(xO ) = f,,(b,(xO) ) t\u00a2 f,(b,(xO)) ' 1 - x6 ' (x \u00b0) whence (3.18) and the last of (3.15) imply - 2 ztu(x \u00b0) =< p o ( 2 - xpo) To establish the last of (3.14) for x < 0, take q = - 1/x choose z such that C,~(z) is tangent to OD a t y \u00b0 and n(y\u00b0) \u2022 ( y \u00b0 - z ) < 0 (See Fig. 2). The remainder of the proof for tc < 0 is then entirely analogous to the foregoing proof for x > 0. Consider finally the case x = 0. Fix x \u00b0 ~ D, and let x l , xz designate cartesian coordinates in a frame with its origin on aD at a distance 6(x \u00b0) from x \u00b0, its x2-axis tangent to OD, and x \u00b0 lying on the positive xl-axis (See Fig. 3). Let ~ > 0 be such that 6(x) > xl < Po for all x e S\u00a2(x\u00b0), define u'(x) = f ( x , ) , and proceed as in the case x > 0 to arrive at au(x \u00b0) Au'(x\u00b0). Stress bounds for bars in torsion 7 A\u00a2(~o) = r , ( x o ) = _ L " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003061_j.ymssp.2012.09.012-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003061_j.ymssp.2012.09.012-Figure3-1.png", + "caption": "Fig. 3. Simplified diagram of the gearbox simulation model.", + "texts": [ + " The square values additionally enhance small changes in the signal itself. In the next part the meshing plane method will be applied to the signal of the meshing force generated using the mathematical model of a gearbox. The model approach was chosen as it permits introduction of small, precisely placed faults into the gears. In this study, for the purpose of evaluation of the local meshing plane method, a model which relies on the method of apparent interference was used [14]. The simplified diagram of the 14 degrees of freedom model is presented in Fig. 3. The characteristic feature of the model is the way in which the meshing force between mating teeth is calculated. In the discussed model the mating of toothed wheels is realised by means of a complex flexible element representing meshing. It is assumed that both the gear and the pinion have the possibility of making, without any sliding, an additional rotation in relation to the motion resulting from the revolution of their base circles. Thus the principle of absolute permanency of the transmission ratio is not maintained" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000113_bf00043705-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000113_bf00043705-Figure2-1.png", + "caption": "Figure 2", + "texts": [ + " Thus, the post-buckling state is characterized by (1.8). Now exploring (2.2) one concludes that the post-buckling film forms a lined surface which by symmetry must be a cone of revolution. In the course of transformation of the semi-sphere into the cone all the parallels are contracted forming straight-lined wrinkles. Because of the if T l1>0 , (2.6) positive tension Tll > 0, (2.14) the length of the wrinkle cannot be smaller than its pre-buckling length, i.e., H = R 0 ~ -1, (2.15) where H is the height of the cone (Fig. 2). The contractions (wrinkling) of parallels are given by the formula 20 ,n- sin 0 < 0 if 0 < 5 , (2.16) ~ 2 2 '77\" where 7 r /2 -0 is the latitude of the parallel. Hence, infinitesimal stretching of a semi-spherical film leads to a jump in the shape via snapping which is accompanied by wrinkling. As a result the sphere is transformed into a cone whose geometry is defined irrespective of the elastic properties of the film. (b) Torsion of a convex film of revolution Let us consider a film which forms a convex surface of revolution bounded by two undeformable circumferences with radii R1 and R2 (Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001851_robot.2009.5152196-Figure9-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001851_robot.2009.5152196-Figure9-1.png", + "caption": "Fig. 9. Musculoskeletal System with Two Joints and Six Muscles", + "texts": [ + " 7-(a) can quasi-statically achieve the feedforward positioning by inputting the internal force balancing at desired posture, even though both controlled links are compressed similarly. In the following, the muscular arrangement satisfied with the above conditions is defined as the \u201dstable\u201d arrangement. A. Decomposition of potential In this section, the above discussion is expanded into the two-link system with two joints (the shoulder and elbow joints) and six muscles (two biarticular muscles and four simple joint muscles), which is modeled after the human\u2019s upper limb as shown in Fig. 9. Especially, we fucus attention on the role of the biarticular muscles for the feedforward positioning. In this figure, qi depicts the length of the ith muscle, and \u03b81, \u03b82 mean the shoulder angle and the elbow angle respectively. The muscles labeled as i = 1...4 are simple joint muscles, meanwhile, the rest (i = 5, 6) are biarticular muscles. This system simply arranges the fixed points between the muscles and skeletons symmetrically. This section analyzes the quasistatic motion converge when inputting the muscular internal force balancing at \u03b8d = (\u03b8d1 \u03b8d1) T = (\u03c0/2 \u03c0/2)T " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003714_piee.1970.0022-Figure8-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003714_piee.1970.0022-Figure8-1.png", + "caption": "Fig. 8 Geometry of strands m(i and n n, as shown in Fig. 8. If the strand n carries a current /, the mutual flux is obtained in the shaded area of Fig. 8 which may be expressed as two isosceles triangles. 114 The area of an isosceles triangle CDE (CE = DE) may be expressed as (CD2/4) tan EDC. Using this expression, the area of mutual flux within the depth of the conductor is N N and the mutual inductance m - n The same expression also applies if in is the upward-going strand, as long as the correct strand numbers specified in Fig. 6 are used [(IV \u2014 m) for an upward strand in from the top]. This expression is shown as a function of (/;/ \u2014 njN) in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002628_speedam.2010.5542276-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002628_speedam.2010.5542276-Figure4-1.png", + "caption": "Fig. 4 Torque map (Wheel torque over Car velocity) of an electric machine in combination with a two speed transmission. Index 1 refers to gear 1, Index 2 to gear 2. mges indicates the total mass of e-machine and transmission. [2]", + "texts": [ + " Thus the e-machine(s) would either be in the middle or low speed range. Another possibility is to combine a high speed electric machine with an additional higher reduction ratio. A high speed electric machine in combination with a two speed automated manual transmission (AMT) system has benefits as the eSmart prototype developed by Getrag shows for example. The power train configuration of the eSmart is equivalent to the picture on the right in Fig. 3 and the wheel torque over the car velocity for both gears of a 100 kW high speed electric drive is shown in Fig. 4. Since the weight of the e-machine is predominantly depending on the torque level, the vehicle contains a high speed/low torque machine with reduced weight. The first gear with a high gear ratio ensures a high starting torque and consequently a good acceleration while the second gear allows suitable vehicle top speed. A further important benefit of the two speed transmission is an enhanced operating area with high efficiency. Electric machines are said to have a good operating area with a high starting torque and high efficiencies even without multispeed transmission" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003608_640047-Figure21-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003608_640047-Figure21-1.png", + "caption": "Fig. 21 shows the flywheel contrageared to the annulus now located at 250 rpm, that is, contra to an input rotation of 500 rpm as this is the sun/annulus ratio with the planet carrier (and output shaft) stationary. If 500 rpm corresponds to the motor idling speed, the motor can be \"solidly\" clutched to the input shaft at zero torque. Yet, immedi", + "texts": [], + "surrounding_texts": [ + "FLYWHEEL ENERGY 517\nenergy. The energy topping-up time at suitably sited \"trol ley\" standards would be of the order of 30 sec to transform and store some 1-1/2 kwhr of energy, but if the standards were sited up to 2-1/2 miles apart it might then take four times as long. It will be gathered from this that the flywheel\ncan store up to 9 kwhr of energy (24 x 106 ft-lb), 2/3 ' s of which comes within the usual operating range.\nWhen the \"pantograph\" fingers are retracted, the fly wheel motor becomes an alternator that is capacitor reso nance excited when connected to the roadwheel motor. In reality, this is a triple-pole changing motor (Fig. 17) offer ing six different synchronous output speeds, the torque/speed curves at maximum capacitance being shown in Fig. 18. Consecutive selection of the six-pole motor combinations is controlled by two pedals, one for upshifting and one for downshifting. Downshifting ahead of the speed decrement provides useful but inefficient regenerative braking. Whether accelerating or braking, tractive effort (or retardation) is controlled by a capacitance handlever.\nAlthough capable of operating between 2950-1850 rpm, the normal and more efficient operating limits are between\n2900-2100 rpm, equivalent to 4 kwhr (10.7 x 106 ft-lb) or 80 sec topping up from the mains supply. If after topping up, the stored energy is not immediately used to drive the bus, the windage and bearing losses within the casing will drag the flywheel speed down again to the lower limit within 1 - 1/2 hr, or right down to zero in about 12 hr. However, it is considered to be advantageous to hold the speed overnight to 1800 rpm by connection to a low voltage supply.\nThe performance imparted to the bus is: 3.5 mph/sec at maximum acceleration; 2 mph/sec at average accelera tion from standstill to 25 mph; and 37 mph maximum speed at full charge. The bus will perform well on short gradients but would have to stop frequently for protracted recharging if operated on any substantial grade.\nWhy did the Gyrobus fail commercially? Why did it not replace the trolley bus instead of dying prematurely with it? Its economics were good, and technically it was sound. In the writer's opinion, there are three main reasons:\n1. The \"frustrating delay\" while the bus stands appar ently idle during the topping up.\n2. Poor gradient capability detracting from the Gyrobus route adaptability.\n3. Initial driver reaction to the exacting controls, and precision stopping in relation to the \"trolley\" standards.\nNevertheless, the electrogyro still has advantages and aptitude for such operations as mine road haulage.\nGyreacta Recuperative Transmission\nSome form of energy recuperation when stopping, to be subsequently utilized to assist acceleration, is more than a mere wish \u2014 it is almost an economic necessity.\nIt has been shown that there is no great problem in kinetic energy storage, nor even much difficulty in utilizing it provided the control demanded is not too stringent. But when it comes to recuperating the energy efficiently and under precise control, the problems really begin. Of course, a robust and efficient zero range infinitely variable gear would readily solve the problem, except that this presup poses problems of its own.\nHow can we efficiently couple a decelerating vehicle to an accelerating flywheel and, conversely, a decelerating flywheel to an accelerating vehicle? One solution is the Gyreacta principle. Its essential feature is the differenti ating and integrating planetary geartrains. These serve either to integrate the flywheel energy output proportionate with the driver controlled engine input, in order to augment the tractive effort applied by the summation element of the integrating train to the vehicle, or, in the case of the other train, to control the tractive retardation by differentiation between input control and output to the flywheel. A pecul iar \"byproduct\" of this arrangement is that the flywheel speed can be contrageared to precisely match the engine idling speed. This can therefore remain \"solidly\" clutched in gear with the bus stationary, and achieve a smooth clutchless start (without the slip normally associated with torque converters or other automatic transmissions) merely by in creasing engine speed.\nThese features are shown schematically in Figs. 19-23. The first shows a normal epicyclic train, with the annulus", + "518 R. C. CLERK\nlocated to zero datum by a static brake whose input/output ratio as depicted would be 3:1. Fig. 20 shows the same train but with the annulus located at 1500 rpm datum by gearing to a flywheel of high inertia. The speed ratio is conditioned by superimposing 1000 rpm on output shaft speed, added to the 1/3 of input speed; yet the torque ratio is still 3:1. Thus, at an input speed of 3000 rpm the apparent speed ra tio would be 3:2.\nately as the motor is throttled up, the increased input torque is transmitted threefold to the still stationary output, until the output resistance is overcome and the output shaft be gins to rotate at a speed which will be 1/3 of the increase of motor speed above the \"geared idling\" speed of 500 rpm. Thus, at 4100 rpm motor input speed, the output speed would be 1200 rpm. If at this point, a shift were made in the \"da tum location\" change speed gearing (not shown) between the flywheel and the planetary annulus (so as to achieve the configuration of Fig. 20), the motor speed corresponding to 1200 rpm output would, of course, be 600 rpm. From this, it could again accelerate to 3600 rpm, which is equivalent to an output speed of 2200 rpm.\nObviously, if the \"datum location\" had a further shift ratio to \"locate\" the planetary annulus at 3000 rpm (equiv alent to a superimposed 2000 rpm at the output), this would again pull the motor speed back to 600 rpm preparatory to accelerating to 3600 input rpm (equivalent now to 3200 rpm output speed), still with output torque at three times motor torque.\nIt must, of course, be appreciated that the foregoing is an illustrative oversimplification in that no account has been taken of the fractional increase of flywheel speed when ac celerating in the \"geared idling\" stage, the slight drop in flywheel speed in the \"1500 datum\" stage, and the rather greater drop in the \"3000 datum\" stage. These have the effect of moderating the output speed very slightly at the maximum input speed shown for each stage. This can be offset by appropriately increasing the maximum input speed used in the latter two stages.\nIt will also be apparent that by neutralizing the \"datum shift\" so that the flywheel spins freely without relationship to the planetary annulus, direct drive (top gear) may be", + "FLYWHEEL ENERGY 519\nestablished between motor input and output shaft with 1:1 ratio. Thus, there are only two torque ratios between input and output, that is, inverse 3:1 for acceleration and 1:1 for cruising. By adding a still further \"datum stage\" (say 4500 datum), acceleration on the 3:1 ratio can be continued right through to maximum vehicle speed. Top gear axle ratio can be the optimum cruising ratio without compromise for top gear acceleration.\nLet us now examine the converse possibilities of retarding the vehicle and regaining flywheel speed, with wheelbrakes regarded as an overriding emergency braking system.\nFirst, it will be realized that, while in any accelerating stage, if the throttle is closed, the motor compression torque will be magnified threefold as a retarding torque at the out put shaft. The twofold reaction difference will have an effect in increasing flywheel speed. However effective this might be made as a means of retardation, the energy loss to input (in conjunction with the rolling and wind resistance losses during retardation) would prevent the certain and complete recuperation of the flywheel energy. Thus, there would be a progressive reduction in the accumulated energy with succeeding acceleration braking cycles.\nThis difficulty is obviated in the Gyreacta by employing a differentiating (relative to output) epicyclic train for motor controlled braking (Fig. 22), the sun gear still ac cepting the motor input, but the elemental connections of the flywheel and output shaft being reversed as compared with the \"accelerating\" epicyclic train. Thus, the annulus of the \"braking\" train is connected to the output via the planet carrier \"spider\" of the \"accelerating\" train. The planet carrier of the \"braking\" train is connected to the flywheel \"datum gearing\" via the annulus of the \"acceler\nating\" train, as illustrated in Fig. 23 showing both trains together (but with no provision for datum shift ing.)\nNow, it must be appreciated that the arrows in Fig. 22 represent rotation rather than torque, at least insofar as out put is concerned, for the annulus (output) will always have opposite torque to the sun (input) regardless of its rotation. In this case, assuming the vehicle is moving forward, rota tion will be in the same direction as the sun. Let us assume that the vehicle speed is such that the output shaft (an an nulus) is rotating at 2000 rpm and that the flywheel datum speed applied to the planet carrier is 1500 rpm (1500 da tum). Then since the speed differential between the carrier and annulus (for example, 500 rpm) will double and be of opposite sign between carrier and sun (1000 rpm), the motor input (sun) will rotate at 500 rpm.\nIf the motor is now throttled up to generate input torque, this will be transmitted via the planet pinions to the annulus (and output shaft) as a twofold retarding torque contra to the direction of output shaft rotation. The sum of the two torques (threefold input value) will react on the planet carrier, increasing flywheel speed. As the retarding torque slows the output shaft, the input will be accelerated by twice the decrement, continuing while they both pass through equation (1500 rpm) until, if the input speed was carried to 4500 rpm the output would have to come to rest \u2014 again neglecting flywheel datum speed increase which might be of the order of 3 or 4% depending upon the relationship of maximum vehicle kinetic energy to maximum flywheel energy.\nIf in the above example the input speed were increased further by a small amount, the output shaft and vehicle would creep backward, providing a \"geared idling\" reverse. In practice, of course, a lower flywheel datum speed would" + ] + }, + { + "image_filename": "designv11_7_0002977_1.1719476-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002977_1.1719476-Figure4-1.png", + "caption": "FIG. 4. High pressure viscometer assembly.", + "texts": [ + " Since the ball and gas bubble gave peaks having opposite sign, the presence of an unwanted gas bubble could readily be detected. A limitation, however, is that the liquid being measured must have a resistivity greater than about 106 Qcm in order that well-defined signals may be obtained. The major components of the high pressure assembly were the bomb which contained the viscometer cell and the high pressure electrical-seal housing. These two com ponents were mounted on an axis which permitted the viscometer to be rocked. Flexible tubing was used to con nect the assembly to the high pressure source (see Fig. 4). The pressure bomb with the dimensions of 5.08 cm o.d., 25.40 cm length, with a 1.27 cm diam, 20.32 cm long bore was made of Haynes Stellite No. 25 and closed by a modified Bridgman seal. The closure was made of tool steel A.I.S.I. No. 42 hardened and tempered to Rockwell \"C\" 55. Annealed silver washers supported by brass washers made the actual sealing gaskets. Pressures up to 2 kbar were generated by mechanical compression of dry argon. Higher pressures were obtained by using a second high pressure bomb (not shown) in tandem with the vis cometer bomb" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003050_tmag.2012.2198051-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003050_tmag.2012.2198051-Figure1-1.png", + "caption": "Fig. 1. Scheme of a long-stroke synchronous permanent magnet planar motor.", + "texts": [ + " According to the operation principle, they can be classified into variable reluctance planar motors [1], [2], induction planar motors [3], [4], synchronous permanent magnet planar motors [5]\u2013[12], DC planar motors [13]\u2013[15] and some other planar motors with special structures, such as ultrasonic planar motor. Among them, synchronous permanent magnet planar motor is the most suitable for long-stroke applications and has bright prospects in semiconductor manufacturing machines system. In this paper, a new long-stroke synchronous permanent magnet planar motor is studied. Fig. 1 shows the scheme of this motor, the mover is made of a copper coil array and the stator are magnets and magnetic conductor, and the motor is driven by composite-current. The main contribution of this paper is to analyze the characteristic of the long-stroke synchronous permanent magnet planar motor. Fig. 2 shows top view of the unit planar motor, the red and green parts represent the magnet N and S, respectively. Each unit planar motor includes nine coils and two permanent magnets, as shown in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000037_811309-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000037_811309-Figure4-1.png", + "caption": "Fig 4 \u2014 Axial force N 0 vs. stretch ratio X, for \u2018fro = 0, and, axial force vs. twist squared, g for final stretch ratio Xo = 0.785.", + "texts": [], + "surrounding_texts": [ + "T*\n[k*NN\nk* k* CrTN TT\n14,1 r\n86\nstatic pre-load deformation as well as frequency since Stj is a parameter and g * (w) is frequency-dependent.\nCOMPUTER CODE IMPLEMENTATION\nThe constitutive laws and associated matrix formulations presented herein have been implanted in the finite element code, MARC (7). This code has the capabilities to model both the material and geometric non-linearities of elastomeric components, and utilizes 8 noded plane strain and axisymmetric isoparametric elements and a 20-node solid brick element.\nA variety of potential functions W(I 1 ,1 1) applicable to incompressible materials has been listed in Ref. 8. It was chosen to implement a form investigated by James and Green (9) and James, Green, and Simpson (10), termed the third order invariant form,\nW (1 1 ,1 2) = C o, (1, -3) + Co , (1,-3) + C\u201e (1,-3) (1 2-3) (30)\n+ C 20 + C,0 (11-3)3\nwhere the Co are parameters to be determined by fitting experimental data.\nThe solution procedure consists of the following steps:\nI. Calculation of the non-linear elastic response of the elastomeric component to a static pre load. The solution based on the potential function given by Eq. (30) is obtained by incremental application of the applied loads/displacements and a Newton-Raphson iteration within each increment to obtain static equilibrium.\n2. Calculation of the complex-valued amplitudes Au*/, AS * at each given frequency w and amplitude for theAB boundary tractions Ail and/or boundary displace-\n-* ments AuI. This portion of the analysis involves the assembly and solution of a symmetric complex-valued stiffness matrix.\nAll information calculated during the analysis can be displayed graphically: this includes deformed plots for both inand out-of-phase displacements and contour plots of the inand out-of-phase components of the incremental stresses AS*AB'\nWe will not attempt here to describe the implementation of the geometric non-linearity capability. This capability is described in volumes F and G of the MARC program [7].\nNUMERICAL EXAMPLES AND DISCUSSION\nI. VIBRATIONS IN A STATICALLY STRETCHED AND TWISTED CYLINDER. \u2014 The first example demonstrates the numerical accuracy of the code by comparing code computations with closed-form solutions for the titled problem. Here we consider a circular cylinder of undeformed length 9, and radius \"a\" comprised of an incompressible viscoelastic solid which is stretched axially to a length X012, and twisted through an angle ifrokl2o by application of forces and torques at the cylinder ends. When the stresses in the material have relaxed to constant equilibrium values, small-amplitude time harmonic torsional vibrations and extensional vibrations of frequency 0.) are applied to the pre-strained cylinder. We wish to compare finite element computations with closed-form solu-\ntions (11) for both the static pre-strain response and the lowfrequency steady-state vibrations of the cylinder, after the decay of any transients. Inertia effects in the rubber were neglected.\nThe experimental data on an unfilled SBR material at 0\u00b0C (12) was used. The static material properties are as follows:\n= 1.008 x 10\" t MPa Co, = 1.612 x 107/ C\u201e = 1.338 x 1073 C1, = 6.206 x 10-4\n= 6.206 x 10-9 The steady-state dynamic material parameters gc(w), gs(w) defined in Eq. (19) were determined from experimental test data for uni-axial storage and loss modulus and the results were fitted to the following:\ngc(w) Acw be' gs (w) = Asw-bs\nThe fitted parameters are as follows: As = 0.192940 Ac = 0.052743 bs = 0.846 be = 0.952\nThe problem was solved numerically on Ford's Cyber 176 computer using sixteen (16) three-dimensional isoparametric elements. Since there is no angular dependence of the displacement and stress fields, it was necessary to model only a wedge from the cylinder (Fig. 2). The full length of the cylinder (9, = 0.5 in.) was represented with four elements in the axial direction and four in the radial direction. The wedge angle was chosen arbitrarily to be 30 degrees; the angular span was represented by one element.\nThe cylinder was compressed to a stretch ratio of A\u00b0 = 0.785 and then subjected to twist increments up to a total twist of ifro = 0.4 radians/inch. The closed form solution for stresses oPzz, croz andthe normal force No, torque To, static str static Green Lagrange strain components Ezz, Ebz are given in the Appendix. A comparison of the finite element solution and the exact solution is given in Figures 3-6; the two results are practically indistinguishable except for the results for the normal stress component a\u00b0zz in which case the finite element solution is off in the worst case by less than two percent.\nWe now suppose that one end of the stretched and twisted cylinder remains fixed while to the other end are applied small amplitude extensional vibrations of amplitude, E and torsional vibrations of amplitude a. The superposed torque T* and normal force N * may be written in matrix form in terms of e, a as follows:\nwhere closed form expressions for k*N.,, k*NT' Ic4TN' kh are given in the Appendix. A comparison of the results for the normal stiffness kNN and torsional stiffness k TT is presented in Figs. 7 and 8 respectively; the difference between the exact solution and the finite element solution is indistinguishable.\nThe static response calculations required 27 load increment steps and used 945 CP seconds of computer time. The harmonic analysis used 48 CP seconds for each frequency for a total of 192 CP seconds.", + "87\ndistance for final deformation state X 0 = 0.785,C =", + "88\nII. BUTYL RUBBER BODY MOUNT \u2014 In this example we consider the axial vibrations of a pre-loaded automotive body mount made of a carbon-black filled butyl rubber (Fig. 9). This example demonstrates the applicability of the code to filled elastomers which exhibit some dependence on dynamic strain amplitude. Inertia effects are included. No closed-form solutions exist for this problem. Therefore, we will compare finite element computations with available test data for both the static force-deflection response and the low frequency steady-state axial vibrations of the mount.\nThe static material properties are as follows: C 10 = 0.8669 x 10-2 MPa Co, = 0.2555 C\u201e -= 0.1329 x 10-2 C\u201e = 2.1474 x 10-2 C,0 = 5.107 x 10-7\nThe steady-state dynamic viscoelastic material parameters gs(w), &(s)) defined in Eq. (19) were determined from uniaxial test data and the results are plotted in Fig. 10.\nThe problem was solved numerically using 104 20-node isoparametric brick elements. Since the mount is cyclically symmetric, it was convenient to model a sector from the mount beginning half way between two consecutive holes and terminating at the center of one of the holes (Fig. 11).\nThe static response calculations required 27 load increment steps and used 7,938 CP seconds of computing effort on the Cyber 176. The harmonic analysis used 1,104 CP seconds.\nThe computed static force-deflection response is plotted in Fig. 12 along with corresponding test results. Good agreement between analysis and test is observed. The test data were taken from four tests; the tests were repeated to eliminate the possibility of experimental error.\nThe dynamic stiffness was calculated from finite element results. Both experimental and finite element results for stiffness are plotted against frequency in Fig. 13. Excellent correlation between analysis and testing was obtained for the loss" + ] + }, + { + "image_filename": "designv11_7_0002128_s12239-010-0023-3-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002128_s12239-010-0023-3-Figure3-1.png", + "caption": "Figure 3. Rollover test process (JASIC, 2006).", + "texts": [ + " The envelope of the vehicle\u2019s residual space is defined by creating a vertical transverse plane within the vehicle, which has the periphery that is described in Figure 2. The SR points are located on the seatback of each forward or rearward facing seat, which is 500 mm above the floor under the seat, 150 mm from the inside surface of the sidewall of the vehicle (JASIC, 1998, 2006). 2.2. Rollover Test This regulation is not only continuously updated based on the actual requirements but also used as an international bus rollover regulation. The current version was issued on Feb 22nd, 2006. The rollover test is a lateral tilting test (see Figure 3). The complete vehicle stands on a tilting platform (the suspension is blocked) and is slowly tilted to an unstable equilibrium position. If the vehicle type does not fit with the occupant restraints, it will be tested at an unladen curb mass. If the vehicle is fitted with occupant restraints, it will be tested as the total effective vehicle mass. The rollover test starts in this unstable vehicle position with zero angular velocity, and the axis of rotation passes through the wheel-ground contact points" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002220_1.4001130-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002220_1.4001130-Figure1-1.png", + "caption": "Fig. 1 Machine tool setting for pinion to generator", + "texts": [ + " The convex side of the gear tooth and the mating concave side of the pinion tooth form the drive side contact. The modifications are introduced to the pinion tooth surfaces by applying machine tool setting variations during the generation of the pinion teeth. As described earlier, these modifications make the spiral bevel gear pair mismatched with a point contact of the meshed tooth surfaces. 2.1 Manufacture of Pinion Teeth on a Traditional CradleType Hypoid Generator. The machine tool setting parameters used for pinion tooth finishing are specified in Fig. 1. The concave side of the pinion teeth is in the coordinate system K1 attached to the pinion , defined by the following system of equations: r 1 1 = M3p \u00b7 M2p \u00b7 M1p \u00b7 r T1 T1 1a v m1 T1,1 \u00b7 e m1 T1 = 0 1b where r T1 T1 is the radius vector of the tool surface points, and matrices M1p, M2p, and M3p provide the coordinate transformations from system KT1 rigidly connected to the cradle and head cutter T1 to system K1 rigidly connected to the being generated pinion . Equation 1b describes mathematically the generation of a pinion tooth surface by the head cutter 31 . The matrices and vectors of the system of equations 1a and 1b are defined as follows. The surface of the head cutter used for finishing the concave side of the pinion teeth is in the coordinate system KT1 attached surface finishing on cradle-type hypoid oth to the tool , and is defined as based on Fig. 1 Transactions of the ASME 6 Terms of Use: http://www.asme.org/about-asme/terms-of-use w m H p s c p t s t l p a a t m w J Downloaded Fr e m1 T1 = M1p \u00b7 e T1 T1 = M1p \u00b7 sin 1 cos 1 \u00b7 cos cos 1 \u00b7 sin 0 4 here r m1 T1 =M1p \u00b7r T1 T1 . Matrices M1p, M2p, and M3p, providing the coordinate transforations based on Fig. 1, are given as r m1 = M1p \u00b7 r T1 = 1 0 0 0 0 sin cp \u2212 cos cp ep \u00b7 cos cp 0 cos cp sin cp \u2212 ep \u00b7 sin cp 0 0 0 1 \u00b7 r T1 5 r 01 = M2p \u00b7 r m1 = cos 1 \u2212 sin 1 0 \u2212 c \u00b7 cos 1 sin 1 cos 1 0 \u2212 f \u2212 c \u00b7 sin 1 0 0 1 g 0 0 0 1 \u00b7 r m1 6 r 1 = M3p \u00b7 r 01 = cos 1 0 sin 1 0 0 1 0 \u2212 p \u2212 sin 1 0 cos 1 0 0 0 0 1 \u00b7 r 01 7 ere, 1= 10+ igp \u00b7 cp\u2212 cp0 for the traditional cradle-type hyoid generators, and igp is the velocity ratio in the kinematic cheme of the cradle-type hypoid generator. Angles 10 and cp0 orrespond to the generation of the \u201cinitial\u201d contact point on the inion tooth surface", + " The coresponding coordinate transformations are defined by the followng equations: r c = Mc \u00b7 r T1 = cos \u2212 sin 0 \u2212 X \u00b7 cos + Y \u00b7 sin sin cos 0 \u2212 X \u00b7 sin \u2212 Y \u00b7 cos 0 0 1 0 0 0 0 1 \u00b7 \u2212 u rT1 + u \u00b7 tg 1 \u00b7 cos CNC rT1 + u \u00b7 tg 1 \u00b7 sin CNC 1 10 r 1 = M1 \u00b7 r c = cos 0 sin \u2212 Z \u00b7 sin 0 1 0 0 \u2212 sin 0 cos \u2212 Z \u00b7 cos 0 0 0 1 \u00b7 r c 11 he coordinate transformation from system KT1 to system K1 perorms the following equation: r 1 = M1 \u00b7 Mc \u00b7 r T1 12 The location and the orientation of the tool with respect to the inion/gear are given in coordinate systems that are represented or a conventional, cradle-type generator Fig. 1 . The goal is to evelop the algorithm for the execution of motions of the CNC achine using the relations in the cradle-type machine. Since the ool is a rotary surface and the pinion/gear blank is related to a otary surface, too, it is necessary to ensure that the relative posiion of the two axes, xT1 and y10, and the axial relative position of he head cutter and the pinion, to be the same in both machines. he origo of the coordinate system KT1 and the axis of the head utter xT1 are defined by the following vectors: r T1 OT1 = 0 0 0 1 e T1 xT1 = 1 0 0 0 13 To ensure the same relative position of the two axes, xT1 and 10, in the case of both machines, on the basis of Eqs" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001612_ma802757g-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001612_ma802757g-Figure2-1.png", + "caption": "Figure 2. (a) Schematic sketch of a nematic elastomer under shear deformation. Cross-links are marked by filled circles; daggers show the dividing points of the network strands into subchains, see text for details. (b) Anisotropic Gaussian network model corresponding to a nematic elastomer presented in Figure 2a. Ellipsoidal beads denote diffusion anisotropy of the subchains inside network strands (white beads) and of the subchains attached to the cross-link points (filled beads).", + "texts": [ + " In Section 4 we fix the dependences of K|, K\u22a5, |, and \u22a5 on the order parameter S using a freely jointed-ellipsoids chain. This will allow us to discuss the dependences of the principal dynamic moduli GD * , GV * and GG * on S. In this section we derive expressions for the principal dynamic moduli, GD * , GV * and GG * as functions of the parameters, K|, K\u22a5, |, and \u22a5 using a generalized network structure built from anisotropic Rouse chains. We build a network model as follows: each network strand of a LC elastomer (Figure 2a) is divided up into identical Gaussian subchains. In Figure 2a, the dividing points are marked by daggers and the network cross-links are denoted by filled circles. As a result, we obtain a network structure built from Gaussian subchains (Figure 2b). Each subchain is characterized by the viscoelastic parameters K|, K\u22a5, |, and \u22a5 (point A in Figure 2, parts a and b). The number of subchains in the strands between junctions can vary in general from chain to chain. The friction coefficients of the jth junction, j,| (jun) and j,\u22a5 (jun), represent a sum of friction coefficients of subchains intersecting at a cross-link point (point B in Figure 2, parts a and b), i.e.: where \u03b3j is the number of chains intersecting at the jth crosslink; \u03b3j is independent of S. As a result, we have a network structure of a rather arbitrary topology (Figure 2b); the polydispersity of network strands, the multifunctionality of branching points and the presence of dangling chains are all taken into consideration. However, we do not discuss hydrodynamic and excluded volume effects as long as dense polymer systems display screening of both hydrodynamic and volume interactions (Flory\u2019s theorem).38 For a fixed network structure one can, of course, calculate the relaxation spectrum for motions parallel and perpendicular to the LC director. However, to derive expressions for the dynamic moduli of an anisotropic network structure is a special problem. In the literature, there are no molecular theories which provide expressions for the dynamic moduli for anisotropic networks taking the chain structure of the network strands explicitly into account. Below, we present such derivation. We follow a standard method described, e.g., by Doi and Edwards38 for isotropic systems. As in ref 38, we consider an infinitesimal periodic shear deformation applied along the x-axis to a sample, Figure 2b. This leads to the shear flow38 where v(R,t) ) (vx,vy,vz) is the macroscopic velocity field at the point R ) (Rx,Ry,Rz) and \u03ba(t) is the shear rate which is related to the shear displacement \u03b4L(t) as follows,38 see Figure 2b: Here Ly is the dimension of a sample along the y-direction. We consider geometries when the LC-director n lies along one of U({Rn}) ) 1 2 K|\u2211 n)1 N (R|,n - R|,n-1) 2 + 1 2 K\u22a5 \u2211 n)1 N (R\u22a5,n - R\u22a5,n-1) 2 (4) KR ) 3kT lRL (R ) |, \u22a5) (5) j,|| (jun) || ) j,\u22a5 (jun) \u22a5 \u2261 \u03b3j ) const (6) vx(R, t) ) \u03ba(t)Ry, vy ) vz ) 0 (7) \u03ba(t) ) d dt \u03b4L(t) Ly (8) the axes x, y, or z of the shear flow. Note that the macroscopic velocity field v(R,t) represents an average of the microscopic one.38 This means that the velocity of a given bead, R\u0307I, is related to its average position \u2329RI\u232a as follows: Here the averaging goes over the statistical ensemble, and the index I runs over all the beads", + " The force Fx,I includes the contribution of the Brownian force Fx,I (Br) and of the elastic force Fx,I (El) \u2261 -\u2202U/\u2202Rx,I; it can be written as follows:38 where A )(AIJ) is the connectivity matrix, see refs.39-45 for details. The nondiagonal element AIJ of A equals -1 if the Ith and Jth beads are connected and is 0 otherwise; the diagonal element AII of A equals the number of bonds emanating from the Ith bead. Inserting eq 12 into eq 11 and using \u2329Fx (Br)Ry\u232a ) 0, we have the following for \u03c3xy(t): Equation 13 contains two contributions: (i) from the beads which are inside the network and (ii) from the beads which are fixed on the plate (Figure 2b). The equation of motion for the beads inside the network represents a balance between elastic, Brownian, and viscous forces and, according to the Lagrange equation, is written as follows:38-45 Here and in the following we will view small indices (i, j,...) as running over beads inside the network, small indices with primes (i\u2032, j\u2032,...) as running over beads at the plate and large ones (I, J,...) as running over all the beads both inside the network and at the plate. The position of each bead, RI, is determined by its average value, \u2329RI(t)\u232a, which follows the macroscopic velocity field, and by the fluctuating displacements, \u03b4RI, from the average value: Inserting Equation 15 into eq 13 we can rewrite \u03c3xy as follows where Let us consider, first, the contribution \u03c3xy (1)", + " 9-12,16,22 As a result, a produced monodomain sample turns out to be in a supercritical state which is characterized by a continuous increase of the order parameter with decreasing temperature. Such a continuous dependence S ) S(T) distinguishes the monodomain nematic elastomers from the low-molecular-weight LCs which show a jump of the order parameter, S, at the N-I phase transition.9 In order to calculate the temperature dependences of the principal moduli, we use the experimental dependence S ) S(T) given by Figure 2b of ref 10, which is reproduced here in Figure 9. We note that in the supercritical state, the nematic and the isotropic phases cannot be differentiated anymore and, therefore, the N-I phase transition temperature, TNI \u2248 359 K (or TNI \u2248 86 \u00b0C), determined in ref.10 (Table 1) by differential scanning calorimetry (DSC) is a pseudo N-I phase transition temperature, see also the discussion on pages 371 and 372 of ref 22. Parts a-d of Figure 10 show temperature dependence of the storage moduli G\u2032D,V,G, which have been calculated using the dependence S ) S(T) given in Figure 9" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002132_cdc.2010.5718000-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002132_cdc.2010.5718000-Figure1-1.png", + "caption": "Fig. 1. 2D SpiderCrane mechanism", + "texts": [ + " The heavy elements of the mechanical structure are fixed and the positioning is done by cables that carry the load. As a result, this crane can work at considerably higher speeds which makes it an ideal choice as a fast weight handling equipment. The 2D SpiderCrane studied here was inspired by the 3D version at EPFL and essentially captures all control-theoretic challenges of the larger system. 978-1-4244-7746-3/10/$26.00 \u00a92010 IEEE 1122 Consider the planar 2D SpiderCrane mechanism as shown in Figure 1. The positioning of the load is done by ad- justing the lengths l1 and l2. The model represents the underactuation of degree one and is subject to two holonomic constraints. Here, the position of the load is given by (xp, yp) with the load mass being m. The positions of the two motors are (xa, ya) and (xb, yb) with the corresponding rotary inertias taken as Ia and Ib. The ring has mass M and the position (xr, yr). The load is attached to the ring using a cable with fixed length of L3. In this mechanism the ring functions as the cart to carry the load as in the conventional overhead gantry crane system" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001860_tmech.2010.2057440-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001860_tmech.2010.2057440-Figure4-1.png", + "caption": "Fig. 4. Test bed for the calibration of the gyroscopes.", + "texts": [ + " The range of these gyroscopes is increased by changing a resistor external to the gyroscope chip. Notice that the chosen range corresponds to the angularvelocity range required from the hand-held human\u2013machine interface under development in our laboratory. The bandwidth of the ADXRS300 is set to 88 Hz using the on-chip analog low-pass filter, which is enough to pick up trajectories that are generated by hand. The gyroscopes were calibrated over their linear range of \u00b140 rad/s using a simple test bed, a photograph of which appears in Fig. 4. Each gyroscope was attached at its turn to the shaft of a servomotor. The servomotor rotation axis and the gyroscope sensitive axis were both aligned with the vertical. A harmonic rotation was generated with the servomotor, at a frequency of 0.5 Hz and an amplitude of 40/\u03c0 rad \u2248 2 turns, so as to cover the desired angular-velocity range of \u00b140 rad/s. The motor angular positions given by an optical encoder of 0.18\u25e6 resolution (500 pulses per revolution in quadrature) were recorded and differentiated over time, which yielded accurate estimates \u03c9E of the angular velocity" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000900_j.cirp.2008.03.028-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000900_j.cirp.2008.03.028-Figure2-1.png", + "caption": "Fig. 2. Geometrical parameters of laser free form heading process.", + "texts": [ + " Moreover, the advantage of a laser-based accumulation process over other thermal accumulation processes is the fact, that the laser process allows a very precise energy application in time and space. This leads to a robust and efficient free form heading process. Furthermore, it opens possibilities to process more complex geometries as well as to control the material microstructure. In the laser free form heading process a laser beam with beam radius v0 and divergence angle Q irradiates a cylindrical sample * Corresponding author. 0007-8506/$ \u2013 see front matter 2008 CIRP. doi:10.1016/j.cirp.2008.03.028 with diameter dS (Fig. 2). The laser beam melts the material up to a length of l0 which results in a spherical material accumulation with diameter da due to surface tension. The centre of the sphere has a distance of h to the initial end surface AC of the cylindrical sample. The energy balance of the laser free form heading process can be described by the energy needed for the material heating and melting as well as the mechanisms of energy coupling and defocusing. In the following, these terms are discussed in detail. For an adiabatic process the amount of energy Ea which is needed for a material accumulation of volume Va is given by [5] where the material and setup specific parameters are defined as r, the density; cp, the heat capacity; HM, the heat of fusion; TM, T0, the melting and working temperature; b, the offset term (e" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003869_s00419-012-0608-6-Figure17-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003869_s00419-012-0608-6-Figure17-1.png", + "caption": "Fig. 17 The mode shapes corresponding to frequency \u03c917 (the first mode)", + "texts": [], + "surrounding_texts": [ + "As mentioned earlier, in the geometrical model of the gear, the geometry of the teeth is omitted. It allows us to reduce the system\u2019s FE model size. The simplified geometrical model of the system consists of five sectors (see Fig. 1) that have the cyclic symmetry feature. Each of these segments is meshed by using standard procedures of the ANSYS software. The 3-D solid mesh is elaborated and as mentioned earlier, the ten-node tetrahedral element (solid92) with three degrees of freedom in each node is used to realize each sector. During the mesh generation process, it is assumed that the maximum length of each element\u2019s side needs to be no more than 2.7 [mm]. The developed FE model is displayed in Fig. 2, and it consists of 19,620 elements and 36,188 nodes, respectively. The particular sectors are glued as a whole at the geometrical model preparing the stage by using standard procedure of the ANSYS program. The analysed gear is mounted in the roller bearings. Such bearings typically have slight load capacity under loads perpendicular to the primary supported direction. The gear shaft neck surfaces on which the bearings are assembled are denoted \u201cbearing\u201d (see Fig. 3a). The gear mates with the other devices by the splines. The splines is simplified down to a regular cylinder of the diameter assumed as equal to the splines pitch diameter. The surface denoted \u201cjoint\u201d (see Fig. 3a) is located on the pitch diameter of the splines. Parameters of the analysed system are shown in Table 1a\u2013b. The calculation results for natural flexural oscillations taking into account angular speed of the gear are shown in the paper. In the case of circular discs and annular plates, for each solution where nodal lines are nodal diameters, one obtains two identical arrangements of straight nodal lines, rotated by an angle of \u03b1 = \u03c0/(2n) one to another, where n is the number of nodal diameters. In accordance with the circular and annular plate vibration theory [5,6,12], the particular natural frequencies of vibration are denoted as \u03c9mn , where m refers to the number of nodal circles and n is the mentioned number of nodal diameters. As the shape of the gear model is fairy elaborate, the flexural modes of the system are subject to deformation (as compared to the system without any holes) to such extent that establishing which particular node it refers to becomes rather difficult. This problem is even worse if the angular speed of the gear is varying. The problem of influence of the angular speed on the flexural gear models deformation is analysed. For the purpose of identification of these modes, an algorithm of tagging oscillation modes, which determines the correspondence between vibration of the circular disc versus disc with holes, is used. For this purpose, an auxiliary model of annular plate in the form shown in Fig. 3b is used. The geometrical dimensions of the auxiliary model were taken from the gear geometry (shown in Fig. 1). They are as follows: addendum circle diameter dz , rim mounting diameter dp, root circle diameter dw2, and thickness h p and hz (see Table 1). Dynamic analysis is performed for the auxiliary model cases rotating at predetermined angular speed, where diameter of though holes d01 (see Fig. 3b) varies as seen in Table 2. Findings are compared to each other both quantitatively and qualitatively. This method makes it possible to investigate deformations of nodal lines associated with nodal diameters and circles due to through holes and then determine correspondence between oscillation modes of solid circular disc and a plate with holes. In the final step, solutions found for the auxiliary model are compared with the solution for the system whose FEM model is shown in Fig. 2 (the principal model). As for the principal model case, the 3-D solid mesh and the ten-node tetrahedral element (solid92) are used to discretize the auxiliary models. For all models subject to analysis, the boundary conditions were applied to the nodes. For each model, 1 d f associated with node radial displacement was subtracted from the nodes found on the surface identified as a bearing (see Fig. 3a,b). Furthermore, 1 d f associated with the displacement of nodes along the centreline of each model was subtracted from the nodes found on the surface, identified as a joint (see Fig. 3a,b). For the models obtained in this way, calculations were kept conducted as long as the natural frequency \u03c918 was determined. The calculations were performed assuming that the systems rotate as angular speed of \u03b8 , within the range of 0\u20131047 [ rad/s]. During the computing process, the angular speed values were gradually increased by 80[ rad/s], which made fourteen variants of the results (the natural frequencies and corresponding natural modes), which were subject to further interpretation. The rotation effect was taken into account by determining stress distribution due to rotation, for each model during the computational step associated with static analysis (the so called pre-stress effect). This stress distribution was then included in the computation step associated with modal analysis. The results of the numerical calculations related to the procedure of identifying deformed natural modes of flexural vibration of the gear under consideration are shown below. The results displayed here relate to the determination of the correspondence between the natural frequencies \u03c916 and \u03c925 at high angular speed (\u03b8 = 1047 [ rad/s]) as well as to the correspondence between oscillation modes and the natural frequency \u03c931 at lower angular speeds (\u03b8 = 80 [ rad/s]). The results as shown in Figs. 4, 5, 6, 7, 8, 9 allow for tracking deformations of nodal lines associated with nodal circles and diameters, due to varying diameter of the through holes. With respect to the natural frequency \u03c925, there is marked difference in shapes of natural modes. When one compares the results between each other, one can notice that in order to identify correctly deformed natural modes of the flexural oscillations in the gear under consideration at lower angular speeds, larger number of auxiliary models is required to be included during calculations, as compared to the higher angular speeds. It comes from the fact that additional stresses through the centrifugal effects appear. This effect causes the gear flexural stiffness to be an apparent function of rotational speed (stiffness grows for higher speed). In the next part, results of the numerical calculations associated with the extent of the influence of the angular speed to deformation of mode shapes of oscillations. For each discussed case, both mode solutions related to nodal diameters are shown. These analysed results are sorted by the order of their occurrence. For the frequencies \u03c923 and \u03c918, the results were obtained at angular speeds of \u03b8 = 0 and \u03b8 =1,047 [ rad/s] respectively. For the other cases, results were obtained at angular speeds \u03b8 of, 0, 320, 720, and 1,047 [ rad/s], respectively. Natural frequencies for these modes are included in Table 3. To determine this mode (see Figs. 10, 11), the procedure of tagging natural oscillation modes was required. Nodal lines associated with the circle and diameter are deformed. Minor influence of the angular speed to deformation of the nodal lines is noticeable. The task of determining modes in this case was not too difficult (see Figs. 12); no procedure of tagging natural oscillation modes was required. The slight impact of the gear angular velocity on the distortion of the nodal lines is observed. For these modes (see Figs. 13, 14), procedure of tagging natural oscillation modes was required. It is noticeable that angular speed affects markedly deformation of the nodal lines. Once the angular speed of 720 [ rad/s] is exceeded, the oscillation mode takes different shape. Major deformation of mode shape attributable to the shaft vibrations is evident at this speed. Moreover, additional problem associated with some similarity of the mode being tagged to the mode associated with frequency of \u03c931, emerged during mode identification. Establishing the correspondence between these modes was a complex task (see Figs. 15, 16) due to the shape of oscillation modes similarity to the case discussed earlier. The angular speed affects deformation of nodal lines markedly. Major shape mode variations emerge at \u03b8 = 400 [ rad/s]. The identification process in this mode was not easy (see Figs. 17, 18) . One can notice that angular speed affects the deformation of nodal lines. Major variation in mode shape emerges at \u03b8 = 720 [ rad/s]. Moreover, additional annular shaft vibration emerges at the highest considered angular speed. Finding correct correspondence between the modes in this case was fairly easy (see Figs. 19). High repeatability in deformations of nodal lines on circular plate at various angular speeds is noticeable. As a consequence of the conducted analysis (see Table 3), the Campbell diagram was plotted for the gear under consideration. This is a convenient method of displaying the relationship between gear natural frequencies and transmission system excitations [4]. Excited frequencies are plotted on a vertical axis, and the gear speed of rotation is plotted on the horizontal axis (see Fig. 20). Natural frequencies achieved from numerical analysis are plotted as near-horizontal curves. The forced frequency due to the meshing is determined by the following relation (as in Ref. [4]) f = n0 \u00b7 z 60 (4) where n0 [rpm] is the rotational speed and z is the number of teeth in the gear. For this system, the gear teeth number is z = 59. Vibration resonance phenomenon occurs when forcing frequency (4) matches as to its value with some natural oscillation frequency of the gear. The points where the near-horizontal \u03c9mn curves intersect the straight line (4) indicate the speeds at which the gear resonance will be excited (see Fig. 20). For instance, the rated excitation speed for the natural frequency of \u03c923 is 764 [rpm]. It may be inferred from both the Campbell diagram and Table 3 that the rotating movement makes flexural stiffness of the gear under consideration to increase. Moreover, at speed of 3,820 [rpm], one can notice major surge associated with the mentioned earlier changing of the shape of the natural mode frequency in the case of the frequency of \u03c931. The growth of the gear transversal stiffness observed during gyrate of the gear comes from the appearance of the additional stresses in the toothed gear through the centrifugal effects. The higher rotational speed generates higher centrifugal forces, higher stress level, thereby causing the transversal stiffness of the system to increase. Moreover, the growth of the gear flexural stiffness through the gyrate effect causes reduction of the needed numerical calculations connected with identifying the proper distorted mode shapes." + ] + }, + { + "image_filename": "designv11_7_0003942_j.jmatprotec.2012.09.002-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003942_j.jmatprotec.2012.09.002-Figure1-1.png", + "caption": "Fig. 1. Die geom", + "texts": [ + " The dies made out of AISI H13 which re preheated to 240 \u25e6C and have been heat treated to a tempered artensitic structure (52\u201354RC). The tooling is nitrided to form a 10 m thick nitride layer with an 11 m thick compound layer. he workpiece has a 30\u201350 m thick glass coating and water based raphite is sprayed upon the dies before each stroke. The heading peration occurs immediately after the extrusion operation. The eformation time for each operation is around 0.25 s. The extrusion ies separate vertically for workpiece removal and the ram acts orizontally as illustrated in Fig. 1. Fig. 1(a) shows an elevation view of the closed tooling with the orkpiece inserted. Fig. 1(b) and (c) shows the isometric cross secion of the tooling before and after deformation of the workpiece. ig. 1(d) shows the damage of interest on the workpiece where coring marks are observed along the extruded surface. An improved understanding of the dominant failure mode(s) of he extrusion tooling is required in order to make effective changes o improve tool life. This study is the first stage in a wider package of ork aimed at developing a general die life model based on material icrostructure" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003975_s11044-011-9287-2-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003975_s11044-011-9287-2-Figure1-1.png", + "caption": "Fig. 1 3D Collision; side (left) and top views on S\u0303", + "texts": [ + " vPi , the velocity of Pi in N , a Newtonian reference frame, can be expressed in terms of u1, . . . , up , q1, . . . , qn and time t as vPi = p\u2211 r=1 vPi r ur + vPi t (i = 1, . . . , \u03bd) (2) where vPi r , called the r th partial velocity of Pi , and vPi t , called the remainder partial velocity of Pi , are vector functions of q1, . . . , qn and t . Let B and B \u2032 be bodies of S, and let P be a point of B coming into contact with point P \u2032 of B \u2032 during the collision of B with B \u2032 occurring between two instants t1 and t2 (Fig. 1). Under these circumstances, collision hypotheses [11, 13, 14] can be used to bring the effect of this collision into (1). To this end, let vR be the relative velocity of points P and P \u2032, defined as vR=\u0302vP \u2212 vP \u2032 , (3) and note that vR can be written similarly to vPi in (2), hence vR r = vP r \u2212 vP \u2032 r (r = 1, . . . , p), (4a) vR t = vP t \u2212 vP \u2032 t , (4b) where vR r is the coefficient of ur in vR . Suppose that, during collision, P \u2032 exerts on P a force R, so that P exerts on P \u2032 a force \u2212R. Then (1) give way to equations that bring into evidence the contributions of R, i", + " , p; t1 \u2264 t \u2264 t2) (5) or, in view of (4a), Fr + F \u2217 r + R \u00b7 vR r = 0 (r = 1, . . . , p). (6) During the collision, P is assumed to maintain contact with P \u2032, i.e., to coincide with P \u2032; and a plane S\u0303 exists which passes through P \u2032 (\u2261 P ) and is tangent to B and B \u2032 at P \u2032 if both are locally smooth, or to B \u2032 at P \u2032 if only B \u2032 is locally smooth. Name B and B \u2032 such that n, a unit vector perpendicular to S\u0303, makes vR(t1) \u00b7 n a non-positive quantity. Align t, a unit vector lying in S\u0303, with the projection of vR(t1) on S\u0303, making vR(t1) \u00b7 t a non-negative quantity (see Fig. 1) and vR(t1) \u00b7 s, where s=\u0302n \u00d7 t, vanish. Then vR(t) = vR(t) \u00b7 nn + vR(t) \u00b7 tt + vR(t) \u00b7 ss, (7a) vR(t1) \u00b7 n \u2264 0, (7b) vR(t1) \u00b7 t \u2265 0, (7c) vR(t1) \u00b7 s = 0. (7d) vR(t1) and vR(t2) (at times denoted vA and vS [17]) are called velocity of approach and velocity of separation, respectively. Equation (6) can thus be replaced with Fr + F \u2217 r + R \u00b7 nvR r \u00b7 n + R \u00b7 tvR r \u00b7 t + R \u00b7 svR r \u00b7 s = 0 (r = 1, . . . , p; t1 \u2264 t \u2264 t2). (8) If it is assumed that t2 \u2212 t1 is \u2018small\u2019 compared to time constants associated with the motion of S, and that, consequently, q1, ", + " Regarding E2, the change in the system mechanical energy following a collision, a straightforward extension of the proof given in [28] for the planar case shows that E2 = 1/2In2(vn2 + vn1) + 1/2It2(vt2 + vt1) + 1/2Is2(vs2 + vs1) (23) (= 1/2u2(\u2212M)uT 2 \u2212 1/2u1(\u2212M)uT 1 , where u=\u0302|u1 \u00b7 \u00b7 \u00b7up|) for the 3D case, provided \u2212In2vR t \u00b7 n \u2212 It2vR t \u00b7 t \u2212 Is2vR t \u00b7 s + \u03bd\u2211 i=1 miv Pi t \u00b7 [vPi (t2) \u2212 vPi (t1) ] = (2) 0, (24) a condition \u2018neutralizing\u2019 specified motions implied by vR t and vPi t (i = 1, . . . , \u03bd). One can start with the differential form of (20)\u2013(22) given by dvn = mnndIn + mntdIt + mnsdIs, (25) dvt = mntdIn + mttdIt + mtsdIs, (26) dvs = mnsdIn + mtsdIt + mssdIs . (27) Let the slip speed s of P relative to P \u2032 and the orientation angle \u03c6 be defined so that vt = sc\u03c6, (28a) dvt = c\u03c6ds \u2212 ss\u03c6d\u03c6, (28b) vs = ss\u03c6, (28c) dvs = s\u03c6ds + sc\u03c6d\u03c6, (28d) where s\u03c6 = sin\u03c6 and c\u03c6 = cos\u03c6 (Fig. 1); and note that as long as there is slip R \u00b7 t = \u2212\u03bcR \u00b7 nc\u03c6, R \u00b7 s = \u2212\u03bcR \u00b7 ns\u03c6 ([(R \u00b7 t)2 + (R \u00b7 s)2]1/2 = \u03bc|R \u00b7 n|), in accordance with Coulomb\u2019s friction law, or, in view of (10a)\u2013(10c), dIt = \u2212\u03bcdInc\u03c6, dIs = \u2212\u03bcdIns\u03c6, (29) where \u03bc is Coulomb\u2019s coefficient of friction. With f,g and h defined as f =\u0302dvn/dIn, g=\u0302dvt/dInc\u03c6 + dvs/dIns\u03c6, h=\u0302 \u2212 dvt/dIns\u03c6 + dvs/dInc\u03c6 (30) one can show, dividing (25)\u2013(27) throughout by dIn and using (29), that f = mnn \u2212 \u03bcmntc\u03c6 \u2212 \u03bcmnss\u03c6, (31) g = mntc\u03c6 + mnss\u03c6 \u2212 \u03bcmttc 2\u03c6 \u2212 \u03bcmsss 2\u03c6 \u2212 2\u03bcmtss\u03c6c\u03c6, (32) h = \u2212mnts\u03c6 + mnsc\u03c6 \u2212 \u03bcmts(c 2\u03c6 \u2212 s2\u03c6) + \u03bc(mtt \u2212 mss)s\u03c6c\u03c6, (33) and that dvt and dvs can be eliminated from (25), (28b) and (28d), which reduce to d\u03c6/dIn = h/s, (34a) ds/dIn = g, (34b) dvn/dIn = f, (34c) dIt/dIn = \u2212\u03bcc\u03c6, (34d) dIs/dIn = \u2212\u03bcs\u03c6" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000208_robot.2005.1570615-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000208_robot.2005.1570615-Figure1-1.png", + "caption": "Fig. 1 Initial Position Final Position", + "texts": [ + " The paper is organised as follows: section 2 reviews the basic principles of a tentacle manipulator; section 3 presents the general model of this system; section 4 introduces the unconstrained control problem; section 5 discusses the constrained control problem; section 6 verifies by computer simulations the control laws for a 2D and a 3D tentacle manipulator. II. BACKGROUND We will study a class of tentacle arms, of variable length, that can achieve any position and orientation in 3D space and that can increase their length in order to get a better control in the operator space with a constraint area (Fig. 1, 2, 3). 0-7803-8914-X/05/$20.00 \u00a92005 IEEE. 3274 The technological model can be considered as one with a central, highly flexible and elastic backbone. We will assume that the backbone never bends past the \"smallstrain region\" where an applied stress produces a strain that is recoverable and obeys an approximately linear stress-strain relationship. Each element of the arm has two types of deformations: bending and axial tension/compression. Thus, we will use an extensible model that closely matches the characteristics of the prototype arm" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001706_s11003-010-9252-x-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001706_s11003-010-9252-x-Figure2-1.png", + "caption": "Fig. 2. Joints of the oval disk with curvilinear trihedral (a) and tetrahedral (b) holes; joint of the curvilinear trihedral disk with oval hole (c); joint of the curvilinear tetrahedral disk with oval hole (d); joint of the curvilinear trihedral disk with curvilinear trihedral hole (e); joint of the curvilinear tetrahedral disk with curvilinear trihedral hole (f).", + "texts": [ + " After simple transformations, we arrive at the equation for the parameter t specifying the contact point of the contours in the coordinate system x1O1y1 : f (t) = 1 S2 [4b2S3 + (a1 + b1 cos 2t) sin t] [2b1 sin 2t cos t + (a1 + b1 cos 2t) sin t] S [4b2S (1 S2 ) (a1 + b1 cos 2t) sin t][2b1 sin 2t sin t (a1 + b1 cos 2t) cos t] = 0. (8) To find S = S(t) , we solve this equation approximately. The initial contact angle = arcsin S(t) . The co- ordinates of the contact point in the system x1O1y1 are as follows: x1 = (a1 + b1 cos 2t) cos t and y1 = (a1 + b1 cos 2t) sin t . The displacement of the point O2 to the point of contact of the disk with the hole is given by the formula = [(a1 + b1 cos 2t) cos t (a2 b2 cos 2 ) cos ] . Scheme 2 (Fig. 2 ). In this case, the parametric equations of the contours take the form x1 = (a1 + b1 cos 3t) cos t , y1 = (a1 + b1 cos 3t) sin t, x2 = (a2 b2 cos 2 ) cos + , y2 = (a2 b2 cos 2 ) sin . Scheme 3 (Fig. 2b). In this case, the parametric equations of the contours take the form x1 = (a1 + b1 cos 4t) cos t , y1 = (a1 + b1 cos 4t) sin t , x2 = (a2 b2 cos 2 ) cos + , y2 = (a2 b2 cos 2 ) sin . The procedure of determination of the function f (t) is the same as above. Depending on the type of facet- ing, the generalized expression for this function takes the form f (t) = 1 S2 [4b2S3 + (a1 + b1 cos t) sin t][ b1 sin t cos t + (a1 + b1 cos t) sin t] S [4b2 S(1 S2 ) (a1 + b1 cos t) sin t][ b1 sin t sin t (a1 + b1 cos t) cos t] = 0, where = 2, 3, 4,\u2026 is the coefficient of faceting of the contour (oval, trihedral, etc.) and X(t) = 1 4b2 (a1 + b1 cos t) sin t + 1 4b2 (a1 + b1 cos t)2 sin2 t + 2 b2 a2 b2 3 3 3 . Scheme 4 (Fig. 2 ). In this case, the parametric equations of the contours take the form x1 = (a1 b1 cos 2t) cos t , y1 = (a1 b1 cos 2t) sin t , x2 = (a2 b2 cos 3 ) cos + , y2 = (a2 b2 cos 3 ) sin . The cubic equation for the angle t takes the form sin3 t + a1 + b1 2b1 sin t + 1 2b1 (a2 b2 cos 3 ) sin = 0 . Scheme 5 (Fig. 2d). In this case, the parametric equations of the contours take the form x1 = (a1 b1 cos 2t) cos t , y1 = (a1 b1 cos 2t) sin t , x2 = (a2 b2 cos 4 ) cos + , y2 = (a2 b2 cos 4 ) sin . The cubic equation for the angle t is as follows: sin3 t + a1 + b1 2b1 sin t + 1 2b1 (a2 b2 cos 4 ) sin = 0 . Since the discriminant of the cubic equation = 1 16b1 2 (a2 b2 cos )2 sin2 2 b1 a1 + b1 2 3 is negative, it is impossible to use the Cardano formula in the form (7) for the determination of the angle t . This equation has three different real solutions: sin t1 = S1( ) = 2 a1 + b1 6b1 cos 1 3 arccos 3 3b1 (a2 b2 cos ) sin 2(a1 + b1)3 , sin t2 = S2( ) = 2 a1 + b1 6b1 cos 1 3 arccos 3 3b1 (a2 b2 cos ) sin 2(a1 + b1)3 + 2 3 , (9) sin t3 = S3( ) = 2 a1 + b1 6b1 cos 1 3 arccos 3 3b1 (a2 b2 cos ) sin 2(a1 + b1)3 2 3 ", + " (10) As a result of the approximate solution of Eq. (9), we find the angle by using the most suitable root from the collection of three roots. In the presented schemes of the joints, disk 2 (or hole 1) is oval and the initial contact angle is determined by using the Cardano formula. However, one may also consider contacting bodies with more complicated types of faceting of the contours (Figs. 2 , f). In these cases, the Cardano formula can be used neither in the form (7), nor in the form (9). For schemes 6 (Fig. 2 ) and 7 (Fig. 2f), the angular parameters t and are found as a result of the approximate solution of the system of equations of type (5): (a2 b2 cos t) sin = (a1 + b1 cos ) sin , b1 sin t sin t + (a1 + b1 cos t) cos t b1 sin t cos t (a1 + b1 cos t) sin t = b2 sin sin + (a2 b2 cos ) cos b2 sin cos (a2 b2 cos ) sin . (11) Determination of Contact Pressures The general equation for pressure in the case of two-region contact is as follows [4]: k1 cot 2 p ( , ) d k3 p( , ) d k4 cos 1 2 p( , ) cos 1 2 1 2 d = R2 1 1 2 D1 ( )( ) 2 2 D2 ( )( ) , (12) where = + , = + , 0 , 0 , 1 2 , 1, 2 = \u00b1 0.5( 0 (1) 0 (1) ) , k1 = 1 8 1+ 1 G1R1 + 1+ 2 G2R2 , k3 = 1+ 1 8 G1R1 , k4 = 1 2 1 G1R1 + 1 G2R2 , = 3 4\u03bc , R = R2 , and G and \u03bc are the shear moduli and Poisson\u2019s ratios of the materials, respectively. The characteristics of faceting of the contours D1 ( )( ) and D2 ( )( ) for the analyzed joints are given by the formulas [4]: D1 (2) = D2 (2) = 1+ 3 cos 2 (Fig. 1); D1 (3) = 1+ 8 cos 3 , D2 (2) = 1+ 3 cos 2 (Fig. 2 ); D1 (4) = 1+15 cos 4 , D2 (2) = 1+ 3 cos 2 (Fig. 2b); D1 (2) = 1+ 3 cos 2 , D2 (3) = 1+ 8 cos 3 (Fig. 2c); D1 (2) = 1+ 3 cos 2 , D2 (4) = 1+15 cos 4 (Fig. 2d); D1 (3) = D2 (3) = 1+ 8 cos 3 (Fig. 2e), and D1 (4) = D2 (4) = 1+15 cos 4 (Fig. 2f). For the approximate solution of Eq. (12) of the contact problem, we use the collocation method [1, 3]. Thus, in the simplest case, it is possible to take a single collocation point = 0.5 and to choose the function of contact pressure in the form p( , ) E tan2 2 tan2 2 , where E = e4 cos2 ( / 4) R2 , = , = 1 1 2 D1( ) 2 2 D2( ) , = , e4 = 4E1E2 Z , Z = (1+ 1)(1+ \u03bc1)E2 + (1+ 2 )(1+ \u03bc2 )E1 , and E1, E2 = 2G 1+ \u03bc are the elasticity moduli of the materials. The maximum contact pressure is formed at the two points P1 and P2 (Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002295_mats.201100089-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002295_mats.201100089-Figure5-1.png", + "caption": "Figure 5. Schematic of the liquid crystal polymer network configuration used in the polydomain model. The cross-section view shows the finite element boundary conditions of a sub-set of the entire film. Simply supported mechanical constraints are applied to predict free displacement bending. The simulations include rotating the polarization of light in the X1\u2013X3 plane.", + "texts": [ + " This behavior is then coupled to the liquid crystal phase field simulations and polymer mechanics. All photomechanical phase field simulations were conducted on a polydomain model for comparison Macromol. Theory Simu 2011 WILEY-VCH Verlag Gmb iew Publication; these are NOT the final pag with polydomain experiments. The geometry in all simulations is 75 15 mm2 which includes a typical film thickness and a subsection along the length of the film. The boundary conditions for the problem are illustrated in Figure 5. These boundary conditions allow for free bending using a roller boundary condition while applying light via l. 2011, 20, 000\u2013000 H & Co. KGaA, Weinheim www.MaterialsViews.com e numbers, use DOI for citation !! Figure 6. Evolution of polydomain liquid crystal networks from an initial random distribution in (a) to the equilibrium state in (b). The surface plot corresponds to the director component ~n 1 . More detailed, colored version is in the Supporting Information. the tangential field on the top surface", + " Due to the small differences in light attenuation for the different absorption tensors, isotropic absorption is coupled to the liquid crystal evolution and polymer mechanics model to simplify numerical simulations of photomechanics bending for both trans\u2013cis and trans\u2013cis\u2013trans photoisomerization. This provides a qualitative estimate on light induced bending deformation. Additional discussion on this approximation is given after presenting the photomechanical bending results. Photomechanical deformation is simulated using the phase field approach to quantify differences that occur during trans\u2013cis and trans\u2013cis\u2013trans photoisomerization in a polydomain film. The models are simulated under free displacement boundary conditions with light applied on the top as illustrated in Figure 5. To facilitate computational Macromol. Theory Simu 2011 WILEY-VCH Verlag Gmb rly View Publication; these are NOT the final pag efficiency, the small strain approximation is used to study the glassy polymer network. This is a reasonable assumption since photomechanical strain is typically on the order of 1% in these glassy films. This assumption allows the Landau coefficients in Equation 13 and 15 to be independent of the deformation gradient. This gives only one-way coupling where the liquid crystal Cauchy stress given by Equation 18 is still present, but any changes in the liquid crystal structure that may occur during large deformation is neglected" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002278_icelmach.2012.6349905-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002278_icelmach.2012.6349905-Figure2-1.png", + "caption": "Fig. 2. Configuration of a 3M-PC PM motor.", + "texts": [ + " Hashimoto is with the Department of Electrical, Electronic, and Computer Engineering, Toyo University, 2100 Kujirai, Kawagoe-shi, Saitama 350-8585, Japan (e-mail: gz1000045@toyo.jp). drive motor with energy saving. In this paper, we propose a novel PM motor (3M-PC PM motor: 3 torque Mode Pole-Changing PM motor) that can change the number of poles and produce three different types of torque. As shown in Fig. 1, the motor operates with 8 poles and produces a PM torque in the low-speed area. When the motor changes to 4 poles, it produces a PM torque and reluctance torque at medium speed. At top speed, the motor produces only a reluctance torque. Fig. 2 shows the basic configuration of a 3M-PC PM motor. The rotor of the 3M-PC PM motor has a salient core and PMs with low coercive force (variable magnetized magnet) embedded at the iron core. Next, we discuss the change of poles and torque modes. First, we describe the 8- pole mode. When all the variable magnetized magnets have the same direction of magnetization, the magnetic poles (image poles) with reverse polarity to the magnets are formed in the rotor core between the magnets. Thus, the rotor forms 8 poles (Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003409_s1560354711060050-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003409_s1560354711060050-Figure1-1.png", + "caption": "Fig. 1. Purcell\u2019s three-linked robotic swimmer the simplest design capable to overcome the \u201coyster paradox\u201d [39]. The shape space is the rectangle (\u03b81, \u03b82) \u2208 (\u2212\u03c0, \u03c0) \u00d7 (\u2212\u03c0, \u03c0).", + "texts": [], + "surrounding_texts": [ + "In the limit of nearly zero Reynolds number, the motion of a rigid object is determined by its 6 \u00d7 6 resistance matrix which relates linearly the force and torque to the linear and angular velocities. It is common wisdom that the effects of boundaries can be safely neglected, unless the object is in a close vicinity [22]. For a helix moving with linear velocity v in the direction of its axis and angular velocity \u03c9 one has \u23a1 \u23a3 F N \u23a4 \u23a6 = \u23a1 \u23a3 A B B D \u23a4 \u23a6 \u23a1 \u23a3 v \u03c9 \u23a4 \u23a6 . (2.3) In this S1 equivariant setting only three resistance coefficients are needed. Purcell calls the attention that for a right handed helix the coefficient B < 0, implying that \u201ca helical filament does tend to move like a corkscrew in a cork when it is rotated\u201d. 2)An earlier paper by Ludwig [34] was unnoticed then. REGULAR AND CHAOTIC DYNAMICS Vol. 16 No. 6 2011 For a sphere of radius a, it is well known since Stokes that Bo = 0, Ao = 6\u03c0\u03b7a, Do = 8\u03c0\u03b7a3. (2.4) where \u03b7 is the viscosity. How does the gauge theory of microswimming comes into play here? Consider Fig. 2. The shape space has one angular coordinate \u03b8 \u2208 S1, measuring the relative rotation between propeller and cell, varying with motor\u2019s speed \u03c9m = \u03c9 \u2212 \u03a9. For a axisymmetric cell the organism translates and rotates smoothly3). The conditions of vanishing total force and total torque are Ao v + (Av + B\u03c9) = 0, Do\u03a9 + (B v + D \u03c9) = 0 . (2.5) Purcell avoids complicated hydrodynamical calculations by imposing the \u201cadditive rule\u201d for resistance matrices, correct in first order. We present highlights of his analysis in Appendix A, requiring only high school algebra: the quantities v, \u03c9, \u03a9 and the motor torque N are expressed in terms of the motor\u2019s speed \u03c9m. As we mentioned, Purcell\u2019s paper [40] was published posthumously. A manuscript was found by H. Berg, together with a logbook of experiments where the coefficients A,B,D were determined for several helical shapes. We reproduce the table; for convenience Purcell normalized the coefficients dividing by 6\u03c0\u03b7. In our estimates we use the helix that gives the best efficiency \u03b5 = 0.78% when propelling a sphere. The helix length is L = 7.8cm, L/\u03bb = 5 (\u03bb = wavelength), \u03b1 = 39 degrees (pitch angle). For this helix A = 0.71 cm, B = 0.038 cm2, D = 0.06 cm3. (2.6) Purcell did not present the value of the radius of the cylinder containing the helix, but it can be readily computed with the formula r = 1 2\u03c0\u03bb tan(\u03b1) so that r = (1/2\u03c0)(7.8/5)0.81 \u223c 0.2 cm, (2.7) about 1/40 of its length. It is actually quite thin! In general, if an object is scaled by \u03c3, then A \u2192 \u03c3A, B \u2192 \u03c32B, D \u2192 \u03c33D . (2.8) The main point in [40] is to find \u03c3 (given the cell radius) so that the propeller maximizes the efficiency. Purcell concludes that the best scaling occurs when A(\u03c3) = Ao, \u201cjust the condition under which the force required to drag the cell through the fluid . . . is equal to the force required to drag the locked propeller at the same speed\u201d. 3)If the S1 symmetry is borken, the body will stroboscopically cover an helical path, each marked point corresponding to a 2\u03c0 variation of \u03b8. REGULAR AND CHAOTIC DYNAMICS Vol. 16 No. 6 2011 Thus for the above model helical wire of L = 7.8 the radius of the sphere is a = 0.71. This means that the optimal length of an external propeller is about 5.5 times the diameter of the sphere. The need of a rather long flagellum seems to have been overlooked in many artificial swimmer proposals we found in the literature. We can infer the Reynolds number Re = av/\u03bd, where \u03bd = \u03b7/\u03c1 is the kinematic viscosity. In Purcell\u2019s experiment he used a silicon oil of kinematic viscosity \u03bd = 105 cSt, (1 cSt = 10\u22122 cm2/sec), or viscosity \u03b7 = 103 g/(cm sec). For a sphere of radius a = 0.71 cm moving at 20 \u00d7 0.71 cm2/sec Re = 0.71 \u00d7 20 \u00d7 0.71/105 \u223c 10\u22124. Note that if the velocity is measured in body lengths per second, it becomes independent of scale. Equations (2.5) rewrite as [(A + Ao)a](v/a) + B\u03c9 = 0, (Ba)(v/a) + D\u03c9 + Do\u03a9 = 0, (2.9) where the coefficients scale homogenously in size. Hence the frequencies appearing in Table 1 (Fig. 3) would be the same, regardless we consider a toy swimmer or an E. coli. For completeness, we present the main lines of Purcell\u2019s analysis. He focuses on how the efficiency4) depends on the relative sizes of cell and flagellum. Purcell shows that for B2 AD the expression \u03b5 \u223c AoB2 (Ao + A)2D = AoB2 p Dp \u03c3 (Ao + \u03c3Ap)2 . (2.10) (where the suffix \u201cp\u201d means a prototype propeller and \u03c3 is a geometric scaling parameter) is a very good approximation for the efficiency (Eq. (16) in his paper). In in the second equality the scaling (2.8) is introduced. The best choice of \u03ba is given by \u03c3 = Ao/Ap for which A = Ao, and \u03b5\u2217 = Bp 4ApDp . (2.11) The values in Table 1 on Purcell\u2019s paper were divided by 6\u03c0\u03b7, so the rule A = Ao implies that one chooses the size of the cell equal to the value of A, dimensionalized in cm. For the propeller we chose, A = 0.71 cm and L = 7.8 cm so the best size for the flagellum is 7.8/0.71 roughly 5.5 times the diameter of the cell as already mentioned above5). 4)Efficiency, following Lighthill\u2019s definition [31], is the ratio of the minimum possible hydrodynamical power expenditure \u2014 towing the cell or robot with motors shut down at a given velocity \u2014 to the hydrodynamical power expenditure required for self propulsion with that same velocity. This efficiency notion \u03b5Lighthill does not depend on the chosen velocity, fluid viscosity, or scaling, and it is always < 1. 5)Incidentally, we observed slight discrepancies from the reported values in Table 1 and the results we computed with (2.11). For the helix with L = 5.2 cm we got \u03b5\u2217 = 0.5 % instead of 0.48 %, for the L = 7.8 cm we got \u03b5 = 0.85 % instead of 0.78 %. REGULAR AND CHAOTIC DYNAMICS Vol. 16 No. 6 2011 There is an interesting observation, that does not appear in Purcell\u2019s paper. By direct substitution one can check that N\u03a9m = (Aov 2 + Do\u03a92) + (Av2 + 2Bvw + Dw2). (2.12) The left hand side is the power expenditure as \u201cseen by the little man\u201d inside the cell rotating the external flagellum. The right hand side is the sum of the propeller\u2019s energy expenditure plus the cell power expenditure, some sort of \u201cPythagoras law\u201d." + ] + }, + { + "image_filename": "designv11_7_0001865_vr.2010.5444756-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001865_vr.2010.5444756-Figure1-1.png", + "caption": "Figure 1: Rigid endoscope model for virtual endoscopy", + "texts": [ + " The STEPS system [4], simulates the movements of the endoscope and its access to the tumor by navigating with a force feedback joystick, however the navigation model proposed do not take into account tissue deformations for having a real haptic response. The Sinus Endoscopy system [3], shows a realistic rendering using the GPU with a low load of CPU at interactive frame rates, but without haptic response. Rigid endoscope movements can be represented as a four degrees of freedom mechanical joint (pitch, yaw, roll and dolly) which is equivalent to study it as a simple lever, transforming the the user\u2019s force to one applied over the nasal tissue. Figure 1 shows the characterized endoscope with a mass M = M1 +M2, length D = d1 +d2, and using the nostril as a pivot point. Due to the anatomical restrictions of the nasal cavity, there is a limited space to rotate the endoscope (pitch and yaw degrees of freedom (DOF)) therefore the \u03b8 angle is small and its behavior in terms of system\u2019s forces and velocities can be represented by the equations 1 on the user side, 2 on the collision site and 3 between soft and osseous tissue 0 =\u2212 f +m1v\u03071 + f1 (1) 0 =\u2212 f2 +m2v\u03072 +K1 \u222b v2\u2212 v3 dt +B1(v2\u2212 v3) (2) 0 = K1 \u222b v3 \u2212 v2 dt +B1(v3\u2212 v2)+m3v\u03073 +K2 \u222b v3 dt (3) The elastic properties of the osseous tissue are modeled from the K2 spring and M3 mass and the elastic and damping properties of soft tissue are modeled from K1 spring and B1 damper, the viscous friction of the mucus" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001192_b719320c-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001192_b719320c-Figure1-1.png", + "caption": "Fig. 1 Schematic illustration of porous membrane controlled polymerization. A porous membrane is used to separate the monomer and oxidant solutions, resulting in careful control of nucleation and growth of nanofibers.", + "texts": [ + " X-Ray patterns were taken with Cu Ka radiation (l \u00bc 1.54059292 A\u030a). A 50 nm thin layer of the four Au strips (2 mm in width) patterned by a shadow mask was thermally evaporated onto the top of the cast uniform thin film and the pressed pellet of doped polyaniline nanofibers was put under a pressure of 8 10 7 Torr for the measurement of the conductivity. Each strip was equally separated by 3 mm. The pressed pellets of nanofibers and nanofibers\u2013KBr were prepared under highpressure mechanical stress, e.g. 4000 psi, using KBr pellet die. Fig. 1 shows the concept of porous membrane controlled polymerization. The monomer dissolved in an aqueous acid solution is J. Mater. Chem., 2008, 18, 2085\u20132089 | 2085 D ow nl oa de d by V an de rb ilt U ni ve rs ity o n 13 /0 5/ 20 13 1 5: 36 :0 0. Pu bl is he d on 0 4 A pr il 20 08 o n ht tp :// pu bs .r sc .o rg | do i:1 0. 10 39 /B 71 93 20 C separated by a permeable membrane from an aqueous oxidant\u2013acid solution in a reaction chamber. Monomer (or oxidant) diffuses through the membrane at a controlled rate and is subsequently polymerized in the oxidant/acid solution (or monomer/acid solution) according to known reactions" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003276_tasc.2013.2283238-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003276_tasc.2013.2283238-Figure1-1.png", + "caption": "Fig. 1. Schematic diagram of the proposed cross section of HTS rotor.", + "texts": [ + " The magnet torque is realized by means of HTS squirrel-cage windings, and the reluctance torque is generated by means of the HTS shield bulk. Electromagnetic field analysis and experimental results are reported and discussed. The basic structure of the original HTS motor is the squirrelcage-type induction motor. The detailed structure and characteristics of such motor is described in [3]\u2013[6]. In this study, HTS reluctance torque is further added to the abovementioned induction/synchronous torque (hereafter, stated as magnet torque). Fig. 1 illustrates the schematic diagram of the cross section of the proposed rotor. HTS squirrel-cage windings are installed in the slots, which are located at the outer parts of the rotor core. The HTS magnetic shield bodies (4 in this figure) are also installed in the slots. Fig. 2 shows the conceptual explanation of the maximum torque for different rotational speed. As shown in the figure, there are roughly two kinds of operation modes for the drive motor, i.e., constant torque operation mode at low speed and constant power operation mode at high speed", + " In other words, the abovementioned HTS reluctance torque is automatically generated by sensing the magnetic condition of the rotor core. It is commonly said that the reluctance torque will decrease the power factor, and this occurs the enlargement of the reactive current. Hence, the magnet torque should only be utilized for the steady-state (medium or light torque) operation mode. At starting, however, high torque is more important than efficiency. In order to verify the abovementioned idea, electromagnetic field analysis is carried out. Fig. 1 is modeled for 2-D finiteelement analysis (FEA). A normal conducting (copper) stator (three-phase, four-pole, distributed windings, star connection) is considered, and the rotor windings are made of HTS tapes. The air-gap length between the stator and the rotor is 0.3 mm. At present, the analysis is only available for the static condition of the rotor due to the difficulty in the characterization of the HTS. Fig. 3 shows the examples of analysis results of magnetic flux density contours. As can be seen in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000522_11505532_3-Figure3.3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000522_11505532_3-Figure3.3-1.png", + "caption": "Fig. 3.3. Illustration of the LOS angles.", + "texts": [ + "15) contains no control inputs. To regulate the cross-track error to zero, we will control the surge speed u, the pitch angle \u03b8 and the yaw angle \u03c8 in such a way that the cross-track error converges to zero. This will be done with the help of LOS guidance. For LOS guidance, we pick a point that lies a distance \u2206 > 0 ahead of the vehicle, along the desired path. The angles describing the orientation of the xz- and xy-projection of the line of sight are referred to as the LOS angles. With reference to Fig. 3.3, the LOS angles are given by the following two expressions: \u03b8LOS(t) = tan\u22121 ez(t) \u2206 , \u03c8LOS(t) = tan\u22121 \u2212ey(t) \u2206 . (3.16) In the next subsections we will propose three controllers. The first controller regulates the surge speed u to asymptotically track some commanded speed signal uc(t). The second controller makes the pitch angle \u03b8 track \u03b8LOS . We will show that this will result in the cross-track error ez and pitch angle \u03b8 exponentially converging to zero. The third controller makes the yaw angle \u03c8 asymptotically track \u03c8LOS " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001518_13506501jet327-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001518_13506501jet327-Figure1-1.png", + "caption": "Fig. 1 Geometry of a squeeze film short bearing", + "texts": [ + " [46] analysed the effect of viscosity variation on the static performance of a narrow journal bearing operating with couple stress fluids. The present paper predicts theoretically the effect of viscosity variation on static characteristics of a short squeeze film bearing operating with couple stress fluid. Lin\u2019s study [35] static and dynamic behaviours of pure squeeze films in couple stress fluid-lubricated short journal bearings has been extended to include the viscosity variation for constant load. Figure 1 represents the physical configuration of a short squeeze film bearing. The shaft of radius r approaches the bearing surface with velocity V. The film thickness h is a function of u, that is h \u00bc c \u00fe e cos u, where c is the radial clearance and e is the eccentricity of the journal centre. The lubricant in the system is taken to be a Stokes couple stress fluid. According to the Stokes microcontinuum theorem, the constitutive equations of an incompressible fluid with couple stress are [12] r\u2020V \u00bc 0 \u00f01\u00de r dV dt \u00bc rp\u00fe rF \u00fe 1 2 rr C \u00fe mr2V hr4V \u00f02\u00de where the vectors V, F, and C represent the velocity, body force per unit mass, and body couple per unit mass; r the density; p the pressure; m is the shear viscosity, and h is a new material constant responsible for the couple stress fluid property @u @x \u00fe @v @y \u00fe @w @z \u00bc 0 \u00f03\u00de Proc" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003869_s00419-012-0608-6-Figure18-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003869_s00419-012-0608-6-Figure18-1.png", + "caption": "Fig. 18 The mode shapes corresponding to frequency \u03c917 (the second mode)", + "texts": [], + "surrounding_texts": [ + "As mentioned earlier, in the geometrical model of the gear, the geometry of the teeth is omitted. It allows us to reduce the system\u2019s FE model size. The simplified geometrical model of the system consists of five sectors (see Fig. 1) that have the cyclic symmetry feature. Each of these segments is meshed by using standard procedures of the ANSYS software. The 3-D solid mesh is elaborated and as mentioned earlier, the ten-node tetrahedral element (solid92) with three degrees of freedom in each node is used to realize each sector. During the mesh generation process, it is assumed that the maximum length of each element\u2019s side needs to be no more than 2.7 [mm]. The developed FE model is displayed in Fig. 2, and it consists of 19,620 elements and 36,188 nodes, respectively. The particular sectors are glued as a whole at the geometrical model preparing the stage by using standard procedure of the ANSYS program. The analysed gear is mounted in the roller bearings. Such bearings typically have slight load capacity under loads perpendicular to the primary supported direction. The gear shaft neck surfaces on which the bearings are assembled are denoted \u201cbearing\u201d (see Fig. 3a). The gear mates with the other devices by the splines. The splines is simplified down to a regular cylinder of the diameter assumed as equal to the splines pitch diameter. The surface denoted \u201cjoint\u201d (see Fig. 3a) is located on the pitch diameter of the splines. Parameters of the analysed system are shown in Table 1a\u2013b. The calculation results for natural flexural oscillations taking into account angular speed of the gear are shown in the paper. In the case of circular discs and annular plates, for each solution where nodal lines are nodal diameters, one obtains two identical arrangements of straight nodal lines, rotated by an angle of \u03b1 = \u03c0/(2n) one to another, where n is the number of nodal diameters. In accordance with the circular and annular plate vibration theory [5,6,12], the particular natural frequencies of vibration are denoted as \u03c9mn , where m refers to the number of nodal circles and n is the mentioned number of nodal diameters. As the shape of the gear model is fairy elaborate, the flexural modes of the system are subject to deformation (as compared to the system without any holes) to such extent that establishing which particular node it refers to becomes rather difficult. This problem is even worse if the angular speed of the gear is varying. The problem of influence of the angular speed on the flexural gear models deformation is analysed. For the purpose of identification of these modes, an algorithm of tagging oscillation modes, which determines the correspondence between vibration of the circular disc versus disc with holes, is used. For this purpose, an auxiliary model of annular plate in the form shown in Fig. 3b is used. The geometrical dimensions of the auxiliary model were taken from the gear geometry (shown in Fig. 1). They are as follows: addendum circle diameter dz , rim mounting diameter dp, root circle diameter dw2, and thickness h p and hz (see Table 1). Dynamic analysis is performed for the auxiliary model cases rotating at predetermined angular speed, where diameter of though holes d01 (see Fig. 3b) varies as seen in Table 2. Findings are compared to each other both quantitatively and qualitatively. This method makes it possible to investigate deformations of nodal lines associated with nodal diameters and circles due to through holes and then determine correspondence between oscillation modes of solid circular disc and a plate with holes. In the final step, solutions found for the auxiliary model are compared with the solution for the system whose FEM model is shown in Fig. 2 (the principal model). As for the principal model case, the 3-D solid mesh and the ten-node tetrahedral element (solid92) are used to discretize the auxiliary models. For all models subject to analysis, the boundary conditions were applied to the nodes. For each model, 1 d f associated with node radial displacement was subtracted from the nodes found on the surface identified as a bearing (see Fig. 3a,b). Furthermore, 1 d f associated with the displacement of nodes along the centreline of each model was subtracted from the nodes found on the surface, identified as a joint (see Fig. 3a,b). For the models obtained in this way, calculations were kept conducted as long as the natural frequency \u03c918 was determined. The calculations were performed assuming that the systems rotate as angular speed of \u03b8 , within the range of 0\u20131047 [ rad/s]. During the computing process, the angular speed values were gradually increased by 80[ rad/s], which made fourteen variants of the results (the natural frequencies and corresponding natural modes), which were subject to further interpretation. The rotation effect was taken into account by determining stress distribution due to rotation, for each model during the computational step associated with static analysis (the so called pre-stress effect). This stress distribution was then included in the computation step associated with modal analysis. The results of the numerical calculations related to the procedure of identifying deformed natural modes of flexural vibration of the gear under consideration are shown below. The results displayed here relate to the determination of the correspondence between the natural frequencies \u03c916 and \u03c925 at high angular speed (\u03b8 = 1047 [ rad/s]) as well as to the correspondence between oscillation modes and the natural frequency \u03c931 at lower angular speeds (\u03b8 = 80 [ rad/s]). The results as shown in Figs. 4, 5, 6, 7, 8, 9 allow for tracking deformations of nodal lines associated with nodal circles and diameters, due to varying diameter of the through holes. With respect to the natural frequency \u03c925, there is marked difference in shapes of natural modes. When one compares the results between each other, one can notice that in order to identify correctly deformed natural modes of the flexural oscillations in the gear under consideration at lower angular speeds, larger number of auxiliary models is required to be included during calculations, as compared to the higher angular speeds. It comes from the fact that additional stresses through the centrifugal effects appear. This effect causes the gear flexural stiffness to be an apparent function of rotational speed (stiffness grows for higher speed). In the next part, results of the numerical calculations associated with the extent of the influence of the angular speed to deformation of mode shapes of oscillations. For each discussed case, both mode solutions related to nodal diameters are shown. These analysed results are sorted by the order of their occurrence. For the frequencies \u03c923 and \u03c918, the results were obtained at angular speeds of \u03b8 = 0 and \u03b8 =1,047 [ rad/s] respectively. For the other cases, results were obtained at angular speeds \u03b8 of, 0, 320, 720, and 1,047 [ rad/s], respectively. Natural frequencies for these modes are included in Table 3. To determine this mode (see Figs. 10, 11), the procedure of tagging natural oscillation modes was required. Nodal lines associated with the circle and diameter are deformed. Minor influence of the angular speed to deformation of the nodal lines is noticeable. The task of determining modes in this case was not too difficult (see Figs. 12); no procedure of tagging natural oscillation modes was required. The slight impact of the gear angular velocity on the distortion of the nodal lines is observed. For these modes (see Figs. 13, 14), procedure of tagging natural oscillation modes was required. It is noticeable that angular speed affects markedly deformation of the nodal lines. Once the angular speed of 720 [ rad/s] is exceeded, the oscillation mode takes different shape. Major deformation of mode shape attributable to the shaft vibrations is evident at this speed. Moreover, additional problem associated with some similarity of the mode being tagged to the mode associated with frequency of \u03c931, emerged during mode identification. Establishing the correspondence between these modes was a complex task (see Figs. 15, 16) due to the shape of oscillation modes similarity to the case discussed earlier. The angular speed affects deformation of nodal lines markedly. Major shape mode variations emerge at \u03b8 = 400 [ rad/s]. The identification process in this mode was not easy (see Figs. 17, 18) . One can notice that angular speed affects the deformation of nodal lines. Major variation in mode shape emerges at \u03b8 = 720 [ rad/s]. Moreover, additional annular shaft vibration emerges at the highest considered angular speed. Finding correct correspondence between the modes in this case was fairly easy (see Figs. 19). High repeatability in deformations of nodal lines on circular plate at various angular speeds is noticeable. As a consequence of the conducted analysis (see Table 3), the Campbell diagram was plotted for the gear under consideration. This is a convenient method of displaying the relationship between gear natural frequencies and transmission system excitations [4]. Excited frequencies are plotted on a vertical axis, and the gear speed of rotation is plotted on the horizontal axis (see Fig. 20). Natural frequencies achieved from numerical analysis are plotted as near-horizontal curves. The forced frequency due to the meshing is determined by the following relation (as in Ref. [4]) f = n0 \u00b7 z 60 (4) where n0 [rpm] is the rotational speed and z is the number of teeth in the gear. For this system, the gear teeth number is z = 59. Vibration resonance phenomenon occurs when forcing frequency (4) matches as to its value with some natural oscillation frequency of the gear. The points where the near-horizontal \u03c9mn curves intersect the straight line (4) indicate the speeds at which the gear resonance will be excited (see Fig. 20). For instance, the rated excitation speed for the natural frequency of \u03c923 is 764 [rpm]. It may be inferred from both the Campbell diagram and Table 3 that the rotating movement makes flexural stiffness of the gear under consideration to increase. Moreover, at speed of 3,820 [rpm], one can notice major surge associated with the mentioned earlier changing of the shape of the natural mode frequency in the case of the frequency of \u03c931. The growth of the gear transversal stiffness observed during gyrate of the gear comes from the appearance of the additional stresses in the toothed gear through the centrifugal effects. The higher rotational speed generates higher centrifugal forces, higher stress level, thereby causing the transversal stiffness of the system to increase. Moreover, the growth of the gear flexural stiffness through the gyrate effect causes reduction of the needed numerical calculations connected with identifying the proper distorted mode shapes." + ] + }, + { + "image_filename": "designv11_7_0002447_iet-epa.2010.0192-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002447_iet-epa.2010.0192-Figure2-1.png", + "caption": "Fig. 2 Block diagram of the identification algorithm", + "texts": [ + " Furthermore, the input/output data must capture both transient and steady state behaviour for an appropriate characterisation. Hence, it is assumed that To represents the length of the time window used for identification purposes. Furthermore, the data are stored digitally at a sampling frequency Fs, then N represents number of measurements captured after ac/dc conversion. Therefore given the input voltages (ud, uq) and load torque TL in the experiment, the objective is to obtain the best parameters vector Q such that the error in the estimated output (i\u0302ds(Q), i\u0302qs(Q), v\u0302m(Q)) by SIM is minimal (see Fig. 2). Hence, the identification problem can be translated into a finite-dimensional optimisation problem over a closed domain. The performance cost function can be defined in terms of the estimation error as follows Y(Q) W d2(ids, i\u0302ds(Q)) d2(ids, i\u0302ds(Q)) + 1 + d2(iqs, i\u0302qs(Q)) d2(iqs, i\u0302qs(Q)) + 1 + d2(vm, v\u0302m(Q)) d2(vm, v\u0302m(Q)) + 1 (3) where d2(u, v) W To 0 (u(t) \u2212 v(t))2dt \u221a denotes the two- metric of time signals (u(t), v(t)); or if the measurements are considered as discrete signals (u[k], v[k]), then d2(u, v) W \u2211N k=1 (u[k] \u2212 v[k])2 \u221a " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003404_isma.2013.6547379-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003404_isma.2013.6547379-Figure2-1.png", + "caption": "Figure 2. Vertical movement", + "texts": [ + " The Quadrotor main idea was to have a helicopter that can handle larger capacity and can maneuver in areas that were difficult to reach. Generally it consists of four propellers (front, rear, right and left), as shown in Figure 1 [10]. By changing the control command to these motors \u03a9i, their speed will vary and the quadrotor direction is updated, accordingly the quadrotor can navigate in different directions. For instance, the quadrotor can move in the vertical Z direction by varying the speed of all propellers at the same time and by the same amount as shown in Figure 2. To command the quadrotor to move in the X direction, the speed of the front and rear propellers should be changed by the same amount and in opposite directions as shown in Figure 3. Moving the quadrotor in the Y direction can be done by changing the speed of the right and left propellers by the same amount and in opposite directions as shown in Figure 4. 978-1-4673-5016-7/13/$31.00 \u00a92013 IEEE ISMA13-2 To control quadrotor heading, the speed of all propellers is commanded by the same amount but in different directions, front and rear propellers with the same direction and right and left the propellers with opposite direction, as shown in Figure 5" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001492_tmag.2007.916391-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001492_tmag.2007.916391-Figure1-1.png", + "caption": "Fig. 1. (a) Edge and (b) facet model of a tetrahedron.", + "texts": [ + " The aim is to facilitate the connection between field equations due to such currents and the equations of the supplying circuitry. Coupling between magnetic and electric networks is also considered for models of electric windings. It was shown in [1] that finite-element formulations using potentials may be seen as equivalent to network models of either edge elements (EN), with branches coinciding with element edges, or facet elements (FN), where the branches connecting the nodes are associated with the facets, while the nodes are positioned in the middle of the volumes. Fig. 1 depicts the edge and facet models of a tetrahedron. The nodal equations of EN are equivalent to the nodal element description (NEM) of the scalar potential formulation, while the loop equations of FN correspond to the edge element formulation (EEM) using vector potential. The edge values of the vector potentials and represent the loop fluxes and currents in loops around the edges, respectively [1]. In regions with conduction currents, a conductance network (CN) may be created from an electric edge model, whereas a resistance network (RN) stems from an electric facet model", + " The edge networks (EN) are analysed using the nodal method, thus branch sources need to be introduced. On the other hand, a loop method is applied to evaluate the facet networks (FN), hence either branch or loop sources may be used. In the models under consideration, the branch mmfs and emfs are established from loop currents and fluxes. In the case of EN, currents and fluxes \u201caround\u201d the edges are relevant, whereas for the FN case currents and fluxes of the loops associated with facets need to be used (see Fig. 1). Loop mmfs in EN represent facet values of , whereas loop emfs arise from time derivatives of facet values of . The loop sources of FN, on the other hand, may be defined using branch currents and fluxes corresponding to element edges. Table I collects expressions that describe branch and loop currents, fluxes, mmfs, and emfs for electric and magnetic networks. 0018-9464/$25.00 \u00a9 2008 IEEE In field analysis of simply connected conducting regions, e.g., solid parts of a core with no \u201choles,\u201d it is possible to use the \u2013 combination of potentials, as well as \u2013 or \u2013 " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002685_978-1-4419-1674-7_23-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002685_978-1-4419-1674-7_23-Figure4-1.png", + "caption": "Fig. 4 Schematic of the THz chipless tag structure", + "texts": [ + " As long as the relative phase shifts between the multiple reflection depend on the frequency of the CW incoming wave, on the one hand, and on the geometrical and optical properties of the tag, on the other hand, a frequency sweep of the CW source involves specific intensity modulation of the total reflected (or transmitted) EM wave. In turn, a detector reads a spectral signature: the tag information is coded in the frequency domain. Below we present some results obtained with this latter approach, and more specifically how it is possible to code several bits with a simple multilayer structure as a RFID chipless tag in the THz domain. The studied THz tag on Fig. 4 consists of non-magnetic dielectric media arranged in a well-defined order, ensuring three different functions, which are required to identify precisely the tag and its information. The periodical stack of layers A and B is well-known as Bragg mirror. This periodic structure has a transmission coefficient, which depends on the frequency of the incident signal. As depicted in Fig. 5b, this Bragg mirror prevents an incoming wave from being transmitted through the structure if its wavelength is included within a certain bandwidth whose spectral characteristics (rejection level, position and width) depend on the dielectric and geometrical properties of each periodically stacked layers A and B. The Bragg mirror is a 1-D photonic crystal, presenting a Photonic Band Gap (PBG) that allows coding spectral information. Indeed, introducing a layer C (defect layer Fig. 4) embedded by two 1-D photonic crystals, one creates a Fabry-Pe\u0301rot cavity [25] having frequency-dependent reflectivity since the bandwidth separating two consecutive transmission peaks depend on the optical length of the defect. Thus, either none or several peaks occur within the PBG. Then, presence or absence of those transmission peaks, called defect mode, code the useful information. As example of results, we consider the multi-layer structure on Fig. 4, to develop a THz tag whose spectral signature presents an orientation-free dependence: the reader must identify the tag regardless its relative orientation. The spectral response of the developed structure must be also independent of the polarization state of the incoming THz EM wave in order to fit the RFID applications requirements. The transmitted and reflected EM waves (Et and Er, respectively) are numerically calculated with the transfer matrix method [26], considering TE or TM planar incoming wave Ei, with any orientation \u2122 about the tag surface" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003560_978-1-4613-4560-2_2-Figure8.51-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003560_978-1-4613-4560-2_2-Figure8.51-1.png", + "caption": "Fig. 8.51. As a consequence of the vertical shift of one linear curve, the critical activation energy is altered.", + "texts": [ + " But the argument is valid for any change of potential across the interface. Thus, if the double-layer potential is initially iJrpe (i.e., the interface is at equilibrium) and then the potential is changed to iJrp, the Morse curve for the initial state is shifted vertically through an energy F(iJrp - iJrpe)' or FrJ. As a consequence of the vertical shift of one linear curve, the critical activation energy for the reaction (the main factor upon which its rate depends) is altered from E/ at equilibrium (i.e., AF in Fig. 8.51) to Ery* at the overpotential rJ (i.e., HD of Fig. 8.51). The difference iJE* between the two activation energies has resulted from the electrical energy F'Yj that has been introduced into the reaction. What is the relationship between L1E* and F'Yj? The change L1E* in activation energy decides the net current output; the F'Yj is the input electrical energy channeled into the interface. One seeks to know: How much did the activation energy decrease for the given energy input F'Yj? In terms of the linear analogue, the question is answered by a trivial exercise in geometry (see Fig. 8.51). One has E* AB = FE = -\"-[from L1AEF] tan y and AB = GE - E/ [from L1ABG] tan e and, therefore, E * = tan Y (G E - E *) e tan e e (8.84) E* CD = _'1_ [from LI CD H] and tan Y CD = GH - Eq* [f L1CDG] tan e rom Hence, E '*' = tan Y (GH - E'*') 'I tane q (8.85) By making use of Eqs. (8.84) and (8.85), it follows that change in activation energy or LJE* = E/ - E'I* = tan Y (G E - G H) - (E * - E'*') tan e e\" = tan Y (F - LJE*) tan e 'Y} LJE* -- ( tany ) F - tan y + tan e 'Y} (S.S6) This is a basic result", + " Is the fJ in the Butler-Volmer Equation Independent of Over potential? In order to consider the influence of the current-producing (or current-produced) overpotential 'Y} on the activation energy, the Morse curves used to synthesize the potential-energy barrier were linearized, and then one linear curve was shifted vertically through an energy Frj- During this shift brought about by a change of interfacial potential difference, the slopes tan y and tan () of the linear curves were maintained constant (Fig. 8.51). On this approximate basis, the symmetry factor, which is a function only of the slopes y and () of the linear curves, appears to remain constant during a change of potential. Is this result a feature of barriers at interfaces or merely a consequence of shifting a linear curve? It is clear that, once a linear curve is displaced vertically, it cannot but yield a parallel shift of the curve and therefore a constant fJ. The apparent constancy of fJ with potential is a result of the linearization of the potential-energy-distance curves" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002596_s0022-0728(69)80015-x-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002596_s0022-0728(69)80015-x-Figure2-1.png", + "caption": "Fig. 2.", + "texts": [ + " Accordingly, they concluded that a second-order step is rate-determining for the reaction of propionate. Although their t reatment was somewhat ambiguous, the idea of pulsating current electrolysis is unique and interesting. FLEISCHMANN et al. 1\u00b04 developed this technique in a more rigorous form. They applied potentiostatic pulse electrolysis to a solution of aqueous acetate in order to determine the mechanism. A plot of the rate of ethane formation against the pulse width applied is shown in Fig. 2. I t is obvious that the appreciable change in the rate of ethane formation appears in a very short pulse time, i .e . , less than IO -a sec. For longer pulses, the rate becomes virtually constant. Unfortunately, this very interesting experiment cannot be compared with a rigorous mathematical analysis, since the evolution of oxygen as well as the formation of the surface oxide of the platinum electrode took place simultaneously during this short period of time. The transient current during a pulse had a discontinuous break which was, no doubt, due to these complications" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000514_ijcnn.2006.247123-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000514_ijcnn.2006.247123-Figure1-1.png", + "caption": "Fig. 1. Overhead crane", + "texts": [ + " In [28], the nonlinear antiswing control based on the singular perturbation method is presented. Also, these anti-swing controllers are modelbased. In this paper, we will give a model-free anti-swing controller, which has PID structure. To the best of our knowledge, model-free anti-swing controller and its stability analysis with neural compensator has not yet been established in the literatures. A experimental comparison of various antiswing controllers is realized on our 3D crane system. 0-7803-9490-9/06/$20.00/\u00a92006 IEEE 4697 The overhead crane system described schematically in Fig.1 (a) can be formed into a system structure which is shown in Fig.1 (b). The dynamics of the 3D crane system can be obtained by Lagrangian method. The kinetic energy of the overhead crane can be divided into three parts, K = K1 +K2 +K3 where K1 is rail kinetic energy K1 = Mrv 2 Mr 2 , xr = 0, yr = y, zr = 0, Mr and vMr are mass and velocity. K2 is cart kinetic energy K2 = Mmv 2 Mm 2 , xm = x, ym = 0, zm = 0. K3 is payload kinetic energy K3 = Mcv 2 Mc 2 . Because vMr = y\u0307w, vMm = x\u0307w. So K1 = 1 2 y\u03072wMr, K2 = 1 2 x\u03072wMm, v2Mc = v2Mxc + v2Myc + v2Mzc. For the payload, its position is given by xc = xw +R sin\u03b1 cos\u03b2 yc = yw +R sin\u03b2 zc = \u2212R cos\u03b1 cos\u03b2 where where \u03b1 and \u03b2 are payload angles with respect to the vertical and its projection angle along the X-coordinate axis, so vMxc = x\u0307c = x\u0307w +R cos\u03b1\u03b1\u0307 sin\u03b2 +R sin\u03b1 cos\u03b2\u03b2\u0307 vMyc = y\u0307c = y\u0307w \u2212R sin\u03b1\u03b1\u0307 vMzc = z\u0307c = \u2212R cos\u03b1\u03b1\u0307 cos\u03b2 +R sin\u03b1 sin\u03b2\u03b2\u0307 Finally we have K = 1 2 Mc \u239b\u239c\u239c\u239c\u239c\u239c\u239c\u239c\u239c\u239c\u239d y\u03072w + x\u03072w +R2 sin2 \u03b2 cos2 \u03b1\u03b1\u03072 +R2 sin2 \u03b1 cos2 \u03b2\u03b2\u0307 2 +2x\u0307wR cos\u03b1\u03b1\u0307 sin\u03b2 + 4x\u0307wR sin\u03b1 cos\u03b2\u03b2\u0307 +y\u03072w \u2212 2y\u0307wR sin\u03b1\u03b1\u0307+R2 sin2 \u03b1\u03b1\u03072 +R2 cos2 \u03b2 cos2 \u03b1\u03b1\u03072 \u22122R2 cos\u03b2 sin\u03b1 cos\u03b1\u03b1\u0307 sin\u03b2\u03b2\u0307 +R2 sin2 \u03b1 sin2 \u03b2\u03b2\u0307 2 \u239e\u239f\u239f\u239f\u239f\u239f\u239f\u239f\u239f\u239f\u23a0 + 1 2 y\u03072wMr,K2 + 1 2 x\u03072wMm The potential energy can also be divided into three parts, V = V1 + V2 + V3 where V1, V2, V3 are rail, cart and payload potential energies, obviously V1 = 0, V2 = 0, V3 =McgR (1\u2212 cos\u03b1 cos\u03b2) where Mcg is gravity of the payload, R is length of the lift-line" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002731_elan.201000424-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002731_elan.201000424-Figure1-1.png", + "caption": "Fig. 1. a) Picture of a packaged microelectrochemical cell ; b) detail of a microelectrochemical cell (Design 2) after modification of the reference electrode. CE: Counter electrode, WE: Working electrode array and RE: Reference electrode; c) Schematic representation of the working electrode array for Designs 1 to 4. Dimensions are given in Table 1.", + "texts": [ + " Following fabrication, the individual chips were diced and attached on a PCB board. The electrodes were then connected to the PCB tracks with gold wire bonds. The chip edges and the wire bonds were subsequently protected by covering in a polymeric encapsulant (Amicon 50300 HT from Emerson and Cuming) cured at 150 8C for 2 hours. Four microelectrochemical cells have been designed on a 4 mm 4 mm silicon chip. Each of the cells has a counter electrode, a reference electrode and an array of working microelectrodes, all made of Pt (Figure 1) which is essential to work in seawater. The electrode geometry, dimensions, electrode centre-to-centre spacing, number of electrodes in the array and total geometric surface areas are given in Table 1. The counter electrode is L-shaped with a total geometric surface area of 0.003 cm2 for Designs 1 and 2 and of 0.015 cm2 for Design 3 and 4. The total geometric surface area refers to the geometric surface area of one microelectrode multiplied by the number of electrodes in the array. The Pt pad for the reference electrode is a 200 mm by 200 mm square" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000055_978-1-4684-1500-1-Figure7.1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000055_978-1-4684-1500-1-Figure7.1-1.png", + "caption": "Figure 7.1 Frame construction is identified when discrete items are fitted to a three-dimensional larger object.", + "texts": [ + " Either way, the method of evaluating a design for compatibility with robots is the same. The only additional considerations are incurred costs due to any changes to the design of components or processes (eg stocks of existing components being scrapped), and/or the need for compatibility with products that have or are being assembled manually because of servicing, stocking or approval reasons. 88 Product and process design for assembly Each product and subassembly can be described by one of four classifications: 1. Frame construction (Figure 7.1). Items such as television sets or computers are frame constructed as they need a frame onto which other items can be mounted. 2. Stacked construction (Figure 7.2). Designs that require the components to be assembled one on top of another (eg armatures). 3. Base component construction (Figure 7.3). Items that incorporate a base onto which all components are fitted and transported through the assembly process (eg printed circuit boards). 4. Modular (Figure 7.4), in which individual sub assemblies are combined to form different products (eg manufacture of automobiles in which different combinations of similar 'options' are used to produce a wide range of models)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002376_j.fusengdes.2011.01.018-Figure6-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002376_j.fusengdes.2011.01.018-Figure6-1.png", + "caption": "Fig. 6. Kinematic chain of the base in the Stewart.", + "texts": [ + " The bearing house and the U-joint orm the base of Stewart platform, and each has configurationndependent stiffness, while the stiffness of the base of the Stewart latform is configuration-dependent as a function of the orientaion of the hydraulic limb. The stiffness of the hydraulic limb is also onfiguration-dependent as a function of its length. The up-joint in he end-effector is considered as rigid. 3.1. Stiffness evaluation of base in parallel mechanism The composition of the base by the bearing house and the U-joint is in a serial form. Herein, its stiffness is investigated by employing the virtual joint method and the principle of virtual work. The kinematic chain of the base is shown in Fig. 6. The hexagon in the figure is the basement of the Stewart, in which the frame Xg 4 Yg 4 Zg 4 is defined as the local reference coordinate. Under the external force Fft applied to the point Ou 6, the compliance of the base will cause the point Ou 6 to experience a twist[ T ft T ft ]T in terms of translational and rotational deformations in the frame Xg 4 Yg 4 Zg 4 . Applying the kinematic relationship in the base results in: ft = Jft[ T u T bearh ] T , Jft = [ Ju dx Ju dz Jbearh dy Jbearh dz Jbearh x Jbearh z ] (5) where u and bearh represent the deformations of the U-joint and the bearing house while Ji is the Jacobian of the ith local joint deformation" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000055_978-1-4684-1500-1-Figure7.13-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000055_978-1-4684-1500-1-Figure7.13-1.png", + "caption": "Figure 7.13 In the lefthand column, these simple components will tangle since they each have hooks that will engage in adjacent", + "texts": [ + " Another variation of this principle is to use adhesives or 'snap in' plastic legs to achieve assembly. Both methods are used in place of traditional fasteners (eg bolts, screws, dowels or rivets) which require the costly manufacture of a hole, which is then filled with an expensive item. It is necessary to ensure that the component is presented at a known and consistent rate to the robot pickup station by the feeder device. Unless items are specifically designed for auto matic processing, problems of tangling, nesting, telescoping and shingling are likely to occur: 1. Figure 7.13 shows three types of components that can be functionally 'reduced' to hooks and eyes to engage into each other. Tangling is avoided if the design concepts shown in Figure 7.13 are followed. 2. Figure 7.14 shows a plain conical item. Adjacent items to this design will nest and lock together. To avoid this a stepped inner shoulder is used to prevent locking of 102 Product and process design for assembly WILL TANGLE WILL NOT TANGLE components. The simple solutions are shown in the righthand column. The closed spring is a common occurrence and the closed split ring will still permit assembly to another component through radial pressure at the joint line. The third example is perhaps more radical, but under certain conditions could be cost effective" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002957_kem.473.75-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002957_kem.473.75-Figure2-1.png", + "caption": "Fig. 2 Schematic drawing of the cross section of a deposited specimen", + "texts": [ + " It is also possible to define the Power Density [W/mm 2 ], as derived parameter, a function of P and Aspot (area of the laser beam focus), according to Eq. 1. 2 4 spot P P Power Density dA \u03c0 = = \u22c5 . (1) The mathematical model used in this work, is based on the following hypotheses: 1) The deposition process is stationary: the quantity of powder at each deposited track is identical; the cross section area of each track is uniform [7]. 2) The cross section of the deposited track is geometrically similar, with some degree of approximation, to a circular segment of height H and width W (Fig. 2). The area of this section is also calculated as a function of the only variable W, once fixed a certain value of the ratio between H and W (RH/W ratio). This approximation is justified, neglecting gravitational forces and the variation of the density of the melt zone with the temperature and with the concentration of alloy components. In fact, if the surface tension remains constant, the balance of forces that occurs at the interface molten zone/air ensures that its profile has radius constant r [6, 7]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000742_09544054jem913-Figure9-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000742_09544054jem913-Figure9-1.png", + "caption": "Fig. 9 Three scanning modes of the multi-outline sections: (a) jumping mode; (b) dividing mode; (c) splitting mode", + "texts": [ + " Although the problem of the former two scanning modes could be avoided by adopting a high energy density of the electron beam, a high energy density would lead the temperature of the upper layer to rise to a high value that will induce a large amount of volatilization of elements. Unlike the former two scanning modes, the rotated scanning mode can reduce the first line to a point, which will increase the heat input of the initial scanning by reducing the speed of heat transfer; therefore, the powder will be fully melted and the bonding quality between the two layers will greatly improve. The two common zigzag scanning modes of multioutline sections are shown in Figs 9(a) and (b). In Fig. 9(a), the scanning lines jump back and forth between subzone 2 and subzone 3. As for the forming of full-density parts which have less space between the filling lines, this scanning method will Proc. IMechE Vol. 221 Part B: J. Engineering Manufacture JEM913 IMechE 2007 at Universidad de Valencia on July 20, 2015pib.sagepub.comDownloaded from result in many vacancy paths and decrease the forming efficiency. In addition, the scanning interval between the two filling lines in the subzone is long as the scanning sequence of filling lines is dc!jump! ba!ef!jump!gh, which is shown in Fig. 9(a). The interval between dc and gh in subzone 2 includes not only the scanning time between ba and ef in subzone 3 but also two jump times. When scanning the filling line gh of subzone 2, the filling line dc has already solidified or will solidify. So this jump on\u2013off scanning mode makes it more difficult than the continuous scanning mode to realize tight bonding of the two filling lines dc and gh. In Fig. 9(b), the multi-outline section is divided into several scanning subzones by making the filling lines parallel, and these subzones are connected to each other end to end to make up a continuous scanning path, such as 1!2!3!4. Although the vacancy path could be reduced, the length of the first scanning line is increased too. According to the scanning sequence 1!2!3!4, the two first scanning lines ab (subzone 3) and cd (subzone 4) of each subzone will appear, which originally did not exist, and the scanning flaws are inclined to rise. Therefore, a new kind of scanning mode, which is called a split mode, is proposed according to the rule of heat transfer in EBSM. The process of the split mode is shown in Fig. 9(c); the multi-outline section is divided into two separated subzones along the perpendicular of the filling lines with a slice and the number of subzones is fewer than in Fig. 9(b). By this split mode, the length of filling lines is greatly reduced compared with those Figs 9(a) and (b) and the heat transfer speed within the section will be reduced too, which will increase the forming quality. Furthermore, the scanning process of each subzone is continuous, and the path of heat transfer is the least, which ensures continuity of the thermal field. In Fig. 9(c), the length of the filling lines is approximately the same as the others for each subzone, which ensures stability of the EBSM process too. In the split mode, there are common edges between subzones 1 and 2. Since the thickness of the interspace is nearly zero and the heat-affected zone of the electron beam has an effect on the edges, the common edges will be joined by the electron beam. In conclusion, the method of the split mode is that the multi-outline section must be divided along the perpendicular of filling lines; the principles of the split mode are as follows" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003909_j.scient.2011.08.026-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003909_j.scient.2011.08.026-Figure2-1.png", + "caption": "Figure 2: Spatial mobile robot in a real environment.", + "texts": [ + " In this paper, the environmental objects are generally modeled as ellipsoids, and due to obstacle avoidance ofmobilemanipulator in cluttered environment, the new dimensionless potential functions are defined. Furthermore, it should be mentioned that a lot of ellipsoids can be enclosed to the convex object, but fitting the best ellipsoid to the object can be treated as an optimization problem. Moreover, mobile robot parts (the platform and the arms), walls, etc. are usually rectangular objects, and it is obvious that the rectangular cuboid must be enclosed with the optimal ellipsoid. Figure 2 shows a non-holonomic spatial mobile manipulator in a real environment, and Figure 3 depicts the enclosed ellipsoid to mobile manipulator parts in the presence of some common obstacles. In addition, for obstacle avoidance of colliding objects, potential function is applied to performance index, where it is a function of the dimensionless parameter, dij, and can bewritten as: \u2016Li\u20162 wobij = wobij 1 d2ij . (6) The value of the potential function is increasedwhen themobile robots move closer to the environmental obstacles" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003169_0369-5816(65)90020-7-Figure8-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003169_0369-5816(65)90020-7-Figure8-1.png", + "caption": "Fig. 8. Vessel with short pad reinforcement.", + "texts": [ + " The main s t rengthening effect of the ext ra th ickness a s so - ciated with a > l or /~>1 is the hoop force aoat or e0/3T which is l inear with thickness . For design use , therefore , a or /3 f rom eqs. (10a), ( l l a ) or fig. 7 should be mult ipl ied by ~ to obtain t rue full s t rengthening. 4. SHORT PAD REINFORCEMENT The l imit p r e s s u r e for a vesse l with a nozzle opening re inforced with a short pad, as shown in Pad: Nozzle: Qc = UcX - Clc , (12a) Mxc = \u00bdUcX2 + C l c X + C2c . (12b) Qp = Upq) + Clp , (12c) M~b p = \u00bdApUpqb 2 + Clpq~ + C2p. (12d) fig. 8, may be found with the methods of the p r e - vious section. The same 3-hinge c i rc le col lapse mechan i sm is the assumed mode of fa i lure . The hinge c i r c l e s in the nozzle at X = X 0 and at the junct ion are as before, and the one in the vesse l at q~ = ~b 0 is a ssumed to l ie in the shell beyond the pad. The hoop s t r e s s for 0 -< X -.< XO, dp i --< -< ~b 0 is at yield and the prev ious genera l solut ion found for eqs. (2) holds for both pad and shell . In tegrat ion constants for the pad a re det e rmined by equi l ibr ium enforcement between pad and shell. Otherwise the same condit ions exist and these a re used to find the r ema in ing in tegrat ion cons tants , hinge c i r c l e locat ions, and l imi t p r e s su r e . With re fe rence to fig. 8, the following notation is adopted t Uc:P-aoO, = \u00bdPn s U s - Tse 0 , % = \u00bd p A p - 0 . Solutions to the equi l ib r ium equations for the three pa r t s are as follows Shell: Qs = Us4 + Cls , (12e) M4s = \u00bdAsUs~b2 + C l s 4 + C2s . (12f) The integration constants are determined f rom the following boundary conditions: a t X = X 0 , Qc = 0 , t MXc =Me0 =(~0-- ' (/ a t 4 = 4 , , Qp = Q s , M 4 p = M4 s , a t ~ = 4 s Qs =0, 2T s Mdp s = MxO = a 0 A s After resolution of the integration constants, eqs" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002201_6.2009-6286-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002201_6.2009-6286-Figure1-1.png", + "caption": "Figure 1. Schematic of a Hypersonic Vehicle with Air-Breathing SCRAMJET Engine", + "texts": [ + " In this work it is assumed that these forces and moments are computed as a function F(x,u) of the state and control vectors by a computer program. Explicit analytical use of the right hand side of Eq. (1) is not made anywhere in the controller design. ),(][ uxFGMTDL ip = (2) As mentioned earlier apart from the state components such as velocity, altitude and angle-of-attack it is also of interest to compute and control variables such as Mach numbers and temperatures at various locations of the hypersonic vehicle as shown in Figure 1. Computation of these variables is essential for the computation of forces and moments, therefore, it is assumed in this work that these variables are also obtained from a computer program as a function z(x, u) of the state and control vectors. [ ] ),(..222111 uxzmTpMTpM tip =\u2206& (3) III. Discretization Model predictive controller formulations are inherently discrete-time formulations. Therefore, the first step in designing a model predictive controller involves discretization of the nonlinear dynamic system" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000220_0040517506053911-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000220_0040517506053911-Figure1-1.png", + "caption": "Figure 1 Scheme of the electrochemical cell consisting of PVC plates 1\u20134, two electrodes, rubber ring fittings and a PVC tube.", + "texts": [ + " Due to this lack of information phenomena such as non-reproducibility and unpredicted behavior cannot be explained. In order to provide a first answer to this problem a tool is presented in this paper that offers the possibility to measure and control the quality of the electrodes used in intelligent textiles. This tool is an electrochemical conductivity cell that is characterized in this paper and used for the study of different types of textile electrodes. The electrochemical cell consisted basically of four PVC plates, as shown schematically in Figure 1. The electrodes were positioned between the outer and the inner plates (between plates 1 and 2 and between plates 3 and 4), the inner plates having a hole that allowed contact between electrode and electrolyte. The distance between the electrodes was determined by the length of the tube positioned between plates 2 and 3, which was filled with electrolyte solution. The complete structure was kept together with screws and rubber fittings were used to avoid leaking of electrolyte solution between electrode and plate 2, plate-2 and tube, tube and plate-3 and plate-3 and electrode" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000706_j.triboint.2007.12.003-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000706_j.triboint.2007.12.003-Figure1-1.png", + "caption": "Fig. 1. Two types of tilting pad: (a) rocker backed", + "texts": [ + " The previous studies reported that the bearing performance is affected by turbulent flow, thermo-elastic interactions, pad and pivot deformation, and inlet pressure [1\u20134]. The studies contribute to revealing characteristics of the tilting pad journal bearing. It, however, was reported that the bearing performance can be greatly affected by supporting mechanism of the pad which had hardly been considered as a factor when predicting the performance. In 1999, Wygant et al. [5,6] performed experiment on the performance of tilting pad journal bearing, such as journal locus and dynamic coefficient of the bearing. Fig. 1 depicts two pads with ee front matter r 2007 Elsevier Ltd. All rights reserved. iboint.2007.12.003 ing author. Tel.: +8242 869 3215; fax: +82 42 869 3210. ess: taeho@kaist.ac.kr (K.W. Kim). different supporting mechanism used by Wygant et al. Fig. 1(a) shows the rocker backed tilting pad and Fig. 1(b) represents the ball and socket tilting pad. It was found from their experiment that the results for the ball and socket tilting pad were not explained by the previous theories, whereas the results for the rocker backed tilting pad coincided with the previous theories. In the results for the ball and socket tilting pad, the eccentricity direction of journal did not coincide with the load direction and the cross-coupled dynamic coefficients had non-zero values. These phenomena are not explained by the existing theories. It was also found from another research that the bearing performance can be affected by supporting mechanism of the pad. In 1999, Pettinato and Choudhury [7,8] measured pad temperature profiles for the two pads depicted in Fig. 1 and reported the differences. In 2005, Sabnavis [9] studied for shaft tracking behavior of pads in a ball and socket type tilting pad journal bearing and tried to explain the relation between the shaft tracking behavior and the pad\u2013pivot friction. The largest difference between the rocker backed tilting pad and the ball and socket tilting pad is the friction mechanism. The tilting pad of ball and socket type slides ARTICLE IN PRESS Nomenclature Ad pulse amplitude (m) ep eccentricity of the journal center (m) d preload (m) Ff friction force on the pad (N) fpx, fpy force caused by fluid film pressure (N) h local film thickness (m) Ip moment of inertia for the pad (kgm2) L bearing length (m) Lg distance between pads (m) Mf pad moment caused by pad\u2013pivot friction (Nm) Mp pad moment caused by fluid film pressure and shear stress (Nm) Mt Mf+Mp, total pad moment (Nm) p film pressure (Pa) R bearing radius (m) Re VCpr/Z, Reynolds number (\u2013) Rei Vh(ys)r/Z, local Reynolds number at the pad inlet (\u2013) rf radius of ball pivot (m) t time (s) td pulse interval (s) uim mean fluid velocity at the pad inlet (m/s) V velocity of journal surface (m/s) w, wx, wy external load on the journal (N) wp normal force on the pad (N) X, Y coordinates for relative position of journal center to bearing center (m) xb, yb displacement of bearing center (m) xj, yj displacement of journal center (m) x, z coordinates for bearing surface (m) G Lg/h(ys), non-dimensional distance between pads (\u2013) g tilt angle of pad (rad) Z lubricant absolute viscosity (Pa s) y x/R, angular coordinate (rad) yo attitude angle (rad) ys, yp start, pivot angle of each pad (rad) m friction coefficient between ball and pad (\u2013) o angular velocity (rad/s) z axial coordinate at pad inlet (\u2013) fd pulse direction (deg.) S.G. Kim, K.W. Kim / Tribology International 41 (2008) 694\u2013703 695 on the ball whereas the tilting pad of rocker back type rolls on the bearing housing. Therefore, the resistance against pad motion of the ball and socket tilting pad is larger than the rocker backed tilting pad\u2019s. The resistance against pad motion is generated from the pad\u2013pivot friction and causes the difference between bearing characteristics of the two types depicted in Fig. 1. Thus, the pad\u2013pivot friction might be considered as an external force when calculating the tilt angle of pad if the pad\u2013pivot friction is large. In 1995, Nicholas and Wygant [10] pointed out the need for considering the pad\u2013pivot friction as a factor when predicting the bearing performance. There, however, are a few theoretical researches taking into account the pad\u2013 pivot friction and no mathematical models for the pad\u2013 pivot friction based on the physical meaning of the friction. In 1999, Kozanecki [11] reported that the pad\u2013pivot friction changes the dynamic behaviors of the tilting pad gas journal bearing in his numerical study" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000004_robot.1986.1087601-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000004_robot.1986.1087601-Figure1-1.png", + "caption": "Figure 1. Screw and Screwdriver.", + "texts": [ + ") A f A FEW ILLUSTRATIONS: This section shows applications to simulation of tool-workpiece contact (a screw-driver) and biped ice-skating. The concern in these examples is not so much that the stated constraints are accurate (they are purely pedagogical), as to illustrate that constraints are conveniently implemented once devised. Although these illustrations are for fixed constraints, the matrices could reflect a full articulated-body inertia [3, 41 such as might arise if the robot manipulates another kinematic chain. Screwdriver: (See figure 1.) The slots in the head of the screw constrain the screw-driver tip to be translationally motionless in the x and y directions. The z translational acceleration a, is the pitch p of the screw threads (divided by 2 ~ ) times the angular acceleration a, about L. None of the angular accelerations nor translational forces are constrained by the problem geometry. (However, if the forces in the x or y directions grow too large the robot has pushed the screw over; and if the force in the I: direction becomes negative the robot has lifted the tool from the screw" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002376_j.fusengdes.2011.01.018-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002376_j.fusengdes.2011.01.018-Figure2-1.png", + "caption": "Fig. 2. Schematic diagram of hybrid robot.", + "texts": [ + " The remainder of this paper is organized as follows: Section 2 introduces a general methodology of the MSA; Section 3 describes the modeling of the typical Stewart structure; Section 4 gives a finial stiffness model by integrating the parallel mechanism and the serial mechanism; Section 5 presents the numerical results of stiffness; and Section 6 summarizes the main contributions of this work. 2. Description of matrix structural analysis The schematic representation of the kinematic chain of the IWR is presented in Fig. 2. The coordinate Xg 0 Yg 0 Zg 0 is defined as the global frame, and all local coordinates are related to the global frame: Xg 1 Yg 1 Zg 1 moves along the gear track and Xg 2 Yg 2 Zg 2 along the ball screw; Xg 3 Yg 3 Zg 3 rotates around the Zg 2 axis; Xg 4 Yg 4 Zg 4 is the basement coordinate of the Stewart and rotates around the Xg 3 axis; Xg 5 Yg 5 Zg 5 is fixed in the centre of the end-effector as the tool frame. The analytical stiffness model of the basic element evaluated in this paper is based on MSA", + " 4, the coordinate frame Xg 4 Yg 4 Zg 4 is attached to the base- ent in the geometric centre. The coordinate frame B (Xg 5 Yg 5 Zg 5 ) is ttached to the moving platform, and its origin is located at the mass entre. Taking account of the deformations in the six base joints and ydraulic limbs, the stiffness matrix of the parallel mechanism is btained in the same way achieving Eq. (8) stw = (Jstw[diag[Kli]] \u22121JT stw) \u22121 (10) here Jstw is the Jacobian matrix of the Stewart, and li = diag[Khy i Kft i]. . Stiffness modeling of hybrid robot The hybrid robot (Fig. 2) is composed of the Stewart, the elevatng part and the track basement. Through the mechanism analysis, he elevating part is considered as a crank-slider mechanism: the ase frame of Stewart platform is regarded as the crank while the ydraulic limb is the actuator of the mechanism. The stiffness of he actuator is transformed into the local compliant spring located t the crank joint Og 3 and denoted by k 4. The stiffness of the gear air in the track is denoted by kx1. The rotation around Zg 2 axis is riven by an epicycle gear, and its stiffness is denoted by k 3", + " Employing the principle of virtual work on the hybrid robot joints leads to: C = J \u22121JT (12) where C is the 6 \u00d7 6 compliance matrix of the whole hybrid robot, and = diag[Kstw k 4 k 3 ky2 kx1] is a 10 \u00d7 10 diagonal matrix of the stiffness of all joints. The stiffness of the whole hybrid robot is obtained as the inverse of the compliance matrix: K = C\u22121. 5. Numerical evaluation results Based on the above model, the deformations of some certain workspace are investigated under the external loads. One example is given for demonstration. The work space of the end-effector was a 200 mm \u00d7 200 mm \u00d7 200 mm cube (Fig. 2); the end-effector frame has no rotation with respect to the basement frame of the Stewart. The robot worked along the borders of the workspace and the external load of 5 kN was vertical to the Stewart basement. The deformations are illustrated in Fig. 7. 1 g and o w w d t r e b r r m t p c r [ [ 842 M. Li et al. / Fusion Engineerin Due to the redundant freedom in the robot, the configuration f the serial part in the robot is pre-determined, while the cubic orkspace is reached by the Stewart. In Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001321_09544100jaero509-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001321_09544100jaero509-Figure1-1.png", + "caption": "Fig. 1 Schematic of the variable stability projectile configuration", + "texts": [ + " The system consists of two major components, namely a main projectile body and an internal translating mass. The main projectile body is largely a typical projectile with the exception of an internal cavity that hosts an internal mass. The internal mass is free to translate within the main projectile cavity. An actuator inside the projectile exerts a force on the internal mass as well as the main projectile to move the mass inside the cavity to a desired location. A schematic of the variable stability projectile is shown in Fig. 1. Note that the cavity is aligned with the body centre-line (axis of symmetry). Two reference frames are used in development of the equations of motion for the system, namely the inertial and projectile reference frames. The two frames are linked by the following orthonormal transformation matrix\u23a7\u23a8 \u23a9 I P J P K P \u23ab\u23ac \u23ad = \u23a1 \u23a3 c\u03b8 c\u03c8 c\u03b8 s\u03c8 \u2212s\u03b8 s\u03c6s\u03b8 c\u03c8 \u2212 c\u03c6s\u03c8 s\u03c6s\u03b8 s\u03c8 + c\u03c6c\u03c8 s\u03c6c\u03b8 c\u03c6s\u03b8 c\u03c8 + s\u03c6s\u03c8 c\u03c6s\u03b8 s\u03c8 \u2212 s\u03c6c\u03c8 c\u03c6c\u03b8 \u23a4 \u23a6 \u23a7\u23a8 \u23a9 I I J I K I \u23ab\u23ac \u23ad = [TIP] \u23a7\u23a8 \u23a9 I I J I K I \u23ab\u23ac \u23ad (1) The cavity containing the internal translating mass is fixed and extends along the projectile\u2019s axis of symmetry, in this case the I P axis" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002708_acc.2010.5530997-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002708_acc.2010.5530997-Figure2-1.png", + "caption": "Fig. 2. Dubins path based waypoint(DWP) [11, 12].", + "texts": [ + " 1) Dubins path based waypoint (DWP) [11, 12]: Dubins path [10] is well-known as the shortest path for a vehicle in two-dimensional plane from an initial position and heading to a final position and heading under a bounded turning radius, which consists of three segments, e.g. -- a minimum radius arc, a straight line segment and another minimum radius arc, referred to as a circle-line-circle (CLC) Dubins path. The Dubins path can be easily obtained from the geometrical relations as can be seen in Ref. [13]. The DWP for the UAV guidance is determined as the end of the line segment in CLC Dubins path as shown in Fig. 2. 2) Waypoint based on a tangent to a circular path (TWP): The tangent to the circle is much simpler than the CLC Dubins path and therefore, is easily implementable onboard. The tangent point is set as the final turning waypoint and is determined as the tangent point of the nearest circle as shown in Fig. 3. C. Prediction of rendezvous point and time Time-to-rendezvous can be estimated using the current UAV position, velocity, and heading, and those of the future target information at rendezvous that is estimated from the current target position, heading, velocity, and turn rate" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001395_bf00045793-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001395_bf00045793-Figure1-1.png", + "caption": "Figure 1. (K > 0).", + "texts": [ + "15) 1 - - xs po(2-- xpo) and tha t these, together with (3.13) imply u e c~(D) and du u = 0 , - - = - l o n ~ D . On Consider now the last o f (3.14), and assume first tha t ~c > 0. I f D is a disk, po = l /x , and (3.12) gives igs 2 f ( s ) = s-- - - . 2 Thus, in this instance 1 = p o - r - -- (po- r) 2 p o where r is the distance between x and the center o f D. Therefore 2 Au = - - - Po which confirms the last o f (3.14) for D a disk. Suppose that D is not a disk. Choose x0 ~ D, and let yO e OD be such tha t 5(x \u00b0) = Ix \u00b0 - y \u00b0 l (See Fig. 1). Put t/ = 1/x, and let z be such tha t C,(z) is tangent to aD at yO and n(y\u00b0) \u2022 ( y O _ z ) > 0. Define 6' o n D by 5 ' (x) = min [ y - x l Y~Cn(z) for every x ~ D. Let ~ > 0 be such that ~ 6(x) < 6'(x) < Po for every x ~ Sc(x\u00b0), and set u'(x) = f ( a ' ( x ) ) 1) The existence o f ( is ensured by the a s sumpt ion tha t po > P. for all x e S;(x\u00b0). By (3.15), u ' e c~2(S;(x\u00b0)). (3.16) Since 6'(x \u00b0) = 6(x \u00b0) and 6'(x) > 6(x) for every x ~ S~(x\u00b0), and because f ' > 0 o n [0, Po], there follows u(x) < u'(x), u'(x \u00b0) = u(x\u00b0)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000825_978-1-4020-9137-7_15-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000825_978-1-4020-9137-7_15-Figure2-1.png", + "caption": "Fig. 2 Twister mini UAV. a Free-body diagram. b Actuators of the vehicle", + "texts": [ + " Additionally, the fact that the propellers are mounted over the same axis of center of gravity (CG), represents a mechanical advantage because the inherent adverse torque gyroscopic and blade\u2019s drag torques) is considerably reduced. The vertical roll motion is controlled the rudder\u2019s deflection . The vertical pitch is controlled by the elevator deflection . Due to the counterrotating capabilities the yaw motion is auto-compensated, however the blade geometry is not exactly the same, therefore we handle the yaw remanent by propellers differential angular speed (see Fig. 2). 2.1 Longitudinal Dynamic Model In this section we obtain the longitudinal equations of motion of the Twister through the Newton-Euler formulation. Let I={iIx , kI z } denote the inertial frame, B={iBx , kB z } 1hobby-lobby.com/pogo.html. denote the frame attached to the body\u2019s aircraft whose origin is located at the CG and A= { iAx , kA z } represent the aerodynamical frame (see Fig. 3). Let the vector q = (\u03be, \u03b7)T denotes the generalized coordinates where \u03be = (x, z)T \u2208 2 denotes the translation coordinates relative to the inertial frame, and \u03b7 = \u03b8 describes the vehicle attitude" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001640_j.mechmachtheory.2009.09.010-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001640_j.mechmachtheory.2009.09.010-Figure3-1.png", + "caption": "Fig. 3. The local coordinate system of the ith strut.", + "texts": [ + " Thus, the rotation matrix is: oRo0 \u00bc Rot\u00f0z;/z\u00deRot\u00f0y;/y\u00deRot\u00f0x;/x\u00de \u00f01\u00de Schematics of the 8-PSS redundant parallel manipulator and its non-redundant counterpart\u20146-PSS parallel manipulator. (a) Sequence numbers of SS are written in black. (b) Sequence numbers of the 6-PSS are written in violet. (For interpretation of the references in colour in this figure legend, der is referred to the web version of this article.) The angular velocity of the moving platform is given by [12] x \u00bc _/x _/y _/z T \u00f02\u00de The orientation of each kinematic strut with respect to the fixed base can be described by two Euler angles. As shown in Fig. 3, the local coordinate system of the ith strut can be thought of as a rotation of /i about the z axis resulting in a Ci x0iy 0 iz 0 i system followed by another rotation of ui about the rotated y0i axis. So the rotation matrix of the ith strut can be written as: oRi \u00bc Rot\u00f0z;/i\u00deRot\u00f0y0i;ui\u00de \u00bc c/icui s/i c/isui s/icui c/i s/isui sui 0 cui 2 64 3 75 \u00f03\u00de where s/ denotes the sine of angle / while c/ denotes the cosine of angle /. The unit vector along the strut in the coordinate system O xyz is wi \u00bc oRi iwi \u00bc oRi 0 0 1 2 64 3 75 \u00bc c/isui s/isui cui 2 64 3 75 \u00f04\u00de So the Euler angles /i and ui can be computed as the following: cui \u00bc wiz sui \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi w2 ix \u00few2 iy q ; \u00f00 6 ui < p\u00de s/i \u00bc wiy=sui c/i \u00bc wix=sui ifui \u00bc 0; then /i \u00bc 0 8>>>>>< >>>>: \u00f05\u00de 2" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003865_j.jtbi.2011.12.003-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003865_j.jtbi.2011.12.003-Figure2-1.png", + "caption": "Fig. 2. (a) Lateral and (b) dorsal view of Cataglyphis bicolor and Cataglyphis fortis, respectively. The body parts (head H, thorax T, petiolus P, gaster G) and measured dimensions (see Table 1) are indicated. The white dot in (b) marks the center of gravity when the gaster is in a horizontal position. Drawings adapted from Wehner (1983) and Wehner et al. (1994).", + "texts": [ + " Some Saharan desert ants of the genus Cataglyphis, especially those belonging to the bicolor species group (e.g., C. bicolor) and the albicans species group (e.g., C. fortis) are able to raise the gaster until its major axis is vertical (Fig. 1). This position contrasts with the lowered orientation in which the major axis of the gaster is nearly horizontal, and aligned with the ant\u2019s other body parts (Wehner, 1982, 1983). The ability of raising the gaster is associated with a nodiform or cubiform rather than squamiform petiolus (Fig. 2) (Wehner et al., 1994). The squamiform petiolus, which is typical for formicine ants in general, is still present in some more original Cataglyphis species such as C. emmae, the members of the cursor species group, and C. bombycina (Agosti, 1990). These species \u2013 most remarkably C. bombycina, the \u2018\u2018silver ant\u2019\u2019 of the Sahara, the Sinai and the deserts of the Arabian Peninsula \u2013 are unable to raise the gaster. Even though they reach high running speeds, they proceed along almost straight lines and decelerate or even stop when turning (Wehner and Wehner, 1990)", + " Here we test the hypothesis, promoted almost 30 years ago (Wehner, 1982, 1983), that the erect position of the gaster reduces the ant\u2019s moment of inertia and hence facilitates maneuverability. A lowered moment of inertia would allow the ant to perform fast turns with reduced levels of torque generated from the motion of its legs. We investigate this concept quantitatively by modeling the moment of inertia for the ant with its gaster raised and lowered. In addition, we consider an ant running on circular and sinusoidal paths to estimate the relative levels of torque and foot-thrust required when the gaster is erect and lowered. As illustrated in Fig. 2, Cataglyphis has four main body parts. They are the head, the thorax (alitrunk), the petiole (petiolus) and the gaster (metamosa) (Wehner, 1983; Wehner et al., 1994). In addition, there are legs, mandibles, antennae and other small appendages, whose geometry we ignore for the purpose of estimating the insect\u2019s moment of inertia. The dimensions (defined in Fig. 2) and mass of each body part are listed in Table 1 for workers of C. bicolor and C. fortis. The mass of each body part was measured on freshly killed animals, and all appendages of the head were attached. Negligible desiccation occurred in the few seconds involved in handling, as is confirmed by the data for wet brains provided by Wehner et al. (2007). In each case, measurements were made on 3 animals, and the mean values used to prepare Table 1. The measured ants were all taken while on foraging runs outbound from the nest, and therefore following tortuous paths", + " As a consequence, the dimensions and masses in Table 1 are those relevant to the ant\u2019s inertia when it is making its rapid turns. After securing food, the ant returns to the nest on relatively straight paths. The inertia of the animal carrying a food item is not relevant to our study. In view of the shapes of the body parts, we model the head, thorax and gaster as ellipsoids and the petiolus as a sphere. The lay-out of our geometric model is shown in various states in Fig. 3. As can be seen in Fig. 2a, the head is oriented so that its short axis, (i.e. height) is oriented at approximately 451 to the horizontal axis of the ant (Wehner, 1982), which we define to be the x-axis (see Fig. 3a). The y-axis is parallel to the width dimension of all body parts and the z-direction is vertical. The long axis (i.e. the length LT) of the thorax is, in the first instance, assumed to be aligned with the x-axis, as illustrated in Fig. 3. We also consider the case where the thorax is inclined by f\u00bc201, sloping downwards from the head to the petioles", + " the length LG) is assumed to be aligned with the x-axis, as shown in Fig. 3a. When fully elevated, it is assumed to be vertically above the petiole, as shown in Fig. 3b. The gaster may be at an orientation intermediate to the horizontal and the vertical, in which case it will have an angle of inclination, c, to the horizontal as shown in Fig. 3c. Thus c\u00bc0 is a horizontal gaster, whereas c\u00bcp/2 is a vertical one. The head is assumed to be attached to the thorax such that the center of its crown, as marked in Fig. 2, is vertically above the proximal end of the thorax. The origin of the Cartesian coordinate system is taken to lie at the center of mass of the ant in the x\u2013y plane, as shown in Fig. 3a. Note that throughout this paper we use the general term \u2018\u2018thorax\u2019\u2019 rather than \u2018\u2018alitrunk\u2019\u2019 for the middle part (mesosoma) of the body. In the nomenclature of hymenopteran morphology \u2018\u2018alitrunk\u2019\u2019 would be the more appropriate term (see also legend of Table 1). We first compute the center of mass of the whole ant", + " A is the area of the elliptical cross section in the sagittal plane at yC and therefore having semi-axes xo ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 y2 C=y2 o q and zo ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 y2 C=y2 o q . Given that the area of an ellipse is p times the product of the 2 semi-axes, and that the volume of an ellipsoid is 4p/3 times the product of the 3 semi-axes, we obtain the result in Eq. (7). In addition we use yo \u00bcWI=2, where WI is the width of the body part, as defined in Fig. 2 and tabulated in Table 1. To allow for a gaster and a thorax that may be raised above the horizontal orientation, and to account for the head, we introduce a change of variables for xC given by xC \u00bc xcosc zsinc \u00f08\u00de where the coordinates \u00f0x,z\u00de are indicated in Fig. 3c. When xC in Eq. (8) is squared, the term containing the product xz gives no contribution to the resulting integral, and we then deduce that rI Z VI x2 C dV \u00bc 1 20 mI\u00f0L 2 I cos2c\u00feH2 I sin2c\u00de \u00f09\u00de on similar grounds to those that gave us the result in Eq" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003592_978-3-319-06698-1_33-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003592_978-3-319-06698-1_33-Figure2-1.png", + "caption": "Fig. 2 Watt I six-bar linkage that passes through eight specified task positions", + "texts": [ + " The total degree of these equations is (2 \u00b7 32 \u00b7 5)N\u22121, which for N = 8 is approximately 4.78\u00d7 1013. To compute the multihomgeneous degree, we introduce the N + 1 groups, For N = 8 this grouping yields a nine-homogeneous Bezout degree of 3.43\u00d7 1010. The synthesis equations were validated by generating a few solutions using an implementation ofNewton\u2019smethod provided by theMathematica computational software package called FindRoot. We solved for the task positions listed in Table 1. Example solutions are listed in Table 2. Solution 1 is shown in Fig. 2. Newton\u2019s method was used to solve the synthesis equations for a randomized set of 100,000 of start points. The computation took 46min. All computations of this chapter were done in parallel on a 64 core machine. The start point values of the isotropic coordinate pairs (A, A\u0304), . . . , (H, H\u0304) were randomized within a 10 \u00d7 10 box centered on the origin of the complex plane. The start point values of (S j , S\u0304 j ), j = 1, . . . , 7 were specified to be random complex numbers of unit magnitude. All isotropic coordinate start points maintained conjugate relationships throughout randomization" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002651_j.jnnfm.2011.08.003-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002651_j.jnnfm.2011.08.003-Figure1-1.png", + "caption": "Fig. 1. Schematic diagram of the squeeze flow between two parallel disks (dark region is the core of the fluid with high viscosity).", + "texts": [ + " Then, the effects of fluid properties, disks velocity, gap width and slip coefficient upon pressure, pressure gradient and squeeze force are presented according to the three dimensionless variables (viscosity ratio, slip coefficient and yield number). The paper is organized as follows. First, the mathematical models are presented in Section 2. Afterwards, the analytical solutions are detailed in Section 3. Next, the results are discussed in Section 4. Finally, concluding remarks are given in Section 5. The flow system shown in Fig. 1 consists of the squeeze flow of a fluid within a narrow gap between two parallel disks. The plates of radius Ra are separated by 2h and translated towards each other with a relative velocity 2 _h. This squeezing speed is obtained by the squeeze force F applied to the disks. The governing differential equations are written in cylindrical polar coordinate system(r,h,z). For symmetry reasons, the dependence on coordinate h terms can be omitted. Besides, for a small aspect ratio h/Ra 1, the pressure may be considered as constant in the z-direction and the lubrication theory can be used to balance pressure and shear forces", + " In the case of the analysis of the fluid squeezing flow with slip at the walls, the slip condition is given by: u \u00bc bsrz\u00f0z \u00bc h\u00de \u00bc b dp dr h; \u00f05\u00de where b is the slip coefficient. While the situation in which b = 0 corresponds to no slip, full lubrication is described in the limit b ?1. It is worth noting that the slip coefficient should be quite small to be able to consider the lubrication approach. The flow field is divided into a Newtonian region with high viscosity and a bi-viscosity region with yielded/unyielded fluids, intersecting the disks at r = R0 (Fig. 1). In the first stage of this development, the dimensional expressions of radial velocity and continuity equation for both regions will be given. In the second stage, the dimensionless expressions of the pressure gradient, pressure and squeeze force will be developed according to three dimensionless parameters which are the viscosity ratio, slip coefficient and yield number. A Newtonian region of r 6 R0 and a bi-viscosity region of r > R0 are separately considered with different solutions. In the Newtonian region, the fluid can be considered as a Newtonian fluid with high viscosity, whose constitutive relation is described by Eq" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001789_s00707-008-0132-5-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001789_s00707-008-0132-5-Figure1-1.png", + "caption": "Fig. 1 Orbiting satellite with fluid rings", + "texts": [ + " These aspects are discussed in the present paper along with the detailed analyses of the system including stability analyses and numerical simulations. The system parameters are presented in dimensionless form so that the scope of application of the results no longer depends upon the particular satellite size, mass and inertia properties or fluid properties. The system under study comprises of three fluid rings attached to a satellite at its three principal pitch, roll, and yaw axes, respectively (Fig. 1). The fluid inside the ring provides inherent damping to the satellite attitude motion. But as the damping torque is found to be low, it may take longer for the attitude motion of the satellite to reach desired attitude angles. With a view to stabilize the satellite attitude motion effectively, each fluid ring is equipped with a pump. A simple controller inside the pump is designed to regulate the fluid flow in each ring. The liquid propellant present in the satellite can be used in the fluid rings if feasible; otherwise a different fluid could be supplied", + " The Euler\u2019s moment equations are used to obtain the governing ordinary differential equations of motion for the proposed system. In Sect. 3, the linearized system model is derived and the stability analysis is presented. The control laws are derived in Sect. 4. Finally, for a detailed assessment of the proposed attitude stabilization strategy, the set of governing equations of motion is numerically integrated and the effects of various system parameters on the system response are examined in Sect. 5. The system model comprises a satellite and three fluid rings (Fig. 1). Each fluid ring is fitted with a pump to regulate the flow of the fluid. The system center of mass \u2018S\u2019 lies on the center of mass of the satellite. As the focus is on studying the effects of fluid motion on the satellite attitude, the distance of the fluid ring from the center of mass is assumed negligible. The coordinate frame XoYoZo passing through the system center of mass S represents the orbital reference frame. Here the Xo-axis is taken along the normal to the orbital plane, the Yo-axis points along the local vertical and the Zo-axis represents the third axis of this right handed frame taken" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002969_j.proeng.2013.12.146-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002969_j.proeng.2013.12.146-Figure1-1.png", + "caption": "Fig. 1. (a) Picture of the friction test-rig available at the virtual vehicle competence center with engine under test; (b) Exemplary results obtained from the friction test-rig for an inline four cylinder gasoline engine (see also [1])", + "texts": [ + ": 0043 873 4006; fax: 0043 873 4002. E-mail address: hannes.allmaier@v2c2.at 13 The Authors. Published by Elsevi r Ltd. Selection and peer-review under responsibility of The Malaysian Tribology Society (MYTRIBOS), Department of Mechanical Engineering, Universiti Malaya, 50603 Kuala Lumpur, Malaysia Before any efficient measures to reduce friction in engines can take place, the main friction sources need to be known. At the Virtual Vehicle Competence Center, we use our friction test-rig as shown in Fig. 1(a) to investigate the sources of friction for a typical four cylinder gasoline engine; exemplary results for this engine are shown in Fig. 1(b). The chart confirms the commonly regarded main sources of friction: the piston-liner contact is the cause for about 60% of the total mechanical losses, while the journal bearings in the crank train (main and big end bearings) contribute together about 25%. Finally, the valve train represents the third main source of friction and typically causes losses that equal roughly about the half of the power losses in the journal bearings, or, more precisely, 15% of the total power losses shown in Fig. 1(b). These results differ significantly from the results for special single cylinder research engines [6], which shows the importance of measuring the actual engine to be investigated. Modern lubricants as they are used in ICEs show a complex rheological behavior, where the lubricant\u2019s dynamic viscosity strongly depends on temperature, pressure and shear rate in the contact [7]. To be able to simulate accurately the tribological working conditions in the journal bearings, these lubricant properties need to be taken into account [4-5]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001528_gt2008-50806-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001528_gt2008-50806-Figure2-1.png", + "caption": "Figure 2. Cutaway view of the rotordynamic simulator Test", + "texts": [ + " Since angular contact ball bearings are typically used in the class of machines for which GFBs are considered as replacements, it is appropriate to compare the misalignment tolerance of the two. The amount of misalignment ball bearings can tolerate depends on the size, load, speed, and required life, but according to Zaretsky [9], a typical allowable maximum angle of misalignment for angular contact ball bearings is 3E-4 radians. The current test program was instigated to quantify the level of misalignment GFBs can tolerate for comparison and to help guide future oil-free turbomachinery engineering design programs. The rotordynamic simulator test rig at NASA Glenn Research Center (Fig. 2)[10] was used to conduct misalignment tests on two journal GFBs. The specific geometry of the individual bumps is proprietary and the reader is referred to the patent for more details on the design [3]. However, the bearings are classified as generation III bearings as defined in [8] and the basic geometry used is listed in Table 1. Table 1. Gas Foil Bearing Geometry Nominal Shell Outside Diameter 63.5 mm Nominal Shell Inside Diameter 52.6 mm Nominal Shaft Diameter 50.8 mm Nominal Length 40.6 mm Number of Circumferential Bumps 35 2 Copyright \u00a9 2008 by ASME l=/data/conferences/gt2008/69978/ on 03/12/2017 Terms of Use: http://www", + ") and is roughly symmetric such that each journal bearing supports half the rotor weight for a loading of 6.0 kN/m2. The journal bearings are housed in independent structures that can be moved relative to each other in transverse and angular directions. The independent bearing supports allow the operator to impose a known misalignment on the two journal bearings using a laser based alignment system. Each foil bearing is mounted in a ball bearing supported rotating bearing carriage, as illustrated in figure 2. The alignment system, shown in figure 3, consists of two laser loaded From: http://proceedings.asmedigitalcollection.asme.org/pdfaccess.ashx?ur heads, each having a laser emitter and sensor. One head attaches to each rotating bearing carriage. The bearing carriages rotate through 180 degrees, and at three distinct angular positions, the laser alignment heads take measurements: \u00b1 90 degrees from top dead center, and top dead center. From these three measurements, the lateral and angular alignment of the central axis of the rotating bearing carriages is calculated" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000583_j.cma.2008.11.014-Figure8-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000583_j.cma.2008.11.014-Figure8-1.png", + "caption": "Fig. 8. Comparison of the perfect plastic process and wrinkling.", + "texts": [ + " For small strains, the energy error is insignificant and hypoelastic descriptions of the elastic response are often adequate, and in turn, this model is not recommended for the case of large elastic strains. Wrinkling is related to the elastic\u2013 plastic process as follows: (i) An analogy between the wrinkling strain Ew and the plastic strain Ep is adopted as E \u00bc Ee \u00fe Ep; Ep Ew: \u00f016\u00de (ii) When wrinkles occur, compressive stiffness in the direction of those wrinkles vanishes suddenly. This phenomenon resembles a perfect plastic process without any hardening. An illustration in Fig. 8a represents the relation between stress and strain for a 1D perfect plastic process with the boundary of the elastic domain oEr. Nearby, Fig. 8b depicts a 1D wrinkling process of a tension structure, e.g., a membrane. In this figure, one observes that a constraint on the condition of no-compressive stress can be fulfilled by two different approaches, either the Lagrange multiplier or the penalty method (see [2]). Obviously, these figures exhibit a resemblance between wrinkling in membranes and the perfect plastic process. (iii) With a known wrinkling direction, the corresponding modified stress field is determined in such a way that the plastic flow direction r and the wrinkling direction w0 (see Fig", + "\" # fEg\u00fefSpreg \u00bc \u00bdC I j U2UT 2\u00bdC UT 2\u00bdC U2 !\" # fEg\u00fefSpreg \u00bc \u00bdC \u00f0I H\u00defEg\u00fefSpreg \u00bc \u00bdC UfEg\u00fefSpreg \u00bcNfEg\u00fefSpreg: \u00f026\u00de After putting everything together, factor j is the modification factor whose magnitude is adjustable between 0 and 1. This value corresponds to the degree of modification for the constitutive tensor in such a way that the original constitutive tensor is recovered when j disappears. In contrary, as the magnitude of j is tuned up a modified constitutive tensor comes out (for an illustration see Fig. 8b). When j reaches unity Eq. (13) is recovered. Here U is the projection tensor that projects a nominal Green\u2013Lagrange strain tensor E onto a modified one eE in presence of wrinkles. This modified strain includes both influences of the prescribed allowable compressive stress with factor q and the reduction factor c, which accounts for the effects of prestress, on the wrinkling direction. The second term N stands for a modified constitutive tensor which maps a nominal Green\u2013Lagrange strain tensor E onto a modified PK2 stress field regarding to the occurrence of wrinkles" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001596_0094-114x(73)90020-7-Figure8-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001596_0094-114x(73)90020-7-Figure8-1.png", + "caption": "Figure 8. Dynamics of a b inary group.", + "texts": [ + " An Assur group consisting of n members is described by 3n equations that are linear with respect to the desired reaction forces and whose number is 3n. The subprogram for each group is again applicable to all of its modifications, independently of the combination of turning and prismatic pairs. The kinematic analysis always precedes the dynamic analysis and provides the necessary kinematic quantities (Xs,. ys. .~s~. ~s~, ~,. i~,. etc.). The mathematical model of a binary group for example according to Fig. 8 has the form Ay+ By = mlas,y+ V,y A . + B. = re,as,.+ V,. where - A,l~, cos \u00a2~,~ + A~I,, sin \u00a2 . ~ - Bvl~, cos ~;B, + B~l~ sin \u00a2~ --/s~< + M, - B,.+ C cos \u00a2 = re:as:,+ V:,, - B ~ - C sin \u00a2 = m:as:~ + V._. B,I~: cos \u00a2~_. - B,I~. sin \u00a2~_. - C[~-: cos (\u00a2 - \u00a2c_-1 + Mc = [~:e: + M: as,~ = -~:s,. as,, = j.~,. e, = ~, etc. The third part of the program KIDYAN is the investigation of the motion of a mechanism having one degree of f reedom in the phase plane. The equation of motion of such a mechanism has the known form d~ 1 dM(q)_" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001544_6.2008-4506-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001544_6.2008-4506-Figure4-1.png", + "caption": "Figure 4. Herringbone groove design.", + "texts": [ + " This is essential to reducing hysteresis in the seal. The 21.6-cm-diameter test rotor is made of Grainex MAR-M-247, a nickel-base alloy with excellent high-temperature properties. The seal runner surface on the rotor outer diameter is coated with chrome carbide applied by high-velocity oxygen fuel thermal spraying. A herringbone-groove pattern was machined into this coating by plunge electro-discharge machining. A pre-test photo of the grooves is shown in Fig. 3. The groove design geometry is shown in Fig. 4. The groove geometry and rotor surface finish was measured with a profilometer. The measured groove depth and land surface finish is 20 and 0.2 \u03bcm, respectively. The seal is positioned so that the lift pad rides over the herringbone-grooves with the groove ends beginning at the middle of the circumferential groove on the lift pad and extending past the low pressure edge. Based on the inspected inner diameter of the seal prior to machining the slots to create the fingers and the inspected rotor outer diameter, the radial clearance between the seal and the rotor at room temperature is 25" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000702_09544070jauto469-Figure8-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000702_09544070jauto469-Figure8-1.png", + "caption": "Fig. 8 24-wire grasshopper linkage", + "texts": [ + " The output voltage of the strain gauge circuit is directly proportional to the gauge factor, strain, and excitation voltage. The orientation of the gauges in the Wheatstone bridge and on the connecting rod were such that the bridge was bending and temperature compensated. Jaguar Cars, a partner in this research, kindly carried out the finite element analysis on the connecting rod to determine the most appropriate position for installing strain gauges. A special device called a grasshopper linkage was used to lead the wires from the strain gauges on the connecting rod to the side of the crankcase (Fig. 8). To measure friction using the IMEP method, very accurate measurement of forces acting on the complete piston assembly is necessary including the piston assembly inertial force, As the experiments are carried out on a single-cylinder four-stroke gasoline engine, the engine speed varies throughout complete engine cycle, thus account must be given to crankshaft angular acceleration. The piston assembly axial acceleration can be calculated as d2 dt2 S~{Rc a sin hz l 2 sin 2h\u00f0 \u00deffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1{l2 sin2 h p \" #( zv2 cos hz l cos 2h\u00f0 \u00dezl3sin4 hffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1{l2 sin2 h 3 q 2 64 3 75 9>= >; \u00f032\u00de The information from the encoder 0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003534_978-1-4419-6022-1-Figure7.14-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003534_978-1-4419-6022-1-Figure7.14-1.png", + "caption": "Fig. 7.14 Circuit diagram of Task 1", + "texts": [], + "surrounding_texts": [ + "around 1 nm (see Fig. 7.12) and can focus radiation to a spot as small as 1 mm in diameter. One disadvantage of laser diodes (compared to gas or other types of lasers) is that its beam is divergent, typically elliptical or wedge-shaped, and astigmatic, requiring refocusing.\nLaser diodes are most commonly used in CD, DVD and blu-ray players, laser printers, and barcode/UPC scanners. They are also becoming very important in many biosensor applications, especially when the light needs to be irradiated to the small area of interest, such as microcapillary channels, and when the light source needs extremely narrow spectrum width.\n\u2022 A breadboard, wires, wire cutter/stripper, a power supply, and a DMM. \u2022 20 kO pot, and a screw driver. \u2022 1 O resistor. \u2022 Planar diffused silicon photodiode (metal package; PIN-040A from UDT\nSensors, Inc.).\n\u2022 Incandescent light bulbs: 15, 40, and 60 W. \u2022 Sockets for light bulbs. \u2022 Ruler.\nFigures 7.14, 7.15, and 7.16 show the circuit layout. The photodiode is aligned in reverse bias, indicating this is a photoconductive operation. Without light, a depletion region forms between the P- and N-type semiconductors (because it is set to reverse bias), and no current flows. With light, this depletion region gradually disappears and the current starts to flow.\nThe 1O resistor is used formeasuring the current flowing through the photodiode. Before applying the voltage to the circuit, make sure that the voltage output from the 20 kO pot is less than 10 V, so that a huge current is not applied to the photodiode.\nExpose the photodiode to the 60 W light bulb (630 lm) by bringing the light bulb\nas close as possible, as shown in Fig. 7.16.\nWhile changing our pot from 0 to 10 V, measure the voltage applied to the system (Va \u00bc V), and the voltage drop across the 1 O resistor (Vab) to evaluate current (I). The following chart summarizes the experimental results (current against voltage), indicating almost constant current readings over the voltage range. Take the average of the currents that are \u201cplateaued.\u201d This is your sensor reading.\nRepeat the experiments with a 40 W light bulb (480 lm), with a 15 W light bulb (110 lm), and with ambient light. Plot the average current readings against the light bulb output (W), provided by the bulb manufacturer (Fig. 7.17).\n7.7 Laboratory: Photodiode 113", + "We notice that the I light bulb output graph is quite linear.\nQuestion 7.1 The experimental data shown above indicates almost no current for the ambient light, and the I light bulb output curve passes thru the origin. If the current for ambient light is 0.1 mA, can you estimate the light intensity of ambient light using the above data (in W)?\n7.7 Laboratory: Photodiode 115" + ] + }, + { + "image_filename": "designv11_7_0002210_9781782420545.178-Figure6.5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002210_9781782420545.178-Figure6.5-1.png", + "caption": "Fig. 6.5 - Cyclic voltammograms for a reversible process, 0 + e ^ R when only 0 is initially present in solution. The potential sweep rates are (a) v, (b) 10v, (c) 50*, and (d) lOO*", + "texts": [ + " The solution is quite difficult because of the time dependent potential term, but is can be shown that for planar diffusion [1, 2, 3] inF\\112 j p = -0.4463 \u00ab F \u2014 I c S \u00a3 V V / 2 (6.4) This is called the Randles-Sevttik equation, and at 25\u00b0C this reduces to the form L = -(2.69 X 10s) w ^ c o ^ W 2 (6.5) where 7p, the peak current density (measured as shown in Fig. 6.4) is in A cm-\"2, D is in cm2 s~\\ v is in V s\"1, and CQ is in mol cm - 3 . Thus we see that the peak current density is proportional to the concentration of electroactive species and to the square roots of the sweep rate and diffusion coefficient. Fig. 6.5 shows a set of typical cyclic voltammograms obtained for a reversible system over a range of sweep rates. 184 Potential sweep techniques and cyclic voltammetry [Ch. 6 Having obtained such results, a test of the reversibility of the system is to check whether a plot of/p as a function of y^2 is both linear and passes through the origin (or alternatively whether Ip/i'1^2 is a constant). If this is found to be true then there are further diagnostic tests to be applied, all of which should be satisfied by a reversible system" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002010_1.4002342-Figure6-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002010_1.4002342-Figure6-1.png", + "caption": "Fig. 6 Wheel profiles", + "texts": [ + " Also, note that the location of the lead/lag ange contact or the back of flange contact can be accurately redicted using Eq. 9 , as shown in Fig. 5. Numerical Examples 4.1 Wheel/Rail Profiles. In this section, numerical examples re presented in order to demonstrate the use of the numerical rocedure presented in this investigation and the effect of wheel nd tongue rail profiles on the location of contact point in turnout ection is discussed. Three different wheel profiles are considered n this example, as shown in Fig. 6. That is i conical wheel rofile, ii arc wheel profile, and iii severely worn arc wheel rofile obtained by measurement. The track gauge is assumed to e 1067 mm narrow gauge . The stock rail profile is assumed to e 50 kg N of Japan Industrial Standard JIS while the tongue ail is JIS 70 S. The wheel and rail contact on the point section of simple turnout is considered, as shown in Fig. 7, and the tongue ail cross-section profiles available from the drawing at points A to are given in this figure as well", + " Using the stock and tongue rail profiles, the contact geometry in turnout section can be analyzed using the two-point contact geometry procedure discussed in Sec. 3. 4.2 Two-Point Contact Analysis on Turnout. In the numerical example, the six rail profiles along the track are used in order to discuss the contact transfer from the stock to tongue rails in APRIL 2011, Vol. 6 / 024501-3 27/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use t i t t t w i c w t c s w t d a l 0 Downloaded Fr urnout section using the three different wheel profiles, as shown n Fig. 6. The contact configurations of left wheel subjected to wo-point contact are presented from Fig. 10 i to Fig. 10 iii . In he case of conical wheel profile, both the contact points are on he stock rail in section A while in sections B and B-C , the heel tread is in contact with the stock rail and the wheel flange is n contact with the tongue rail. In section C , the wheel tread omes in contact with both stock and tongue rails. Finally, the heel loses its contact with the stock rail and travels over the ongue rail after passing section C-D . A slightly different contact onfiguration is observed in the case of arc wheel profile, as hown in Fig. 10 ii . That is, the wheel has already lost its contact ith the stock rail in section C while contacts on both stock and ongue rails are kept in the case of conical wheel profile. This ifference is due to the difference in tread shapes of two wheels, s shown in Fig. 6, and such a small difference in wheel shape eads to a noticeable difference in contact configuration in turnout 24501-4 / Vol. 6, APRIL 2011 om: http://computationalnonlinear.asmedigitalcollection.asme.org/ on 01/ section. In the case of severely worn profile, as shown in Fig. 10 iii , significantly different and unwanted contact configurations are observed. Due to severe wear on the wheel tread, the flange angle becomes very steep and this leads to an unwanted flange contact with the side of the tongue rail in all the sections" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002534_12.907113-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002534_12.907113-Figure2-1.png", + "caption": "Figure 2: Blueprinter 5 using the DLP-technology for processing highly filled slurries - close-up of the production-area (a), schematic of the process (b) [5]", + "texts": [ + " Depending on the intensity of this dark field, premature gelling of the resin might occur. This reduces the number of build jobs which can be run with one batch of slurry, furthermore the viscosity of the resin increases constantly, leading to inconsistent buildresults [4]. AMT setup A prototype system (Blueprinter) developed by the Vienna University of Technology is able to process highly filled photosensitive slurries. The mainly difference to commercially available systems is related to the fact that the described system includes modifications (Figure 2) in the recoating system. These modifications facilitate the processing of high-viscosity resins. Proc. of SPIE Vol. 8254 82540E-2 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 11/04/2015 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx During the printing process the light engine projects a single cross sections from below through the glass bottom of the vat onto the slurry. The control software consecutively sends the images, corresponding to the cross-section of an individual layer, to the light engine, which controls the individual micro-mirrors of the DMD chip" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000839_978-3-540-75759-7_6-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000839_978-3-540-75759-7_6-Figure3-1.png", + "caption": "Fig. 3. Schematic view of the respiratory liver motion simulator", + "texts": [ + " Preparation: We prepared each porcine liver according to the following procedure: (a) Based on the method proposed by Zhang et al. [5], a 5% agar dilution was prepared and mixed with contrast agent (1:15 v/v dilution). (b) Three to four agar nodules of volume 2 ml were then injected into the liver (Fig. 2a). In case of a spherical lesion, a volume of 2 ml corresponds to a diameter of approximately 1.5 cm. (c) The liver was sewn to the diaphragm model (i.e., the Plexiglas R\u00a9 plate) of the motion simulator introduced in [9] (Fig. 3). (d) Two 5 Degrees-of-Freedom (5DoF) navigation aids [7] were inserted into the liver (\u201cdiagonal arrangement\u201d, Fig. 4b). (e) A planning CT scan of the motion simulator with the integrated porcine liver was acquired (Somatom Sensation 16 multidetector row scanner; Siemens, Erlangen, Germany). A fine resolution (0.75 mm slices) was necessary because our evaluation relies on accurate computation of the center of gravity of the agar nodule in both the planning CT and the control CT. (f) The motion simulator was used to simulate several breathing cycles (cranio-caudal displacement of the liver \u2248 15 mm [9]) reflecting the fact that the patients cannot hold their breaths between acquisition of the planning CT and registration" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000934_taes.1974.307798-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000934_taes.1974.307798-Figure1-1.png", + "caption": "Fig. 1.", + "texts": [ + " This paper is devoted to an error analysis of two commonly used integration schemes, namely, cirection cosines and quaternions. Scale, skew, and drift errors are defined, and the susceptibility of the integration schemes to these types of error is examined. It is concluded that the quaternion scheme offers an advantage because it intrinsically yields zero skew error. The paper is presented in two parts, for convenience. Let us begin with a two-dimensional example. Consider Figs. 1 and 2. In both figures, the x andy axes are depicted as correctly aligned and mutually perpendicular. In Fig. 1, the x%yt pair of axes are shown as rotated through an angle 6 relative to the x' y pair. The x', y' pair retains perpendicularity, but as a coordinate frame it is no longer correctly aligned. This is called drift error. Manuscript received July 26, 1973. The author is also a Consultant to Computer Software Analysts, Inc., Los Angeles, Calif. In Fig. 2, both the x' and y' axes have again been rotated, but this time in opposite directions through an angle a The x' and y' axes now form the sides of a parallelogram rather than a square. In some sense, the x',y coordinate frame could still be considered to be correctly aligned, but it is now an oblique or skew frame rather than a rectangular frame. This is called skew error. By rotating the y' axis alone, we could convert the situation shown in Fig. 2 into a situation similar to that shown in, Fig. 1. This would eliminate skew error at the expense of incurring drift error. There is really no virtue in doing this, especially if it is possible actually to eliminate the skew error without just converting it to drift error. IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. AES-10, NO. 4 JULY 1974 451 In addition to skew error and drift error, already described, there is a third kind of possible distortion of a coordinate frame called scale error. Pure scale error exists when the x' and y' axes, respectively, coincide with the x and y axes, but the unit of length in the primed system is normalized incorrectly; i" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002476_0278364909357644-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002476_0278364909357644-Figure1-1.png", + "caption": "Fig. 1. (a) A kinematic tree and (b) its connectivity graph.", + "texts": [ + " Finally, Section 8 presents the new sparse-matrix algorithms and Section 9 presents a table of computational cost formulae, an analysis of computational complexity, and the actual costs incurred in the ASIMO example. A rigid-body system can be regarded as a collection of rigid bodies connected together by joints. The connectivity of such a system can be described by means of a graph in which the nodes represent the bodies and the arcs represent the joints. We use the term kinematic tree to describe any rigid-body system for which the connectivity graph is a tree. In practical terms, a kinematic tree is a mechanical system without kinematic loops. An example of a kinematic tree is shown in Figure 1(a), and its connectivity graph is shown in Figure 1(b). In general, a kinematic tree will consist of N bodies, N joints and a fixed base. We treat the fixed base as a special body, so the connectivity graph will contain N arcs and N 1 nodes. If the kinematic tree describes a mobile robot, then one body in the robot is identified as the floating base, and a sixdegree-of-freedom (6-DoF) joint is inserted between the fixed and floating bases. This joint is not physically a part of the robot, but the six joint variables associated with it are necessary for describing the robot\u2019s location", + " Next, the remaining nodes are numbered consecutively from 1 in any order such that each node has a higher number than its parent. The arcs are then numbered such that arc i connects between node i and its parent. Finally, the bodies and joints are given the same numbers as their corresponding nodes and arcs. Once the bodies have been numbered, the connectivity of a kinematic tree can be described by its parent array, . This is an N -element array such that i is the body number of the parent of body i . The parent array for the example in Figure 1 is [0 1 1 2 2 3 3], meaning that 1 0, 2 1, and so on. The node-numbering rules ensure that has the property 0 i i , which is exploited in many algorithms. Given , the following sets can be defined, which describe various properties of the connectivity graph: i : the set of children of body i , defined by i j j i i : the set of joints that support body i , defined by i i i and 0 (the empty set) and i : the set of bodies supported by joint i , defined by i j i j . A joint is said to support a body if it lies on the path between that body and the root node. Thus, i is the set of all joints on the path between body i and the root, and i is the set of all bodies in the subtree starting at body i . These sets have various properties that follow from their definitions. For example, j i implies i j and vice versa, and i j if and only if j i . For the connectivity tree in Figure 1, we have 1 2 3 , 2 2 4 5 , 4 1 2 4 , 5 , and so on. A kinematic tree is branched if at least one set i contains more than one element. Most mainstream dynamics algorithms can be couched in terms that use only . Nevertheless, i , i and i can be useful in the mathematical descriptions of these algorithms, and in the analysis of their properties. at UNIV OF GEORGIA LIBRARIES on May 27, 2015ijr.sagepub.comDownloaded from The phenomenon of branch-induced sparsity refers to a pattern of zeros appearing in certain important matrices as a direct consequence of branches in the kinematic tree", + " The third case in Equation (2) is the one that gives rise to branch-induced sparsity. It states that Hi j will be zero for every i and j such that joint i does not support body j and joint j does not support body i . This condition will be true if and only if bodies i and j lie on separate branches of the connectivity graph, hence the name \u201cbranch-induced sparsity\u201d. To give a pictorial example, Figure 2(a) shows the sparsity pattern (i.e. the pattern of zeros) that would appear in H as a consequence of the branches in the kinematic tree in Figure 1 and Figure 2(b) shows a lower-triangular matrix having the same sparsity pattern below the main diagonal. In both cases, the gray areas denote non-zero elements1 or submatrices. We regard both of these patterns as examples of branch-induced sparsity. 1. A non-zero element in a sparse matrix is one that is free to take any value, including zero. In effect, \u201cnon-zero\u201d means \u201cnot constrained to be zero\u201d. A formal definition of branch-induced sparsity can now be stated as follows. For a given , which can be any array of integers such that 0 i i for all i : 1", + " (15) Thus v is a 6N -dimensional vector, and S is a 6N n matrix S is also an N N block matrix composed of rectangular blocks Si j having dimensions 6 n j . If it is important to identify what coordinate system is being used, then add a leading superscript thus, i S j is the motion subspace of joint j expressed in link i coordinates, and so on. Equation (15) implies that S has the same sparsity pattern, expressed at the block-matrix level, as an element of L . For example, the value of S for the kinematic tree in Figure 1 is S S1 0 0 0 0 0 0 S1 S2 0 0 0 0 0 S1 0 S3 0 0 0 0 S1 S2 0 S4 0 0 0 S1 S2 0 0 S5 0 0 S1 0 S3 0 0 S6 0 S1 0 S3 0 0 0 S7 (16) Having obtained a formula for S in Equation (12), the next step is to find a formula for R. In order to preserve as much sparsity as possible, we assume that each element in x depends on the velocity of a single body in the robot mechanism, and introduce an m-element array of body numbers, b, such that b i is the number of the body upon which xi depends. As the relationships between velocities are linear, it follows that xi can be expressed in the form xi Ri vb i (17) where Ri is a 1 6 matrix. Collecting the equations for each variable, we have x R v (18) where R R11 R1N Rm1 RmN and Ri j Ri if j b i 0 otherwise. (19) Thus, R is a sparse m N block matrix composed of submatrices Ri j having dimensions 1 6, with the property that exactly one block on each row is non-zero. To give a concrete example of the sparsity patterns that arise, suppose that an operational space is defined for the kinematic tree in Figure 1 such that m 2 and b [4 7]. In this case, we have R 0 0 0 R1 0 0 0 0 0 0 0 0 0 R2 and J R1S1 R1S2 0 R1S4 0 0 0 R2S1 0 R2S3 0 0 0 R2S7 Observe that the sparsity patterns in the two rows of this matrix are the same as the patterns in rows 4 and 7 of Equation (16). In general, submatrix Ji j of the task Jacobian is non-zero if and only if j b i . It was shown by Featherstone (2005) that any H SPD can be factorized into H LT L using the LTL factorization, or into H LT d DLd using the LTDL factorization, where L is lower-triangular, D is diagonal, Ld is unit-lower-triangular, and L Ld L ", + ") Conceptually, e and be can be regarded as the parent and body-number arrays for an expanded version of the original connectivity graph, in which each joint having more than one DoF is replaced by a chain of single-DoF joints. Another useful quantity is e i , which is the support set for node i in the expanded connectivity graph. These sets are used in the analysis and cost figures, but not directly in the algorithms. The idea of an expanded connectivity graph is illustrated in Figure 3. In this example, joint 2 in the mechanism from Figure 1 has 3 DoFs, while the other joints each have only a single DoF. The expanded connectivity graph is therefore obtained from the original by replacing arc 2 with a chain of three arcs. This alteration implies the addition of two new nodes, and it necessitates a renumbering of the nodes and arcs. The latter is performed in such a manner that arc i in the expanded graph refers specifically to element i in q (or q or ). An algorithm to calculate e and be from and b is presented in Figure 4. It is an extension of an algorithm appearing in Featherstone (2008) that calculates only e" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003966_s0040579514050224-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003966_s0040579514050224-Figure1-1.png", + "caption": "Fig. 1. Alternative approaches for parameter identification: (a) by fitting a simulated system output to the measurements y; (b) by fitting a reconstructed input to the true input u using an inverse process model. y\u0302", + "texts": [ + "94 1INTRODUCTION Virtually all mathematical models of chemical or biochemical processes contain unknown parameters that have to be identified from experimental data. Parameter identification is therefore a central step during the development of mathematical models and a prerequisite for model based process control and pro cess design. In most cases, parameters are identified from experiments as shown in Fig. 1a, see e.g. [1]. A process model is set up to reproduce the experiments in sim ulations, using the operation conditions or inputs as in reality and an estimate of the unknown model parameters \u03b8. In most cases, this requires a numerical solution of the differential equations of the model. The simulated process output or measurement is then compared to the true output y. If there are deviations, the estimate of the parameters is refined iteratively in an optimization step. Nowadays, the numerical solu tion of differential or differential algebraic systems is usually not very challenging, but it may become tricky when the guesses of the parameter values or of unknown initial conditions are poor and far away from the true values", + " Further, numerical inte gration underlying an optimization procedure may be 1 The article is published in the original. \u03a3\u0302 u \u03b8\u0302 y\u0302 quite expensive and consume the biggest share of the spent computation time. Finally, the dependence of the system outputs on the model parameters is often strongly nonlinear, resulting in non convex cost func tions with local minima for parameter identification. The mentioned difficulties motivate the search for alternative approaches for parameter identification. One possibility, which is shown in Fig. 1b, is to look at an inverse system model Instead of computing simulated system outputs from given inputs u, one could use the inverse model to compute estimated sys tem inputs from given outputs y and to use the differ ence between u and for parameter fitting. This approach is rarely used and only makes sense if it is much easier to solve the inverse model than the usual model But actually, there is a large class of sys tems, so called differentially flat systems, with exactly this property. The concept of differential flatness was initially introduced by Fliess et al" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001956_oceanssyd.2010.5603565-Figure6-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001956_oceanssyd.2010.5603565-Figure6-1.png", + "caption": "Fig. 6 The moment exerted by T5 is in balance with the moment exerted by the gravitational force (W) and the buoyant force (B) during descending, and this produces non-zero pitch angle (\u03b8e).", + "texts": [ + " When rank(BH)>dim(TH) AND rank(BV)>dim(TV) There are two cases to be discussed: one is the case when neutral buoyancy is applied to the AUV and the other is when a slight amount of positive buoyancy is applied. First, when neutral buoyancy is applied, the depth (or altitude) control can be achieved using only one vertical thruster, because the moment balance between the one exerted by the single vertical thruster and the one by the distance between the gravity center and the buoyancy center maintains the pitch angle a constant value during ascending or descending as shown in Fig. 6; however, if the AUV reaches the goal depth and the thrust of the single vertical thruster becomes zero, the pitch angle automatically grows to zero by the gravitational and buoyant forces. Hence, the control methods presented in Subsection C can be used for this case. Next, when a slight amount of positive buoyancy is applied, the pitch angle cannot be zero even if the AUV reaches the goal depth since the single vertical thruster should continually exert a force to maintain the goal depth due to the positive buoyancy. However, if the buoyancy force is small (this is usual case), the pitch angle (\u03b8e in Fig. 6) produced by the moment balance is also small. Consequently, the fault-tolerant control methods in Subsection C can be adopted for this case like the former case. Additionally, in upper two cases, the AUV descends and ascends obliquely. In order to verify the effectiveness of the presented faulttolerant control methods, simulations were carried out. The following three examples were selected: (i) when the #1 and #2 thrusters are malfunctioned; (ii) when the #2 and #3 thrusters are malfunctioned; and (iii) when the #3, #4, and #6 thrusters are malfunctioned" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000898_978-0-387-28732-4_4-Figure4-8-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000898_978-0-387-28732-4_4-Figure4-8-1.png", + "caption": "Figure 4-8. Subretinal implant with a subretinal vision chip with 1500 integrated receivers and stimulation electrodes (right), infrared receiver for energy supply (middle) and electrical charge storage (left) assembled on a thin polyimide foil which serves as printed circuit board. By courtesy of H. Haemmerle (NMI, Reutlingen, Germany).", + "texts": [], + "surrounding_texts": [ + "Worldwide, scientific research groups and companies work on the development and commercialisation of retinal vision prostheses. The different approaches have to take into account the anatomical restrictions of the eye globe and the physiology of the human retina. The developments in which the electrode arrays have to be placed under the retina (subretinal) or on the retina (epiretinal) have yet to become feasible by the degree of miniaturization made by means of micro system technology. Retina prostheses simulate the physiological function of the deceased receptor cells and stimulate the visual system at a very proximal level. As a result they benefit from the retinotopic organization of the retina and the further information processing of the entire visual pathway [153]." + ] + }, + { + "image_filename": "designv11_7_0001745_physreve.81.031920-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001745_physreve.81.031920-Figure2-1.png", + "caption": "FIG. 2. Two-dimensional solvent field around a bead moving with velocity v in a fluid at rest. A bead moving in a dilute Stokesian solvent at rest induces a solvent flow around it. The induced solvent flow at any point can be determined as radial vr and tangential v velocities, which are functions of the radial separation r and angle from the flow . In this study, the cubic-order term in the solvent velocity equations is neglected.", + "texts": [ + " The Method of Reflections improves on the first-order estimate by iteratively adding corrections so that the superposed solvent 031920-2 flows are induced by the hydrodynamic velocities and not the observed velocities of the neighbors 10 . We use the same idea to improve on the first-order superposition estimate of the solvent field. However, instead of iteratively correcting for the hydrodynamic velocities as in the Method of Reflections, we solve for them implicitly. We illustrate this in more details below in the context of the hydrodynamic interaction between two beads moving alongside each other. 1. First-order linear superposition Fig. 2 shows the two-dimensional solvent velocity field around a bead moving in a fluid at rest. The solvent field around the bead can be resolved into radial and tangential velocities, which can be determined at any point using the distance to the bead center and the angle relative to the bead velocity. Now consider two beads, I and II, moving with velocity v1 and v2 perpendicular to the line joining their centers Fig. 3 a . A simple first-order superposition of their solvent velocity fields would estimate their relative velocities1 v1 H and v2 H as, v1 H = v1 \u2212 3a 4 r12 v2, 1a v2 H = v2 \u2212 3a 4 r12 v1", + " 2 would be v1 H = v1 \u2212 3a 4 r12 v2 H 3a v2 H = v2 \u2212 3a 4 r12 v1 H 3b By solving these two equations simultaneously, the hydrodynamic velocities, and therefore the hydrodynamic drags, of the two beads can be determined. Figure 4 shows the predictions of the implicit technique for the change in the drag of a bead in the presence of another bead. Both beads are of the same radius, moving with the same velocity perpendicular and parallel to the line through their centers see insets in Fig. 4 . Note that the prefactor 3/4 in Eq. 3 changes to 3/2 for two beads moving parallel to their center line see solvent field equations in Fig. 2 . The drag correction is determined as the ratio of the bead\u2019s hydrodynamic velocity to its apparent relative velocity, vH /v. The predictions of the implicit method show a better match to rigorous calculations 15,16 and experimental observations 17,18 , than the predictions of a first-order superposition. The implicit technique predicts a smaller drag reduction than the first-order superposition technique. This is because a component of a bead\u2019s velocity comes from drifting in the solvent flow induced by its neighbor", + " In the implicit technique, that component does not exert a dragreducing hydrodynamic influence on the bead\u2019s neighbor. Finally, note that the solution of the first-order superposition is the same as that given by the first reflection in the Method of Reflections, and the solution of the implicit technique is the same as that given by infinite reflections in the Method of Reflections. The error between the implicit and the experimental/rigorous solutions in Fig. 4 is not because of Stokes superpositions, but comes from the approximations in the equations describing solvent flow around a bead Fig. 2 10 . The hydrodynamic drag along a rigid rod can be estimated by idealizing it as a string of beads, and solving for the hydrodynamic velocities of the beads. We resolve the velocities of a rigid rod and a bead in the following way. The 031920-4 two-dimensional motion of a rigid rod can be described completely by three velocities: the translational velocity of the rod center in the direction normal to the rod Vn , the translational velocity of the rod center in the direction parallel to the rod Vp , and the rotational velocity about the rod center W ", + " For a rigid rod in pure parallel and tangential motion, the parallel velocity of each bead is uniform along the rod. In Figs. 5 c and 5 d , we show the parallel hydrodynamic velocities of the beads, for rods of 20 and 100 bead sizes. The hydrodynamic velocities are scaled by the parallel velocity of the rod. The profile shows large bead-to-bead fluctuations in hydrodynamic velocities, with no definite overall trend. We found these fluctuations to be mathematical artifacts. They disappear upon inclusion of the cubic term in the Stokes solution for the solvent field around a bead Fig. 2 , and the profile takes on a U shape similar to that of the normal hydrodynamic velocities in Fig. 5 a data not shown . However, we omit the cubic-order term and the attendant increase in mathematical complexity because 1 the omission of the cubic-order term leads the less than 5% error in the total drag calculations for a rigid filament, and 2 the fluctuations disappear when the hydrodynamic velocities are determined as section averages see Sec. II B . In Fig. 6 we show validations of the filament hydrodynamic profile obtained with the implicit method", + " The one-step implicit solving of hydrodynamic variables is equivalent to infinite superpositions of the bead solvent fields or infinite reflections in the Method of Reflections because 1 each superposition serving to enforce the no-slip boundary condition at a bead can be mathematically interpreted as requiring that solvent flow be induced by the hydrodynamic velocity of a particle alone, 2 infinite orders of explicit iteration are equivalent to one implicit solution. The predictions of the implicit technique deteriorate at very small distances between beads. This is not because of the Stokesian superpositions, but because the presence of a bead in the solvent is represented by a point perturbation in the velocity field. In other words, the equations for the solvent flow around a bead Fig. 2 do not respect the impenetrability of the bead. However, in spite of this limitation, the predictions of an implicit or infinite-order superposition is vastly superior to that of a first-order superposition, especially in that it captures the hydrodynamic influence of stationary particles while being relatively easy to implement. A string-of-beads approach is traditionally limited by the computational size of even modeling a single filament. The proposed method addresses this limitation by assuming sections of beads, excepting the beads at the ends of filaments, to have the same average hydrodynamic velocities" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003351_j.engfracmech.2012.12.001-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003351_j.engfracmech.2012.12.001-Figure1-1.png", + "caption": "Fig. 1. Graphical representation of the rail chill effect.", + "texts": [ + " In the third stage, the Generalised Frost\u2013Dugdale approach [29,30] is used to model thermal fatigue crack growth. In order to consider the influence of rail chill effects on the crack growth, no mechanical loading or residual stresses (due to the manufacturing process) are included in this analysis. During the braking process, the friction generated by the brake-shoe on the moving tread produces heating. The heat generation at the braking shoe\u2013wheel interface and heat transfer to the rail is shown schematically in Fig. 1. A break cycle includes breaking to full stop. As the wheel rotates points on the wheel tread, experience both heating and cooling. The conditions at the two thermal contact interfaces which are associated with the wheel\u2013rail and brake\u2013wheel interfaces are very complex. Many factors, such as roughness of the surfaces, oxides, lubricant, organic material and sand, may cause a non-zero thermal contact (i.e. imperfect contact). In this analysis the interface thermal contact resistance has been ignored and the widely used assumption [10\u201313,21\u201323] of perfect thermal contact between the two surfaces has been adopted", + " The braking heat transfer flux of a wheel can be estimated from: qwheel\u00f0t\u00de \u00bc Q wheel\u00f0t\u00de A1 \u00bc 2Q wheel A1 1 t tb \u00bc Q0 wheel A1 1 t tb \u00f01\u00de where Q wheel \u00bc PV2 2gtb \u00bc Q shoe Average instantaneous braking (friction) power (kW) Q 0 wheel \u00bc 2Q wheel Starting average braking power (kW) In order to account for the dissipation of the thermal heat to the surroundings, a convectional boundary condition is applied to the surface of the wheel. As the wheel rotates the tread surface is subjected to periodic heating and cooling. A method to account for the cooling influence from the rail is transformed to convection cooling to the area of wheel\u2013rail contact. The cooling flux of rail chill effect is modelled using the equation: qchill\u00f0t\u00de \u00bc Q rail A2 \u00bc hrail\u00f0Twheel\u00f0t\u00de Trail\u00f0t\u00de\u00de \u00f02\u00de Here Qrail is the heat into rail from wheel/rail contact surface and A2 is the contact area of wheel and rail, see Fig. 1. The value of A2 can be obtained by using software such as \u2018GENSYS\u2019, and \u2018Vampire\u2019 to model the wheel/rail contact conditions. In this paper we used Hertzian contact theory, as a first approximation, to evaluate contact area [32]. The value of hrail is the coefficient of rail convection. The temperature of wheel and rail on the contact surface at time t are represented by Twheel(t) and Trail(t) respectively. The rail convection heat transfer coefficient was taken from [21,33]. During braking longitudinal conduction has the effect of heating up a rail section ahead of the wheel" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001640_j.mechmachtheory.2009.09.010-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001640_j.mechmachtheory.2009.09.010-Figure4-1.png", + "caption": "Fig. 4. Nodal elastic displacement of the element.", + "texts": [ + " (4) The transverse deflections are modeled as a cubic polynomial of the nodal displacement, the longitudinal deflections and the torsional deflections are modeled as a first-order polynomial of the nodal displacement. The manipulator is divided into several substructures, namely one moving platform substructure and some kinematic chain substructures which are composed of the lead-screw assembly and the strut. Each strut is divided into three elements and the nodal elastic displacement of the element is shown in Fig. 4. The moving platform and the sliders are regarded as the rigid bodies since their deformations are small relative to the elastic deformations. 3.2. Strut dynamics equation 3.2.1. Element model It is well known in the study of kineto-elastodynamics analysis of mechanism that the kinematic differential equation of the strut element within ith kinematic chain can be written in the following form by applying Lagrange equation [13,14]: m\u20acd\u00fe kd \u00bc f m\u20acdr \u00f07\u00de where f denotes the resultant of the applied and the internal forces exerted at the element, k and m are the element stiffness matrix and element mass matrix, respectively, d and \u20acd are the nodal elastic displacement and acceleration of the element, \u20acdr is the nodal acceleration of the rigid body motion" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003161_j.jsv.2012.09.043-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003161_j.jsv.2012.09.043-Figure1-1.png", + "caption": "Fig. 1. Lumped-parameter model for the in-plane vibration of a tuned planetary gear and generalized coordinates. The fe1 ,e2 ,e3g basis rotates at the constant speed Oc about e3.", + "texts": [ + " Eigenvalue speed dependency has been investigated in many physical gyroscopic systems, such as spinning disks [1\u20136], axially moving materials [7,8], pipes conveying fluid [9], spinning disk-spindle systems [10\u201312], spinning rings [13,14], spinning shafts [15\u201317], and high-speed planetary gears [18,19]. All these systems have speed-dependent eigenvalues that may result in vanishing eigenvalues (at speeds called critical speeds) and divergence and flutter instabilities. While many of these systems show common eigenvalue behavior that is considered typical, this study demonstrates unique, atypical eigenvalue behavior observed in a lumped-parameter planetary gear model from Refs. [18\u201320]. The lumped-parameter model for the in-plane vibration of a tuned planetary gear is shown in Fig. 1. All coordinates are measured with respect to the reference frame fixed to the carrier, which rotates at constant speed. The central members (the carrier, ring, and sun) have translations xh and yh, and rotations uh for h\u00bc c,r,s. The planets have radial (zi) and tangential (Zi) deflections, and rotations ui for i\u00bc 1,2, . . . ,N (N is the number of planets). The planetary gear model is described in detail in Ref. [20]. The non-dimensional gyroscopic eigenvalue problem for the planetary gear shown in Fig. 1 is [18] l2M/\u00felOcG/\u00fe\u00f0Kb\u00feKm O2 c KO\u00de/\u00bc 0, (1) . All rights reserved. igan-Shanghai Jiao Tong University Joint Institute, Shanghai Jiao Tong University, Shanghai r). where the non-dimensional carrier speed is Oc . The matrices of Eq. (1) are defined in Ref. [18]. The eigenvalue problem in Eq. (1) is a standard gyroscopic eigenvalue problem characterized by symmetric mass (M) and stiffness (Kb\u00feKm O2 c KO) matrices and a skew-symmetric gyroscopic matrix (G). Gyroscopic systems have specific properties [21,22]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002071_s0091-0279(71)50004-1-Figure12-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002071_s0091-0279(71)50004-1-Figure12-1.png", + "caption": "Figure 12.", + "texts": [ + " In the dog, the strides of the fore- and hindlimbs have a very predictable normal pattern in the walking and running gaits, an exception be!ng the leaping gait. This predictable stride is of great advantage in the diagnostic examination. To picture the normal stride of the front leg of the dog, one can draw an imaginary line from the spine of the sea pula to the ground. This is the anterior contact point. The limb will stay in contact with the ground until the anterior half of the body has passed over this point, thus terminating the stride (Fig. 12). The hindlimb also has a calculable stride of great importance. In motion, the hindlimb is extended to the middle ofthe body and is placed in contact with the ground a split second after the forelimb has been lifted. The hindlimb then stays in contact with the ground to about an equal distance past the normal stance position (Fig. 13). In anteroposterior views of limb placement, normal variations will occur between the two basic shapes of dogs. Long legged, deep chested dogs-mostly the hunting breeds, where endurance necessi tates the conservation of energy- walk by placing one limb in a direct line with the limb of the opposite side (single tracking)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000113_bf00043705-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000113_bf00043705-Figure4-1.png", + "caption": "Figure 4", + "texts": [ + " Consequently, the initial curve C is transformed into the corresponding hyperbola h. Clearly, the larger the difference is between the curves C and h the greater is the effect of snapping-through. As in the previous case such a buckling is accompanied by a jump in the intensity of wrinkling because of the contraction of parallels. For infinitesimal torsion the post-buckled state of the film can be defined without involving of the whole system of Eqs. (1.3)-(1.7). Indeed, let us write the equation of the hyperbola h (Fig. 4) as where \u00b1 , ( a ) \u00b12(8) A = - - B = (2.21) A(~) ' a (~) ' 82 and H is the height of the body of revolution formed by the film. The unknown parameter 8 can be found by taking into account that for small torsion the lengths of the curves C and h must be equal, i .e., I 2 1 ( 1 A 2 x 2 ~ 1/2 gc = 1 d B A x 2 - 1/ dx 2 [ 1 \"~l/2f ['/ A.~112 1/2 -]~ =tA) 1Ettl+B -) ' ~ ' ] -E [ ( I+A) '~2]~ =y(8)' (2.23, where E is the elliptical function of the second kind in Legendre's form, and qh, q~2 A x e - B y 2= 1, A > 0 , B > 0 , (2" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001269_1.3197178-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001269_1.3197178-Figure1-1.png", + "caption": "Fig. 1 Residual displacements used in normal problem", + "texts": [ + " 3 Normal and Tangential Problems in Elastoplasticity Both normal and tangential displacements of a surface point due to a cuboid of uniform plastic strain should be carefully considered when solving EP contact problem in the stick/slip regime. The normal displacement was given in an integral form by Chiu 26 , which was analytically integrated in Ref. 5 . It is also given MARCH 2010, Vol. 77 / 021014-110 by ASME 6 Terms of Use: http://www.asme.org/about-asme/terms-of-use i m c s T p 4 v w m a o i T w a v 0 Downloaded Fr n terms of Galerkin vectors in Ref. 27 . The knowledge of noral displacements, see Fig. 1, is sufficient for most frictionless ontact problems. For frictional contacts the tangential problem, ee Fig. 2, must be solved to correctly define shears in stick-zones. angential displacements induced by plasticity are useful in this roblem, but have not yet been studied nor considered. Maxwell\u2013Betti Reciprocal Theorem Consider two independent loads applied to an elastic body of olume and of boundary . The first state u , , , f i exists ith initial strains \u00b0. The second state is undefined for the moent and will be noted u , , , f i " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003761_j.compstruc.2012.08.005-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003761_j.compstruc.2012.08.005-Figure5-1.png", + "caption": "Fig. 5. Concentrated radial load.", + "texts": [ + " The estimation of this number is explained in the next section. The results are given on Fig. 4. Several discretizations of the curved beam by straight beam finite elements were performed to ensure convergence with the results given by the FE model. Very good convergence of the finite element solutions with the continuous element response is observed. 4.2. Concentrated radial load Then, the ring structure is subjected to a concentrated radial force at the point located on the middle line at h = 0 (see Fig. 5). Free boundary conditions are taken into account and the harmonic response is determined at the point where the force is applied. The only non zero force component is fg. This load system is given by: fg\u00f0h\u00de \u00bc Fd\u00f0h\u00de \u00f028\u00de with d(h) the Dirac delta function which is defined such that:Z \u00fe1 1 d\u00f0h\u00deu\u00f0h\u00dedh \u00bc u\u00f00\u00de \u00f029\u00de The Fourier expansion of the applied load has the following form: Fig. 4. Dynamic response of t fg\u00f0h\u00de \u00bc F 2p \u00fe X1 m\u00bc0 F p cos mh \u00f030\u00de Thus according to the notations of (21), we obtain: F1m \u00bc \u00f00;0;0;0;0;0\u00de F20 \u00bc 0;0;0; F 2p ;0;0 F2m \u00bc 0;0;0; F p ;0;0 8>< >: \u00f031\u00de Eq" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000077_2006-01-0358-Figure6-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000077_2006-01-0358-Figure6-1.png", + "caption": "Figure 6: Radial expansion of cage subject to centrifugal forces.", + "texts": [ + " EXPERIMENTAL VALIDATION OF THE ANSYS CAGE MODEL In order to validate the force-deflection relationship obtained from the ANSYS cage model, actual cage specimens were tested using an MTS machine. Figure 4 illustrates the loading applied to the ANSYS cage model and the experimental investigation. Figure 5 demonstrates that the results from ANSYS and experiments are in very good agreement. To obtain the circumferential stiffness, an energy balance was performed on a pocket under steady state expansion of the cage at a specified angular velocity, \u03c9. The steady state expansion of the cage was compared to results obtained from the ANSYS cage model under the same conditions. Figure 6 shows a cage with four pockets initially undeformed and deformed radially by a displacement, \u0394Rc, due to centrifugal force. The strain energy stored in the cage deflections at steady state expansion is equated to the work done by the centrifugal loads. Solving for the circumferential stiffness, kc, gives [ ] ( ) 2 p c c c c a m 2R R k R 2 2cos r \u03c9 + \u0394 = \u0394 \u2212\u23a1 \u23a4\u23a3 \u23a6 (1) where mp is the mass of a cage pocket, Rc is the centerline radius of the cage, \u0394Rc is the radial expansion of the cage, \u03c9 is the angular velocity of the cage and ra is 360\u00b0/N" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000385_s00170-006-0604-5-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000385_s00170-006-0604-5-Figure3-1.png", + "caption": "Fig. 3 Rp revolute joint in prismatic form", + "texts": [ + " As all of the actuators are locked, the kinematic screws change to be: $2 \u00bc S2; S02\u00bd \u00bc l2; m2; n2; 0; 0; 0\u00bd $3 \u00bc S3; S03\u00bd \u00bc l3; m3; n3; 0; 0; 0\u00bd $4 \u00bc S4; S04\u00bd \u00bc l4; m4; n4; O2 S4\u00bd $5 \u00bc S5; S05\u00bd \u00bc l5; m5; n5; O2 S5\u00bd (13) The constraint screws for the kinematic screws in Eq. 13 are $r1 and $r2, as shown in Fig. 2c. The axis of $r2 is the intersection of the two planes PR2R3 and PR4R5. Similar to the 5-RRR(RR) manipulator, five $r2 and the common $r1 are six linear independent screws. So, the selection of base actuators is feasible. 3.3 Manipulator 5-(RRpR)(RR) A kind of revolute joint in a prismatic form (Rp) shown in Fig. 3 is adopted to build some novel parallel manipulators in this study. The relative motion of the kinematic pair is that a slider moves on an arc-track. It is equivalent to a revolute joint, since the slider rotates around the axis S. The manipulator 1\u20139, 5-(RRpR)(RR), is taken as the example, as shown in Fig. 4. Different to the 5-(RRR)(RR) manipulator, the second kinematic pair adjacent to the base platform is an Rp pair. The constraint screws and input selection analysis for this manipulator are omitted as they are similar to that of manipulator 5-(RRR)(RR)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002392_j.matdes.2012.02.002-Figure10-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002392_j.matdes.2012.02.002-Figure10-1.png", + "caption": "Fig. 10. Laser-welding joint geometric position relationship of the multi-sheet cylinder sandwich structure.", + "texts": [ + " Taking the problem of loading and unloading of parts in laser welding process into account, the adjustment range of the fixture diameter is between 218 mm and 228 mm. The key diagram of the fixture diameter variation is shown in Fig. 9. The principle of operation is as follows: when the adjustable bar forces the adjustable oblique block move axially, the adjustable oblique drives the adjuster roller to move radially due to the axial motion of the roller forbidden in the slot limit. Therefore, the changes in diameter can be achieved. The geometry relations and the number of laser welding joint on the cylinder structure are shown in Fig. 10. So as to make superplastic forming of multi-sheet cylinder sandwich structure successful, the core cylinder can not be welded together with the inner cylinder during the welding preparation for outer cylinder and core one. Otherwise the superplastic forming of the multisheet cylinder sandwich structure can not be successful. In addition, the welding seam appearance should be also no welding defects such as dents, undercut. Consequently it is very important to select appropriate welding parameters to ensure that the welding request of the multi-sheet cylinder sandwich structure can be met and the welding joints have high strength as well as good weld quality and appearance at the same time", + " The laser butt welding parameters for the inner cylinder and the outer cylinder are: Power 900 W; Welding speed 1400 mm/min; Defocusing amount 1 mm; Shielding gas flow 0.6 L/min. After the butt welding of the inner cylinder, the laser penetration welding between the core cylinder and the inner one is performed. After the core cylinder is stuck on the inner cylinder, the butt welding position of the core cylinder is welded on the inner cylinder according to the penetration welding parameters. With this laser welding seam on the core cylinder as the baseline, the laser scratching is carried out on the core cylinder according to Fig. 10 so that the geometric location of the other penetration welding seams is precise. After the scratching, the rest of the laser penetration welding between the core cylinder and the inner cylinder is conducted. The photo after finishing the laser penetration welding between the inner cylinder and the core cylinder is shown in Fig. 12. re. ing amount (mm) Shielding gas flow (MPa/min) Joint penetration 0.1 Depth 0.1 Penetration 0.1 Penetration 0.1 Shallow 0.1 Depth 0.1 Penetration 0.1 Shallow 0.1 Depth 0.1 Penetration -sheet cylinder sandwich structure under the different parameters. A basis line about laser penetration welding between core cylinder and outer cylinder is scratched with laser on the core cylinder according to the geometric relationship shown in Fig. 10, before the outer cylinder is loaded on the core cylinder. The outer cylinder is loaded on the core cylinder according to the baseline on the core cylinder. Because the longitudinal seam of the outer cylinder is long, a uniform laser spot welding is carried out in the laser butt welding of the outer cylinder. And then the laser scratching is proceeding on the outer cylinder as the baseline with the laser butt welding seam according to Fig. 10. The laser penetration welding of the outer cylinder is performed after the laser scratching. After all the laser penetration welds are completed, the longitudinal seam welding is finalized. The workpieces photo after finishing the laser penetration welding is shown in Fig. 13. Higher demands are presented to the SPF die material because of the complexity of multi-sheet core cylinder structure. The die material should have the following properties: good mechanical properties in high temperature; good performance in rapid thermal and quench; good oxidation resistance in high temperature; good machining properties; high phase transition temperature" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001768_j.robot.2009.09.014-Figure6-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001768_j.robot.2009.09.014-Figure6-1.png", + "caption": "Fig. 6. Pair of AttractObstacle behaviors based on the robot\u2019s scanning IR array. Each behavior is bounded by two IR sensor readings, shown with active distances within behavior view regions.", + "texts": [ + " The purpose of this behavior is to provide more localization data points by attempting to maximize obstacles that are within the range array\u2019s coverage. As the robot navigates the environment, it can therefore bettermap the locations of obstacles. This behavior is weighted in such a way that allows obstacle avoidance to take over when the robot is too close to an obstacle. Its weight has also been empirically found to avoid getting stuck in corners (i.e., avoidance has a higher weight when obstacles are abundant and close). Two AttractObstacle behaviors are utilized by each robot. Fig. 6 illustrates the two obstacle attraction behaviors based on the IR array\u2019s FOV. As with the AvoidObstacle behavior set, the range and magnitude are computed, with the range linearly mapped to [0,1] for both behaviors. These behaviors are considered active out to 100 cm, and are triggered in the same manner as described for the AvoidObstacle behaviors. AvoidPast: This behavior causes the robot to favor making progress away from areas that have already been explored, especially those that are most recent" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003909_j.scient.2011.08.026-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003909_j.scient.2011.08.026-Figure3-1.png", + "caption": "Figure 3: Enclosed ellipsoid in the presence of the general obstacles.", + "texts": [ + " In this paper, the environmental objects are generally modeled as ellipsoids, and due to obstacle avoidance ofmobilemanipulator in cluttered environment, the new dimensionless potential functions are defined. Furthermore, it should be mentioned that a lot of ellipsoids can be enclosed to the convex object, but fitting the best ellipsoid to the object can be treated as an optimization problem. Moreover, mobile robot parts (the platform and the arms), walls, etc. are usually rectangular objects, and it is obvious that the rectangular cuboid must be enclosed with the optimal ellipsoid. Figure 2 shows a non-holonomic spatial mobile manipulator in a real environment, and Figure 3 depicts the enclosed ellipsoid to mobile manipulator parts in the presence of some common obstacles. In addition, for obstacle avoidance of colliding objects, potential function is applied to performance index, where it is a function of the dimensionless parameter, dij, and can bewritten as: \u2016Li\u20162 wobij = wobij 1 d2ij . (6) The value of the potential function is increasedwhen themobile robots move closer to the environmental obstacles. For determining the parameter, dij, suppose that each robot\u2019s part is modeled by ellipsoid, and a point obstacle is in the robot\u2019s workspace (Figure 3). In fact, the distance between point obstacle and enclosed ellipsoid can be computed via optimization method, which leads to a complex equation. But on the other point of view, the relative position of the point obstacle with respect to the ellipsoid can be easily described according to its describing equation. If the equation of the ellipsoid is considered in the local coordinate system, xyz, attached to its center, for the collision avoidance between the point obstacle with the local coordinates pi(xobi , yobi , zobi), and the enclosed ellipsoid, the parameter dij is defined as follows: dij = x2obi a2 + y2obi b2 + z2obi c2 \u2212 1 1 2 , (7) where dij is a dimensionless parameter and implies the obstacle avoidance of ellipsoid, if it has the real positive value" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000445_s00216-005-0267-3-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000445_s00216-005-0267-3-Figure2-1.png", + "caption": "Fig. 2 Schematic diagrams of a CL flow cell body and b perspective view of the CL flow cell with cell holder", + "texts": [ + " Apparatous The schematic flow diagram used in this work is shown in Fig. 1. AWatson Marlow 505Du peristaltic pump propelled carrier and reagent solutions using silicon manifold tubing of 1.02-mm and 0.76-mm i.d., respectively. The flow lines were made from Supelco Teflon tubing (0.5-mm i.d.). The sample solution was injected via a Rheodyne four-way Teflon rotary valve type 50 into the carrier solution. The CL signal intensity was measured using a Varian Cary Eclipse fluorescence spectrophotometer equipped with a home-made CL flow-through cell (Fig. 2). The body of the flow cell was made from a block of Plexi-glass. Grooves with a depth and width of 1 mm were machined on the surface of the cell body to make inlet and outlet channels on the surface. A piece of transparent glass window was mounted on the grooved surface and then was tightened by a holder. Incoming solutions from two inlets pass through two inlet channels (at right angles) on the surface of the cell, mix together at the confluence point, and then pass through the outlet channel, where the chemiluminescence reaction takes place; the emitted light then passes through the transparent glass window" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000145_epepemc.2006.4778416-Figure10-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000145_epepemc.2006.4778416-Figure10-1.png", + "caption": "Fig. 10 The flux density distribution for rated speed and load.", + "texts": [ + " The FEM model has been created in two dimensional magnetostatic solver with 15.000 elements approximately. The SRM model was supplied with non sinusoidal phase current, which has been obtained from measurement. The simulation of magnetic flux and flux density distribution under FEM was made step by step for each current and rotor position. The output value from FEM analysis was flux density in whole crosssection area of investigated SRM model, for different speed and load. The flux density distribution can be seen in Fig. 10 for rated speed and rated load. The flux density waveforms have been constructed for stator and rotor poles and yokes and the harmonic analysis has been done. In the Fig. 11, there are the magnitudes of flux density harmonic components for stator pole. The accuracy is very good in comparison with Fig.4b and the difference is not higher than 3%. The accuracy is also very good for all calculations and the difference is not higher than 6%, which is acceptable value in electrical machines. The core losses (both of eddy current and hysteresis loss components) calculations have been made in the same way than in analytical approaches described above" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000026_tuffc.2006.193-Figure9-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000026_tuffc.2006.193-Figure9-1.png", + "caption": "Fig. 9. Reference contours of X-Y axes. (a) Window contour. (b) Circle contour. (c) Butterfly contour.", + "texts": [ + " Moreover, in practical applications the motion commands of X-axis, Y-axis, and \u0398-axis are designed individually through contour planning to achieve three dimensions motion control. In this study, the window, circle, and butterfly contours for the X-Y axes are used to show the control performance of the proposed recurrent RBFN-based FNN controller. For the \u0398-axis, the sinusoidal and trapezoidal reference trajecto- ries are used to show the control performance of the proposed recurrent RBFN-based FNN controller. 1. Contour Planning for X-Y Table: The window contour is shown in Fig. 9(a) and can be divided into nine parts from a to i. The window contour can be described as shown in (32)\u2013(41) (see next page), where i is the number of samples; \u2206\u03d5 is the variation value of the angle; R is the radius of the circle; \u03be is a constant. The size of the contour 2458 ieee transactions on ultrasonics, ferroelectrics, and frequency control, vol. 53, no. 12, december 2006 \u03d5i = \u03d5i\u22121 + \u2206\u03d5, (32) a trajectoryXi = Xi\u22121, Yi = \u03be + Yi\u22121, (33) b trajectory ( \u03d5i 5 4 \u03c0 \u2192 2\u03c0 ) , Xi = Ox1 + R cos (\u03d5i) , Yi = Oy1 + R sin (\u03d5i) , (34) c trajectoryXi = \u03be + Xi\u22121, Yi = Yi\u22121, (35) d trajectory ( \u03d5i \u03c0 \u2192 5 4 \u03c0 ) , Xi = Ox2 + R cos (\u03d5i) , Yi = Oy2 + R sin (\u03d5i) , (36) e trajectoryXi = Xi\u22121, Yi = \u2212\u03be + Yi\u22121, (37) f trajectory ( \u03d5i 1 2 \u03c0 \u2192 \u03c0 ) , Xi = Ox3 + R cos (\u03d5i) , Yi = Oy3 + R sin (\u03d5i) , (38) g trajectoryXi = \u2212\u03be + Xi\u22121, Yi = Yi\u22121, (39) h trajectory ( \u03d5i 0 \u2192 1 2 \u03c0 ) , Xi = Ox4 + R cos (\u03d5i) , Yi = Oy4 + R sin (\u03d5i) , (40) i trajectoryXi = Xi\u22121, Yi = \u2212\u03be + Yi\u22121" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001970_demped.2009.5292798-Figure15-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001970_demped.2009.5292798-Figure15-1.png", + "caption": "Fig. 15. Induction motor rotors: healthy, one, two and three broken bars.", + "texts": [ + " However, they can only be used for nonsinusoidally voltage-fed motors. These components are also useful as tools to identify and separate rotor faults from oscillations due to load, mainly in those cases where the oscillating load frequency is next to 2sfs. In such cases, the analysis of sidebands around the fundamental component does not allow a correct diagnosis. Technical data and parameters of the induction motor for simulations and laboratory experimental results are shown in Table 1. The rotors used in the experiments are shown in Fig. 15. [1] A. Bellini, F. Filippetti, G. Franceschini, C. Tassoni, and G.B. Kliman, \"Quantitative evaluation of induction motor broken bars by means of electrical signature analysis,\" IEEE Trans. on Industry Applications, vol. 37, no. 5, pp. 1248-1255, 2001. [2] C.J. Verucchi, G.G. Acosta, and E. Carusso, \"Influence of the motor load inertia and torque in the fault diagnosis of rotors in induction machines,\" IEEE Latin America Transactions, vol. 3, no. 4, pp. 48-53, 2005. [3] C. H. De Angelo, G. R. Bossio, J" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001907_s10514-010-9205-0-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001907_s10514-010-9205-0-Figure2-1.png", + "caption": "Fig. 2 A team of three point-model robots manipulate a payload in three dimensions. The coordinates of the robots in the inertial frame W are qi = [xi, yi , zi ] and in the body-fixed frame (attached to the payload) B are q\u0303i = [x\u0303i , y\u0303i , z\u0303i ]. The rigid body transformation from B to W is A \u2208 SE(3). Additionally, we denote the projection of the robot position q\u0303i along qi \u2212 pi to the plane z\u0303 = 1 as q\u0302i = [x\u0302i , y\u0302i ,1]", + "texts": [ + "1 Mechanics of a cable-suspended payload We begin by considering the general problem with n robots (quadrotors in our experimental implementation) in three dimensions. We consider point robots for the mathematical formulation and algorithmic development although the experimental implementation requires us to consider the full twelve-dimensional state-space of each quadrotor and a formal approach to realizing these point abstractions, which we provide in Sect. 5. Thus our configuration space is given by Q = R 3 \u00d7 \u00b7 \u00b7 \u00b7 \u00d7 R 3. Each robot is modeled by qi \u2208 R 3 with coordinates qi = [xi, yi, zi]T in an inertial frame, W (Fig. 2). The ith robot cable with length li is connected to the payload at the point Pi with coordinates pi = [xp i , y p i , z p i ]T in W . We require P1, P2, and P3 to be non-collinear and span the center of mass. The payload has mass m with the center of mass at C with position vector r = [xC, yC, zC]T. The payload\u2019s pose A \u2208 SE(3) can be locally parameterized using the components of the vector r and the Euler angles with six coordinates: [xC, yC, zC,\u03b1,\u03b2, \u03b3 ]T. The homogeneous transformation matrix describing the pose of the payload is given by: A = \u23a1 \u23a2\u23a2\u23a2\u23a3 R(\u03b1,\u03b2, \u03b3 ) \u239b \u239d xC yC zC \u239e \u23a0 0 1 \u23a4 \u23a5\u23a5\u23a5\u23a6 . (1) Note that R is the rotation matrix going from the object frame B to the world frame W (as depicted in Fig. 2). Additionally, for this work we follow the Tait-Bryan Euler angle parametrization for {\u03b1,\u03b2, \u03b3 }. The equations of static equilibrium can be written as follows. The cables exert zero-pitch wrenches on the payload which take the following form after normalization: wi = 1 li [ qi \u2212 pi pi \u00d7 qi ] . The gravity wrench takes the form: g = \u2212mg [ e3 r \u00d7 e3 ] , where g is the acceleration due to gravity and e3 = [0,0,1]T. For static equilibrium: [ w1 w2 \u00b7 \u00b7 \u00b7 wn ] \u23a1 \u23a2\u23a2\u23a2\u23a3 \u03bb1 \u03bb2 ... \u03bbn \u23a4 \u23a5\u23a5\u23a5\u23a6 = \u2212g, (2) where \u03bbi \u2265 0 is the tension in the ith cable" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001199_biorob.2008.4762786-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001199_biorob.2008.4762786-Figure3-1.png", + "caption": "Fig. 3. Setting handrail position, final height of bed and foot position", + "texts": [ + " The handrail position, the final height of the bed and the foot position are determined from the hand position and the hip joint position of the human model simulated for satisfying the conditions explained in the previous section. A procedure of deriving candidates of these parameters of the support system is described as follows: 1) The position of the toe of the foot is set at the origin of the base coordinate frame and the xy plain is divided by rectangular elements whose intervals are \u0394x and \u0394y as shown in Fig. 3. 2) The hand position and the hip joint position are set in each rectangular element and the joint angles of the human model are calculated according to both set hand and hip joint positions, while \u03b8neck and \u03b84 are changed every interval of \u0394\u03b8 within the joint range of motion for considering the redundancy of the human model. 3) The evaluation indexes xG, \u03c4i are calculated in the cases that the joint angles are within the joint range of motion. Note that we ignore forces applied to the hands for calculating the evaluation indexes, because they are within the each acceptable range even if the user releases the gripe of the handrail accidentally during the sit-to-stand movement" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000084_s00170-005-0312-6-Figure25-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000084_s00170-005-0312-6-Figure25-1.png", + "caption": "Fig. 25 Collision-free cutter orientation on the hub", + "texts": [ + " After calculation by software, it is known that there are 9,834 and 9,648 cutter contact points on the hub and single blade, respectively. The numbers of their tool paths are 134 and 138, respectively, as shown in Fig. 24. When the cutter contact points on the blades and hub are determined, and after the original spindle axis orientation (TSa) and suitable clearance value (rcl 0.2 cm) are given, the collision-free cutter orientation can be acquired by using the abovementioned two stages detection methods, and through the programming usingEUKLID software. Figure 25 is the simulated diagram of collision avoidance during cutting hubs. The cone body used for collision checking is marked as the dashed line. Figure 26 is the simulated diagram on cutting blades. The determined cutter contact points and cutter orientation data are entered into the post processor of the fiveaxis machining tool, MAHO 600E. Then the five-axis joints variables of the five-axis machining tool can be acquired. Supplemented by suitable cutting conditions, such as feed-rate and spindle speed, the required NC program of the blade and hub can be machined, as shown in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000648_bf03027056-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000648_bf03027056-Figure4-1.png", + "caption": "Fig. 4. Test rig.", + "texts": [ + " In case of contact, which means IrN 1=\u00b00 , the desired distance I rN desired I follows: The system consists of an elastic rotor with one disc, which is mounted on two isotropic ball bearings. The auxiliary bearing is attached to the foundation via two unidirectional magnetic actuators. The air gap between the rotor and the auxiliary bearing is O. 3 mm. A magnetic bearing is used to create realistic excita tions to the rotor such as a sudden arising unbalance, so that the rotor comes into contact with the auxiliary bearing. A direct current disc-servomotor allows a rotational speed up to 3500 rpm. Several sensors are used to gather information, as it is shown in Fig. 4. There are two eddy current dis placement sensors to measure the position of the rotor beside the auxiliary bearing. The same sensors are installed inside the actuators. Load washers in each actuator are measuring the actuator forces, from which the contact forces are determined indirectly. With the help of accelerometers the load of the bearings are recorded. 3. Test rig (5) (4) IrN desired 1=/rN I-f (jrN j.vpmwJdt =/rN 11- f(jrN I-A ea/r'/)dt with !perm the desired contact force during the d 1 " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002359_s00170-010-2783-3-Figure12-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002359_s00170-010-2783-3-Figure12-1.png", + "caption": "Fig. 12 Temperature distribution of a steel die and b bimetallic die", + "texts": [ + " hc \u00bc 0:023 k D Re0:8Pr0:4 \u00f03\u00de 2; 500 < Re < 125; 000 and 0:6 < Pr < 100 Where, hc heat transfer coefficient k thermal conductivity of coolant (water) D Diameter of the cooling channels Re Reynolds number Pr Prandtl number 4.3 Results of finite element analysis Simulation result shows that for a given solidification time, bimetallic die cools the casting part at a much higher rate than that of a traditional steel die. Norwood et al. [19] reported from their experimental work that the die surface temperature reduces to 150-200\u00b0C after solidification of the casting part. For our analysis, Fig. 12a and b show the temperature distribution over the entire die after the completion of solidification. From the figures, it is noted that the final die surface temperature after the solidification process is 174\u00b0C. Figure 13 depicts the overall transient thermal behavior of the steel die and bimetallic die for the entire solidification process. For both dies, the temperature rises to its maximum value and then decreases to the ejection temperature. The steel die requires 24.6 s to reduce the temperature to the ejection point where as the bimetallic die takes only 7" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002189_ijrapidm.2010.036116-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002189_ijrapidm.2010.036116-Figure5-1.png", + "caption": "Figure 5 Laser engineered net shaping (LENS) (a) LENS process; (b) A pair of dies made using LENS; (c) A turbine blade made using LENS; (d) LENS used for refurbishing a turbine (see online version for colours)", + "texts": [ + " Of late, electron beam is becoming popular for these applications due to its better energy efficiency (15%\u201320%) but it requires high vacuum for the working environment (Kruth et al., 2005; Rannar et al., 2007; Wanjara et al., 2007). Laser engineered net-shaping (LENS) originally developed at Sandia National Laboratory (USA) and further developed and marketed by OptoMec (USA) is the most popular commercial RM process capable of handling a variety of metallic powders including titanium alloys (Griffith et al., 1998). Its deposition head uses 1 kW or 2 kW laser positioned at the centre and is surrounded by two or four nozzles [Figure 5(a)]. This head is mounted on a 3-axis manipulator. When the head is moved over a substrate, it creates a moving molten metal pool into which the powders from the nozzles dive and get integrated. As the powder used is fine, fluidised feeding using Argon is employed. By moving the welding head along appropriate raster and contouring paths, the object is built in layers. It permits usage of different powders through different nozzles with the ability to control their flow rates independently. Thus, LENS is capable of building gradient objects. This machine also comes with other types of manipulators. LENS has been successfully tested not only for fresh objects but also for repair of aerospace components [Figure 5(b\u2013d)]. LENS is a pure additive process and hence produces only a near-net shape which requires finish-machining on a separate machine. Furthermore, building the near-net object is totally automatic only for the objects free from undercuts. LENS does not use any support mechanism. Therefore, objects with undercuts and intricate shapes have to be built by suitably orienting the substrate; however, the required complex motion planning for such cases have to be created by the user. Apart from poor energy efficiency, this and other powder-deposition processes also suffer from poor powder efficiency of 10%\u201315% and slow deposition rates of 6\u201310 gm/min" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000563_j.fss.2007.05.009-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000563_j.fss.2007.05.009-Figure1-1.png", + "caption": "Fig. 1. (a) An FBF can be represented by a neuron. (b) The expansion of FBFs can be represented by a three-layer neural network (FBFN).", + "texts": [ + " The firing strength can also be defined as the fuzzy basis function (FBF) according to the Gaussian membership functions, and therefore the outputs (1) of the fuzzy system can be viewed as an FBF expansion [28]. Moreover, for ease of calculation, FBF j is simplified as j = n\u220f i=1 Aji (xi), j = 1, . . . , N. (2) An FBF j (x, cj , j ) = e\u2212[ T j (x\u2212cj )]2 (j = 1, 2, . . . , N) with input vector x = [x1, x2, . . . , xn]T, center vector cj = [cj1 cj2 \u00b7 \u00b7 \u00b7 cjN ]T and inverse width vector j = [ j1 j2 \u00b7 \u00b7 \u00b7 jN ]T denotes an neuron in the hidden layer, which represents the entire fuzzy system as the neural network architecture. Thus, Fig. 1 indicates that an FBF expansion can be constructed by a three-layer neural network with Gaussian activation functions and weights wkj connecting the hidden and output layers. Such an architecture representing the expansions of FBFs can be defined as the FBFN. For convenience, the FBFN output is presented in the following vector form: f(x, c, , W) = WT (x, c, ) (3) with f(x, c, , W) = [f1 f2 \u00b7 \u00b7 \u00b7 fm]T \u2208 m, c = [cT 1 cT 2 \u00b7 \u00b7 \u00b7 cT N ]T \u2208 nN , = [ T 1 T 2 \u00b7 \u00b7 \u00b7 T N ]T \u2208 nN , W = [w1 w2 \u00b7 \u00b7 \u00b7 wm] with wk \u2208 N(k = 1, 2, " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003741_icelmach.2012.6350105-Figure9-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003741_icelmach.2012.6350105-Figure9-1.png", + "caption": "Figure 9 - Phasor diagram of PM motor at no load. (Iq is neglected, very small positive Id is assumed)", + "texts": [ + " In the following tests it is assumed that the current required for core loss and friction windage loss remains unchanged, when the motor is operated under different loads and operating conditions. M A series of tests are done on the test motor while it is operating under no-load. A vector controlled drive is used to inject a phase current, which has a component along the daxis. The d-axis current component is gradually increased from zero to about 20 A first in the direction of the magnet flux and then in the demagnetizing direction. Under this condition the phasor diagram of the motor looks like the one shown in Figure 9. Since the motor is operating at no-load, the load angle is very small and may be taken to be zero, for the purpose here. In other words, the terminal voltage is approximately equal to Vq, i.e. its quadrature axis component. Note that the current component providing power to meet core loss is in alignment with the terminal voltage. In that case, the value of the direct axis inductance can be calculated from (5). In this equation bold symbols represent complex quantities. -, = \u2212 *+ |(\", \u2212 \"7)\u03c9'| (5) In (5) Ic is the no-load current" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001686_10407780903266489-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001686_10407780903266489-Figure4-1.png", + "caption": "Figure 4. A typical multiblock nonorthogonal grid and a typical enthalpy field.", + "texts": [ + "0 which means that the powder is heated to near melting-point temperature. The conductivity enhancement factor F k\u00bc 1.5 is used to partially offset the effect of convective circulation on heat transfer for h? 1 [22]. A higher conductivity enhancement factor of more than 2 has also been used elsewhere [25, 34]. The center of the laser beam is fixed at the location x?\u00bc 6.0 on the symmetry plane (i.e., z?\u00bc 0) for all of the test cases. 3.1. Effect of the Process Parameters on the Process Characteristics Figure 4 shows the multiblock nonorthogonal grid and contours of specific sensible enthalpy for P 10, U \u00bc 1.25, and m? p \u00bc 1:4. Only a part of the surrounding area near the molten pool is shown in the figure. The molten pool is recognized by the dark region where specific sensible enthalpy value h?> 1. The effect of scanning speed on the enthalpy field can be seen in the plot due to which there is a high enthalpy gradient in the upstream side and a low enthalpy gradient in the downstream elevated side. Also, there is a long hot zone trailing behind the laser beam due to the presence of convective term on the left-hand side of the energy equation Eq" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001911_s0580-9517(08)70593-2-Figure7-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001911_s0580-9517(08)70593-2-Figure7-1.png", + "caption": "FIG. 7. A Clark electrode and reaction vessel-this design is similar to that provided by Yellow Springs Instrument Company, Yellow Springs, Ohio.", + "texts": [ + " This coating procedure not only lowers the sensitivity of the electrode but also increases the response time by SO-lOO%. The commercial availability and robustness of the Clark type membrane covered electrode makes this the electrode of choice for most laboratories. I t differs from those previously described only by the separation of the anode and cathode from the reaction medium by a thin semi-permeable membrane through which oxygen readily diffuses into the electrolyte that immerses the anode and cathode (Fig. 7). The membrane material is usually Teflon or polyethylene and the electrolyte used is half-saturated KC1 solution or a similar paste formulation. As with most mass transfers across membranes, diffusion gradients are set up and these must be removed by continuous replenishment of fluid across the surface. This is easily achieved with a magnetic stirrer and a flea impeller (Fig. 7). Membrane electrodes are not poisoned so readily as open electrodes, unless left in contact for extended periods with cells or proteins. Usually a change of membranes, which takes 1-2 min, is sufficient to restore the efficiency of the electrode. The use of a membrane to isolate the anode and cathode, and their electrolyte, from the solution being measured also allows measurements to be made in gaseous phases and in non-conducting fluids. Another big advantage of the membrane electrode is that some of the classical inhibitors of respiration; e", + " The requisite minimum depths below which the tip of the electrode should be are listed in Table 2. These data (calculated from the equation described by Hill (1928)) refer to diffusion in a stationary medium, great care should be taken to control the possible continuous electrode error due to the enhanced oxygen concentrations which might be caused by either stirring the reaction medium directly or with rotating and vibrating electrodes. It therefore becomes essential with stirred (but not usually vibrating) systems that enclosed systems are used and that air bubbles are not trapped (see Fig. 7). Electrode measurements are very sensitive to temperature and agitation variations. Thus Clark electrodes have temperature coefficients of 2-8% of the reading per \"C change in temperature. Agitation conditions can only be assessed by showing that increased agitation produces no further increase in the response of the electrode system. This is easily done in stirred or rotating systems; fortunately, vibrating electrodes usually operate at frequencies beyond those that limit the oxygen measurements" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001288_j.robot.2008.10.021-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001288_j.robot.2008.10.021-Figure1-1.png", + "caption": "Fig. 1. The spatial configuration of the helicopter.", + "texts": [ + " The computational load of the proposedmethod is also analyzed, and is compared to that of the classical gradient descentmethod [25]. The computational load analysis proves the feasibility of the real-time implementation. Finally, the performance of themethod is studied through some simulated flight scenarios. The simplified dynamic equations of a helicopter, which are detailed enough for control development for quasi-steady maneuvers, are introduced. The aerodynamic tractions are assumed to be the control inputs. The spatial configuration of the helicopter is shown in the Fig. 1. Using the Newton\u2013Euler equations of motion, one can link the absolute linear and angular accelerations of the helicopter to the aerodynamic tractions exerted by the main and tail rotors. The inertial position of the helicopter is defined by vector pI , where the index I indicates the vector is expressed in the inertial frame {I}. Through the following vector: pI = [ xI yI zI ]T . (1) The indices I and B determine whether a vector is expressed in the inertial or body coordinate system, respectively" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003035_s12555-011-0132-4-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003035_s12555-011-0132-4-Figure2-1.png", + "caption": "Fig. 2. Quadrotor\u2019s configuration frame system.", + "texts": [ + " Unmanned Quadrotors [27] base their operation in the appropriate control of four rotors, and have received a growing attention, mainly due to their capability to outperform most of other types of quadrotors on the issues of maneuverability, survivability, simplicity of mechanics and increased payloads [11]. In addition, quadrotors is a very popular platform to develop control laws and examine their characteristics in order to draw conclusions that can be expanded to the whole rotorcraft family [28]. The modeling of the unmanned quadrotor depicted in Fig. 2, assumes that the structure is rigid and symmetrical, the center of gravity and the body fixed frame origin coincide, the propellers are rigid and the thrust and drag forces are proportional to the square of propeller\u2019s speed. Using the Euler-Lagrange formulation the system can be described by the following set of twelve order nonlinear ODEs of the form [19]: ( )f= ,X X U (1) with f a non-linear function, 12 \u2208\u211cX the state vector, and 5 \u2208\u211cU the input vector, or more analytically: 1 2 1 2 3 4 2 3 5 3 4 1 1 1 cos cos ) (cos sin cos sin sin ) (cos sin sin sin cos ) r r a a bU a a b U a b U z z z U m x x x U m y y y U \u03c6 \u03c6 \u03c6 \u03b8\u03c8 \u03b8 \u03b8 \u03b8 \u03c6\u03c8 \u03d5\u03b8 \u03c8\u03c8 \u03b8\u03d5\u03c8 \u03c6 \u03b8 \u03c6 \u03b8 \u03c8 \u03d5 \u03c8 \u03c6 \u03b8 \u03c8 \u03d5 \u03c8 \u23a1 \u23a4 \u23a2 \u23a5 \u23a2 \u23a5 + \u03a9 + \u23a2 \u23a5 \u23a2 \u23a5 \u23a2 \u23a5 \u2212 \u03a9 + \u23a2 \u23a5 \u23a2 \u23a5 \u23a2 \u23a5 + \u23a2 \u23a5= = \u23a2 \u23a5 \u23a2 \u23a5 /\u23a2 \u23a5 \u23a2 \u23a5 \u23a2 \u23a5 + /\u23a2 \u23a5 \u23a2 \u23a5 \u23a2 \u23a5 \u2212\u23a2 \u23a5\u23a2 \u23a5\u23a3 \u23a6 X " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002156_robot.2009.5152525-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002156_robot.2009.5152525-Figure5-1.png", + "caption": "Fig. 5. Fingertip contact model", + "texts": [ + " The stopper attached to the link is used to set a constant initial condition between the link and the disk. As shown in Fig. 3, the velocity, angular velocity, and direction of the ball after the release from the link are measured by image processing using a camera. Two dynamic models are presented based on the condition of contact between the ball and robot link: (1) the fingerlink contact model, and (2) the fingertip contact model. The finger-link contact model shown in Fig. 4 represents the dynamics where the ball and link keep a rolling contact condition. The fingertip contact model shown in Fig. 5 represents the dynamics where the ball is in contact with an edge of the link (fingertip). The relationship between the two contact models is illustrated in Fig. 6. The finger-link contact model is initially applied since the initial condition (see the most-left image in Fig. 3) is given under this condition. The ball is released from the link if the contact force fh acting on the ball from the link becomes zero. In this paper we don\u2019t discuss the case where the link contacts again with a ball once released" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003736_tac.2012.2232376-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003736_tac.2012.2232376-Figure2-1.png", + "caption": "Fig. 2. Parking problem for the car with a trailer, is a constant.", + "texts": [ + " The kinematic model is (4) Example 4: The ball with a trailer is as in example 3, where the trailer\u2019s position is known from the angle as described in Fig. 1(d). The distance between the ball and its trailer is denoted by : (5) Typical motion planning problems are: 1) for example (2), the parking problem: the non-admissible curve is , 2) for example (3), the full rolling with slipping problem, , where is the identity matrix. In Figs. 2 and 3, we show our approximating trajectories for both problems, that are in a sense universal. In Fig. 2, of course, the -scale of the trajectory is much larger than the -scale. The basic academic kinematic problems have a lot of symmetries, and most of them have finite dimensional Lie algebras. Due to these symmetries, the associated subriemannian problems are often integrable in Liouville sense (roughly speaking minimizers can be explicitly computed up to quadratures). These explicit solutions, of course, could be used directly to solve the motion planning problem. The drawback of our method is that it forgets about these particular structures since in the nilpotent approximations along the symmetries are not preserved" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002443_s12239-011-0023-y-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002443_s12239-011-0023-y-Figure1-1.png", + "caption": "Figure 1. Schematic of brake dynamics.", + "texts": [ + " These two deceleration performances are essential criteria used to confirm the braking performance. Consequently, many related laws and regulations have been established based on these two deceleration performances. Vehicle deceleration changes in proportion to the braking force. Braking force is determined by brake torque, which is calculated from brake line pressure and brake pad friction coefficient. Therefore, the vehicle deceleration can be expressed as a function of brake line pressure and the brake pad friction coefficient. Figure 1 shows the schematic of brake dynamics. Equation (1) represents these brake dynamics. The equation shows the relation between deceleration and brake line pressure. The pressure generating brake torque is not equal to the brake line pressure. There is a pad threshold pressure that is obstructive to movement of the brake pad. Thus, the threshold pressure will reduce the brake line pressure, and this reduced brake line pressure is the actual pressure resulting in brake torque (Limpert, 1992). (1) The friction in the brake system is usually assumed to be constant in most of the prediction program, but the actual friction coefficient of the brake pad is changing due to its non-linearities, such as braking pressure, velocity and temperature" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003869_s00419-012-0608-6-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003869_s00419-012-0608-6-Figure2-1.png", + "caption": "Fig. 2 The complete FE model of the system (a) and the cyclic symmetry sector of the FE model (b)", + "texts": [ + " The simplified geometrical model of the system consists of five sectors (see Fig. 1) that have the cyclic symmetry feature. Each of these segments is meshed by using standard procedures of the ANSYS software. The 3-D solid mesh is elaborated and as mentioned earlier, the ten-node tetrahedral element (solid92) with three degrees of freedom in each node is used to realize each sector. During the mesh generation process, it is assumed that the maximum length of each element\u2019s side needs to be no more than 2.7 [mm]. The developed FE model is displayed in Fig. 2, and it consists of 19,620 elements and 36,188 nodes, respectively. The particular sectors are glued as a whole at the geometrical model preparing the stage by using standard procedure of the ANSYS program. The analysed gear is mounted in the roller bearings. Such bearings typically have slight load capacity under loads perpendicular to the primary supported direction. The gear shaft neck surfaces on which the bearings are assembled are denoted \u201cbearing\u201d (see Fig. 3a). The gear mates with the other devices by the splines", + " Dynamic analysis is performed for the auxiliary model cases rotating at predetermined angular speed, where diameter of though holes d01 (see Fig. 3b) varies as seen in Table 2. Findings are compared to each other both quantitatively and qualitatively. This method makes it possible to investigate deformations of nodal lines associated with nodal diameters and circles due to through holes and then determine correspondence between oscillation modes of solid circular disc and a plate with holes. In the final step, solutions found for the auxiliary model are compared with the solution for the system whose FEM model is shown in Fig. 2 (the principal model). As for the principal model case, the 3-D solid mesh and the ten-node tetrahedral element (solid92) are used to discretize the auxiliary models. For all models subject to analysis, the boundary conditions were applied to the nodes. For each model, 1 d f associated with node radial displacement was subtracted from the nodes found on the surface identified as a bearing (see Fig. 3a,b). Furthermore, 1 d f associated with the displacement of nodes along the centreline of each model was subtracted from the nodes found on the surface, identified as a joint (see Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000069_841057-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000069_841057-Figure4-1.png", + "caption": "Fig. 4 - Liapunov stability results using the modified kinetic energy function for data set 2", + "texts": [ + " The v2 = - 12 ii y '12\"z 16\\y 5 B17Vynz + B18Vyflz + B19az' B^ 0", + "8) of the function given by Eq. (8.1), we obtain of oSi of oeS i \u00bc 4 S3 q eS 3 2 dq deS 3 6 0: Therefore, Drucker\u2019s postulate is fulfilled for the part of the loading surface given by Eq. (8.1). As a corner point arises on the loading surface, i.e. f cannot be expressed in an explicit form, the fulfillment of Drucker\u2019s postulate, d~S d~eS P 0; may be studied by means of verifying of the above inequality for each plane: d~S d~eS N P 0; \u00f08:2\u00de where d~eS N is an increment of plastic strain vector for a plane with normal ~N (Fig. 13a). It is clear that if the inequality (8.2) is valid for one plane, the vector d~eS, being the sum of components d~eS N , also satisfies this inequality or, in other words, it makes an acute angle with vector d~S. Therefore, our object now is the angle, g, between vectors d~eS N and d~S. The projections of the vector d~eS N on S1- and S3axis can be determined on the base of Eqs. (3.8), (3.12) and (3.31): d~eNS 1 \u00bc duN cos a cos b cos k~g1; d~eNS 3 \u00bc duN sin b cos k~g3: \u00f08:3\u00de Eq. (8.3) gives that d~eS N3 d~eS N1 \u00bc tan H \u00bc tan b cos a : This formula determines the angle H which the increment vector d~eS N makes with S1-axis. Angles H, d, and g are shown in Fig. 15, from which it is evident that g = p/2 + d H, and the angle g must satisfy inequality g 6 p/2 or d 6 arctan tan b cosa : It is sufficient to show that d 6 b for a \u00bc 0 \u00f08:4\u00de because 0 < cosa 6 1 for a1 6 a 6 a1. As follows from Fig. 13a, the inequality (8.4) is always fulfilled because angle b falls into the region d 6 b 6 b1 for any plane located on the endpoint of vector d~S. For the planes tangential to sphere (3.23) and for the boundary planes constituting the generator of cone (b = \u00b1b1), Drucker\u2019s postulate is automatically satisfied because the incremental strain vectors are perpendicular to these planes. The fulfillment of Drucker\u2019s postulate, examined through Eqs. (8.2)\u2013(8.4), can be extended for an arbitrary state of stress employing the procedure in Section 5" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003268_j.ymssp.2012.10.005-Figure12-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003268_j.ymssp.2012.10.005-Figure12-1.png", + "caption": "Fig. 12. Friction and separator discs after 10,000 duty cycles, courtesy of Dana Spicer Off Highway Belgium.", + "texts": [ + " In order to prepare for the forthcoming duty cycle, both driving motors are braked at the time instant tb, such that the driveline can stand still for a while. The ALT procedure discussed above is continuously repeated until a given total number of duty cycles is attained. For the sake of time efficiency in measurement, all the ALTs are performed for 10,000 duty cycles. Moreover, when testing the clutch pack is sprayed by the ATF due to the centrifugal force effect, which represents the actual operation. The ATF is continuously filtered, such that it is reasonable to assume that the used ATF has not degraded during all the tests. Fig. 12 shows the photographs of friction and separator discs of a wet friction clutch after 10,000 duty cycles, taken from the first clutch pack. It can be seen that the surface of the friction discs has become smooth and glossy, see Fig. 12. Nevertheless, it is evident that the separator discs are still in good condition. The change of the color (darkening, see Fig. 13) and the surface topography (flattening, see Fig. 14) of the friction discs is known as a result of the glazing phenomenon that is believed to be caused by a combination of wear and thermal degradation [9]. The experimental results obtained from all the tests are presented and discussed in this section. The representative measured signals obtained from the run-in tests and ALTs are depicted in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000419_1.2735636-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000419_1.2735636-Figure3-1.png", + "caption": "Fig. 3 The general 7R single-loop mechanism", + "texts": [ + " By the way, the right solutions can also be found when taking the rotary angle 1 but not 6 as the imaginary value. However, the derivation of formulas is much easier when taking 6 as an imaginary value, so we suggest that 6 should be taken as an imaginary value. Forward Kinematic Analysis of the General 7R Mechanism The displacement analysis of the general seven-link 7R mechanism has been a very significant and important problem in the theory of the spatial mechanisms. The configuration of the general 7R single-loop mechanism is shown in Fig. 3. The displacement analysis of this mechanism can be stated as follows: given input angle 7, and structural parameters, determine six rotary angles i i=1\u20136 . Given input angle 7, we can convert the 7R serial robot problem to the 6R serial robot problem. Accordingly, the forward kinematics problem of the general 7R single-loop mechanism is coincident with the inverse kinematics problem of the general 6R serial robot in nature, so its computing method and steps are omitted here. Numerical Examples Example 1", + "364396051,1.537440730 Structural parameters are shown below l1 = 0 l2 = 0.56 l3 = 0.61 l4 = 0.32 l5 = 0.43 l6 = 0.35 l7 = 0.23 a1 = 0.76 a2 = 1.36 a3 = 0.81 a4 = 1.31 a5 = 1.43 a6 = 1.26 12 = 1.2 23 = 0.5 34 = 1.4 45 = \u2212 /4 56 = \u2212 /3 67 = 1.9 here the angular unit is radian, and other units are millimeter. With the help of the software, Matlab7.0, all the real solutions re obtained and shown in Table 1. Example 2. The general 7R single-loop mechanism with the ame dimensions as those in Ref. 6 is shown in Fig. 3, and the imensions are given as follows l1 = 0.59 l2 = 1.09 l3 = 0.50 l4 = 0.70 l5 = 0.80 Table 1 The real solutions to inverse kine o. 6 deg 5 deg 4 deg \u2212167.378529 \u2212164.555197 116.163 2.863131 126.648935 \u221254.710 121.583545 123.169018 \u2212171.604 132.849530 \u2212105.429355 150.690 Table 2 The real solutions to forward kinematics o. 6 deg 5 deg 4 deg 9.678847 60.523803 \u221211.822 39.073405 42.210142 26.082 56.932017 176.843726 \u221266.850 82.533411 21.696183 \u2212119.607 84.529335 22.237055 151.813 105.991053 94" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003560_978-1-4613-4560-2_2-Figure8.31-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003560_978-1-4613-4560-2_2-Figure8.31-1.png", + "caption": "Fig. 8.31. In the narrow region of small overpotentials, the i versus 1] relationship is linear, and, at sufficiently high positive or negative overpotentials, the i versus 1] relationship becomes exponential.", + "texts": [ + " Hence, equal magnitudes of 'fJ on either side of the zero produce equal currents; and, conversely, equal de-electronation and electronation currents should produce equal overpotentials, or current produced potentials, 'fJ. This means that the interface cannot rectify a periodically varying potential or current (Fig. 8.29). On the other hand, if fJ \"* to then the i versus rJ curve would not be symmetrical and the inter face would have rectifying properties (Fig. 8.30). The effect, known as faradaic rectification, was discovered by Doss. The hyperbolic sine function has two interesting limiting cases (Fig. 8.31). The first limiting case is when the overpotential rJ [Eq. (8.31)] or the excess field (JX [Eq. (8.35)] is numerically large. This is the high-over potential or high-field approximation. Under these conditions of large rJ (if the example of a net de-electronation reaction is taken), and, since the e-F~/2RT term tends to zero, 2 sinh ~ '\" eF~/2RT 2RT - (8.39) (8.40) Hence, under high fields, the Butler-Volmer equation reduces [from (8.38)] to (8.41 ) i.e., the current density increases exponentially with the overpotential 'YJ or with the driving force of the excess electric field across the double layer" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003102_j.rcim.2013.03.002-Figure8-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003102_j.rcim.2013.03.002-Figure8-1.png", + "caption": "Fig. 8. The 3-CUP parallel mechanism close to (a) singular configuration (i) and (ii), (b) singular configuration (iii) and (iv).", + "texts": [ + " (20) results in J f \u00bc C\u03b1\u00f016C\u03b22b1 \u00fe 4 ffiffiffi 3 p S\u03b1S2\u03b2\u00f0\u2212b2 \u00fe b3\u00de \u00fe \u00f011\u00fe 6C2\u03b1C\u03b22\u2212C2\u03b2\u00de\u00f0b2 \u00fe b3\u00de\u00de2 8\u00f0b1 \u00fe b2 \u00fe b3\u00de\u00f0b2b3 \u00fe b1\u00f0b2 \u00fe b3\u00de\u00deqD \u00f021a\u00de where qD \u00bc \u00f012S\u03b1S2\u03b2\u00f0\u2212b2 \u00fe b3\u00de \u00fe 6 ffiffiffi 3 p C2\u03b1C\u03b22\u00f0b2 \u00fe b3\u00de \u00fe ffiffiffi 3 p \u00f016C\u03b22b1\u2212\u00f0\u221211\u00fe C2\u03b2\u00de\u00f0b2 \u00fe b3\u00de\u00de\u00de \u00f021b\u00de From inspection of Eq. (21a), is determined that jJf j \u00bc 0 when: (i) \u03b1\u00bc 901 and (ii) \u03b1\u00bc \u2212901. Note that these configurations are not reachable, since either the stroke d2 or d3 tend to have an infinite value in those poses. In this case the actuators would have act on the same plane, and this cannot occur without disassembling the mechanism. Fig. 8a shows a CAD model of the 3-CUP parallel mechanism close to the singular configurations. Furthermore, singular configurations (iii) \u03b2\u00bc901 and (iv) \u03b2\u00bc\u2212901 were obtained by analyzing the motion and constraint screws. In order to obtain the configuration in which the P joint represented by $15 becomes redundant due to the action of the P joint represented by $11 (this means that both screws are linearly dependent), it is necessary to determine the value of \u03b2 where the result is a loss of 1 DOF in leg 1", + " (27) indicates that the platform shows two DOF for the singular configurations (iii) and (iv), namely: one translation along the Z axis, and a rotation that will produce linear parasitic motions along the XY plane. Note that the platform mobility is changed considerably by losing one DOF, hence this singular configuration is known as serial singularity [1], since it is present due to the singularity of the open kinematic chain of leg 1. The linear dependency of screws $15 and $11 indicates that the prismatic joint of the cylindrical pair and the passive parasitic joint will act on the same axis resulting in a loss of DOF. Fig. 8(b) shows the CAD model of the PM close to the singular configurations (iii) and (iv). The following section presents a study of the orientation workspace of the platform. Furthermore, the parasitic position workspace is introduced and discussed. The approach followed in this paper for having an insight into the possible orientations reached by the manipulator, considers the unit vector that is normal to the platform from Eq. (9). The components of this unit vector change according to the platform orientation and is calculated by using all the possible combinations of strokes magnitudes" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000727_j.aca.2008.01.049-Figure8-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000727_j.aca.2008.01.049-Figure8-1.png", + "caption": "Fig. 8 \u2013 Effect of LDH concentration on fluorescence intensity under different states. Each point on the curve in", + "texts": [ + " For comparing the catalysis efficiency of the liquid and immobilized-LDH enzymes, the following experiment was done. The concentration of LDH immobilized in IE-ECBR was 5 kU L\u22121, and the concentration of liquid LDH also was 5 kU L\u22121. Used concentration of NAD+ all was 5.0 mmol L\u22121 in both methods. Other conditions are as in Section 3.6. A series of the lactate standard solutions were used as the test samples. Under the same experimental conditions, it was conducted the detection for the fluorescence intensities of the testing solutions. Obtained result in Fig. 8 presents the analytical characteristics of these capillaries with immobilized and liquid LDHs. It can be seen that IE-FCA method employing the immobilized LDH showed more advantages than the liquid LDH. Although the linearity of the FCA using liquid LDH and IE-FCA are all better, but if LDH was immobilized (solid dots) on inner surface of the capillaries, its analytical sensitivity was much better than that of the liquid LDH (hollow dots). So after the LDH was immobilized on the capillaries, it has not only the better selectivity, but also has better catalysis efficiency than the liquid LDH" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003404_isma.2013.6547379-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003404_isma.2013.6547379-Figure5-1.png", + "caption": "Figure 5. Changing the quadrotor heading.", + "texts": [ + " To command the quadrotor to move in the X direction, the speed of the front and rear propellers should be changed by the same amount and in opposite directions as shown in Figure 3. Moving the quadrotor in the Y direction can be done by changing the speed of the right and left propellers by the same amount and in opposite directions as shown in Figure 4. 978-1-4673-5016-7/13/$31.00 \u00a92013 IEEE ISMA13-2 To control quadrotor heading, the speed of all propellers is commanded by the same amount but in different directions, front and rear propellers with the same direction and right and left the propellers with opposite direction, as shown in Figure 5. The quadrotor\u2019s model, mainly includes the nonlinear aero dynamical equations of the quadrotor along with the actuators dynamics and saturation limits [10-13]. The model is represented as follows: 1(sin sin cos sin cos ) U X m = \u03a8 \u03a6+ \u03a8 \u0398 \u03a6 (1) 1( cos sin sin sin cos ) U Y m = \u2212 \u03a8 \u03a6+ \u03a8 \u0398 \u03a6 (2) 1(cos cos ) U Z g m =\u2212 + \u0398 \u03a6 (3) 2yy zz xx xx I I U p qr I I \u2212 = \u2212 (4) 3zz xx yy yy I I U q pr I I \u2212 = \u2212 (5) 4xx yy zz zz I I U r pq I I \u2212 = \u2212 (6) where , ,X Y Z are the position of the center of mass WRT inertial frame, , ,\u03c6 \u03b8 \u03c8 are the Euler angles, , ,p q r are the body rates, m is the quadrotor\u2019s mass, , , xx yy zz I I I are the moments of inertia, 1 2 3 4 , , ,U U U U are the throttle, roll, pitch and yaw forces and moments respectively" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003869_s00419-012-0608-6-Figure19-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003869_s00419-012-0608-6-Figure19-1.png", + "caption": "Fig. 19 The mode shapes corresponding to frequency \u03c918 (the first and second mode)", + "texts": [], + "surrounding_texts": [ + "As mentioned earlier, in the geometrical model of the gear, the geometry of the teeth is omitted. It allows us to reduce the system\u2019s FE model size. The simplified geometrical model of the system consists of five sectors (see Fig. 1) that have the cyclic symmetry feature. Each of these segments is meshed by using standard procedures of the ANSYS software. The 3-D solid mesh is elaborated and as mentioned earlier, the ten-node tetrahedral element (solid92) with three degrees of freedom in each node is used to realize each sector. During the mesh generation process, it is assumed that the maximum length of each element\u2019s side needs to be no more than 2.7 [mm]. The developed FE model is displayed in Fig. 2, and it consists of 19,620 elements and 36,188 nodes, respectively. The particular sectors are glued as a whole at the geometrical model preparing the stage by using standard procedure of the ANSYS program. The analysed gear is mounted in the roller bearings. Such bearings typically have slight load capacity under loads perpendicular to the primary supported direction. The gear shaft neck surfaces on which the bearings are assembled are denoted \u201cbearing\u201d (see Fig. 3a). The gear mates with the other devices by the splines. The splines is simplified down to a regular cylinder of the diameter assumed as equal to the splines pitch diameter. The surface denoted \u201cjoint\u201d (see Fig. 3a) is located on the pitch diameter of the splines. Parameters of the analysed system are shown in Table 1a\u2013b. The calculation results for natural flexural oscillations taking into account angular speed of the gear are shown in the paper. In the case of circular discs and annular plates, for each solution where nodal lines are nodal diameters, one obtains two identical arrangements of straight nodal lines, rotated by an angle of \u03b1 = \u03c0/(2n) one to another, where n is the number of nodal diameters. In accordance with the circular and annular plate vibration theory [5,6,12], the particular natural frequencies of vibration are denoted as \u03c9mn , where m refers to the number of nodal circles and n is the mentioned number of nodal diameters. As the shape of the gear model is fairy elaborate, the flexural modes of the system are subject to deformation (as compared to the system without any holes) to such extent that establishing which particular node it refers to becomes rather difficult. This problem is even worse if the angular speed of the gear is varying. The problem of influence of the angular speed on the flexural gear models deformation is analysed. For the purpose of identification of these modes, an algorithm of tagging oscillation modes, which determines the correspondence between vibration of the circular disc versus disc with holes, is used. For this purpose, an auxiliary model of annular plate in the form shown in Fig. 3b is used. The geometrical dimensions of the auxiliary model were taken from the gear geometry (shown in Fig. 1). They are as follows: addendum circle diameter dz , rim mounting diameter dp, root circle diameter dw2, and thickness h p and hz (see Table 1). Dynamic analysis is performed for the auxiliary model cases rotating at predetermined angular speed, where diameter of though holes d01 (see Fig. 3b) varies as seen in Table 2. Findings are compared to each other both quantitatively and qualitatively. This method makes it possible to investigate deformations of nodal lines associated with nodal diameters and circles due to through holes and then determine correspondence between oscillation modes of solid circular disc and a plate with holes. In the final step, solutions found for the auxiliary model are compared with the solution for the system whose FEM model is shown in Fig. 2 (the principal model). As for the principal model case, the 3-D solid mesh and the ten-node tetrahedral element (solid92) are used to discretize the auxiliary models. For all models subject to analysis, the boundary conditions were applied to the nodes. For each model, 1 d f associated with node radial displacement was subtracted from the nodes found on the surface identified as a bearing (see Fig. 3a,b). Furthermore, 1 d f associated with the displacement of nodes along the centreline of each model was subtracted from the nodes found on the surface, identified as a joint (see Fig. 3a,b). For the models obtained in this way, calculations were kept conducted as long as the natural frequency \u03c918 was determined. The calculations were performed assuming that the systems rotate as angular speed of \u03b8 , within the range of 0\u20131047 [ rad/s]. During the computing process, the angular speed values were gradually increased by 80[ rad/s], which made fourteen variants of the results (the natural frequencies and corresponding natural modes), which were subject to further interpretation. The rotation effect was taken into account by determining stress distribution due to rotation, for each model during the computational step associated with static analysis (the so called pre-stress effect). This stress distribution was then included in the computation step associated with modal analysis. The results of the numerical calculations related to the procedure of identifying deformed natural modes of flexural vibration of the gear under consideration are shown below. The results displayed here relate to the determination of the correspondence between the natural frequencies \u03c916 and \u03c925 at high angular speed (\u03b8 = 1047 [ rad/s]) as well as to the correspondence between oscillation modes and the natural frequency \u03c931 at lower angular speeds (\u03b8 = 80 [ rad/s]). The results as shown in Figs. 4, 5, 6, 7, 8, 9 allow for tracking deformations of nodal lines associated with nodal circles and diameters, due to varying diameter of the through holes. With respect to the natural frequency \u03c925, there is marked difference in shapes of natural modes. When one compares the results between each other, one can notice that in order to identify correctly deformed natural modes of the flexural oscillations in the gear under consideration at lower angular speeds, larger number of auxiliary models is required to be included during calculations, as compared to the higher angular speeds. It comes from the fact that additional stresses through the centrifugal effects appear. This effect causes the gear flexural stiffness to be an apparent function of rotational speed (stiffness grows for higher speed). In the next part, results of the numerical calculations associated with the extent of the influence of the angular speed to deformation of mode shapes of oscillations. For each discussed case, both mode solutions related to nodal diameters are shown. These analysed results are sorted by the order of their occurrence. For the frequencies \u03c923 and \u03c918, the results were obtained at angular speeds of \u03b8 = 0 and \u03b8 =1,047 [ rad/s] respectively. For the other cases, results were obtained at angular speeds \u03b8 of, 0, 320, 720, and 1,047 [ rad/s], respectively. Natural frequencies for these modes are included in Table 3. To determine this mode (see Figs. 10, 11), the procedure of tagging natural oscillation modes was required. Nodal lines associated with the circle and diameter are deformed. Minor influence of the angular speed to deformation of the nodal lines is noticeable. The task of determining modes in this case was not too difficult (see Figs. 12); no procedure of tagging natural oscillation modes was required. The slight impact of the gear angular velocity on the distortion of the nodal lines is observed. For these modes (see Figs. 13, 14), procedure of tagging natural oscillation modes was required. It is noticeable that angular speed affects markedly deformation of the nodal lines. Once the angular speed of 720 [ rad/s] is exceeded, the oscillation mode takes different shape. Major deformation of mode shape attributable to the shaft vibrations is evident at this speed. Moreover, additional problem associated with some similarity of the mode being tagged to the mode associated with frequency of \u03c931, emerged during mode identification. Establishing the correspondence between these modes was a complex task (see Figs. 15, 16) due to the shape of oscillation modes similarity to the case discussed earlier. The angular speed affects deformation of nodal lines markedly. Major shape mode variations emerge at \u03b8 = 400 [ rad/s]. The identification process in this mode was not easy (see Figs. 17, 18) . One can notice that angular speed affects the deformation of nodal lines. Major variation in mode shape emerges at \u03b8 = 720 [ rad/s]. Moreover, additional annular shaft vibration emerges at the highest considered angular speed. Finding correct correspondence between the modes in this case was fairly easy (see Figs. 19). High repeatability in deformations of nodal lines on circular plate at various angular speeds is noticeable. As a consequence of the conducted analysis (see Table 3), the Campbell diagram was plotted for the gear under consideration. This is a convenient method of displaying the relationship between gear natural frequencies and transmission system excitations [4]. Excited frequencies are plotted on a vertical axis, and the gear speed of rotation is plotted on the horizontal axis (see Fig. 20). Natural frequencies achieved from numerical analysis are plotted as near-horizontal curves. The forced frequency due to the meshing is determined by the following relation (as in Ref. [4]) f = n0 \u00b7 z 60 (4) where n0 [rpm] is the rotational speed and z is the number of teeth in the gear. For this system, the gear teeth number is z = 59. Vibration resonance phenomenon occurs when forcing frequency (4) matches as to its value with some natural oscillation frequency of the gear. The points where the near-horizontal \u03c9mn curves intersect the straight line (4) indicate the speeds at which the gear resonance will be excited (see Fig. 20). For instance, the rated excitation speed for the natural frequency of \u03c923 is 764 [rpm]. It may be inferred from both the Campbell diagram and Table 3 that the rotating movement makes flexural stiffness of the gear under consideration to increase. Moreover, at speed of 3,820 [rpm], one can notice major surge associated with the mentioned earlier changing of the shape of the natural mode frequency in the case of the frequency of \u03c931. The growth of the gear transversal stiffness observed during gyrate of the gear comes from the appearance of the additional stresses in the toothed gear through the centrifugal effects. The higher rotational speed generates higher centrifugal forces, higher stress level, thereby causing the transversal stiffness of the system to increase. Moreover, the growth of the gear flexural stiffness through the gyrate effect causes reduction of the needed numerical calculations connected with identifying the proper distorted mode shapes." + ] + }, + { + "image_filename": "designv11_7_0003865_j.jtbi.2011.12.003-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003865_j.jtbi.2011.12.003-Figure4-1.png", + "caption": "Fig. 4. A sinusoidal path in the x1\u2013x2 plane on which the ant is assumed to run at a constant speed v.", + "texts": [ + " Recall that i is the unit base vector parallel to the x-axis previously defined in conjunction with Eq. (4). The velocity vector, v P , in the x1 x2 plane of point P, with the ant\u2019s gaster at a fixed elevation, is thus v P \u00bc dr P dt \u00bc dr dt \u00fexP di dt \u00bc v C \u00fexP da dt j \u00bc v C \u00fexPoj \u00f013\u00de where v C is the velocity vector in the x1 x2 plane of the ant\u2019s center of mass, j is the unit base vector parallel to the y-axis previously defined in conjunction with Eq. (4), and a is the angle between the x1-axis and the x-axis, i.e. between the x1-axis and the long dimension of the ant\u2019s body as shown in Fig. 4. In Eq. (13), it has been recognized that, due to the fact that the ant must turn to follow a curved path, di=dt\u00bc j da=dt, and that da/dt is the angular velocity, o, of the ant. The situation is illustrated in Fig. 4, though this figure is for a sinusoidal path that will be explored below. Nevertheless, the significance of the parameters illustrated in Fig. 4 is general. Assume that the ant has no sideways motion, and runs at speed v parallel to its long axis, i.e. the velocity is always parallel to the x-axis (fixed in the ant) as shown in Fig. 3. However, the path may be tortuous, and the ant controls the motion of point P. Thus, we take the velocity vector, v P , of the point P within the ant to be v P \u00bc vi \u00f014\u00de As a consequence, the acceleration of the center of mass of the ant is dv C dt \u00bc dv dt \u00fexPo2 i\u00fe\u00f0vo xP _o\u00dej \u00f015\u00de where we have used dj=dt \u00bc oi", + " In addition, we note that the circular path is different from a tortuous one in that covering the circular path at steady speed involves no angular acceleration, in contrast to the twisting back and forth that is required when the ant zig-zags. Furthermore, it seems unlikely that the ant will persist in running for long times on circular paths, as this behavior gains it little, other than perhaps a transient ability to escape a predator. For this reason, we now turn to an ant running at constant speed on a sinusoidal path possessing characteristics that typify a tortuous trajectory. Let the ant\u2019s sinusoidal path have the form x2 \u00bc b 2 sin 2x1p l \u00f026\u00de as illustrated in Fig. 4, with b the amplitude of the sinusoid and l its wavelength. Note that tana\u00bc dx2 dx1 \u00bc pb l cos 2x1p l \u00f027\u00de Differentiation of Eq. (27) with respect to time provides o\u00bc 2p2bvsin\u00f02x1p=l\u00de l2 \u00bd1\u00fe\u00f0p2b2=l2 \u00decos2\u00f02x1p=l\u00de 3=2 \u00f028\u00de where we have used dx1=dt\u00bc vcosa, a result that arises by projection of the ant\u2019s velocity on the x1-axis. We then use Eq. (15) to calculate the acceleration of the ant\u2019s center of gravity at constant speed, v, and with xP\u00bc0 as dv C dt \u00bc 2p2bv2 sin\u00f02x1p=l\u00de l2 \u00bd1\u00fe\u00f0p2b2=l2 \u00decos2\u00f02x1p=l\u00de 3=2 j \u00f029\u00de which is maximized at x1\u00bc(2n 1)l/4, where n is a positive integer" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001962_j.engfracmech.2010.05.001-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001962_j.engfracmech.2010.05.001-Figure5-1.png", + "caption": "Fig. 5. Comparison of notch stress and bending stress distribution.", + "texts": [ + " For the simulation of fatigue crack growth in hollow wheelset axles with NASGRO 3.0.16 two types of crack growth models are useful: \u2013 Thumbnail in a hollow cylinder (NASGRO model SC05) (Fig. 4a). \u2013 Surface crack in a plate (NASGRO model SC02) (Fig. 4b). With model SC05 only linear bending stresses and constant tensile stresses can be applied. However, a wheelset axle in the fillet region is exposed to a non-linear notch stress distribution superimposed by non-linear stresses induced by the press fit of the wheel or other components (Fig. 5). Using the analytical model SC05 the linear nominal bending stress distribution rN is multiplied by the stress concentration factor at the surface. This scaled bending stress distribution is superimposed by a constant positive press fit stress rP, which is reached at the surface in the region of the crack, i.e. the R-ratio shifts from 1 to higher values. By this method it is ensured that the stresses at the surface are identical with the superimposed notch and press fit stresses. In the inner of the wheelset axle the stresses are overestimated and in general a conservative result is obtained" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000084_s00170-005-0312-6-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000084_s00170-005-0312-6-Figure4-1.png", + "caption": "Fig. 4 Tilting and yaw angle on the local coordinate", + "texts": [ + " Assuming Pa as the contact point between cutter and surface, the tool tip Pt can be indicated as: where R is the radius of cutter, ns is surface normal, and Ta is the tool orientation vector. Therefore, while the data of tool tip Pt is known, the five joint variables of the five-axis machine tool can be calculated through the postprocessor, and the NC program can be completed. During the five-axis machining, the rotational axes change with the effect of part surface shape or interference between cutter and workpiece. Therefore, the cutter orientation being relative to the local coordinate system of the surface has to be defined. As shown in Fig. 4, the CC point of ball-end cutter is at point Pa on the planes XL\u2013YL. If the cutter orientation firstly turns around the axis XL on the local coordinate system at an angle \u03b1s, and turns around the axis ZL at an angle \u03b2s, where \u03b1s is called tilting angle and \u03b2s is called yaw angle, then the axis vector (Ta) of the cutter orientation after rotation is: Ta \u00bc sin\u03b1s sin \u03b2siL sin\u03b1s cos\u03b2s jL \u00fe cos\u03b1skL: (4) In this equation, iL, jL and kL represent the unit vectors of local coordinate system on the axes XL, YL, and ZL, respectively" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003551_rnc.3118-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003551_rnc.3118-Figure1-1.png", + "caption": "Figure 1. Directed interaction topology G.", + "texts": [ + " Although sufficient or even necessary and sufficient conditions for swarm systems to achieve state containment have been proposed in [30\u201333], the relative information about the states of the neighbors of the agents is required available to construct the protocols by these approaches. In some practical applications, only outputs of agents are available and only output containment is required to be achieved. In this case, the state containment approaches proposed in [30\u201333] will become invalid. In this section, a numerical example is given to illustrate the effectiveness of theoretical results obtained in the previous sections. Consider a fifth-order swarm system with thirteen agents. The interaction topology of the swarm system in the example is shown in Figure 1. For simplicity, it is assumed that the interaction topology has 0 1 weights. The dynamics of each agent is described by (1) with AD 2 6664 8 8 6 2 6 3 2 3 1 2 2 2.5 0.5 0.5 2 6 8.5 4.5 0.5 5 4 2 3 2 2 3 7775 ,B D 2 6664 0 1 0 1 0 1 1 0 0 1 1 0 0 1 1 3 7775 ,C D 2 4 1 0 0 1 0 0 0 1 0 1 0 1 1 0 0 3 5 . Assume that there are eight followers and five leaders in the swarm system. Choose NC D 1 0 0 1 1 1 1 1 0 1 . It can be verified that . NA22, NA12/ is not completely observable, then choose a nonsingular matrix OT as follows OT D 1 1 1 1 " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002982_elan.201200443-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002982_elan.201200443-Figure1-1.png", + "caption": "Fig. 1. A scheme of the tubular detector of silver solid amalgam (TD-AgSA). 1) Teflon capillary (inner diameter ID1 =0.5 mm, outer diameter OD1 =1.6 mm), 2) Teflon tube (ID2 =1.6 mm, OD2 =3.1 mm), 3) column of silver solid amalgam (ID1, OD1, length L=6.0, 7.5, or 13.5 mm), 4) platinum contact, 5) Teflon capillary (ID1, OD1, length 2.0 mm).", + "texts": [ + " In this paper, the tubular detector based on silver solid amalgam (TD-AgSA) is described and tested. For this purposes Zn2+ and Cd2+ were selected as representatives of inorganic reducible analytes and 4-nitrophenol as an organic one. It is shown that this TD-AgSA represents a miniature detector with a simple, robust and inexpensive construction which provides sufficient sensitivity and a good repeatability of measurements even at highly negative potentials. Construction of the detector: A piece of PEEK capillary with the same ID1 and OD1 as the inlet Teflon capillary 1 (see Figure 1) is inserted into the Teflon tube 2 in place of the planned beginning of the silver solid amalgam column. A steel needle with ID1 and length of a few mm larger than tube 2 is moved via PEEK capillary and then the tube 2 is placed in the vertical position. A silver powder (flakes 10 mm, Sigma-Aldrich) is gradually added into the upper hole of the tube 2 and it is pressed by another piece of a PEEK capillary with ID1 and OD1. As soon as the length of the silver powder column will be 2\u2013 3 mm, a hole is created in the tube 2 just above the silver column" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001907_s10514-010-9205-0-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001907_s10514-010-9205-0-Figure1-1.png", + "caption": "Fig. 1 A rigid body suspended by n cables with world-frame pivot points qi . Analysis techniques for cable-actuated parallel manipulators assume that qi is fixed while li varies in magnitude, while for cooperative aerial manipulation we fix li and vary qi by changing the positions of the aerial robots", + "texts": [ + " (2008), the authors consider the problem of cooperative towing with a team of ground robots, where under quasi-static assumptions there is a unique solution to the motion of the object given the robot motions. This approach is not directly extensible to three-dimensional manipulation where frictional ground forces are absent and gravity introduces dynamics into the problem. The cooperative aerial towing problem is similar to the problem of controlling cable-actuated parallel manipulators in three dimensions, where in the former the payload pose is affected by robot positions and in the latter pose control is accomplished by varying the lengths of multiple cable attachments (see Fig. 1). Thus the work on workspace analysis (Stump and Kumar 2006; Verhoeven 2004), control (Oh and Agrawal 2007), and static analysis (Bosscher and Ebert-Uphoff 2004) of such parallel manipulators is directly relevant to this paper. Also relevant to this paper is the work on the dynamics of a cable-suspended payload (Henderson et al. 1999) and control strategies that ensure the placement and stability of the payload in flight (Etkin 1998; Sgarioto and Trivailo 2005; Williams et al. 2006). More generally, we are interested in the mechanics of payloads suspended by n cables in three dimensions" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003752_iecon.2011.6119355-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003752_iecon.2011.6119355-Figure1-1.png", + "caption": "Fig. 1. The diagrams of the relative distance and angle between the \ud835\udc56-th unmanned aircraft and the virtual leader.", + "texts": [ + " The first level is contributed to design a control strategy for the formation of unmanned aircrafts based on the virtual structure. In this section, the objective is to design a control strategy which can provide various formations of unmanned aircrafts in three dimensions. The control strategy is based on controlling the distance between the \ud835\udc56-th unmanned aircraft and a virtual leader which its desired value is shown by \ud835\udc5f\ud835\udc56 \u2208 \u211d+. To provide a rigid formation, it is feasible for the unmanned aircraft to control the angle of the line linking it to the virtual leader in its body frame coordinate. As shown in Fig. 1, this angle has two terms. A term which defines the relative position between the unmanned aircraft and the virtual leader on the ?\u0302?\ud835\udc56 \u2212 \ud835\udc66\ud835\udc56 plane, and its desired value is shown by \ud835\udf12\ud835\udc56 \u2208 \u211d, and the other term which represents the relative height between the unmanned aircraft and the virtual leader on the ?\u0302?\ud835\udc56 \u2212 \ud835\udc66\ud835\udc56 \u2212 \ud835\udc67\ud835\udc56 axes which its desired value is shown by \ud835\udf0d\ud835\udc56 \u2208 [\u2212\ud835\udf0b 2 , \ud835\udf0b 2 ]. In this figure, ?\u0302?\ud835\udc56\u2212\ud835\udc66\ud835\udc56\u2212\ud835\udc67\ud835\udc56 axes and ?\u0302?\ud835\udc63\u2212\ud835\udc66\ud835\udc63\u2212\ud835\udc67\ud835\udc63 axes show the frames of the unmanned aircraft and the virtual leader, respectively" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002449_03093247v014313-Figure9-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002449_03093247v014313-Figure9-1.png", + "caption": "Fig. 9. Measurements on the deformedgrid pattern-plane strain", + "texts": [ + " (26) is indistinguishable from one representing the matrix (1 l), whereas in a rectangular grid, the square becomes a rectangle in equation (26) and a parallelogram in matrix eccos+ -e-'sin+ cos+ -sin+ 0 (1 1). Plain strain The grid pattern for a particular application should not be too fine, because fine grids are tedious to inscribe, and difficult to print and measure accurately; nor should it be too coarse, otherwise a square becomes a figure with curved sides. It is assumed in the following that the grid is sufficiently fine to show substantially homogeneous deformation in every square. Let the sides of the undeformed square be lo and let it be deformed into a parallelogram as in Fig. 9, which shows the most general case. Since the matrix for the general case of two-dimensional deformation involves three independent variables, at least three measurements must be taken on the dotted parallelogram in Fig. 9. The choice of the measurements to take is dictated by the convenience of measurement and calculation. Suppose the measurements taken are I , , Q and tan-l y. The three most descriptive variables mentioned before, +, E and (++w) may be easily derived from l , , Q J O U R N A L O F S T R A I N A N A L Y S I S V O L I NO 4 1966 317 at University of Bath - The Library on June 20, 2015sdj.sagepub.comDownloaded from exp (-;) o 0 0 exp (-2) o a11 a12 0 0 a12a21+ 1 a21 all and y by considering first the deformation in Fig. 10 and setting up the equation cash E sinh E . sin 24 sinh E .sin 24 cosh E cos 6 -sin S sin 8 cos 6 + sinh E . cos 24 - sinh E . cos24 Y . 11/10 0 =I: 11 ( 0 lo/l11 (27) Solving equation (27), rL2 112+ lo2 tan S = -- 1 sin 24 = -(11 sin &)/(lo sinh E) J It is obvious from the comparison between Fig. 9 and Fig. 10 that Thus, 4, c and (++w) can all be calculated from equations (28) and (29). The angles 4 and (++w) can each be represented graphically by two sets of mutually perpendicular curves, one set for 4 (or 4+w) and another for 90\u00b0+4 (or 90\"+++~) ; and E can be represented in an isometric drawing as a surface at distance E above the base. w = 8+CL . . - (29) Ad-symmetrical deformation In axi-symmetrical deformations, the meridian plane remains plane, by symmetry, hence it is convenient to measure the deformation in such a plane", + " A square is deformed in general into a parallelogram, not necessarily of the same area, owing to the circumferential strain (perpendicular to the paper, or the meridian plane) due to the radial displacement. Four quantities are now required to represent the deformation : the circumferential strain eC, 4, E and ($+u). It is convenient to consider the deformation to be in two steps, first the square becomes smaller owing to the circumferential strain (see the two squares in in order to determine the deformation fully and let these be Ro, R1 (Fig. ll), I , , CL and tan-' y (Fig. 9). The circumferential strain is In Fig. 11, it can be seen that Therefore, by analogy to equations (28), we may write J . . . (32) As before, w is equal to (&+a). Some reflection will show that the two principal finite strains in the meridian plane are (E-5) and -(c+:)- Coaxial finite strains-particular cases of large deformations In some particular cases the product of two matrices remains unchanged if the two matrices are interchanged in position; for example, the axi-symmetrical deformation discussed above, which was, in effect, analysed as a product of two matrices whose relative position may be interchanged, as follows : 319 J O U R N A L OF S T R A I N A N A L Y S I S V O L I N O 4 1966 at University of Bath - The Library on June 20, 2015sdj" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000084_s00170-005-0312-6-Figure21-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000084_s00170-005-0312-6-Figure21-1.png", + "caption": "Fig. 21 Illustration of cutter\u2019s yaw angle on the second coordinate system", + "texts": [ + " Therefore, assuming that the original spindle axis (TSa) being relative to the unit vector of workpiece coordinate is \u00bdiSa; jSa; kSa T0 ; the original spindle axis related to the unit vector of the second coordinate (TSa)L2 is: iSa jSa kSa 2 4 3 5 L2 \u00bc L2RL1 L1R0 iSa jSa kSa 2 4 3 5 0 (13) where L2RL1 and L1R0 , respectively, are the orientation transformation matrixes in comparing the second detecting coordinate system with the first detecting coordinate system, as well as comparing the first detecting coordinate system with the workpiece coordinate system. And [iSa, jSa]L2 are the unit vectors of the original spindle axis projected on the XL2\u2013YL2 plane. Referring to Fig. 21, if the included angle between the vectors of original spindle axis projected on the XL2\u2013YL2 plane and \u2013YL2 axis is (\u03b8Sa)L2, \u03b8Sa\u00f0 \u00deL2 \u00bc 180 tan 1 iSa jSa iSa 0; jSa 0 tan 1 iSa jSa iSa 0; jSa 0 180 \u00fe tan 1 iSa jSa iSa 0; jSa 0 360 tan 1 iSa jSa iSa 0; jSa 0 8>>>>< >>>>: (14) There are two situations in determining the yaw angle \u03b2S2 of cutter on the second detecting coordinate system: 1. If the original spindle axis of the cutting tool falls within the collision-free region, there is no change of the yaw angle. That is (refer to Fig. 21a): \u03b2S2 \u00bc \u03b8Sa\u00f0 \u00deL2 (15) 2. Otherwise, re-elect the tool spindle axis to have the closed end direction and collision-free. That is (refer to Fig. 21b): where (\u03b8ci)max&min represents the extreme values (maximum or minimum) of collision area in the ith collision angle range. In Eq. 17, the upper and lower symbols represent the tool spindle axis is near the maximum or minimum extreme values of collision area, respectively. Therefore, when referring to Fig. 22, the axis vector (Ta)L2 on the second coordinate is (please refer to Eq. 4): Ta\u00f0 \u00deL2 \u00bc sin\u03b1S2 sin \u03b2S2iL2 sin\u03b1S2 cos\u03b2S2jL2 \u00fe cos\u03b1S2kL2 (18) The final cutter orientation should be relative to the workpiece coordinate system" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001269_1.3197178-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001269_1.3197178-Figure3-1.png", + "caption": "Fig. 3 Cuboid of uniform plastic strain", + "texts": [ + " The method and the analytical functions F3ij that describe the normal displacement of a surface point due to a cuboid of uniform plastic strain are recalled in the Appendix to gather all important analytical solutions in a single paper. What now follows focuses on the tangential displacement of a surface point due to a cuboid of uniform plastic strain. Let us consider a virtual state corresponding to the application of a unit force Qx along the x-axis applied on the elementary surface area centered at point A, as shown in Fig. 3. The displacements generated are expressed by Cerruti 28 U x = Qx 4 \u00b7 \u00b7 G \u00b7 1 R + x2 R3 + 1 \u2212 2 \u00b7 \u00b7 1 R + z \u2212 x2 R \u00b7 R + z 2 U y = Qx 4 \u00b7 \u00b7 G \u00b7 x \u00b7 y R3 \u2212 1 \u2212 2 \u00b7 \u00b7 x \u00b7 y R \u00b7 R + z 2 U z = Qx 4 \u00b7 \u00b7 G \u00b7 x . z R3 + 1 \u2212 2 \u00b7 \u00b7 x R \u00b7 R + z 4 The reciprocal theorem is used to express the surface displacements as a function of contact forces and plastic strains within the p body under the assumption that Tr =0 as follows: Transactions of the ASME 6 Terms of Use: http://www.asme.org/about-asme/terms-of-use w P T i T t f d a m J Downloaded Fr u1 r A = 2 \u00b7 \u00b7 n=1 Nv ij p Cn \u00b7 p 1ij A,M d = n=1 Nv ij p \u00b7 Dkij A,Cn 5 ith U defined by Eq" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000996_fedsm2007-37502-Figure6-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000996_fedsm2007-37502-Figure6-1.png", + "caption": "Figure 6. Trade-off patterns.", + "texts": [ + " Using these two methods, we demonstrated how design rules were extracted from the optimization database. Brief explanations of these methods are given in section 4 together with the results. The population was set to 40, and 12 generations were altered within the allowed turn around time. The total number of evaluations might not be sufficient, but we thought this result was satisfactory because the obtained optimum dominated the current model\u2019s performance. All the solutions in the objective function space are shown in Fig. 6. Seven non-dominated solutions were obtained and the corresponding shapes were visualized. An apparent trade-off relationship was found between two objectives. The shapes are described from three different viewpoints. From the top row, axial view, side view, and bird view near the leading edges are shown. Efficiency-weighted and uniformity-weighted design candidates are shown toward the right and left, respectively. ownloaded From: http://proceedings.asmedigitalcollection.asme.org/pdfaccess.ash Although there are clear distinctions in the leading edge shapes, the tendency is not clear. Regarding other parts, it is also difficult to identify any tendency in these figures. Table 2 compares two dimensions of the non-dominated solutions P1, P2, \u2026, and P7 shown in Fig. 6. D2s/D2h indicates how much the trailing edge inclines in the meridian plane. There is a clear tendency that efficiency-weighted designs are D2s>D2h and uniformity-weighted designs are D2s hc (distorted nematic film), \u201clong wavelength\u201d stripes are expected. The control parameter is K24 (possibly also K13)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003868_2014-01-1085-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003868_2014-01-1085-Figure4-1.png", + "caption": "Figure 4. Distorted bore section (magnified 300 times)", + "texts": [], + "surrounding_texts": [ + "Analytical solutions of the deflection of thin curved beams under simple loading have been developed at the beginning of the 20th century [19]. It is used to check the accuracy of the proposed curved beam finite element model. In addition, a comparison with straight beam finite elements previously used to model piston rings is made. The structural problem used to make the comparison between analytical, curved, and straight beam solutions is the bending of a circular ring in its plane of curvature. Figure 7 illustrates this problem: The ring forms a quarter of a circle of radius R and is submitted to a radial load at its tip Fr. Its base located at \u03b8=0 is clamped. Under the action of the radial force the arch is bent outwards. For deformations that are small compared to the ring radius, the radial displacement of the neutral axis, y, can be expressed as [19]: (28) E and I are the ring Young's modulus and area moment of inertia. The ring is meshed with the curved beam element presented here and a straight beam element found in the literature [11]. Translation and rotation degree of freedoms of the base node are cancelled and the radial force Fr is applied at the end node. The calculation parameters are listed in Table 2. They are chosen to be representative of a steel top ring for mid-size automotive engines. Figure 8 shows a comparison of the neutral axis deflection of analytical, curved, and straight beam solutions. For both finite element methods, the ring is meshed with two elements and squares or circles represent the nodes. The curved beam result with 2 elements is close enough to the analytical solution that it cannot be distinguished on the above graph. On the other hand, the straight beam mesh is too coarse to offer a satisfactory solution. Though there is only 3 nodes in the ring curved beam mesh, an accurate description of the entire ring deflection is obtained using the element shape functions. This shows how contact between the ring and the liner can be calculated on a fine grid even with a coarse structural mesh. The tip displacement of both curved and straight beam methods is compared to the analytical solution. Figure 9 shows the relative error on tip displacement. It can be seen that great accuracy is achieved with only one curved beam element, yet ten straight beam elements are required to keep the relative error below 1%. It takes approximately 30 straight beam element to match the accuracy of 1 curved beam element, which illustrate expected differences in computation time. The high order polynomial spline of the curved beam model is able to describe with precision the ring deformed geometry. Under real engine conditions, the contact pressure acting on a piston ring can vary rapidly around its circumference. The ring would deform locally and a larger number of elements might be required. Nevertheless, based on the previous result, it can be stated that 10 curved beam elements should provide an accurate model of the entire ring structure. One has to keep in mind that this model is only valid for small deformations of the ring neutral axis which is expected during engine operation." + ] + }, + { + "image_filename": "designv11_7_0002327_iccme.2012.6275613-Figure11-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002327_iccme.2012.6275613-Figure11-1.png", + "caption": "Fig. 11 o-ring type magnet", + "texts": [], + "surrounding_texts": [ + "Based on the promotion model, we evaluated propulsive force of the spiral jet type microrobot. It was aimed at the under water. Density of the water is 1000kg/mI\\2, and drag coefficient is 0.5. We simulated propulsive force against the rotating speed of the jet propeller. This result indicated that when rotating speed is 40rps, propulsive force of the robot is 6mN. This value is enough to drive of the robot. We did experiment of the developed spiral jet microrobot. We used acrylics pipe filled with water. Inner diameter of the pipe is 18mm. The result is indicated in Fig. 14. As the frequency becomes higher, moving speed of the robot becomes high. This tendency is the same as the simulation results of the propulsive force. Because of this characteristic, it is thought that it is ideal for the control of the moving speed of the robot. Additionally, the robots can multi DOFs locomotion by this jet motion. This robot can also move forward and backward by changing the direction of the outer magnetic field. We confirmed the robot has equivalent moving speed even backward by experiment." + ] + }, + { + "image_filename": "designv11_7_0000737_035301-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000737_035301-Figure1-1.png", + "caption": "Figure 1. Schematic of the pendulum rolling apparatus. The weight lies directly beneath the centreline of the rubber slab.", + "texts": [ + " This paper explores this effect further by examining oscillating rolling contact, achieved by attaching the rolling cylinder to a simple pendulum, as described below. While the writing of this paper was in progress, Gent et al [28] reported an independent experiment of oscillatory contact in which a steel cylinder was rolled on two different rubbers, one more viscoelastic than the other. We will also compare our results with those of Gent et al. The apparatus in which an effectively rigid cylinder rolls on a flat slab of PDMS is shown schematically in figure 1. The rolling cylinder was made from a borosilicate glass pipette (weight 2.18 g). Its stem was heated and bent back through 130\u25e6 and the narrow end curled into a ring in which was inserted and firmly attached a weight (6.82 g). The thicker part of the pipette (a cylinder radius 3.45 mm) makes contact with the PDMS slab. The positions of the two contact edges, viewed through the transparent slab, are recorded with a high speed camera (model Motion-Pro, Redlake, USA) for subsequent analysis. The axial position of the cylinder is adjusted to obtain a contact strip of constant width" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003344_j.cplett.2012.08.055-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003344_j.cplett.2012.08.055-Figure1-1.png", + "caption": "Figure 1. (a) Schematic illustration for the preparation of penetrated and aligned CNT fil", + "texts": [ + " The resistivity change under bending was monitored by Agilent 34401A digital multimeter. The dye-sensitized solar cells were measured by recording J\u2013V curves with a Keithley 2400 Source Meter under illumination (100 mW/cm2) of simulated AM1.5 solar light coming from a solar simulator (Oriel-94023 equipped with a 450 W Xe lamp and an AM1.5 filter). The stray light was shielded by a mask with an aperture which was a little smaller than the working electrode. Cyclic voltammetry and electrochemical impedance spectroscopy were performed on CHI 660a electrochemical workstation. Figure 1a schematically shows the preparation of penetrated and aligned CNT film. A CNT array was first synthesized by a chemical vapor deposition process [22,23]. Figure S1 shows photograph of a typical CNT array. The CNT array was then pressed down along one direction by a roller. A typical scanning electron microscopy (SEM) image of CNT film by side view is provided in Figure 1b. The CNTs were penetrated from the bottom to the top in the film and highly aligned with an angle of 1.4 relative to the substrate. The aligned structure of CNTs can be also observed from the top view of the film (Figure S2). The resulting CNT film can be easily peeled off from the silicon wafer or stabilized on conductive glass after the further pressing treatment. Figure S3 shows a typical CNT film on fluorine-doped tin oxide (FTO) with thickness of 30 lm (Figure S3a). The CNT film exhibited a smooth surface with a small fluctuation on the level of tens of nanometers (Figure S3b)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000084_s00170-005-0312-6-Figure26-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000084_s00170-005-0312-6-Figure26-1.png", + "caption": "Fig. 26 Collision-free cutter orientation on the blade", + "texts": [ + " The numbers of their tool paths are 134 and 138, respectively, as shown in Fig. 24. When the cutter contact points on the blades and hub are determined, and after the original spindle axis orientation (TSa) and suitable clearance value (rcl 0.2 cm) are given, the collision-free cutter orientation can be acquired by using the abovementioned two stages detection methods, and through the programming usingEUKLID software. Figure 25 is the simulated diagram of collision avoidance during cutting hubs. The cone body used for collision checking is marked as the dashed line. Figure 26 is the simulated diagram on cutting blades. The determined cutter contact points and cutter orientation data are entered into the post processor of the fiveaxis machining tool, MAHO 600E. Then the five-axis joints variables of the five-axis machining tool can be acquired. Supplemented by suitable cutting conditions, such as feed-rate and spindle speed, the required NC program of the blade and hub can be machined, as shown in Fig. 27. It refers to the appearance of the turbine blade (the workpiece is aluminum alloy 7,075, and the radius of turbine blade is 250 mm, and its height is 75 mm)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000809_1.2959095-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000809_1.2959095-Figure5-1.png", + "caption": "Fig. 5 Coordinate senses during the \u201ea\u2026 front foot stance, and \u201eb\u2026 rear foot stance. Point S represents the shoulder joint, and point H represents the hip joint. G is the center of mass.", + "texts": [ + " 5 and 9 can be combined to give yFR = gT a + b p \u2212 1 , yRF = gT a + b p 12 where = Mab Iy 13 The parameter actually measures the relative magnitudes of the impulsive moment about the pitch axis and the impulse of the inertial moment about that axis. Thus, it quantifies the importance of pitch rotation in the model. Energy Loss. We will use the energy loss due to the impact of the feet with the ground to estimate the optimal value of p and hence the optimal time division between the two ballistic saccades that make up the stride. The velocity, wF, with which the front feet strike the ground may be obtained from Eq. 10 with reference to Fig. 5, wF = \u2212 uF + a yRF = gT 2 1 \u2212 2ap 1 \u2212 a + b 14 wR = \u2212 uR \u2212 b yFR = gT 2 1 \u2212 2b 1 \u2212 p 1 \u2212 a + b The energy lost in each stride due to impact with the ground is UL = mFwF 2 + mRwR 2 15 Differentiation with respect to p to find the extremal value of UL gives Transactions of the ASME ashx?url=/data/journals/jmroa6/27973/ on 04/23/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use a c s v b o s b i l b t E i b v v G t T o B t e F c t = J Downloaded Fr p = mFa a + b \u2212 mRb a \u2212 b 1 \u2212 2 2 1 \u2212 mFa2 + mRb2 16 s the value of p that extremizes the energy consumption" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001403_gt2009-59226-Figure10-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001403_gt2009-59226-Figure10-1.png", + "caption": "Fig. 10 Bevel gearbox for improvement of shrouds", + "texts": [ + "[% ] _ Shroud #1 Shroud #2 Shroud #3 *1\u2026Averaged from 10th to 20th rev. of input gear. *2\u2026The power losses of Shroud#2 were set to 100%. Fig. 7 Averaged power loss *1 *2 *2 4 Copyright \u00a9 2009 by ASME ?url=/data/conferences/gt2009/70580/ on 02/28/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use Do velocity near the area in which the shroud was deleted was small, and because the amount of oil in the area was also small. In order to exclude the influence of the housing, a bevel gearbox with a large housing, shown in Fig. 10, was used. In this bevel gearbox, oil was supplied to the gear mesh besides supplying it to the bearings of each gear shaft. The supplied oil for the bearings flowed into the gearbox through the back space of the bevel gears. The test conditions are shown in Table 3. After an adequate warm-up run was carried out, the 130 0 [m/s] Fig. 8 Oil flow in shroud #1 7th rotation of input gear 13th rotation 10th rotation 130 0 [m/s] 130 0 [m/s] * Isosurface of VOF=0.5 Fig. 9 Velocity contour around output gear 130 0 [m/s] 130 0 [m/s] *at 13th revolutions of input gear 130 0 [m/s] Shroud #1 Shroud #2 Shroud #3 wnloaded From: http://proceedings" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002961_cjme.2012.01.190-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002961_cjme.2012.01.190-Figure1-1.png", + "caption": "Fig. 1. Pure torsional model of 2K-H planetary gear sets", + "texts": [ + " The epicyclical stage of the transmission is more complex due to its multiple components and the orbital motion of the planets. How to simplify the model is the first step to develop the model of 2K-H planetary gear sets. As the stiffness of planet gear support is rigid and internal ring gear is fixed to the top of the transmission casing, we can ignore the central displacement of planet gears and ring gear[5\u20137]. So a lumped parameter, pure torsional dynamical formulation is employed to develop the physical model of 2K-H planetary gear sets. Fig. 1 represents the pure torsional model of 2K-H planetary gear sets. In Fig. 1, Kspi denotes mesh stiffness between sun gear and planet gear, Krpi denotes mesh stiffness between planet gear and ring gear, Cspi denotes mesh damping between sun gear and planet gear, Crpi denotes mesh damping between planet gear and ring gear, \u03b8s, \u03b8pi and \u03b8c denote the rotation angle of sun gear, planet gear and carrier, TD, TL denote driving torque and loading torque. Subscripts s, r, pi and c denote sun gear, ring gear, planet gear i and carrier, and all the subscripts in the paper have the same meaning" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002513_piee.1971.0124-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002513_piee.1971.0124-Figure1-1.png", + "caption": "Fig. 1", + "texts": [ + " This paper describes a numerical approach to the calculation of endregion fields to obtain the voltages produced between strands, and obtains the consequent circulating currents with due consideration of the impedance of the circuits. The reactive effects of the circulating currents are also taken into account. 2 Method of approach The Roebel bars considered are made with strands insulated from each other, except at the end of each bar, where all the strands are soldered together and to the following bars. In the slot length, the strands are transposed through 360\u00b0, as shown in Fig. 1 of Reference 10. 689 The current within each bar is considered as two components : (a) a uniform load current (b) a circulating current which sums to zero over the cross- section of all the strands in one bar. This approach is convenient, because the losses of the two currents may be considered independently. For the purposes of analysis, circulating currents and load currents are treated as if they occurred in different circuits. Their presence superimposed on each other in the same strands does not invalidate the analysis. Each stator bar will contain 30-70 strands in two stacks. Since the depth/width ratio is high (10/1 in the machine analysed), only circulating currents in the depth are considered. It was not practicable to consider each strand pair as a circuit, and each bar has been represented by five line filaments in which four circulating currents flow with a common return. Each line filament is set at the centre of the crosssection of the part of the bar which it represents, as shown in Fig. 1. 5 A \u2022g. i '-element representation of circulating-current paths in top bar irp\u00bb inside circuit 1 is shaded Any circulating-current path (\u00abth) within a stator bar may be considered to have induced in it a voltage Vn, available to drive a circulating current through its resistance, given by: Vn = Ja>MAnlA + ja>MBnIB + j\u00ab)MRnIR 0) m=\\ where MAn, MBn etc. are the mutual inductances of the load currents in phases A, B etc. with the \u00abth current path. MRn is a motional mutual inductance with the rotor-field current", + " With this approach, the solution is resolved into the following steps: (a) the identification of a general set of closed circulatingcurrent paths (b) the calculation of the mutual inductances of the stator phases and the rotor winding with all the closed circulatingcurrent paths to obtain the induced voltages E, as in eqn. 5 (c) the evaluation of the self and mutual impedances of the closed circulating-current paths to obtain the impedance matrix of eqn. 7 (d) the inversion of the impedance matrix and the insertion of the voltages E to obtain the circulating currents / and thereby to obtain the loss. 3 Mutual inductance of stator currents with circulating-current paths Circulating-current paths have been defined in Fig. 1 in each stator bar at each end of the machine. Any one path encloses flux at each end and in the slot portion. The transposition in the slot portion is such as to give zero mutual reactance for each circulating path with a stator-load current (this is its purpose), and coupling with these currents occurs only in each endregion. The calculation is made in steps, each end of each bar being considered in turn. Mutual inductances of each phase with each circulatingcurrent path MAn, MBn and MCn in eqn", + "4 This showed that the effect of the fringing flux from both ends was approximately equal to that in 1-2 times the slot width of untransposed conductor considered to lie within the slot length. winding was considered, at 20 positions, and the flux variation with time for each circulating-current path was obtained. The fundamental component predominated, the third harmonic being only 20% of it. Voltage phasors have been drawn for the instant when phase-A current is a maximum and the machine is on fullload short circuit. Phasor values of the voltage in circuit 1 (see Fig. 1) of a bar in the top layer in two positions are shown in Fig. 7. The difference between the two, apart from the 4 Motional mutual inductance of rotor with circulating-current paths A motional mutual inductance expresses a relationship between a direct current in one circuit and a voltage appearing in a second circuit which is in motion relative to the first. The mutual inductance must also express the correct generation of voltage phasorially, and is a complex quantity with reference to rotor position" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003112_2013.40500-Figure16-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003112_2013.40500-Figure16-1.png", + "caption": "FIG. 16 Normal pressure profiles under a 20 by 3-in. wheel in sandy loam at w equal to 16 percent with 100-lb load.", + "texts": [], + "surrounding_texts": [ + "ducers, the magnitude of angular and linear displacement, torque and sinkages. The pressure cells were calibrated by a device developing a known air pressure and having a maximum capac ity of 20 psi (Fig. 4 ) .\nTests were performed in sand and in sandy loam under laboratory conditions. The soil bin used for this investigation was 40 by 5 by 2 ft in overall dimen sions and was equally divided between sand and sandy loam. During test, the sand was kept air-dry. However, in the case of the sandy loam, water was added after each complete experiment as needed to investigate the effect of soil consistency on pressure distribu tion and slip-sinkage relationship.\nSome important characteristics of the materials tested are tabulated in Table 1. Atterberg limits pertaining to sandy loam are tabulated in Table 2.\nPrior to each test run, the dry sand was leveled with a leveling board at tached to the carriage in order to as sure a reference surface for sinkage measurements. Then the wheel was loaded and the experiment was begun by driving the wheel and tow carriage simultaneously. Drag was applied to the carriage causing it to slow down relative to the wheel and produce a certain magnitude of slip. By increas ing the drag on the carriage, pressuredistribution measurements and slipsinkage measurements at higher slip were possible. This technique was em-\nployed for testing at different slips, since speed of carriage and wheel can not be controlled separately. During this procedure, pressure distribution, angular displacement, linear displace ment, torque and sinkage data were recorded con t inuous ly . The experi mental technique produced data which permitted plotting of normal pressure distribution, sinkage and torque as a function of slip between 0 and 100 percent for each type of soil and load ing condition.\nThe test procedure for sandy loam was essentially the same as for sand. The only difference existed in process ing the material. Sandy loam was mixed at each test run and at each addition of water content with a rotary tiller. Then it was raked until a smooth soil surface was obtained. After this procedure, two passes with a smooth roller, weighing 200 lb, were made. Although this resulted in an increase of soil density, it assured a more uniform soil structure, which is demonstrated by the fact that the deviations from\n1965 \u2022 TRANSACTIONS OF THE ASAE\nthe mean in moisture and density val ues are within acceptable limits. As a matter of interest, it should be noted here that deviation from mean density at least doubled when the roller passes were omitted.\nTEST RESULTS\nThe results of driving moment, pres sure distribution and slip-sinkage meas urements are presented in diagrams and chart forms.\nFig. 5 shows a typical torque vs slip relationship with wheel load as parame^ ter in dry sand. This figure also con firms that, for slip conditions in sand in excess of 30 percent, the assumption that is constant is valid. If shear strength is taken as independent of depth, the torque vs slip relationship depicted can be considered as a shear deformation diagram since torque is proportional to the tangential forces and slip to the corresponding deforma tions. The peak points of these curves were taken for the construction of the Mohr-Coulomb envelop, and the value of (f> was found to be very nearly equal to that determined by sliding friction experiments. The sliding friction ex periments resulted in cfy equal to 24 deg and c equal to 0 while evaluating those from torque-slip relationship when\nthe normal pressures at wheel-soil con tact are known, gave (f) equal to 23 deg and c equal to 0.\nActual, normal pressure-distribution diagrams are shown in the next series of figures. Fig. 6 illustrates the pres sure distribution in sand as a function of the polar angles under a 20 by 3-in. wheel at various loads. The slip is held constant at 0 per cent. The effect of slip on pressure distribution is shown in Fig, 7, when the soil (sand), wheel size and wheel load are kept constant,\nIt is apparent from the latter two pressure-distribution diagrams that, as slip occurs, pressure distribution as well as sinkage become a function of slip. An increased sinkage develops higher motion resistance; therefore, the result ant of the pressure distribution will have a higher angle of inclination rela tive to the vertical.\nAnother important factor is that the pressure distribution extends beyond the point of maximum sinkage. The ex tent of pressure distribution to the trail ing portion of the wheel is about 10 deg or less from the toe of the wheel in most of the pressure profiles reported here. This phenomenon can be at tributed to the flow of the material into the wheel rut in sands, to the rebound of the material in firm soils.\nNote that the pressure distribution in the lateral direction is also shown in the figures. Dots denote the pressure at the center of the wheel and crosses denote the pressure close to the edges of the wheel. The pressure transducers mounted at the edges of the wheel were averaged on the recording device so that the crosses represent the average value of the pressure on the two wheel edges.\n307", + "Fig. 8 shows the same information for a 20 by 5-in. wheel as was shown in Fig. 7 for the 20 by 3-in. wheel in sand. The variation in pressure across the wheel face is very significant in deed for this wheel. The pressures at the center of the wheel were found approximately twice as high, as they were observed close to the edges of wheel. In case of the narrow wheel, the variation of pressure in the lateral direction is negligible, except for those pressure-distribution diagrams which were obtained at very high slip condi tion.\nFig. 9 shows sinkage (maximum vertical deformation) as a function of slip in sand for the 20 by 3-in. wheel. Again, it is apparent that as slip oc curs sinkage rapidly increases. For sand the compaction effects are small, so that the wheel can dig itself into the ground. This process is associated with slip failure in which the wheel removes material from the contact surface and deposits it behind the wheel.\nThe next figure (Fig. 10) shows sinkage as a function of the angle of inclination of the resultant of normal pressures in sand for both wheels tested. This function may be approxi mated by a straight line having the fol lowing equation:\nz = 6.87 oc After some manipulation it may be seen that in sand the normal resultant divides the ground contact arch ap proximately into two equal parts, there by confirming the hypothesis of Tanaka (12) who assumed in general that the angular position of the resultant (N) is half that of the angle of sinkage.\nIf the vertical component of the ground reaction is evaluated by graphi cal integration, a chart plotting Nv and\nRv against W can be made. Nv is the vertical component of the normal re sultant N, while Rv is the vertical com ponent of the resultant of normal and frictional forces. It is found that Nv alone does not satisfy the equilibrium of the vertical forces. This indicates tliat frictional forces must be included to achieve equilibrium, The frictional forces were evaluated from Coulomb's equation for maximum shear stress. The agreement obtained by the inclusion of the frictional forces is shown in Fig. 11, and it can be seen that the mag nitude of the discrepancy is within an acceptable limit.\nThe tests were continued to investi gate the behavior of the wheel in a sandy loam at various moisture con tents.\nThe following illustrations refer to results obtained. Figs. 12 and 13 show typical slip-sinkage relationships for a 20 x 5-in. wheel in sandy loam mix No. 1 and for a 20 x 3-in. wheel in\nsandy loam mix No. 4, respectively. In sandy loam at low moisture contents (w < 9.0 percent) the slip-sinkage re lationships were found to be very simi lar to those obtained in sand. However, at higher moisture contents, sinkage will be independent of slip.\nAn explanation of slip-sinkage be havior of wheels in sand and in sandy loam may be given as follows: in granu lar soils (dry sand and sandy loam as low moisture content) the compaction effects are very small. Therefore, a \"soil transport\" phenomenon exists un derneath the wheel. With added water and the same compactive effort of roller and wheel, greater density can be ob tained up until the water c o n t e n t reaches the value where maximum den sity is achieved. The sandy loam type of soil is highly compactable at higher moisture contents. Movement of the moisture of the wheel-soil interface\nserves as a lubricant; therefore, the transport of soil by wheel does not occur.\nThese series of slip-sinkage tests were performed with the aim of pirir pointing the minimum amount of co^ Lesion at which sinkage may be taken as independent of slip.\nFrom the experiments, it appears that the cohesive properties of soils are re>sponsible for the dependence or inde pendence of sinkage upon slip. The number of experiments conducted sug gests that above 0.5 psi of cohesion sinkage may be regarded as independ ent of slip.\nFig. 14 shows the angular position of the resultant of the normal pressure distribution as a function of slip for a 20 x 3-in. wheel in sandy loam at 16 percent of moisture content. This curve also shows the independence of oc and slip.\nSince the sinkage and oc were found to be independent of slip, the pressuredistribution measurements were pre sented in a superimposed form. Figs.\n308 TRANSACTIONS OF THE ASAE \u2022 1965", + "clay plotted against concentration for a Grenada silt loam soil is shown in Fig. 7. These data indicate that at low concentrations (below 1,000 ppm) the percentage of clay transported from the plot was greater than 90 percent and the percentage of silt transported was less t h a n 10 p e r c e n t . As the concentration increased, the percent age of clay transported from the plot decreased and the percentage of silt transported increased. At a concen tration of 3,000 to 4,000 ppm the per centage of silt and clay transported was about equal. When the concen tration reached 20,000 to 30,000 ppm and above, the percentage of silt and clay transported was almost constantapproximately 70 percent silt and 30 percent clay. This was the approximate percentage of silt and clay in the Gren ada silt loam soil. The results indicate that, when the concentration reached between 20,000 and 30,000 ppm, the entire top layer of soil was being moved from the plot.\nEffect of Ground Cover on Runoff and Erosion Rates\nThe characteristics of runoff hydrographs and soil erosion rate graphs on the three different ground-cover condi tions studied were similar except for the rates. The rates of runoff and ero sion increased as the percentage of ground cover decreased. The rate of soil erosion increased as rainfall and runoff rates increased. Rainfall, runoff and soil erosion data from three dif-\nferent ground-cover conditions are sum marized in Table 2. Runoff and erosion rates fluctuated widely with rapid changes in rainfall intensity during the first part of the storm. There was no apparent change in erosion rates from the fluctuations in rainfall and runoff rates in the low-intensity portion of the storm's later stages. Improved manage ment corn with 60 to 90 percent cover produced no measureable erosion for this storm and produced only 0.03 in. of runoff.\nSUMMARY\nErosion rates and particle-size dis tribution throughout runoff events were determined from runoff samples col lected from unit source areas. Equip ment and procedures were developed to obtain samples of runoff at intervals throughout runoff events from V\u00b1 and 1/45-acre plots. An instantaneous total load sampling device was developed and used to obtain runoff samples from a 1/45-acre fallow plot.\nSediment concentrations were de termined from, each runoff sample. The eroded sediment was separated into sand, silt and clay.\nEleven and one-half tons per acre per hour was the highest erosion rate determined from a ^ -acre unit source area. Rates of soil movement varied in the same manner as the runoff. The peak sediment concentration occurred at about the same time or slightly be\u0302 - fore the runoff peaked.\nData indicated that the proportion of silt increased and the proportion of clay decreased as the sediment concen trations increased up to approximately 20,000 ppm. Above 20,000 ppm the particle-size distribution in the runoff samples was approximately the same as the particle-size distribution in the unit source area soil (Grenada silt loam).\nThere were vast differences in the erosion rates from fallow soil, corn under poor management practice, and corn under improved management prac tices.\nPRESSURE DISTRIBUTION UNDER RIGID WHEELS\n(Continued from page 308) 15, 16 and 17 show the superimposition of all the pressure distribution diagrams regardless of slip at 50, 100 and 150 lb of wheel load, respectively. These measurements were taken in sandy loam mix No. 4. Note that the trend of lateral-pressure distribution reverses; that is, close to the edges of the wheel higher pressures were recorded than at the center of the contact strip in a co hesive type of soil.\nIt can be stated again from the ex periments that the angular position of the resultant approximately bisects the contact angle.\nSimilarly, as was shown for sand, equilibrium considerations pertaining to the above normal pressures, esti mated frictional forces, and imposed loads are shown in Fig. 18. It is seen that the frictional forces must also be included in the description of a wheel operation in a material having cohesion, if equilibrium is to be achieved.\nCONCLUSIONS\n1 An analytically correct equation for pressure distribution must include not only soil properties and wheel geometry, as previously believed, but also the slip-sinkage relationship and tangential forces.\n2 The effect of frictional forces are significant and should be included in equilibrium equations for wheels. The frictional forces may be conveniently estimated from Coulomb's equation for maximum shear strength,\n3 Sinkage is a function of slip in granular soils; however, in cohesive soils sinkage may be taken independ\nent of slip. Further tests are necessary to confirm this statement, since tests in loam with a moisture content in ex cess of 16 percent have not be per formed.\nReferences 1 Bekker, M. G. Theory of land locomotion. University of Michigan Press, Ann Arbor, 1956. 2 Vandenberg, G. E. and Gill, W. R. Pressure distribution between a smooth tire and soil. Transactions of the ASAE 5:(2)105-107, 1962,\n3 Cooper, A. W., Vandenberg, G. E., McColly, H. F., Erickson, A. E. Strain gage cell measures soil pressure. Agricultural Engineering 38: (4) 232-235, 246, April 1957.\n4 Reaves, C. A. and Cooper, A. W. Stress dis tribution in soils under tractor loads. Agricultural Engineering 41:(1)20-21, 31 , January 1960.\n5 Sonne, W. The transmission of force be tween tractor tires and farm soils. Grundlagen der Landtechnik, 1952.\n6 Vincent, E. T. Pressure distribution on and flow of sand past a rigid wheel. 1st International Conference on the Mechanics of Soil Vehicle Systems, Torino, 1961.\n7 Trabbic, G. W. The effect of drawbar load and tire inflation on soil-tire interface pressure. M.S. thesis, Michigan State University, 1959.\n8 Capper, L. and Cassie, F. The mechanics of engineering soils. McGraw-Hill, New York, 1953.\n9 Schuring, D. On the mechanics of rigid wheels on soft soil. V.D.I., June 1961.\n10 Hegedus, E. A preliminary analysis of the force system acting on a rigid wheel. Land Loco motion Laboratory, OTAC, Report No. 74, 1962.\n11 Phillips, J. A discussion of slip and rolling resistance. 1st International Conference on the Mechanics of Soil-Vehicle Systems, Torino, 1961.\n12 Tanaka, T. The statical analysis and ex periment on the force to the tractor wheel. 1st International Conference on the Mechanics of Soil-Vehicle Systems, Torino, 1961.\n1965 \u2022 TRANSACTIONS OF THE ASAE 311" + ] + }, + { + "image_filename": "designv11_7_0002010_1.4002342-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002010_1.4002342-Figure3-1.png", + "caption": "Fig. 3 Interpolation of rail profile", + "texts": [ + " Accordingly, the global position vector of contact point k can be given as 6 rrk = Rrk + Arku\u0304rk, k = 1,2,3 5 where Rrk defines the location of the origin of the rail profile coordinate system, Ark defines the orientation of the profile coordinate system that is also the function of the longitudinal surface APRIL 2011, Vol. 6 / 024501-1 27/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use p w p t g s t s l 0 Downloaded Fr arameter s1 rk, and u\u0304rk is the location of the contact point k defined ith respect to the body coordinate system. 2.3 Interpolation of Rail Profiles. In order to obtain a rail rofile at an arbitrary location along the track in turnout section, he rail profile is generated by longitudinally interpolating the two iven rail profiles, as shown in Fig. 3. To this end, the rail crossection profile is defined using the smoothing cubic spline in order o remove small irregularities and measurement noises first. The moothing of the original date yi is performed such that the folowing function J can be minimized 7 : 24501-2 / Vol. 6, APRIL 2011 om: http://computationalnonlinear.asmedigitalcollection.asme.org/ on 01/ where a ,b is the domain of the data and is the weight coefficient for smoothing cubic spline f xi 7 . It is important to note that higher order derivatives of the cross-section data are also required not only for obtaining the shape of contact ellipse at the contact point but also for achieving faster convergence in solving the nonlinear contact equations" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000871_s0076-6879(78)54028-7-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000871_s0076-6879(78)54028-7-Figure5-1.png", + "caption": "FIG. 5. Furnace, exploded view (not to scale).", + "texts": [ + " Acta, Part B 26, 477. 3.~ Veillon, C. (1976). Chem. Anal. (N.Y.) 46, 123-181. ,~6 Murphy, M. K., Clyburn, S. A., and Veillon, C. (1973). Anal. Chem. 45, 1468. z7 Veillon, C., and Margoshes, M. (1968). Spectrochim. Acta, Part B 23, 503. :~\" Kantor, T., Clyburn, S. A., and Veillon, C. (1974). Anal. Chem. 46, 2205. pyrolysis treatment was developed, leading to long-term stability and freedom from memory effects for the system, a9 A schematic diagram of this system is shown in Fig. 4. The furnace is shown in Fig. 5. The system was first applied to the direct determination of the zinc content and stoichiometry in DNA-dependent RNA polymerase isolated and purified from E. coli, using well-characterized carbonic anhydrase as the standard. 4\u00b0 It was demonstrated that the inorganic and metalloenzyme standards gave comparable results, and that purified RNA polymerase from E. coli contains 1.99 + 0.03 g-atom of Zn per 470,000 molecular weight. Subsequently, the system has been applied to the direct determination of the metal stoichiometry of yeast alcohol dehydrogenase, bovine carboxypeptidase A, E" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003347_tvt.2012.2188822-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003347_tvt.2012.2188822-Figure1-1.png", + "caption": "Fig. 1. Electromagnetic active suspension system.", + "texts": [ + "ndex Terms\u2014Active suspension system, direct instantaneous force control (DIFC), force distribution function (FDF), linear switched reluctance actuator (LSRA). I. INTRODUCTION E LECTROMAGNETIC active suspension systems have been introduced in vehicle applications over the past decade and have become a more competitive candidate than their hydraulic counterparts. To date, various electromagnetic actuators have been proposed by researchers and companies [1]\u2013[4], and the permanent magnetic actuator was extensively investigated for its high force density. The structure of the electromagnetic active suspension system from Bose Corporation is shown in Fig. 1. However, the permanent magnet is quite expensive and tends to lose magnetization as the temperature rises. A linear switched reluctance actuator (LSRA)-based electromagnetic active suspension system has the advantages of robust structure, low cost, high reliability, and fast dynamic response [5]. Moreover, LSRA can be operated in regenerating mode as well. The kinetic energy, which is dissipated to heat in passive suspensions, can be recovered back to the power source or Manuscript received October 25, 2011; revised January 9, 2012; accepted January 25, 2012" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001521_s10514-008-9106-7-Figure24-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001521_s10514-008-9106-7-Figure24-1.png", + "caption": "Fig. 24 Phase plane diagrams of the hip link bouncing and swinging in the simulation of the 12-DOF biped robot. Each diagram represents the reciprocal relationship between the position and velocity of the hip link. Note that position is plotted on the abscissa, velocity is on the ordinate, and the action advances in a clockwise direction in (b) and (c)", + "texts": [ + "15 [m], Hz = 0.693 [m] and kleg = 7500.0 [N/m]. The parameters used in the fight phase trajectories are given in Table 4. Figures 22 and 23 show graphs of the angular momentum and the ZMP during normal running in the simulation of the 12- DOF biped robot, respectively. As a result, these plots show that they does not move out of the predefined stability region. Fig. 23 ZMP trajectory in the simulation of the 12-DOF biped robot. The rectangles denote footprints in the horizontal plane (X\u2013Y plane) Figure 24 shows the phase plane diagrams of the hip in the simulation of the 12-DOF biped robot. The vertical height of the hip link Hz is 0.693 [m] at the moment the biped robot leaves off the ground with the maximum flight height of about 0.698 [m]. The peak foot clearance is about 0.04 [m], as the robot runs at the average speed of about 0.3359 [m/s]. In these phase portraits, the hip of the ro- bot bounces and swings along the forward velocity which Fig. 27 Consecutive snapshots of the 12-DOF biped robot with running gaits", + " The revolute joint is actuated by a permanent magnet DC motor-pulley-single stage timing belt-pulleyharmonic driver system. The flexibility of the supporting leg is briefly modeled into an inverted pendulum model with a rotational spring. If the stiffness of the rotational spring is determined experimentally, the support phase trajectory of the hip link is modified to compensate the elastic deformation of the supporting leg. When comparing the phase portrait of Fig. 25(b) to the corresponding graph of Fig. 24(b), it can be seen that the hip link of the robot is controlled to move within a wider range than that in the simulations. In addition, the force of friction slows the revolute joint down as it rotates. The effect of the joint friction is determined experimentally, and then it is added to (52). The ZMP is calculated using the force data that are measured by six pressure sensors mounted at the sole of the robot during the support phase, as given in Appendix A. Figure 26 shows the ZMP trajectory in the horizontal plane (X\u2013Y plane)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000351_1.2185661-Figure10-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000351_1.2185661-Figure10-1.png", + "caption": "FIG. 10. Vertical cross section of the setup used to calculate E .", + "texts": [ + " The first integral yields EF1 = g 0 x0 r2 \u2212 x2 + h \u2212 L 2 \u2212 r2 \u2212 x2 \u2212 L 2dx = gr2 r 0 \u2212 r 2 sin 2 0 \u00b1 2 2 g 1 \u2212 cos 0 sin 0 sin 0 0, where we have used L = r cos 0 2 g 1 \u2212 cos 0 to represent the distance between the center of the initial cylinder and the height of the fluid at infinity. The second integral is approximated to first order as EF2 = \u2212 g x0 x0\u2212 x bi 2 x dx = gu0 2 x = 2 r 1 \u2212 cos 0 cos 0 0. This completes the characterization of E : E = EG + EW + E + EF1 + EF2 . 21 Now all of the terms on the right-hand side of this equation have been defined in this section. The derivation for E is similar to that of E . Referring to Fig. 10, we see that the fluid profile has been truncated and shifted horizontally to reflect the change in 0. We start by finding the parameters h and x as defined in the figure. h is equal to the change in fluid profile height, which is approximated to first order as du /d 0. We also have x= h cot 0 by definition. This yields h = 2 g sin 0 1 \u2212 cos 0 0, 22 x = 2 g cos 0 1 \u2212 cos 0 0. 23 The change in gravitational energy follows as before: EG = \u2212 mg h = \u2212 m g 2 sin 0 1 \u2212 cos 0 0. 24 The wetting energy remains constant in this configuration and so EW =0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002692_fuzzy.2011.6007430-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002692_fuzzy.2011.6007430-Figure3-1.png", + "caption": "Figure 3. Mechanical structure of SAYA", + "texts": [ + " In order to mimic flexible neck movements of a human cervical spine, we utilize a coil spring in the neck part. Furthermore, the center of rotations for pitch rotation (\u201cPitch1\u201d) and yaw rotation are set in the base of the head part. The forward and backward motions are realized by combining the head rotation (\u201cPitch1\u201d) and the neck bending (\u201cPitch2\u201d). The roll-rotation, both pitchrotations (\u201cPitch1\u201d and \u201cPitch2\u201d) and the yaw-rotation are also actuated by McKibben artificial muscles as shown in Fig. 3. We use electro-pneumatic regulators for controlling contraction of McKibben artificial muscle. III. REMOTE CLASS SUPPORT SYSTEM WITH THE ANDROID ROBOT SAYA Fig. 4 shows the system configuration of the developed remote class support system, and the android robot SAYA is utilized as the interface and it plays the role of a teacher. In a classroom, there are SAYA, control PC, and some control equipment. An air compressor and an electropneumatic regulator are used to control contraction of McKibben artificial muscle" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002955_s12541-013-0054-6-Figure17-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002955_s12541-013-0054-6-Figure17-1.png", + "caption": "Fig. 17 ORION manipulator mounted on Hemire ROV", + "texts": [ + " \u03b4gIMU t( ) \u03b5 wg t( )+ vg t( ) N 0 Q \u00b7 n,( )\u223c,= \u03b5 \u00b7 0= \u03b5 \u03b5\u03c8 \u03b5\u03b8 \u03b5\u03c6[ ]T= \u03b5 0( ) N 0 P \u00b7 n,( )\u223c,, \u2207 PR Path t( ) PR hase A Bt C+( )sin+= PR hase xb yb zb \u03c8b \u03b8b \u03c6b[ ]T= A diag Ax Ay Az A\u03c8 A\u03b8 A\u03c6[ ]= B Bx By Bz B\u03c8 B\u03b8 B\u03c6[ ]T= C Cx Cy Cz C\u03c8 C\u03b8 C\u03c6[ ]T= PR hase PUSBL t( ) SUPR Path t( ) \u03b4uUSBL t( )+ SU I 2 0 2 4\u00d7[ ]=,= PCTD t( ) SCPR Path t( ) \u03b4fCTD t( )+= SC 0 1 2\u00d7 1 0 1 3\u00d7[ ]= VDVL t( ) RR 1\u2013 t( )SDP \u00b7 R Path t( ) \u03b4dDVL t( )+= RR 1\u2013 t( )SD diag AB( ) Bt C+( )cos( ) \u03b4dDVL t( )+= SD I 3 0 3 3\u00d7[ ]= VIMU t( ) SIP \u00b7 R Path t( ) \u03b4gIMU t( )+= SI diag AB( ) Bt C+( )cos( ) \u03b4gIMU t( )+= SI 0 3 3\u00d7 I 3 [ ]= PIMU t( ) VIMU t( ) td t t\u0394\u2013 t \u222b PIMU t t\u0394\u2013( ) VIMU t t\u0394\u2013( ) t\u0394+= = pR hase 10 10 10 0 0 0[ ]Tm= In this simulation, the specification of ORION manipulator1,13 mounted on Hemire ROV is utilized. Fig. 17 shows the kinematic configuration and D-H coordinate system for the workspace control. And TABLE II shows the D-H parameters of the portside manipulator of mounted on Hemire ROV. To evaluate the performance of the proposed control method, we compared the simulation results obtained through the dead reckoning method and the proposed method based on EKF. Fig. 18 and 19 show the ROV paths estimated from its two methods and the position error. As shown in Fig. 18 and 19, we know that the result of EKF follows the desired path better than one of DR" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000768_bf02658331-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000768_bf02658331-Figure3-1.png", + "caption": "Fig. 3-Sketch of laser melted region illustrating the results of an overflowing of the melt pool: (a) Section AA, (b) T o p view, as-irradiated surface, and (c) Section BB.", + "texts": [], + "surrounding_texts": [ + "Solidification of a Laser Me l ted N ickeI-Base Superalloy\nS. L . N A R A S I M H A N , S. M . C O P L E Y , E . W . V A N S T R Y L A N D , A N D M . BASS\nT h i s p a p e r d e s c r i b e s a n i n v e s t i g a t i o n o f t h e m i c r o - s t r u c t u r e of r e s o l i d i f i e d z o n e s f o r m e d by l a s e r m e l t - i n g s i n g l e c r y s t a l s of t h e n i c k e l b a s e s u p e r a l l o y U d i m e t 7 0 0 . * M e l t i n g was c a r r i e d out e m p l o y i n g a\nNi C o C r T i AI M o C B * U d i m e t 7 0 0 , wt p c t Ba l 18.~ 15.O 3 . 5 4 . 3 5.3 0 . 0 8 0 . 0 3 0\nc o n t i n u o u s w a v e c a r b o n d i o x i d e l a s e r o p e r a t e d in the T E M o o m o d e ( G a u s s i a n s p a t i a l d i s t r i b u t i o n of i n - t e n s i t y ) a t i n c i d e n t p o w e r of 200 W . T h e l a s e r b e a m was f o c u s s e d to a d i a m of 140 ~ m ( 1 / e 2 p o i n t in i n - t e n s i t y ) g i v i n g a n i n c i d e n t p o w e r d e n s i t y of 1.3 M W \u2022 c m -2 .\nA s i n g l e c r y s t a l of U d i m e t 700 was m o u n t e d on a t r a n s l a t i o n s t a g e w i t h a {100} s u r f a c e p e r p e n d i c u l a r t o t h e l a s e r b e a m . T h e s u r f a c e was t h e n m e l t e d by i r - r a d i a t i n g i t w h i l e i t was t r a n s l a t e d a l o n g <100) a t a r a t e o f 0.4 c m \u2022 s-1 . T o p , t r a n s v e r s e a n d l o n g i t u d i n a l s e c t i o n s o f l a s e r m e l t e d z o n e s w e r e e x a m i n e d by o p - t i c a l a n d s c a n n i n g e l e c t r o n m i c r o s c o p y , s e e F i g . 1 . A s o l u t i o n c o n s i s t i n g o f 13 v o l pct H2SO4 in m e t h a n o l a n d c o n t a i n i n g n i c k e l i o n s was e m p l o y e d f o r e l e c t r o p o l i s h - hag. T h e s p e c i m e n s w e r e e t c h e d in a s o l u t i o n c o n t a i n - i n g 2 g o f CuC12, 40 m l of HC1, 40 m l of e t h a n o l , a n d 40 m l o f H_~O.\nF i g u r e 2 s h o w s o p t i c a l p h o t o m i c r o g r a p h s of a top v i e w a n d t r a n s v e r s e a n d l o n g i t u d i n a l s e c t i o n s of a r e - s o l i d i f i e d r e g i o n . T h e top v iew, F i g . 2 ( a ) , s h o w s t h e a s - i r r a d i a t e d s u r f a c e . T w o s e t s of c i r c u l a r , p e r i o d i c m a r k i n g s a r e v i s i b l e in t h e m e l t e d z o n e . O n e s e t a p - p e a r s to be a s s o c i a t e d w i t h a p e r i o d i c v a r i a t i o n in s u r f a c e e l e v a t i o n a n d r e p e a t s o v e r a s p a c i n g of a p - p r o x i m a t e l y 100 p m . T h e o t h e r s e t , w h i c h l i e s p a r a l - l e l t o t h e f i r s t but i s m u c h m o r e c l o s e l y s p a c e d ( ~ 5 ~ tm) a p p e a r s t o be a s s o c i a t e d w i t h t h e d e n d r i t i c subs t r u c t u r e \u2022 A l s o v i s i b l e in t h e c e n t r a l z o n e a r e m a r k - i n g s r u n n i n g p e r p e n d i c u l a r t o t h e f i r s t t w o s e t s of m a r k i n g s a n d l y i n g a p p r o x i m a t e l y p a r a l l e l to t h e d i r e c t i o n of m a x i m u m h e a t f l o w . A t e a c h edge of t h e m e l t e d z o n e , t h e r e i s a b a n d of c l o s e l y s p a c e d m a r k - i n g s o r i e n t e d p e r p e n d i c u l a r to t h e e d g e . O u t s i d e t h i s b a n d , t h e u n m e l t e d r e g i o n s h o w s c o a r s e s l ip l i n e s c o r - r e s p o n d i n g t o the p r i m a r y {111}<1]0> s l ip s y s t e m s , w h i c h w e r e p r o d u c e d d u r i n g t h e i r r a d i a t i o n . B e t w e e n e a c h b a n d o f m a r k i n g s a n d t h e u n m e l t e d r e g i o n t h e r e i s a s t e p in t h e s u r f a c e . T h e s t e p a p p e a r s t o o u t l i n e t h e r e g i o n w h e r e m e l t o v e r f l o w h a s o c c u r r e d p a r t i a l l y c o v e r i n g t h e s l ip l i n e s .\nS. L. NARASIMHAN, formerly with University of Southern California, is now Engineering Supervisor, Materials and Processes, Research and Development,Eaton Corporation, Battle Creek, MI 49016. S. M . COPLEY is Kenneth Norris Professor of Metallurgical Engineering and Chairman, Department of Materials Science, University of Southern California, University Park, LA, CA 90007. E. W. VAN STRYLAND, formerly with The Center for Laser Studies, University of Southern California, is now Assistant Professor, North Texas State University,Physics Department, Denton, T X 78203. M . BASS is Director, Center for Laser Studies, University of Southern California, LA, CA 90007.\nManuscript submitted December 23 , 1977 .\n6 5 4 - V O L U M E 10A, M A Y 1 9 7 9\n~1111CO2 CW LASER BEAM, lii/ LONGITUDINALli'\u2022 1 1 ~ _ SECTION\n. .A i iJ :J\n~ O N OF / Z TRANSVERSE SECTION Fig. l-Experimental arrangement for sample irradiation.\nF i g u r e 2(b) s h o w s a t r a n s v e r s e s e c t i o n o f t h e m e l t e d r e g i o n , w h i c h was e t c h e d t o r e v e a l t h e d e n d r i t i c subs t r u c t u r e . It i s c o n v e n i e n t t o d i s c u s s t h i s p h o t o m i - c r o g r a p h in t e r m s o f f o u r c o n c e n t r i c z o n e s w i t h d i f - f e r e n t e t c h p a t t e r n s . T h e f i r s t o r o u t e r m o s t z o n e , w h i c h i s a p p r o x i m a t e l y 10 ~ m wide e x h i b i t s l i t t l e subs t r u c t u r e . T h e s e c o n d z o n e w h i c h v a r i e s f r o m 40 to 7 0 ~zm in w i d t h s o l i d i f i e d by t h e g r o w t h of c e l l u l a r d e n d r i t e s w i t h a s p a c i n g of 3.5 p m , w h i c h g r e w in t h e p l a n e o f the t r a n s v e r s e s e c t i o n a l o n g <100>. T h e t h i r d z o n e , w h i c h i s a p p r o x i m a t e l y 30 /~m w i d e , e x h i b i t s f i n e c i r c u l a r e t c h m a r k i n g s s u g g e s t i n g that s o l i d i f i c a - t i o n o c c u r r e d by t h e g r o w t h of c e l l u l a r d e n d r i t e s in a d i r e c t i o n w i t h a c o m p o n e n t p e r p e n d i c u l a r t o the p l a n e of t h e s e c t i o n . T h e f o u r t h o r i n n e r m o s t z o n e a l so e x - h i b i t s e t c h m a r k i n g , that s u g g e s t c e l l u l a r d e n d r i t i c g r o w t h in a d i r e c t i o n l y i n g out of the p l a n e o f t h e s e c - t i o n . In t h i s z o n e , h o w e v e r , the d e n d r i t e c r o s s - s e c - t i o n s a r e s h a p e d d i f f e r e n t l y than in t h e t h i r d r e g i o n . I n b o t h F i g . 2(b) a n d (c) the top s u r f a c e of the s p e c i - m e n was s l i g h t l y g r o u n d so that t h e s e p h o t o m i c r o g r a p h s do not g i v e a n a c c u r a t e r e p r e s e n t a t i o n o f t h e t o p o l o g y o f the a s - i r r a d i a t e d s u r f a c e .\nF i g u r e 2(c) s h o w s a l o n g i t u d i n a l s e c t i o n of the m e l t e d r e g i o n , w h i c h was e t c h e d . It i s a l so c o n v e n i e n t t o d i s c u s s t h i s p h o t o m i c r o g r a p h in t e r m s of f o u r z o n e s o r l a y e r s , w h i c h c o r r e s p o n d to t h e f o u r z o n e s disc u s s e d in F i g . 2 ( b ) . T h e b o t t o m l a y e r o r f i r s t z o n e e x h i b i t s l i t t l e s u b s t r u c t u r e . T h e s e c o n d l a y e r s o l i d i - f i e d by the g r o w t h of c e l l u l a r d e n d r i t e s p a r a l l e l to <100>. T h e t h i r d l a y e r i s c h a r a c t e r i z e d by side b r a n c h - i n g of t h e v e r t i c a l d e n d r i t e s t o p r o d u c e <100> d e n d r i t e s g r o w i n g so a s to f o l l o w the l a s e r b e a m . In t h e t o p o r f o u r t h l a y e r a m i s o r i e n t e d s u r f a c e g r a i n was o b s e r v e d to g r o w so a s to f o l l o w t h e l a s e r b e a m .\nS e v e r a l i m p o r t a n t f e a t u r e s o f the l a s e r m e l t e d r e - g i o n , F i g . 2 ( a ) , c a n be e x p l a i n e d o n t h e b a s i s of F i g . 3 . A s t h e m e l t p o o l m o v e s , i t i s p r o p o s e d that it o v e r - f l o w s i t s b o u n d a r i e s due t o c o n v e c t i v e p r o c e s s e s in t h e m e l t p o o l a n d v a p o r p r e s s u r e g r a d i e n t s a t t h e m e l t - v a p o r i n t e r f a c e . T h i s o c c u r s a t t h e side edge of the m e l t pool d e p o s i t i n g m a t e r i a l a t (a), F i g . 3 ( b ) . I t a l so o c c u r s a t t h e b a c k edge Of t h e p o o l (c) p r o d u c i n g v a r i a t i o n s in s u r f a c e e l e v a t i o n ( r i p p l e s ) , w h i c h in s o m e p l a c e s p a r t i a l l y c o v e r t h e b a n d o f d e n d r i t e s (b) a t the side edge of t h e m e l t p o o l .\nISSN 0360-2133/79/0511-0654500.7510 \u00a9 1 9 7 9 A M E R I C A N S O C I E T Y F O R M E T A L S A N D M E T A L L U R G I C A L T R A N S A C T I O N S A\nTHE METALLURGICAL SOCIETY OF AIME", + "M a t e r i a l in r e g i o n (a), F i g . 3(b), w h i c h f o r m e d w h e n t h e m e l t f l o w e d o v e r the c o o l s u b s t r a t e , m u s t h a v e c o o l e d v e r y r a p i d l y a n d g i v e s n o i n d i c a t i o n of h a v i n g a d e n d r i t i c s t r u c t u r e . I n c o n t r a s t , m a t e r i a l in r e g i o n (b), w h i c h o v e r l i e s t h e m e l t p o o l , m u s t h a v e c o o l e d m o r e s lowly t h a n in r e g i o n (a) a n d s o l i d i f i e d by the g r o w t h o f c e l l u l a r d e n d r i t e s . T h e l a c k o f s u f f i c i e n t l i q u i d to f i l l b e t w e e n the d e n d r i t e s i n d i c a t e s that r e g i o n (b) was l o - c a l l y t h e h i g h e s t in t h e m e l t p o o l w h e n i t s o l i d i f i e d , F i g . 3 ( a ) . M a t e r i a l in r e g i o n (c), was f o r m e d by f l o w o f the m e l t o v e r t h e b a c k edge of t h e pool a s s h o w n in\nF i g . 3 ( c ) . T h e t e n d e n c y of t h i s p h e n o m e n o n to o c c u r in a p e r i o d i c m a n n e r i s n o t u n d e r s t o o d .\nT h e f o u r z o n e s o b s e r v e d in F i g . 2(b) a n d (c) c a n be u n d e r s t o o d on the b a s i s o f c h a n g e s in t h e l o c a l s o l i d i - f i c a t i o n r a t e a n d t h e r m a l g r a d i e n t . I n i t i a l l y , s o l i d i f i - c a t i o n o c c u r s a l o n g a p l a n a r f r o n t g i v i n g r i s e to t h e f e a t u r e l e s s z o n e 1 . T h i s m a y be a t r a n s i e n t e f f e c t o r m a y r e s u l t f r o m h i g h t h e r m a l g r a d i e n t s a n d l o w g r o w t h r a t e s in t h i s z o n e . I n z o n e 2 , s o l i d i f i c a t i o n o c - c u r s by t h e g r o w t h o f c e l l u l a r d e n d r i t e s a l o n g t h e (100} m o s t n e a r l y p a r a l l e l to t h e d i r e c t i o n of m a x i m u m t h e r - m a l g r a d i e n t a s p r e v i o u s l y o b s e r v e d . 1'2 I n z o n e 3 side b r a n c h e s a p p e a r g r o w i n g a l o n g t h e d i r e c t i o n of m o t i o n o f t h e l a s e r b e a m due to a n i n c r e a s e in the c o m p o n e n t of t h e r m a l g r a d i e n t in t h i s d i r e c t i o n n e a r t h e s u r f a c e o f t h e m e l t p o o l . I n z o n e 4 , a s u r f a c e g r a i n w i t h d e n - d r i t e s o r i e n t e d a p p r o x i m a t e l y p a r a l l e l t o t h e d i r e c t i o n o f m a x i m u m t h e r m a l g r a d i e n t c o m p e t e s f a v o r a b l y w i t h the e p i t a x i a l r e g r o w t h .\n1. E. M. Breinan, B. H. Kear, C. M. Banas, andL. E. Greenwald: Surface Treatment o f Superalloys byLaser Skin Melting,Proc. III Int. Conf. Superalloys, Seven Springs, PA, September 12-15, 1976. 2 . S. L. Narasimhan, S. M. Copley, E. W.Van Stryland, and M. Bass: 1EEEJ. QuantumElectron, 1977,vol. QE-13, p . 2D.\nMETALLURGICAL TRANSACTIONS A VOLUME 10A, MAY 1979-655" + ] + }, + { + "image_filename": "designv11_7_0000055_978-1-4684-1500-1-Figure5.8-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000055_978-1-4684-1500-1-Figure5.8-1.png", + "caption": "Figure 5.8 A sensory controlled gripper. (from Institute for Information Technology at Karlsruhe University, West Germany)", + "texts": [ + " These grippers are known as 'simple sensory grippers', which may be used to distinguish between components of different sizes before they are acti vated by the appropriate program to pick up a component. The sensors also enable a robot to function within a dynamic work station by allowing it to check its sensors before every move to 66 Grippers determine (1) what is happening, (2) if a component is avail able for pickup, (3) the identity of the component, and (4) if the other machines (if applicable) are ready for the process to continue. Figure 5.8 shows various types of sensors that could be fit ted to a gripper. In reality, if the grippers are provided with sensors, they are limited to one or two types. For instance, grippers could be equipped with force sensors so the applied force is known and controlled or, alternatively, vision could be fitted within the gripper so that the robot can 'see' what is hap pening before it is activated (see Figure 5.9). In essence the robot becomes an inspection system that measures, identifies and weighs the items prior to or during pickup", + " An increased system reliability through the removal of mechanically complex feeding and sorting devices. This chapter highlights and discusses sensors which are available at present and which are used with assembly robots. The more sensing capability a robot has, the more 'intelligent' it becomes. If a robot can accurately evaluate its working en vironment and react accordingly, dynamic situations that accurately reflect the true world of the manufacturing industry can be accommodated. The idealized gripper shown in Figure 5.8 is fitted with a multi tude of sensory aids. Of course, in reality, this gripper would 129 Assembly with Robots be expensive and have technical implications, but the intent is valid. Consider, for instance, two components of similar shape, but with different dimensions, being processed by a single robot. This gripper could be used to identify a particular component by the size indicated through a diode array or sim ple tactile sensors, whereas weight could be determined by load cells within the gripper" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003538_sta.2013.6783140-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003538_sta.2013.6783140-Figure1-1.png", + "caption": "Figure 1. Bearing test rig [16]", + "texts": [ + " 7, we finally obtain n i n i=1 x(t)= c (t) r (t) +\u2211 (8) Thus, one can achieve a decomposition of the signal into nempirical modes, and a residue rn, which is the mean trend of x(t). The IMFs c1(t), c2(t) ,\u2026 , cn(t) include different frequency bands ranging from high to low. The frequency components contained in each frequency band are different and they change with the variation of signal x(t), while rn represents the central tendency of original signal x(t). The vibration signals used in this paper were provided by the Center for Intelligent Maintenance Systems (IMS), University of Cincinnati, USA. A schematic of experimental rig is shown as in Fig. 1 [16]. Rexnord ZA-2115 double row bearings are installed on the shaft as shown in Fig. 2. Bearings contain 16 rollers in each row, a pitch diameter of 2.815 in., a roller diameter of 0.331 in., and a tapered contact angle of 15.17\u00b0 [17,18]. The test is carried out for 35 days until a significant amount of metal debris is found on the magnetic plug of the test bearing [17]. Each data set describes a test-to-failure experiment. Data set consists of individual files that are 1-second vibration signal snapshots recorded at specific intervals" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000811_tmag.2008.2002379-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000811_tmag.2008.2002379-Figure1-1.png", + "caption": "Fig. 1. The 3-D geometric model of a coil end with the indexes of the segments marked.", + "texts": [ + " In this study, a commercial software package, COMSOL Multiphysics, was used to carry out the FEA of the magnetic forces as well as the corresponding stresses. A. 3-D Geometric Model A 3-phase, 6-pole squirrel-cage induction machine working as a motor was studied here. Thanks to the symmetry and periodicity, the simulated model was only 1/12 of the machine. The stator windings are two-layer diamond windings. A description of diamond windings can be found in [10], [11]. For the simplicity, the bent parts of the coil ends were replaced by the straight parts. In addition, each coil end was divided into 29 segments to analyze the forces. Fig. 1 shows one of the coil ends. According to the local definition here, in Fig. 1, segments 1\u201312 and 18\u201329 are termed as the lower part and upper part of a coil end, respectively. Table I lists the related specifications of the machine. This model used a linear magnetization characteristic. The laminated iron core was anisotropic in its conductivity and permeability. The tensor of its conductivity was and the tensor of its relative permeability was , where , , and are the unit dyads in the Cartesian coordinate system. The other structures were isotropic. 0018-9464/$25.00 \u00a9 2008 IEEE The stator windings were supplied by a current source" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002653_s10450-010-9270-x-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002653_s10450-010-9270-x-Figure1-1.png", + "caption": "Fig. 1 Molecular dimensions of amitrole", + "texts": [ + "1 Characteristics of the activated carbons and herbicide Surface characteristics of the activated carbons used are compiled in Table 1. Heat treatment of ACC at 1173 K in inert atmosphere to obtain ACCN produced a decrease in total oxygen content, OTPD, reducing the surface acidity and increasing the surface basicity and pHPZC. Therefore, as expected, the heat treatment of ACC gives rise to a more basic carbon surface. There was also a decrease in SBET and W0 and an increase in L0 as a result of the slight gasification produced by the removal of surface oxygen complexes (SOCs). The shape and dimensions of AMT are depicted in Fig. 1. Its molecular area is 0.39 nm2/molecule (Fontecha-C\u00e1mara et al. 2007), and this molecule is completely accessible to the microporosity (\u03b8 < 2 nm) of the carbons used. The AMT speciation diagram (Fontecha-C\u00e1mara et al. 2007) indicates that it exists as neutral species (AMT) at pHs of 6\u20138, as protonated species (AMTH+) at pH < 6, and as deprotonated species (AMT\u2212) at pHs 8\u201313. 3.2 Amitrole adsorption AMT adsorption isotherms at 298 K on ACC are depicted in Fig. 2. Results of application of the Langmuir equation to these isotherms at different pHs are displayed in Table 2, which additionally includes the correlation coefficient, R2, of the Langmuir plots", + " C\u2013\u03c0 + H2O2 \u2192 C\u2013\u03c0+ + OH\u2212 + OH\u2022 (3) C\u2013\u03c0+ + H2O2 \u2192 C\u2013\u03c0 + HO\u2022 2 + H+ (4) The only AMT degradation products found in solution after 10 h of treatment were nitrate and virtually negligible concentrations of ammonium ions. The experimental amount of nitrate ions, NO\u2212 3 (exp), was similar to the theoretical amount, NO\u2212 3 (theor), which was obtained by assuming that only two nitrogen atoms per oxidized amitrole molecule are converted to nitrate ions. The agreement between these values indicates that the rest of N is mainly converted to gaseous nitrogen compounds such as N2, which can be formed (Da Pozzo et al. 2005) from the two proximate N atoms in the pentagonal AMT cycle (see Fig. 1). Oxygen is also fixed on the carbon surface during AMT oxidation as shown in Table 6 for oxidation reactions at pH 7 and 10, with higher amounts of fixed O, Ofixed, at pH 10 than at pH 7 and with higher amounts on ACCN than on ACC at both pHs. This is because H2O2 decomposition is more favored at pH 10 and there are fewer SOC in the basic fresh ACCN versus fresh ACC samples. The percentage of oxygen fixed on the carbon surface was a very small percentage of the total available oxygen from H2O2, ranging from 1 to 2% according to the pH and surface basicity" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003790_j.triboint.2013.05.004-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003790_j.triboint.2013.05.004-Figure1-1.png", + "caption": "Fig. 1. Physical geometry of a wide rough plane slider bearing lubricated with a non-Newtonian micropolar fluid.", + "texts": [ + " Analytical expressions of the steady load capacity and the dynamic coefficients are obtained. The steady performance and the dynamic characteristics of the rough bearing lubricated with micropolar fluids are presented and discussed through the variation of the roughness parameter, the coupling parameter and the interacting parameter as compared to the smooth bearing lubricated with a Newtonian fluid. Some numerical values of plane bearing performances are also presented in tables for engineering references. Fig. 1 shows the physical geometry of a wide inclined plane slider bearing with rough surfaces. The lubricant is taken to be a non-Newtonian incompressible micropolar fluid of Eringen [9]. The local film thickness H can be considered to be composed of two separated parts: H \u00bc h\u00f0x; t\u00de \u00fe \u03b1\u00f0x; y; \u03be\u00de \u00f01\u00de where h(x,t) describes the nominal smooth part of the film profile depending on the horizontal coordinate x and the time t: h\u00f0x; t\u00de \u00bc hs\u00f0x\u00de \u00fe hm\u00f0t\u00de \u00bc \u00f0A\u2212x\u00de d A \u00fe hm\u00f0t\u00de \u00f02\u00de On the other hand, \u03b1(x,y,\u03be) represents the random part as a result of the surface asperities measured from the nominal mean level, and \u03be denotes a random variable describing a definite roughness arrangement" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003869_s00419-012-0608-6-Figure12-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003869_s00419-012-0608-6-Figure12-1.png", + "caption": "Fig. 12 The mode shapes corresponding to frequency \u03c923 (the first and second mode)", + "texts": [], + "surrounding_texts": [ + "As mentioned earlier, in the geometrical model of the gear, the geometry of the teeth is omitted. It allows us to reduce the system\u2019s FE model size. The simplified geometrical model of the system consists of five sectors (see Fig. 1) that have the cyclic symmetry feature. Each of these segments is meshed by using standard procedures of the ANSYS software. The 3-D solid mesh is elaborated and as mentioned earlier, the ten-node tetrahedral element (solid92) with three degrees of freedom in each node is used to realize each sector. During the mesh generation process, it is assumed that the maximum length of each element\u2019s side needs to be no more than 2.7 [mm]. The developed FE model is displayed in Fig. 2, and it consists of 19,620 elements and 36,188 nodes, respectively. The particular sectors are glued as a whole at the geometrical model preparing the stage by using standard procedure of the ANSYS program. The analysed gear is mounted in the roller bearings. Such bearings typically have slight load capacity under loads perpendicular to the primary supported direction. The gear shaft neck surfaces on which the bearings are assembled are denoted \u201cbearing\u201d (see Fig. 3a). The gear mates with the other devices by the splines. The splines is simplified down to a regular cylinder of the diameter assumed as equal to the splines pitch diameter. The surface denoted \u201cjoint\u201d (see Fig. 3a) is located on the pitch diameter of the splines. Parameters of the analysed system are shown in Table 1a\u2013b. The calculation results for natural flexural oscillations taking into account angular speed of the gear are shown in the paper. In the case of circular discs and annular plates, for each solution where nodal lines are nodal diameters, one obtains two identical arrangements of straight nodal lines, rotated by an angle of \u03b1 = \u03c0/(2n) one to another, where n is the number of nodal diameters. In accordance with the circular and annular plate vibration theory [5,6,12], the particular natural frequencies of vibration are denoted as \u03c9mn , where m refers to the number of nodal circles and n is the mentioned number of nodal diameters. As the shape of the gear model is fairy elaborate, the flexural modes of the system are subject to deformation (as compared to the system without any holes) to such extent that establishing which particular node it refers to becomes rather difficult. This problem is even worse if the angular speed of the gear is varying. The problem of influence of the angular speed on the flexural gear models deformation is analysed. For the purpose of identification of these modes, an algorithm of tagging oscillation modes, which determines the correspondence between vibration of the circular disc versus disc with holes, is used. For this purpose, an auxiliary model of annular plate in the form shown in Fig. 3b is used. The geometrical dimensions of the auxiliary model were taken from the gear geometry (shown in Fig. 1). They are as follows: addendum circle diameter dz , rim mounting diameter dp, root circle diameter dw2, and thickness h p and hz (see Table 1). Dynamic analysis is performed for the auxiliary model cases rotating at predetermined angular speed, where diameter of though holes d01 (see Fig. 3b) varies as seen in Table 2. Findings are compared to each other both quantitatively and qualitatively. This method makes it possible to investigate deformations of nodal lines associated with nodal diameters and circles due to through holes and then determine correspondence between oscillation modes of solid circular disc and a plate with holes. In the final step, solutions found for the auxiliary model are compared with the solution for the system whose FEM model is shown in Fig. 2 (the principal model). As for the principal model case, the 3-D solid mesh and the ten-node tetrahedral element (solid92) are used to discretize the auxiliary models. For all models subject to analysis, the boundary conditions were applied to the nodes. For each model, 1 d f associated with node radial displacement was subtracted from the nodes found on the surface identified as a bearing (see Fig. 3a,b). Furthermore, 1 d f associated with the displacement of nodes along the centreline of each model was subtracted from the nodes found on the surface, identified as a joint (see Fig. 3a,b). For the models obtained in this way, calculations were kept conducted as long as the natural frequency \u03c918 was determined. The calculations were performed assuming that the systems rotate as angular speed of \u03b8 , within the range of 0\u20131047 [ rad/s]. During the computing process, the angular speed values were gradually increased by 80[ rad/s], which made fourteen variants of the results (the natural frequencies and corresponding natural modes), which were subject to further interpretation. The rotation effect was taken into account by determining stress distribution due to rotation, for each model during the computational step associated with static analysis (the so called pre-stress effect). This stress distribution was then included in the computation step associated with modal analysis. The results of the numerical calculations related to the procedure of identifying deformed natural modes of flexural vibration of the gear under consideration are shown below. The results displayed here relate to the determination of the correspondence between the natural frequencies \u03c916 and \u03c925 at high angular speed (\u03b8 = 1047 [ rad/s]) as well as to the correspondence between oscillation modes and the natural frequency \u03c931 at lower angular speeds (\u03b8 = 80 [ rad/s]). The results as shown in Figs. 4, 5, 6, 7, 8, 9 allow for tracking deformations of nodal lines associated with nodal circles and diameters, due to varying diameter of the through holes. With respect to the natural frequency \u03c925, there is marked difference in shapes of natural modes. When one compares the results between each other, one can notice that in order to identify correctly deformed natural modes of the flexural oscillations in the gear under consideration at lower angular speeds, larger number of auxiliary models is required to be included during calculations, as compared to the higher angular speeds. It comes from the fact that additional stresses through the centrifugal effects appear. This effect causes the gear flexural stiffness to be an apparent function of rotational speed (stiffness grows for higher speed). In the next part, results of the numerical calculations associated with the extent of the influence of the angular speed to deformation of mode shapes of oscillations. For each discussed case, both mode solutions related to nodal diameters are shown. These analysed results are sorted by the order of their occurrence. For the frequencies \u03c923 and \u03c918, the results were obtained at angular speeds of \u03b8 = 0 and \u03b8 =1,047 [ rad/s] respectively. For the other cases, results were obtained at angular speeds \u03b8 of, 0, 320, 720, and 1,047 [ rad/s], respectively. Natural frequencies for these modes are included in Table 3. To determine this mode (see Figs. 10, 11), the procedure of tagging natural oscillation modes was required. Nodal lines associated with the circle and diameter are deformed. Minor influence of the angular speed to deformation of the nodal lines is noticeable. The task of determining modes in this case was not too difficult (see Figs. 12); no procedure of tagging natural oscillation modes was required. The slight impact of the gear angular velocity on the distortion of the nodal lines is observed. For these modes (see Figs. 13, 14), procedure of tagging natural oscillation modes was required. It is noticeable that angular speed affects markedly deformation of the nodal lines. Once the angular speed of 720 [ rad/s] is exceeded, the oscillation mode takes different shape. Major deformation of mode shape attributable to the shaft vibrations is evident at this speed. Moreover, additional problem associated with some similarity of the mode being tagged to the mode associated with frequency of \u03c931, emerged during mode identification. Establishing the correspondence between these modes was a complex task (see Figs. 15, 16) due to the shape of oscillation modes similarity to the case discussed earlier. The angular speed affects deformation of nodal lines markedly. Major shape mode variations emerge at \u03b8 = 400 [ rad/s]. The identification process in this mode was not easy (see Figs. 17, 18) . One can notice that angular speed affects the deformation of nodal lines. Major variation in mode shape emerges at \u03b8 = 720 [ rad/s]. Moreover, additional annular shaft vibration emerges at the highest considered angular speed. Finding correct correspondence between the modes in this case was fairly easy (see Figs. 19). High repeatability in deformations of nodal lines on circular plate at various angular speeds is noticeable. As a consequence of the conducted analysis (see Table 3), the Campbell diagram was plotted for the gear under consideration. This is a convenient method of displaying the relationship between gear natural frequencies and transmission system excitations [4]. Excited frequencies are plotted on a vertical axis, and the gear speed of rotation is plotted on the horizontal axis (see Fig. 20). Natural frequencies achieved from numerical analysis are plotted as near-horizontal curves. The forced frequency due to the meshing is determined by the following relation (as in Ref. [4]) f = n0 \u00b7 z 60 (4) where n0 [rpm] is the rotational speed and z is the number of teeth in the gear. For this system, the gear teeth number is z = 59. Vibration resonance phenomenon occurs when forcing frequency (4) matches as to its value with some natural oscillation frequency of the gear. The points where the near-horizontal \u03c9mn curves intersect the straight line (4) indicate the speeds at which the gear resonance will be excited (see Fig. 20). For instance, the rated excitation speed for the natural frequency of \u03c923 is 764 [rpm]. It may be inferred from both the Campbell diagram and Table 3 that the rotating movement makes flexural stiffness of the gear under consideration to increase. Moreover, at speed of 3,820 [rpm], one can notice major surge associated with the mentioned earlier changing of the shape of the natural mode frequency in the case of the frequency of \u03c931. The growth of the gear transversal stiffness observed during gyrate of the gear comes from the appearance of the additional stresses in the toothed gear through the centrifugal effects. The higher rotational speed generates higher centrifugal forces, higher stress level, thereby causing the transversal stiffness of the system to increase. Moreover, the growth of the gear flexural stiffness through the gyrate effect causes reduction of the needed numerical calculations connected with identifying the proper distorted mode shapes." + ] + }, + { + "image_filename": "designv11_7_0001503_imtc.2008.4547070-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001503_imtc.2008.4547070-Figure5-1.png", + "caption": "Fig. 5. Circuit scheme for short circuit simulation.", + "texts": [], + "surrounding_texts": [ + "The equation for the shorted turns, coupled to all the other circuits in the machine is:\nO=R I + a .sh + v a .sh (2)\nWhere ish, lsh and Rsh are fault current, total flux linking and resistance of the shorted turns. Assuming the infinitely permeable characteristic of ferromagnetic materials, the rotating sinusoidal magnetomotive force (MMF) is accountable only for the air gaps. Because the stator winding is connected in series, the excitation MMF's for individual poles are the same [12]. Regardless of the air gap variations the amplitude of air gap MMF remains uniform. Fmm = Asin(p80\u00b12iZfs t) = Asin(p80\u00b1ws t) (3)\nWhere A is amplitude of MMF, t is time, O is angular position of rotor, Pn = up, u is number of harmonic (6k \u00b1 1) induced in the rotor flux by the space harmonics (slot) de stator MMF, p is pair of poles. The air gap MMF can be expressed by developing expression (4) in Fourier series for all harmonics, v of stator. The distribution of the stator MMF in the air gap will be affected with the current that will circulate through the shortcircuited turns. There exists stator slot (Z1) harmonics of order sin[vZ1 (pro \u00b1 wst)]j. Analyzing the MMF of the affected coil group can be obtained the following new frequencies [4] in the flux density as can see Fig. 3.\nBvh =A CosrPnl[lTzl]\u00b1 lTZIv( )jw5t] (4) The fault of short turns of stator phase winding leads to\ntwo main effects on the machines flux. The first is that the large current in the shorted turns leads to an increase in the local leakage flux, particularly slot leakage as shows in Fig. 3. This changes the saturation conditions of the teeth locally. Secondly, the currents induced in the shorted coils oppose the establishment of the main, air-gap flux. They thus reduce that flux and the corresponding main flux path saturation along the winding axis of the shorted coil [13].\nIf it is considered the rotor harmonic, n and s = 0 for PMSM, can be obtained the new short circuit frequency starting from the equation (4).\nfsh )~fs (5) p\nTherefore, The new frequency component appears in the stator current spectrum as a result of a fault in the stator windings, only a rise in the rotor slot harmonic frequencies can be expected because under fault conditions a greater number of flux density waves exist in the machine, and all of these waves make a contribution at the same frequencies; and there is a greater probability of flux density waves with the basic number of pole pairs now existing [4].\nIII. WAVELET TRANSFORM ANALYSIS.\nWavelet analysis [14] is capable of revealing aspects of data that other signal analysis techniques miss, like trends, breakdown points, discontinuities in higher derivatives, and also self-similarity. Also allows to denoise signal and chose bands where focus the analysis, by using properly the mother wavelet function and also the scaling function wavelet. The wavelet approach is essentially an adjustable window Fourier spectral analysis with the following general definition is continuous Wavelet transforms (CWT):\nW(a,b,X,y a' 2([)V*(t-b)[ (6)\nWhere, V*(.) is the basic wavelet function, a is the dilation factor and b is the translation of the origin.\nAlthough time and frequency do not appear explicitly in the transformed result, the variable 1/a gives the frequency scale and b, the temporal location of an event. An intuitive physical explanation of (6) is very simple: W(a, b, X, ) is", + "the 'energy' ofXof scale a at t = b. In the case of discrete wavelet transform (DWT), the dilation and translation parameters are restricted only to discrete values leading. Through digital signal processing of a signal, it is possible to obtain the wavelet transform coefficients W(a,b), on a discrete grid corresponding to the discrete time wavelet coefficients. This is achieved when a and b are assigned regularly spaced values: a=maO and b=nb,, where m and n are integer values [14]. A signal can be successively approximated by DWT with different scales. The Fig. 4 shows the decomposition or analysis filter bank for obtaining the forward DWT coefficients.\nIV. SIMULATION AND EXPERIMENTAL RESULTS.\nThe motors under analysis have been a PMSM of 6000 rpm nominal speed, 2.3 Nm nominal torque, and 3 poles pair [7]. Simulations and experiments have been carried out for motors with 4, 8 and 12 short turns of stator phase winding. The short circuit implemented (4, 8, 12 turns) is a few turns one, in relation of whole winding (144 turns of stator phase winding one).\nThe load torque for stationary conditions was always the nominal (2.3 Nm) and for non stationary conditions a speed change of \u00b1500 rpm from stationary speed has been considered. Numerical simulations were developed with the combination of a finite element software, Flux2D [15], and an electronic circuit and control simulation sotware, Matlab-Simulink. The coupling between the circuit control and the finite element model (see Fig. 1. ), automatically links local variations in magnetic flux with electrical variables and viceversa [15]. The AWT ridges algorithm are implemented in Matlab using the Wavelab850 toolbox from Stanford University [16]. A. Stationary working conditions The simulations of the PMSM in stationary conditions are shows from Fig. 6 to Fig. 8 through the stator current harmonic. The curves have been normalized to a rotor frequency for every case. The amplitudes of the stator current harmonics 1, 7, 9 are higher for a fault motor than for a healthy one. Although, at low speed the discrimination is more difficult than for the nominal speed. The harmonic 9 is bigger that others and this will shows even the short circuit at low speed with some difficult. The experimental results can be seen in from Fig. 9 to Fig. 11, for 3000, 1500 and 300 rpm, respectively. The experimental measurements performed corroborate simulations. In the practices cannot be possible to carry out tests at high speeds because the very high value of short circuit current. This current can cause irreparable damages in the stator winding, isolation and the permanent magnet.\nThe motors were driven at nominal (6000 rpm), medium (3000 rpm) and low speed (1500 and 600 rpm). Both, the simulations and the experiments were carried out under stationary and not stationary conditions. For stationary conditions, FFT has been the mathematical transform used to determine the short circuit fault stage and DWT for non stationary conditions.", + "w=3000 rpm - M Healthy --M 4 Short turns on phase A --a- M 8 Short turns on phase A ....0.. M 12 Short turns on phase A\n0 2 4 6 8 10 12 14 16 18 20 22 Harmonics ). Stator current harmonics for PMSM. Experimental results at 3000\n2 4 6 8 10 12 14 16 18 20 22 Harmonics Stator current harmonics for PMSM. Experimental results at 1500\nspeed have been provoked. The working conditions for simulations and experiments were the same than for the stationary conditions (nominal torque). DWT Meyer of 7 levels has been considered in order to perform the feature extraction in these non stationary working conditions. DWT stator current motor analysis has been carried out for speed changes at nominal torque. Next to, the energy for every detail has been obtained to evaluate the short circuit fault. The detail wave forms are shown in\nFig. 12 and Fig. 13 for simulated result for speed change from 3000 rpm to 2500 rpm.\nTable 1 shows the energy of every detail for a DWT applied to stator currents obtained from simulation results. There is shows details 2, 3, 5 as the most promising to identify the failure for a PMSM running at 6000 rpm (100 Hz of rotor frequency). For the DWT done, the detail 2 contains the harmonic from seventh to eleventh, likewise, the detail 5 includes the first harmonic, and the detail 3 contains also the harmonic fifth. The detail 2 is more important because contain fault harmonic number 9. This detail is allows the fault detection of accurate way and visible. Likewise, simulations and experimental results have been obtained for 600, 1500 and 3000 rpm. It is observed that the most interesting details are the same or close to those found in 6000 rpm. In any case, there is always at least one detail containing information about the failure, for every speed.\nThe energy of every detail for a DWT applied to stator currents obtained experiment results are shows in Table 2. In this case for 1500 rpm, the details 4, 5 and 7 show the short circuit failure. The detail 4 is more important for the fault detection and the same way, the detail 5 shows the failure at 600 rpm. This way, it can conclude that indifferent of the detail that contains the harmonic 9, DWT allows detecting of short circuit fault at high, medium and low speeds.\nThe detail wave forms are shown in Fig. 14 and Fig. 15. These have been got from experimental results for speed change from 1500 rpm to 1000 rpm. Specifically, for a 1500 rpm the amplitude of the details 4 increases in case of machine with short circuit.\n-10\n-20 a) -5\nQ\nFig. ( rpm\n0O -10\nm-20\no-30 -a\n40 E _< 50\n-60\n-70L0\nud" + ] + }, + { + "image_filename": "designv11_7_0001596_0094-114x(73)90020-7-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001596_0094-114x(73)90020-7-Figure4-1.png", + "caption": "Figure 4. Polygons characterizing a ternary group.", + "texts": [ + " Equation (4) written for the k-th polygon of the investigated Assur group takes the fo rm m k E i g r t t k _ l + l m~ E i g m k _ l + l (lio cos @o + All cos ~p~o- Aq0d~o sin q~o) = 0, (1,o sin , ,o+Al, sin q~,o + A~,l,o cos q~,o) = 0. (5) The sides of vector polygons are created by connect ions of \"character is t ic points\" *Superscript r denotes a transposed matrix. of kinematic pairs. These points lie in the centre of the joint in the case of a rotating pair; in the case of a prismatic pair they coincide with the foot of certain perpendiculars or with the intersection point of the axes of pairs as is shown by example in Fig. 3 (binary groups) and in Fig. 4 (one of the modifications of a ternary group); also shown are the lists of unknowns. 2.2 Velocity and acceleration analyses Differentiating equation (1) with reslaect to t ime we get m k (/, cos ~, - 1,(~, sin ~,) = O, k = 1,2 . . . . n/2, (6) i=mk_l+l ~k E i = m k _ l \u00f7 [ ([~ sin ~, + l,~, cos q~,) = O. This set of n equations is linear with respect to the desired linear and angular velocities and in the corresponding subprogram it is Soived again by the above-mentioned Gauss-Jordan method. The motions of driving links must of course be given" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002138_j.triboint.2010.04.001-Figure9-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002138_j.triboint.2010.04.001-Figure9-1.png", + "caption": "Fig. 9. Supply groove positions for", + "texts": [ + " This assumption implies that the supply groove remains diametrically opposed to the minimum thickness section when the bearing is in equilibrium. But this situation is unrealistic since the centers line for the equilibrium state depends on eccentricity. In real devices, the supported load usually has a fixed direction, and fixed relative position with the supply groove (even if the centers line OaOc is moving, being its orientation given by the angle f), as it is the case in [7,8]. Thus, a vertical load and a supply pressure, p0, on a fixed groove located in the relative angle c will be here considered (see Fig. 9). In this situation, the angle of the line OaOc is an unknown for each eccentricity. That is, angle a between supply position and centers line must be computed, and, consequently, the angle f\u00bcc a can be determined. To compute the angle a a bisection method can be used. At each iteration the hydrodynamical steady state problem is solved to determine the equilibrium position and the corresponding supported load. That is, for a given angle c and pressure supply p0, and for each eccentricity, the following algorithm is implemented: 1", + " (c) Final time tF: Analyse the shaft center trajectory for the initial perturbation d: if it converges to the equilibrium position (stable) then M04M; if it diverges from this position (unstable) or describes a limit cycle then M0rM . diffe Finally, the critical adimensional mass M0 is bounded by testing different values of M . The numerical scheme proposed has been applied to analyze the supply groove position effect on the stability curves of infinite long bearings, with vertical external force and pressure supply p0 \u00bc 0 (but without inlet starvation). The cases for c\u00bc 0, p=4 and p=2 have been studied (see Fig. 9) by using a coarse mesh of 75 12 nodes for the hydrodynamic problems, and the stability curves are shown in Fig. 10. The curves obtained with analytical forces are drawn with a solid line and those obtained by the numerical method are represented with symbols. The analytical curves (a,b and c) are also presented in the corresponding Fig. 9 of Wang\u2013Khonsari [8], but in another scale. From these results, it is deduced that the margin of stability at high eccentricity decreases when c increases, and the vertical asymptote moves to the right. On the contrary, for low eccentricities, stability rent values of c. increases with c. Thus, the groove position should be chosen taking into account the working eccentricity in order to maximize stability. The numerical scheme can be used for testing the stability of short bearings, where analytical models do not compute the cavitation boundary, or finite bearings, for which analytical solutions are not available" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000385_s00170-006-0604-5-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000385_s00170-006-0604-5-Figure1-1.png", + "caption": "Fig. 1a\u2013d 5-RRR(RR) parallel manipulator", + "texts": [ + " Ten (1\u20131\u223c1\u20137, 1\u201316\u223c1\u201318) are identified from 30 as proposed by Li et al. [12]. The mechanism 1\u20138 is identified from mechanisms proposed by Kong and Gosselin [17]. The parentheses \u201c(ABC)\u201d are used to denote the structure where the axes of kinematic pairs A, B and C intersect at a common point. The underline \u201cABC\u201d denotes a structure where the axes of A, B and C are parallel. Following, the three manipulators (5-RRR(RR), 5-(RRR)(RR), 5-(RRpR) (RR)) are adopted as manipulator examples. 3.1 Manipulator 5-RRR(RR) For a 5-RRR(RR) parallel manipulator shown in Fig. 1a, the movable and base platforms are connected by five identical chains, each with five revolute joints. For all five limbs, the axes of the three joints adjacent to the base platform (R1, R2, R3) are perpendicular to the base platform; the other two axes (R4, R5) intersect at a common point O2. For any instantaneous configuration, let the origin (O1) of the reference frame (O1\u2013xyz) locate in the base platform plane and the line passing through the origin O1 and O2 be perpendicular to the base platform", + " Let the x axis pass through the center point of R1 and the z axis point from O1 to O2. Then, the kinematic screws for that chain are: $1 \u00bc S1; S01\u00bd \u00bc 0; 0; 1; 0; q1; 0\u00bd $2 \u00bc S2; S02\u00bd \u00bc 0; 0; 1; p2; q2; 0\u00bd $3 \u00bc S3; S03\u00bd \u00bc 0; 0; 1; p3; q3; 0\u00bd $4 \u00bc S4; S04\u00bd \u00bc l4; m4; n4; p4; q4; 0\u00bd $5 \u00bc S5; S05\u00bd \u00bc l5; m5; n5; p5; q5; 0\u00bd (8) Then, the reciprocal screw (constraint screw) of the kinematic screws is: $r1 \u00bc 0; 0; 1; 0; 0; 0\u00bd (9) whose axis is perpendicular to the base platform and passes through O2, shown in Fig. 1c. The constraint screws from the five chains are the same. Then, the five constraints acting on the movable platform form a common constraint which constrains the translational freedom along the z axis. So, the movable platform has three rotational and two translational freedoms. As all of the actuators are locked, the kinematic screws change to: $2 \u00bc S2; S02\u00bd \u00bc 0; 0; 1; p2; q2; 0\u00bd $3 \u00bc S3; S03\u00bd \u00bc 0; 0; 1; p3; q3; 0\u00bd $4 \u00bc S4; S04\u00bd \u00bc l4; m4; n4; p4; q4; 0\u00bd $5 \u00bc S5; S05\u00bd \u00bc l5; m5; n5; p5; q5; 0\u00bd (10) Then, $r1 and $r2, shown in Fig. 1c, are reciprocal screws (constraint screws) for the kinematic screws expressed in Eq. 10. The axis of $r2 is the intersecting line of the two planes PR2R3 and PR4R5. PRiRj denotes the plane determined by the axes of the kinematic pair Ri and Rj. In the general configuration, the $r2 of five chains are linear independent and every $r2 is also linear independent with the common constraint $r1. So there are six linear independent constraints acting on the movable platform when all five actuators are locked, namely, r(C1...Cn)=6. Therefore, the selection of the base actuators is feasible. As mentioned in the introduction, the manipulator will be singular if the configurations of all five chains are identical, as shown in Fig. 1a. Under such a configuration, five constraint screws $r2 are distributed on a single hyperboloid of one sheet within one regulus [24]. Since the rank of screws on a hyperboloid of one sheet within one regulus is three, so the rank of the constraints acting on the movable platform is not six, but four (r(C1...Cn)=4) when all of the actuators are locked. This means that the movable platform can still move after the locking of all actuators, and it is the second class of singularity defined by Gosselin and Angeles [27]. To avoid such a singularity, kinematic pairs in different limbs should be assembled with a small difference. For example, two of the five chains of the mechanism, chains 2 and 4, can be assembled in another regulus, as shown in Fig. 1d. This method is valid for all 18 parallel manipulators mentioned in this paper. Fig. 2a\u2013c 5-(RRR)(RR) parallel manipulator 3.2 Manipulator 5-(RRR)(RR) For a 5-(RRR)(RR) manipulator shown in Fig. 2a, the movable and base platforms are connected by five identical chains, each with five revolute joints. For all five limbs, the axes of three revolute joints adjacent to the base platform (R1, R2, R3) intersect at a common point O1. The other two (R4, R5) intersect at another point O2. Let the x axis be along the axis of R1 and the z axis pass through O1O2" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000601_jphys:0197800390100103900-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000601_jphys:0197800390100103900-Figure3-1.png", + "caption": "FIG. 3. - Stabilizing gyroscopic effect. Due to the rotation of the director on a elliptic cone with the axis along z : a fluctuation bn, of the direction induces a fluctuation bn, perpendicular to bn\u00e7; the fluctuation bn, induces a fluctuation \u00f4n, in a direction opposite to the initial one.", + "texts": [ + " 9)) equations read in the new coordinates where Before going on let us do some comments on the torque equations. In addition to the classical elastic and viscous torques one sees new contributions F\u2019 > and IGn > to the torques due to th6 rotation (characterized by Q 1) of the director : This is similar to a gyroscopic effect due to the rotation of the director : a fluctuation bn4 of the direction induces a torque r# ) which in turn creates a fluctuation bnn of the director perpendicular to bn\u00e7 (Fig. 3). Due to the symmetry of the problem, a fluctuation bnn also creates a fluctuation \u00e2n,. This process, considered alone, is stabilizing. The destabilizing effect is induced by the viscous torque depending on the viscosity coefficient (X2. For a nematic with x3 1 1 OC2 I the gyroscopic effect will only give a small correction to the viscous torque depending on OC2. In order to give the rationale for the instability let us consider a director fluctuation of the form bn,, - cos (q\u00e7) cos (kz). Conditions for non trivial solutions of eqs" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003742_s0263574711000397-Figure9-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003742_s0263574711000397-Figure9-1.png", + "caption": "Fig. 9. Comparison of ankle behavior of human normal walking and the proposed model. (a) The torque\u2013angle relationship in ankle joint of human normal walking, adapted from Frigo et al.24 Ankle angle is the relative angle between the shank and the foot. y-axis is the ankle joint torque. (b) The torque\u2013angle relationship in ankle joint of the proposed model. O (the origin point): heel-strike; O \u2192 A: toe-down phase; A \u2192 O: foot-flat phase (the leg is before mid-stance. The ankle stiffness is Ka); O \u2192 B: foot-flat phase (the leg has passed mid-stance and ankle stiffness has a larger value Kb.); B \u2192 C: heel-up phase. The ankle stiffness return to Ka . The line BC is parallel to the line AO; C \u2192 O: swing phase, the foot is reset to the equilibrium position.", + "texts": [ + " Thus, the torsional springs at the knee joints have very low stiffness values, which means that there is little torque at the knee joint. Torsional springs are added at ankle joints to represent ankle stiffness. Several studies indicate that ankle walking behavior in humans is quite similar to that of a torsional spring.22\u201325 To improve the performance of walking and achieve various walking gaits, we set different values of ankle stiffness during the stance phase, which shows a great resemblance with human normal walking21, 27 (see Fig. 9). Similar approach has been used in recent studies.20 The ankle stiffness has a larger value when the leg has passed the vertical line during the foot-flat phase. During the rest of the stance, the ankle stiffness is lower. The ankle torque changes continuously at the switching of ankle stiffness. In toe-down, foot-flat, and swing phases, the ankle joint reaches equilibrium position when the leg is vertical to foot (O \u2192 A, A \u2192 O, and B \u2192 C in Fig. 9b). The equilibrium position has a deviation in heel-off phase (O \u2192 B in Fig. 9b). The foot is supposed to be constrained vertically to the shank to avoid oscillation during swing phase. The ankle does a amount of network as shown by the hatched area in Fig. 9(b), which is taken consider into the calculation of energetic efficiency. In the simulation, stable cyclic walking is searched for various combination of actuation pattern and ankle stiffness. A typical representative of each gait is chosen for comparison. The hip torques of the representatives of the five gaits are shown in Fig. 10. Both the hip actuation mode and the ankle behavior are predefined with no active control during the walking motion. All simulations and data processing were performed using Matlab 7 (The Mathworks, Inc", + " In this paper, walking efficiency is measured by the nondimensional form of \u201cspecific resistance\u201d (energy consumption per kilogram mass per distance traveled per gravity), which is commonly used in the studies of dynamic walking. Note that the energy consumption includes the work done both by the hip torque and the ankle since the change of ankle stiffness injects energy to the walker. The total energy consumption during bipedal walking can be calculated by the following equation: Etotal = \u2211 all joints \u222b Ttotal 0 |P \u03b8\u0307 | dt + Eankle, (16) where Ttotal is the total time of walking. P is the joint torque and \u03b8\u0307 is the joint velocity. Eankle is the work done by the ankle joints, corresponding to the hatched area in Fig. 9(b), which can be calculated by the ankle stiffness. Parameter values used in the analysis are specified in Table I. All masses and lengths are normalized by the total mass and leg length, respectively. Our experimental results indicated that ankle stiffness plays an important role in gait selection. Different ankle stiffness may result in different gaits with the same mechanical parameters. The manner of combination of the two ankle stiffness values Ka and Kb has a great influence on the walking gait" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003869_s00419-012-0608-6-Figure16-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003869_s00419-012-0608-6-Figure16-1.png", + "caption": "Fig. 16 The mode shapes corresponding to frequency \u03c931 (the second mode)", + "texts": [], + "surrounding_texts": [ + "As mentioned earlier, in the geometrical model of the gear, the geometry of the teeth is omitted. It allows us to reduce the system\u2019s FE model size. The simplified geometrical model of the system consists of five sectors (see Fig. 1) that have the cyclic symmetry feature. Each of these segments is meshed by using standard procedures of the ANSYS software. The 3-D solid mesh is elaborated and as mentioned earlier, the ten-node tetrahedral element (solid92) with three degrees of freedom in each node is used to realize each sector. During the mesh generation process, it is assumed that the maximum length of each element\u2019s side needs to be no more than 2.7 [mm]. The developed FE model is displayed in Fig. 2, and it consists of 19,620 elements and 36,188 nodes, respectively. The particular sectors are glued as a whole at the geometrical model preparing the stage by using standard procedure of the ANSYS program. The analysed gear is mounted in the roller bearings. Such bearings typically have slight load capacity under loads perpendicular to the primary supported direction. The gear shaft neck surfaces on which the bearings are assembled are denoted \u201cbearing\u201d (see Fig. 3a). The gear mates with the other devices by the splines. The splines is simplified down to a regular cylinder of the diameter assumed as equal to the splines pitch diameter. The surface denoted \u201cjoint\u201d (see Fig. 3a) is located on the pitch diameter of the splines. Parameters of the analysed system are shown in Table 1a\u2013b. The calculation results for natural flexural oscillations taking into account angular speed of the gear are shown in the paper. In the case of circular discs and annular plates, for each solution where nodal lines are nodal diameters, one obtains two identical arrangements of straight nodal lines, rotated by an angle of \u03b1 = \u03c0/(2n) one to another, where n is the number of nodal diameters. In accordance with the circular and annular plate vibration theory [5,6,12], the particular natural frequencies of vibration are denoted as \u03c9mn , where m refers to the number of nodal circles and n is the mentioned number of nodal diameters. As the shape of the gear model is fairy elaborate, the flexural modes of the system are subject to deformation (as compared to the system without any holes) to such extent that establishing which particular node it refers to becomes rather difficult. This problem is even worse if the angular speed of the gear is varying. The problem of influence of the angular speed on the flexural gear models deformation is analysed. For the purpose of identification of these modes, an algorithm of tagging oscillation modes, which determines the correspondence between vibration of the circular disc versus disc with holes, is used. For this purpose, an auxiliary model of annular plate in the form shown in Fig. 3b is used. The geometrical dimensions of the auxiliary model were taken from the gear geometry (shown in Fig. 1). They are as follows: addendum circle diameter dz , rim mounting diameter dp, root circle diameter dw2, and thickness h p and hz (see Table 1). Dynamic analysis is performed for the auxiliary model cases rotating at predetermined angular speed, where diameter of though holes d01 (see Fig. 3b) varies as seen in Table 2. Findings are compared to each other both quantitatively and qualitatively. This method makes it possible to investigate deformations of nodal lines associated with nodal diameters and circles due to through holes and then determine correspondence between oscillation modes of solid circular disc and a plate with holes. In the final step, solutions found for the auxiliary model are compared with the solution for the system whose FEM model is shown in Fig. 2 (the principal model). As for the principal model case, the 3-D solid mesh and the ten-node tetrahedral element (solid92) are used to discretize the auxiliary models. For all models subject to analysis, the boundary conditions were applied to the nodes. For each model, 1 d f associated with node radial displacement was subtracted from the nodes found on the surface identified as a bearing (see Fig. 3a,b). Furthermore, 1 d f associated with the displacement of nodes along the centreline of each model was subtracted from the nodes found on the surface, identified as a joint (see Fig. 3a,b). For the models obtained in this way, calculations were kept conducted as long as the natural frequency \u03c918 was determined. The calculations were performed assuming that the systems rotate as angular speed of \u03b8 , within the range of 0\u20131047 [ rad/s]. During the computing process, the angular speed values were gradually increased by 80[ rad/s], which made fourteen variants of the results (the natural frequencies and corresponding natural modes), which were subject to further interpretation. The rotation effect was taken into account by determining stress distribution due to rotation, for each model during the computational step associated with static analysis (the so called pre-stress effect). This stress distribution was then included in the computation step associated with modal analysis. The results of the numerical calculations related to the procedure of identifying deformed natural modes of flexural vibration of the gear under consideration are shown below. The results displayed here relate to the determination of the correspondence between the natural frequencies \u03c916 and \u03c925 at high angular speed (\u03b8 = 1047 [ rad/s]) as well as to the correspondence between oscillation modes and the natural frequency \u03c931 at lower angular speeds (\u03b8 = 80 [ rad/s]). The results as shown in Figs. 4, 5, 6, 7, 8, 9 allow for tracking deformations of nodal lines associated with nodal circles and diameters, due to varying diameter of the through holes. With respect to the natural frequency \u03c925, there is marked difference in shapes of natural modes. When one compares the results between each other, one can notice that in order to identify correctly deformed natural modes of the flexural oscillations in the gear under consideration at lower angular speeds, larger number of auxiliary models is required to be included during calculations, as compared to the higher angular speeds. It comes from the fact that additional stresses through the centrifugal effects appear. This effect causes the gear flexural stiffness to be an apparent function of rotational speed (stiffness grows for higher speed). In the next part, results of the numerical calculations associated with the extent of the influence of the angular speed to deformation of mode shapes of oscillations. For each discussed case, both mode solutions related to nodal diameters are shown. These analysed results are sorted by the order of their occurrence. For the frequencies \u03c923 and \u03c918, the results were obtained at angular speeds of \u03b8 = 0 and \u03b8 =1,047 [ rad/s] respectively. For the other cases, results were obtained at angular speeds \u03b8 of, 0, 320, 720, and 1,047 [ rad/s], respectively. Natural frequencies for these modes are included in Table 3. To determine this mode (see Figs. 10, 11), the procedure of tagging natural oscillation modes was required. Nodal lines associated with the circle and diameter are deformed. Minor influence of the angular speed to deformation of the nodal lines is noticeable. The task of determining modes in this case was not too difficult (see Figs. 12); no procedure of tagging natural oscillation modes was required. The slight impact of the gear angular velocity on the distortion of the nodal lines is observed. For these modes (see Figs. 13, 14), procedure of tagging natural oscillation modes was required. It is noticeable that angular speed affects markedly deformation of the nodal lines. Once the angular speed of 720 [ rad/s] is exceeded, the oscillation mode takes different shape. Major deformation of mode shape attributable to the shaft vibrations is evident at this speed. Moreover, additional problem associated with some similarity of the mode being tagged to the mode associated with frequency of \u03c931, emerged during mode identification. Establishing the correspondence between these modes was a complex task (see Figs. 15, 16) due to the shape of oscillation modes similarity to the case discussed earlier. The angular speed affects deformation of nodal lines markedly. Major shape mode variations emerge at \u03b8 = 400 [ rad/s]. The identification process in this mode was not easy (see Figs. 17, 18) . One can notice that angular speed affects the deformation of nodal lines. Major variation in mode shape emerges at \u03b8 = 720 [ rad/s]. Moreover, additional annular shaft vibration emerges at the highest considered angular speed. Finding correct correspondence between the modes in this case was fairly easy (see Figs. 19). High repeatability in deformations of nodal lines on circular plate at various angular speeds is noticeable. As a consequence of the conducted analysis (see Table 3), the Campbell diagram was plotted for the gear under consideration. This is a convenient method of displaying the relationship between gear natural frequencies and transmission system excitations [4]. Excited frequencies are plotted on a vertical axis, and the gear speed of rotation is plotted on the horizontal axis (see Fig. 20). Natural frequencies achieved from numerical analysis are plotted as near-horizontal curves. The forced frequency due to the meshing is determined by the following relation (as in Ref. [4]) f = n0 \u00b7 z 60 (4) where n0 [rpm] is the rotational speed and z is the number of teeth in the gear. For this system, the gear teeth number is z = 59. Vibration resonance phenomenon occurs when forcing frequency (4) matches as to its value with some natural oscillation frequency of the gear. The points where the near-horizontal \u03c9mn curves intersect the straight line (4) indicate the speeds at which the gear resonance will be excited (see Fig. 20). For instance, the rated excitation speed for the natural frequency of \u03c923 is 764 [rpm]. It may be inferred from both the Campbell diagram and Table 3 that the rotating movement makes flexural stiffness of the gear under consideration to increase. Moreover, at speed of 3,820 [rpm], one can notice major surge associated with the mentioned earlier changing of the shape of the natural mode frequency in the case of the frequency of \u03c931. The growth of the gear transversal stiffness observed during gyrate of the gear comes from the appearance of the additional stresses in the toothed gear through the centrifugal effects. The higher rotational speed generates higher centrifugal forces, higher stress level, thereby causing the transversal stiffness of the system to increase. Moreover, the growth of the gear flexural stiffness through the gyrate effect causes reduction of the needed numerical calculations connected with identifying the proper distorted mode shapes." + ] + }, + { + "image_filename": "designv11_7_0002079_3.59009-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002079_3.59009-Figure1-1.png", + "caption": "Fig. 1 F-4 with 370 gallon tank.", + "texts": [ + " Significant frequency changes were obtained by the use of forces proportional to strain gage signals. Unfortunately, however, there was no significant improvement of flutter since a new instability was generated by phase shifts in the feedback electronics. This paper reports on an analytical study of the feasibility of active control of wing/store flutter for the F-4 Phantom aircraft. The particular configuration considered in these studies is with the 370 gallon fuel tank on the outboard store station, as shown in Fig. 1. The analytically predicted flutter boundary for this configuration, as a function of the percent fuel load, is shown in Fig. 2. This boundary was investigated by flight flutter testing. A mildly divergent flutter was encountered with the fuel tank near 90% full. Thus, this configuration provides both an analytical and experimental base for the study. D ow nl oa de d by Y O R K U N IV E R SI T Y o n M ar ch 3 , 2 01 5 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /3 .5 90 09 8001- 700 \u00a3-600 1 500 Flutter Placard Unstable - Flight Line J____I 20 40 60 % Fuel Load 80 100 Fig", + " The major function of the time domain program is to evaluate the rate, displacement and power demands on the control system in the presence of maneuver and gust loading and to assess the effect of system nonlinearities. It is also useful for final verification of the effectiveness of an active flutter control system designed in the frequency domain. Aircraft idealization As mentioned before, the aircraft model for these feasibility studies of active wing/store flutter control is the F-4 with a 370 gallon tank 90% full located on the outboard store station, as shown in Fig. 1. The aileron, which is located at the spanwise station of the store, is used as the force producer. Only existing control surfaces were considered in these studies. In this regard it is interesting to notice that the aileron, spoiler and leading-edge flap are all located at the same spanwise station. Each of these surfaces, either singly or in pairs, is available for use as flutter control force producers. Vibration data for this configuration are given in Table 1. The model consists of a truncated set of normal modes for the aircraft wing based on measured intertia data and structural influence coefficients" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001745_physreve.81.031920-Figure10-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001745_physreve.81.031920-Figure10-1.png", + "caption": "FIG. 10. Capturing the hydrodynamic influence of the beads of section S2 on the representative bead of section S1. a The distance rjc1 and the angle jc1 between c1 and bead j of section S2, vary for each bead when integrating through the beads of S2. b A simple rotation of frame so that section S2 lies along the horizontal axis, makes rjc1 and jc1 a function of only one variable xjc1 .", + "texts": [ + " The equation describes the hydrodynamic influence of one arbitrarily placed bead on another. Here we describe the calculation of the hydrodynamic influence of one section of beads on the representative bead of another section. The hydrodynamic influence of a section on an end bead is similarly calculated, except that the self interaction matrix HS is unity for an end bead the summation terms in HS of Eq. 12 do not exist for an end bead . Consider two sections, S1 and S2, which are parts of two separate rigid rods Fig. 10 . Let V1 p ,V2 p and V1 n ,V2 n be the parallel and normal translational velocities of the sections; 1 and 2 be their orientation angles; and c1 and c2 be their representative central beads. Let c1j and rc1j be the angle and distance between c1 and the jth bead of section S2 Fig. 10 . Let sections S1 and S2 be composed of M interior beads. Using the previously described notation for the hydrodynamic velocities, the equation for the hydrodynamic 031920-9 influence of sections S1 and S2 on the representative bead of section S1 is given as vc1 pH vc1 nH wc1 H \u2022 HS1 = V1 p V1 n W1 \u2212 HS1S2 vc2 pH vc2 nH wc2 H , 14 where HS1 = 3 4 a 1 + j=1,j c M 3a 2 rc1j 1 + j=1,j c M 3a 4 rc1j 1 + j=1,j c M 3a 4 rc1j j S1 , 15 HS1S2 = cos 1 sin 1 sin 1 \u2212 sin 1 cos 1 cos 1 \u2212 sin 1 cos 1 cos 1 \u2212 j=1 M 1 + cos2 c1j rc1j dj \u2212 j=1 M sin c1j cos c1j rc1j dj \u2212 j=1 M rc2j sin c1j cos c1j r1j dj \u2212 j=1 M sin c1j cos c1j rc1j dj \u2212 j=1 M 1 + sin2 c1j rc1j dj \u2212 j=1 M rc2j 1 + sin2 c1j rc1j dj d ds j=1 M sin c1j cos c1j rc1j dj d ds j=1 M 1 + sin2 c1j rc1j dj d ds j=1 M rc2j 1 + sin2 c1j rc1j dj j S2 , 16 where d ds = 1 2a d di c " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000104_tpas.1981.316710-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000104_tpas.1981.316710-Figure1-1.png", + "caption": "Fig. 1 MOD-2 Configuration", + "texts": [ + " This paper is addressed to a study of the transient behavior of large wind turbine generators during electrical disturbances. The MOD-2 is selected as the study system since it is representative of the present design of large wind turbine generators. II. DESCRIPTION OF THE MOD-2 SYSTEM As proposed, the MOD-2 is to have a blade speed of 17.55 rpm geared to a 4-pole, 1800 rpm, 2.5 MW synchronous generator. The generator and most of the controls are housed in the nacelle which is mounted on top of 200 ft tower. The MOD-2 system configuration is shown in Fig. 1. A simplified system diagram is shown in Fig. 2. \u00a9= 1981 IEEE 2205 BLade Dynamics The wind torque on a bLade, TWB, can be expressed TR = 2 p A VW cp rW8~~W~ (1 ) where p is the density of air, A is the swept area of the bLade, Vw is the wind velocity, C is the power coefficient andis hetpspedrtioefinap coefficient and r is the tip speed ratio defined as vw r (2 where is the blade angular velocity. The power coefficient is a function of the tip speed ratio and the bLade pitch angLe. In the studies reported herein the pitch angle was held constant at its low mode position" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002301_mesa.2010.5551993-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002301_mesa.2010.5551993-Figure2-1.png", + "caption": "Fig. 2. Singularity-free regions in the input-space of the 2-DOF RR-B.RR- Fig. 3. Singularity-free regions in the workspace of the 2-DOF RR-B.RRB.RR SPM. B.RR SPM.", + "texts": [ + "(31) multiplied with CO2, we have (32) For leg 3, we have h = (W3 x v3f U3 = 0 (33) I.e. (34) Substituting the second equation of Eq. (6) into Eq.(34) multiplied with CB3, we have (35) It is apparent from Eqs. (20), (25), (32) and (35) that Type I singularities happen if Type II singularity happens. C. Input space Except in the configurations corresponding to the four trivial solutions to the FDA (Section II-B), the entire input space is divided into the following four singularity-free regions (Fig. 2) by the singularity surface (Eqs. (19) and (23)): (a) Singularity free region I: CB2 > 0 and CB3 > 0, (b) Singularity-free region II: CB2 > 0 and CB3 < 0, (c) Singularity-free region III: CB2 < 0 and CB3 > 0, and (d) Singularity-free region IV: CB2 < 0 and CB3 < O. To simplify the control, it might be useful to confine the inputs into the maximum square containing the reference configuration. It can be found that within the input space -(90 - \ufffdd \ufffd B2 \ufffd (90 - \ufffddo and -(90 - \ufffdd \ufffd B3 \ufffd (90 - \ufffd1)O, where \ufffd1 is a small positive number, we always have CB2 > 0 and CB3 > O", + "(36), we obtain two solutions to \u00a23 { C\u00a23 = 61 CB3 (37) S\u00a23 = 61SB3 where 61 = 1 or -1. For each value of \u00a23, from Eq.(6), we may obtain two values of \u00a22 as follows { C\u00a22 = \u00b1CB2C\u00a23/(ai + bi)1/2 (38) S\u00a22 = -a1C\u00a22/b1 Equations (37) and (38) show that there are four solutions to the FDA of the 2-DOF SPM, in addition to the four sets of trivial solutions revealed in Section II-B. In the reference configuration shown in Fig. 1, we have B2 = B3 = \u00a22 = \u00a23 = 0, which leads to CB2 > 0, CB3 > 0, C\u00a22 > o and C\u00a23 > O. Therefore the SPM works in Singularity-free region I (Fig. 2) in the input space and Singularity-free region I in the Cartesian workspace (Fig. 3). In addition, we have h < 0 and h > O. In the following, we will derive the formula of the unique current solution (in Singularity-free region I in the Cartesian space) for a given set of inputs (in Singularity-free region I in the joint space) under the condition of J2 < 0, h > O. For a solution with C(/>3 > 0 to the FDA of the 2-DOF SPM for CB2 > 0 and CB3 > 0, we obtain \u00a23 of the current solution to the FDA using Eq" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002889_s11771-013-1751-0-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002889_s11771-013-1751-0-Figure1-1.png", + "caption": "Fig. 1 Basic principle of ERSM", + "texts": [ + " In the dynamic reliability analysis, the ERSM is used to only calculate the extreme value of output response, which is a processing variation corresponding to different input parameters, instead of all values of the output response within the time domain. The ERSM is equivalent to transform a stochastic process into a random variable for the output response of dynamic reliability analysis. Thus, ERSM promises to reduce greatly the computing time and enhance calculation efficiency [18]. The basic principle of ERSM is shown in Fig. 1. With the j-th input sample Xj, the extremum of the output response Yj(t, Xj) is Yj,max(Xj) within the time domain [0,T]. The data set ,max{ : }( )j j jY X Z consisting of the maximum output responses is employed to fit the extremum response curve Y. ,max( ) { : }( )j jY f jY X X Z (1) Based on the the quadratic function, the extremum response surface function (ERSF) is T 0Y a= + BX + X CX (2) where X is the input vector of random sample values, Y is the extremum output response, a0 is the constant term, B is the coefficient vector of the linear term, and C is the coefficient matrix of the quadratic term" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002376_j.fusengdes.2011.01.018-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002376_j.fusengdes.2011.01.018-Figure4-1.png", + "caption": "Fig. 4. Schematic diagram of frame structure: (i) bear", + "texts": [ + " The coordinate Xg 0 Yg 0 Zg 0 is defined as the global frame, and all local coordinates are related to the global frame: Xg 1 Yg 1 Zg 1 moves along the gear track and Xg 2 Yg 2 Zg 2 along the ball screw; Xg 3 Yg 3 Zg 3 rotates around the Zg 2 axis; Xg 4 Yg 4 Zg 4 is the basement coordinate of the Stewart and rotates around the Xg 3 axis; Xg 5 Yg 5 Zg 5 is fixed in the centre of the end-effector as the tool frame. The analytical stiffness model of the basic element evaluated in this paper is based on MSA. In order to illustrate the application of the MSA on the multi-beam structure, the stiffness modeling of bearing house and U-joint in the base side of Stewart platform in the robot is taken into account (Fig. 3). For simplification, the bearing house, U-joint and the base are described by the frame structure in Fig. 4. For applying the MSA method we firstly define the elements of structure and their nodes. Each element of structure is defined by a number enclosed with a circle, and its two nodes by two numbers. A local coordinate is given for each element. ouse, t i t o F n i In Fig. 4(iii), Ob 0A is the base frame of Stewart platform, Ou 1Ou 6 he frame of U-joint, and ABOu 1 the frame of bearing house includng the U-joint shaft. Firstly, we decompose the bearing house and he U-joint into separate beams in Fig. 4(i) and (ii), and then we btain the stiffness matrix for each beam by applying the MSA. inally all these stiffness matrices are assembled according to the ode connectivity by the superposition principle and expressed n the local coordinate system. Herein, the stiffness modeling (ii) U-joint, and (iii) base of Stewart. of U-joint is: (1) ing house, (ii) U-joint, and (iii) base of Stewart. w a b ( c j U f s o F w u t c U p F w f t 6 h t F w f h a f m h 3 l h t c f i p t c t here the 6 \u00d7 1 vector Fi is the external force exerting on node i, the corresponding deformation of node i, O the 6 \u00d7 6 zero matrix nd Kn ij the 6 \u00d7 6 stiffness matrix of beam n", + " Stiffness of hydraulic limb The assembly of components in the hydraulic limb is deemed to be serial, and the limb\u2019s stiffness varies with the cylinder stroke: Khy = A2 1 (A1x + Vh)/Bw + A1x/Bc + Vh/Bh + A2 2 (A2(l \u2212 x) + Vh)/Bw + A2(l \u2212 x)/Bc + Vh/Bh (9) where A is the area, V the volume, x the cylinder stroke, and l the cylinder length. Bw , Bc and Bh are the bulk modulus of water, cylinder and hose respectively. Subscripts 1 and 2 denote the corresponding chambers of the double-acting cylinder. F op pla ( 3 m a c h o K w K 4 i t b h t a p d s t ig. 7. Deformation of robot workspace: (i) on bottom plane of workspace; (ii) on t v); on back plane of workspace (vi) and on front plane of workspace. .3. Stiffness evaluation of parallel mechanism In Fig. 4, the coordinate frame Xg 4 Yg 4 Zg 4 is attached to the base- ent in the geometric centre. The coordinate frame B (Xg 5 Yg 5 Zg 5 ) is ttached to the moving platform, and its origin is located at the mass entre. Taking account of the deformations in the six base joints and ydraulic limbs, the stiffness matrix of the parallel mechanism is btained in the same way achieving Eq. (8) stw = (Jstw[diag[Kli]] \u22121JT stw) \u22121 (10) here Jstw is the Jacobian matrix of the Stewart, and li = diag[Khy i Kft i]. " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000791_e2007-00358-1-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000791_e2007-00358-1-Figure2-1.png", + "caption": "Fig. 2. Coordinate system for the torus: Local representation in cylindrical coordinates.", + "texts": [ + " We verify our analytical results using the numerical scheme and then extend the calculations to the non-slender limit. The problem of a force free torus moving along a cylindrical rod is addressed next. The force free velocity is calculated in several regimes and comparisons made with existing literature. The calculations are then extended to the lubrication limit. Consider a torus with smaller diameter b and larger diameter a, rotating about its centerline with an angular velocity \u03c9 in a Newtonian fluid, in the zero Reynolds number limit (Fig. 2). In the analysis to follow, we indicate dimensional quantities by a tilde. The governing equations for the fluid are the Navier Stokes equations (continuity and momentum), \u2207\u0303 \u00b7 u\u0303 = 0 (1) \u03c1f [ \u2202t\u0303u\u0303 + u\u0303 \u00b7 \u2207\u0303u\u0303 ] = \u2212\u2207\u0303p\u0303+ \u00b5\u2207\u03032u\u0303 (2) where \u00b5 is the viscosity of the fluid. The physical quantities are non-dimensionalized as follows: The lengths are scaled by a, velocity with \u03c9a, time by 1/\u03c9, the stresses and the pressure by \u00b5\u03c9. With this non-dimensionalization the Navier Stokes equations are given by \u2207 \u00b7 u = 0 (3) Re [\u2202tu + u \u00b7 \u2207u ] = \u2212\u2207p+ \u22072u, (4) where the Reynolds number Re = a2\u03c1f/(\u00b5\u03c9). For micron sized particles with speeds of few microns per second, the Reynolds number is indeed very low. In this work, we consider the limit of low Reynolds number, so that the Navier Stokes equations reduce to the familiar Stokes equations \u2207 \u00b7 u = 0 (5) \u2212\u2207p+ \u22072u = 0. (6) Here we use two coordinate systems (Fig. 2), the Cartesian (ex, ey, ez), and the cylindrical coordinate system (ex, er, e\u03b8). The unit vectors of the two coordinate systems are related by ey = er cos \u03b8 + e\u03b8 sin \u03b8 (7) ez = er sin \u03b8 \u2212 e\u03b8 cos \u03b8. (8) The solution for velocity can be expressed in terms of fundamental solutions of Stokes flow like the rotlet, the Stokeslet, the stresslet and the potential dipole [15,16]. For a rotating torus about its centerline, we assume a uniform distribution of rotlets of strength mex \u00d7 er acting along the center line of the torus, m is a scalar and ex is the unit vector in the direction of the axis of symmetry of the torus" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000698_s11814-007-0037-3-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000698_s11814-007-0037-3-Figure2-1.png", + "caption": "Fig. 2. Section view of the electrochemical cell.", + "texts": [ + " The anolyte and catholyte solutions were circulated through the cell with a ceramic pump (Pan World magnet pump, Model NH-40PX-N). The mediator solution oxidized at the cell was transported to the chemical reactor equipped with a scrubber and an online CO2 analyzer to estimate the amount of CO2 produced during the oxidation of organic wastes. The organic to be destroyed was fed to the chemical reactor from the feed tank. The catholyte part was also provided with a gas scrubber to capture the nitrous vapors produced. Single and double stack electrochemical cells were used. The single stack electrochemical cell (Fig. 2) consisted of a pair of anode and cathode separated by a Nafion\u00ae324 proton exchange membrane (Dupont, USA). The double stack cell consisted of two single stack cells assembled in one unit and electrically connected in series. The electrodes in both cells utilized were IrO2-coated on Ti mesh substrate (area: 140 cm2). A fluoro-polymer sheet (Viton\u00ae) possessing excellent chemical and heat resistance was used as a separator. The anolyte solution was prepared by dissolving 1 M cerium(III) nitrate in 3 M nitric acid" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003375_ac50156a021-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003375_ac50156a021-Figure1-1.png", + "caption": "Figure 1. Electrolysis cell", + "texts": [ + " After fresh tubing had been placed in the pumping channels, the flow rates decreased a few per cent but after about 15 hours' use, they remained constant to within =t0.2%, Electrodes and Cell. Tubular platinum electrodes were constructed by sealing a piece of seamless platinum tubing (purchased from Engelhard Industries) 0.060-inch i.d. by 0.500 inch long, wall thickness 0.010 inch, into soft glass tubing. Care was taken to ensure a smooth transition of the solution from the glass to the platinum to prevent turbulence and ensure a parabolic velocity profile as the solution enters the electrode. The electrolysis cell, illustrated in Figure 1 , was constructed from a piece of 10-mm i d . glass tubing with a side arm connected to an aspirator through which waste solution flows. A saturated KC1-agar salt bridge from the saturated calomel reference electrode dips into the cell from above. A rubber septum placed on the bottom of the cell serves as a strain and shock resistance mount for the tubular platinum electrode. The electrode is mounted in an upright configuration to permit easy clearance of any gas bubbles which may enter or be evolved in the flow stream. The bottom end of the tubular platinum electrode is connected to the glass flow line by a short piece of Tygon tubing to provide a strain-free connection. VOL. 39, NO. 13, NOVEMBER 1967 e 1543 The procedure used to coat the electrode with mercury was similar to that used by Blaedel and Laessig (8). The electrode was cleaned with hot concentrated nitric acid, rinsed with distilled water, and placed into the cell assembly shown in Figure 1. One molar perchloric acid was passed slowly through the electrode at approximately 1 ml/min while a potential of -3 volt US. a platinum coil electrode was applied. The electrode was maintained under these conditions of cathodic hydrogen evolution for 15 minutes. Then about 30 ml of triple-distilled mercury was introduced into the flow system and pumped until it was in contact with the inside of the platinum tube. After 5 minutes of steady contact, the mercury was pumped forward and backward through the electrode for 5 cycles and then out of the flow system" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003078_01691864.2013.854452-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003078_01691864.2013.854452-Figure1-1.png", + "caption": "Figure 1. Free-body diagram of an elastic rod; (a) The kinematics variables; (b) A rod experiencing gravity and a force and a moment at its tip; (c) Forces and torques applied on a piece of the rod; (d) An n-segment robotic arm.", + "texts": [ + " As a summary, the contributions of this paper are as follows: (1) solving the BVP with a new fast algorithm, (2) cancelation of some accumulated error in the rotation matrix, (3) modeling without shear and elongation deformations and showing the accuracy of the results, (4) presenting the application and results of the developed model in a very clear control algorithm. In this section, to model a continuum robotic arm, a simplified spatial model of an elastic rod as the arm backbone is introduced, using the theory of Cosserat Rod. It is assumed that shear and extension deformations are negligible for the considered rod. Figure 1(a) shows a thin flexible rod, while each point position along the rod is specified by a variable s, which shows the distance from the base to that point. Six degrees of freedom is defined at each point, three for the point\u2019s position and three for the rod\u2019s orientation at the point. The points\u2019 positions are represented in Cartesian space by r(s) as r\u00f0s\u00de \u00bc \u00bdx\u00f0s\u00de y\u00f0s\u00de z\u00f0s\u00de T (1) The orientation of the rod at each point is represented by a rotation matrix R(s), which is R\u00f0s\u00de \u00bc \u00bdi\u00f0s\u00de j\u00f0s\u00de k\u00f0s\u00de 3 3 (2) where i(s), j(s), and k(s) are the unit vectors along the local Cartesian axes. This local coordinate is attached to the rod at s, and moves and rotates with the rod, as depicted in Figure 1(a). Using R(s) the transformation of a vector such as r(s), represented on the inertial reference coordinate system and rl(s), represented on the local coordinate system at s is obtained as r\u00f0s\u00de \u00bc R\u00f0s\u00derl\u00f0s\u00de; rl\u00f0s\u00de \u00bc RT \u00f0s\u00der\u00f0s\u00de (3) The rod orientation is varied along its length with respect to s. Since the orientation of the rod was represented by a rotation matrix R(s), Equation (2), the derivative of R with respect to s is defined as R0 \u00bc dR ds \u00bc di ds dj ds dk ds (4) It should be mentioned that since all the variables are functions of s, hereafter, we might omit (s) for abridgment", + " For a unit vector such as i, similar to the derivations of angular velocity, it can be obtained di ds \u00bc X i (5) where \u03a9 shows the orientation variation of the rod along its length, and can be represented as X \u00bc \u00bdXx Xy Xz T \u00f0rad/m\u00de (6) Then, using (2), (3), and (5) we can obtain i0 \u00bc di ds \u00bc \u00f0RXl\u00de \u00f0R\u00bd1 0 0 T \u00de \u00bc R\u00f0Xl \u00bd1 0 0 T \u00de \u00bc R\u00bd0 \u00fe Xl z Xl y T Substituting this result, and its equivalents for j\u2032 and k\u2032 into (4), yields R0 \u00bc R\u00bdXl (7) D ow nl oa de d by [ A st on U ni ve rs ity ] at 0 6: 32 0 3 Se pt em be r 20 14 where \u00bdXl is \u00bdXl \u00bc 0 Xl z \u00feXl y \u00feXl z 0 Xl x Xl y \u00feXl x 0 2 64 3 75 (8) Considering Figure 1(a), for a rod without shear and extension deformations, we have r\u2032(s) = k(s). Then, using (2) gives r0 \u00bc R\u00bd 0 0 1 T (9) Figure 1(b) shows a free-body diagram of an elastic rod, experiencing some applied forces and torques, where F and \u03c4 are external concentrated (point) force and torque, respectively, applied at the tip of the rod. The distributed body forces are specified by f(s) per unit of length at each point. Typically, f(s) only represents gravitational loadings. Likewise, distributed body torques are represented by \u03c8(s). \u03c8(s) may represent distributed actuation torques. Internal forces and moments are specified by n (s) and m(s), respectively, at each point. According to Figure 1(c), the force balance for an element of the rod from a to b can be written as n\u00f0b\u00de n\u00f0a\u00de \u00fe Z b a f\u00f0s\u00deds \u00bc 0 (10) and for moment balance about the base of the rod, it is obtained m\u00f0b\u00de m\u00f0a\u00de \u00fe r\u00f0b\u00de n\u00f0b\u00de r\u00f0a\u00de n\u00f0a\u00de \u00fe Z b a \u00f0r\u00f0s\u00de f\u00f0s\u00de \u00feW\u00f0s\u00de\u00deds \u00bc 0 \u00f011\u00de Differentiating the above equations with respect to s, assuming the length of the rod element goes to zero (or b tends toward a) these equations become n0 \u00fe f \u00bc 0 (12) and m0\u00f0s\u00de \u00fe r0\u00f0s\u00de n\u00f0s\u00de \u00fe r\u00f0s\u00de n0\u00f0s\u00de \u00fe r\u00f0s\u00de f\u00f0s\u00de \u00feW\u00f0s\u00de \u00bc 0 (13) where n0 \u00bc dn ds and so on", + " So, on local coordinates the linear Hook\u2019s law can be written as ml \u00bc EIxx 0 0 0 EIyy 0 0 0 GJ 2 4 3 5\u00f0Xl X l\u00de \u00bc C\u00f0Xl X l\u00de (16) where Ixx and Iyy are the second area moments and J is the polar second moment of the cross sectional area, E specifies the modulus of elasticity, and G is the shear modulus. Considering uniform rods, C is a constant matrix. In nonlinear cases, C can be considered as a function of \u03a9l. Obviously, if the rod is straight at rest, then \u03a9*l is zero. Here, a slender rod is considered that is experiencing a force F and a moment \u03c4 applied at its tip, and its own weight as a distributed force f(s) = \u03c1Ag, as illustrated in Figure 1, were \u03c1 is density, A is cross-sectional area, and g is the vector of gravitational acceleration. Solving (10) for these forces, we obtain n\u00f0s\u00de \u00bc \u00bdFx Fy qAgs qAgsf \u00fe Fz T (17) To consider elasticity, the term m\u2032 is calculated using (3) and (16), as m0 \u00bc d ds \u00f0m\u00de \u00bc d ds \u00f0R ml\u00de \u00bc d ds \u00f0RC\u00f0Xl X l\u00de\u00de \u00bc R0CXl \u00fe RC\u00f0Xl0 X l0 \u00de And substituting R\u2032 by (7), and m\u2032 by (14) gives r0 n W \u00bc R\u00bdXl C\u00f0Xl X l\u00de \u00fe RC\u00f0Xl0 X l0 \u00de Solving this equation for \u03a9l\u2032 yields Xl0 \u00bc C 1\u00bdXl C\u00f0Xl X l\u00de C 1RT \u00f0r0 n\u00fe I\u00de \u00feX l0 D ow nl oa de d by [ A st on U ni ve rs ity ] at 0 6: 32 0 3 Se pt em be r 20 14 and finally, substituting (9) into the above result, it is obtained Xl0 \u00bc C 1\u00bdXl C\u00f0Xl X l\u00de C 1RT \u00f0R\u00bd0 0 1 T n\u00fe w\u00de \u00feX l0 \u00f018\u00de Equations (7), (9), (17) and (18) describe the mathematical model of the elastic rod as the backbone", + " Therefore, r(0) = r0 and R(0) = R0 are the proper boundary conditions for the first two equations of (19). However, in the third equation of (19), \u03a9l(0) is not known. From (16), we have Xl \u00bc C 1ml \u00feX l (20) which shows \u03a9l(0) depends on ml(0), which in turn depends on the moments of all the forces acting on the rod, which depend on the shape of the rod. Thus, \u03a9l(0) cannot be determined, unless we already know the rod\u2019s shape. On the other hand, at the tip of the backbone (at s = sf), we have ml(sf) = \u03c4 (Figure 1(b)). Therefore from (20), the boundary condition for \u03a9l is \u03a9l(sf) = C\u22121\u03c4 + \u03a9*l(sf). In summary, the boundary conditions for the first two equations of (19) are r\u00f00\u00de \u00bc r0 R\u00f00\u00de \u00bc R0 (21-a) and for the third Equation of (19) is Xl\u00f0sf \u00de \u00bc C 1m\u00f0sf \u00de \u00feX l\u00f0sf \u00de \u00bc C 1s\u00feX l\u00f0sf \u00de (21-b) Equations (21) present the boundary conditions at two different points, which forms a BVP. Figure 1(d) shows an n-segment robotic arm, with a force F acting at the robotic arm\u2019s tip, gravitational forces acting as a distributed force along the backbone, with actuation torques \u03c41, \u03c42, \u2026, \u03c4n, acting on n different points s1, s2, \u2026, sn. These torques can be applied by an actuation system such as cable-driven systems or pneumatic muscles. To solve the shape of the backbone, we can use the proposed model. However, because of actuation torques and forces, there are some sudden changes in m(s) and n(s) at the beginning of each segment, as explained above Equation (15)", + " Furthermore, this approach automatically avoids switching between various roots, which was discussed below Figure 2. To choose the first X\u0302 l\u00f00\u00de, we start by choosing an estimation of the rod\u2019s shape, r\u0302\u00f0s\u00de. For instance, in control applications if the configuration in the previous step is known, it can be chosen as r\u0302\u00f0s\u00de for the present step. Otherwise, for the first trial of r\u0302\u00f0s\u00de, the rod\u2019s shape can be considered as a straight line, or a constant curvature model. Then, we calculate the base moment, based on the rod\u2019s shape, as in Figure 1(d), by m\u0302\u00f00\u00de \u00bc X si \u00fe X r\u0302i Fi \u00fe Z \u00f0r\u0302\u00f0s\u00de f\u00f0s\u00de \u00fe w\u00f0s\u00de\u00deds\u00fe ::: (31) From (3), we then have m\u0302l\u00f00\u00de \u00bc RT \u00f00\u00dem\u0302\u00f00\u00de, and from (16) X\u0302 l\u00f00\u00de \u00bc C 1m\u0302l\u00f00\u00de \u00feX l\u00f00\u00de. These two equations yield X\u0302 l\u00f00\u00de \u00bc C 1RT \u00f00\u00dem\u0302\u00f00\u00de \u00feX l\u00f00\u00de (32) Using (32), the model expressed by (19) can be solved using conditions of (29). Then the error ebv can be checked by (30). If the error is not small enough, we can use the resulting r\u0302\u00f0s\u00de to find a new X\u0302 l\u00f00\u00de from (31) and (32). We can repeat this procedure until it converges to a solution with negligible error", + " Finally, this procedure was experimentally verified to show the precision of proposed modeling approach, also to reveal the importance of faster solutions for real-time control. The experiments show that the average error in the robotic arm tip position, introduced as the difference between the tip real position as measured during the experiments, and the position obtained using the proposed method, was about 0.5% of the length of backbones which is significantly better than comparable results in literature. Nomenclature s Backbone reference length parameter, Figure 1 sf The whole length of the backbone r(s) Position vector of the backbone at s R(s) Orientation of backbone l Expressed in local coordinates \u2032 Derivative with respect to s ^ An estimation, or a result of an estimation \u03a9(s) Backbone rate of rotation with respect to s \u03a9*l(s) \u03a9(s), at undeformed configuration (at rest) \u00bdXl The skew-symmetric matrix of \u03a9l, (8) f(s) Body forces (distributions per unit of length) \u03c8(s) Body moments (distributions per unit of length) n(s) Internal (cross sectional) forces of backbone m(s) Internal (cross sectional) moments of backbone F, \u03c4 External concentrated (point) force and torque C Stiffness matrix for bending and torsion, Equation (16) ebv Boundary-value error, (30) Notes on contributors M" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003664_peds.2013.6527224-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003664_peds.2013.6527224-Figure1-1.png", + "caption": "Fig. 1. Relationship between \u03b3\u03b4-frame and dq-frame. The \u03b4-axis is defined as the direction of the output voltage vector of the inverter, and the direction of the q-axis is defined as the electromotive force vector.", + "texts": [ + " After that, the MTPA control method based on V/f control method is confirmed by simulation. In the simulation, it is confirmed that the output current in dq-frame can be corresponded to the MTPA operation point. Furthermore, The proposed MTPA is demonstrated in the experiment using a 1.5-kW IPMSM with a 2-level inverter. As a result, the proposed MTPA reduces the output current by nearly 76 % compared to not use MTPA. 978-1-4673-1792-4/13/$31.00 \u00a92013 IEEE 1322 II. V/F CONTROL BASED ON THE OUTPUT VOLTAGE Fig. 1 shows the relationship between \u03b3\u03b4-frame and dqframe. Generally, in the dq-frame of the IPMSM control, the d-axis is defined as the direction of the flux vector by the permanent magnet and the direction of the q-axis is defined as the electromotive force vector. Therefore, it is very important to identify the flux vector in the vector control. However, the V/f control method is implemented on the \u03b3\u03b4-frame, and the \u03b4axis is defined as the direction of the output voltage vector of the inverter. Therefore, the \u03b4-axis means active power component and the \u03b3-axis means reactive power component" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002359_s00170-010-2783-3-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002359_s00170-010-2783-3-Figure1-1.png", + "caption": "Fig. 1 Schematic diagram of DMD process", + "texts": [ + " In his experiment, they also showed that the top of the processed layer was copper rich which is unfavorable for major applications. Another major difficulty associated with steel and copper is that they are partially soluble and have got very different melting points. But these problems can be overcome using direct metal deposition (DMD), which is a laser cladding process for fabricating fully functional metallic parts directly from CAD data. The DMD process involves the beam from a high power laser creating a melt pool on the surface of a solid substrate into which a metallic powder is injected [13\u201315]. Figure 1 shows a simple schematic diagram of the DMD process. The process allows fabrication of single material or multimaterial parts. The laser melts the powder and fuses it on to the substrate creating a fully dense, metallurgical sound bead. By overlapping the beads, usually by 50%, a continuous layer is produced. With this process, bi-metallic components and tooling can be fabricated to advantage for various casting processes. This paper presents an investigation on developing bimetallic tooling for high-pressure die casting using the DMD process with the aim of identifying the most suitable steel layer thickness on the copper alloy substrate" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000999_s11340-007-9115-z-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000999_s11340-007-9115-z-Figure1-1.png", + "caption": "Fig. 1 The concept of the release phase ground testing setup: two pendulums with nominally equal lengths represent the TM and the finger respectively. A position sensor detects the swing motion of the TM due to the momentum transferred upon pulling the finger away from the contact", + "texts": [ + " Neglecting, for the moment, the stiff constraint along the vertical direction, the simple pendulum model for the inertial isolation system has been chosen to investigate the possible performance of the transferred momentum measurement experiment. As long as the pendulum length is compatible with the typical height of a laboratory ceiling (i.e. meter scale), the preferred practical implementation is the simple pendulum characterized by easily determinable dynamic properties (quality factor and resonant frequency) and still providing good isolation from gravity and micro-seismic noise. The basic concept of the measuring apparatus, illustrated in Fig. 1, is to suspend both the test mass and the release finger from two pendulums. A position sensor detects the weakly damped oscillation of the test mass mock-up due to the momentum transferred upon pulling the contacting finger mock-up away. In the configuration shown in Fig. 1, however, the stress status on the contact patch may be in principle far different in the ground experiment from the in-flight conditions. The in-flight release takes place with an unconstrained test mass, and for equilibrium shear stresses at the contact patch are not allowed along any of the directions lying on the common contact plane. In the ground experiment (see Fig. 2), both the test mass mock-up and the finger mock-up need to be suspended with some constraining stiffness to ground, named Kn, Kt and Ks" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000904_j.mechmachtheory.2008.08.005-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000904_j.mechmachtheory.2008.08.005-Figure3-1.png", + "caption": "Fig. 3. Fault tolerant operation.", + "texts": [ + " Generally speaking, a larger K will force the reduced manipulator to come close to its optimal configurations (away from singularity) at a fast rate,which makes the manipulator have a better fault tolerant ability at the moment of locking joint. But a larger K will cause a larger JVJ at the same time. The motion stability of the manipulator at the moment of locking joint is poorer. Hence, K should be taken as small as possible on the condition that the reduced manipulator is not in singular configurations. Note that how to choose the magnitude of K should also take into account the unit of the index H. Fig. 3 is the simulation results of the fault tolerant operation on condition that joint 4 fails and is locked at the moment of maximum JVJ for the case of K = 100. The configurations of the 4R manipulator in Fig. 3a indicate that the manipulator can continue the desired circle motion when the joint 4 is locked at t = 0.225 s. And, the JVJ of remaining joints does occur during the fault tolerant operation by locking failed joint as shown in Fig. 3b The simulation results of the reduced manipulator with least-norm joint velocity are shown in Figs. 4 and 5. Due to the limited space, only the simulation with K = 100 is presented here. When t = 0.275 s, the JVJ of the joint 3 reaches the maximum 2.46 rad/s shown in Fig. 4, which is larger than 1.78 rad/s for the optimal case shown in Fig. 1b. Fig. 5 indicates that when the joint 4 is locked, although the manipulator can continue the desired task, its motion stability decreases, the larger the K is, the more obvious the decrease is" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001668_j.jsv.2010.11.010-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001668_j.jsv.2010.11.010-Figure2-1.png", + "caption": "Fig. 2. Contour of integration.", + "texts": [ + " The case of B-1 In the case of an absolutely rigid target or a small contact spot, the parameter B tends to infinity, resulting in the following: B 1fg\u00f0p\u00de-p2\u00feg\u00fet ge p2\u00feo2 1pg\u00feo2 0t g e , (66) F \u00f0p\u00de \u00bc V0E1 pg\u00fet gs p2\u00feg\u00fet ge p2\u00feo2 1pg\u00feo2 0t g e , (67) Dw\u00f0p\u00de \u00bc V0 pg\u00fet ge p2\u00feg\u00fet ge p2\u00feo2 1pg\u00feo2 0t g e , (68) w2\u00f0p\u00de\u00few1\u00f0p\u00de \u00bc V0 p2 V0o2 1 pg\u00fet gs p2\u00f0p2\u00feg\u00fet ge p2\u00feo2 1pg\u00feo2 0t g e \u00de : (69) Reference to formulae (67)\u2013(69) shows that relationship (68) within an accuracy of an insignificant multiplier coincides with the image of the Green function for an oscillator based on the fractional derivative standard linear solid model (see Eq. (2.1.1) in the review article [1]), while relationship (67) coincides with the first term of the image of the stress in a viscoelastic rod based on the same model during its normal impact against a rigid barrier (see Eq. (4.4.7) in the review article [1]). During inverse transform from the Laplace domain to the time domain via the Mellin\u2013Fourier transition formula Z\u00f0t\u00de \u00bc 1 2pi Z c\u00fe i1 c i1 Z\u00f0p\u00deept dp, (70) where Z(t) is the function to be found, we use the contour of integration shown in Fig. 2. Applying the main theorem of the theory of residues to a multi-valued function possessing the branch points at p=0 and p\u00bc1, we rewrite integral (70) in the following form: Z\u00f0t\u00de \u00bc 1 2pi Z 1 0 \u00bdZ \u00f0se ip\u00de Z \u00f0seip\u00de e st ds\u00fe X k res\u00bdZ\u00f0pk\u00dee pkt , (71) where pk are the roots of the characteristic equation fg\u00f0p\u00de \u00bc 0: (72) To find the roots of Eq. (72), we put p\u00bc reic, introduce the value x\u00bc \u00f0rte\u00deg, and separate in the resulting relationship the real and imaginary parts. As a result, we obtain r3a1\u00fer2a2\u00fera3\u00fea4 \u00bc 0, (73) r3b1\u00fer2b2\u00ferb3\u00feb4 \u00bc 0, (74) where a1 \u00bc cos3c\u00fexcos\u00f03\u00feg\u00dec, b1 \u00bc sin3c\u00fexsin\u00f03\u00feg\u00dec, a2 \u00bc B\u00bdcos2c\u00fexcos\u00f02\u00feg\u00dec , b2 \u00bc B\u00bdsin2c\u00fexsin\u00f02\u00feg\u00dec , a3 \u00bc C\u00bdo2 0cosc\u00fexo2 1cos\u00f01\u00feg\u00dec , b3 \u00bc C\u00bdo2 0sinc\u00fexo2 1sin\u00f01\u00feg\u00dec , a4 \u00bc B\u00f0o2 0\u00fexo2 1cosgc\u00de, b4 \u00bc Bxo2 1singc: First we fix the anglep=2rcrp in Eqs" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003759_ieem.2012.6838020-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003759_ieem.2012.6838020-Figure4-1.png", + "caption": "Fig. 4. The CAD model of test part", + "texts": [ + " Moreover, the inspection operations are added before a machining operation starts, identifying how much material should be taken off from the deposited feature. If the deposited feature is smaller than its nominal size as identified in the inspection operation, further deposition operations will be added before executing the machining operation. Furthermore, inspection operations are conducted before depositing a child part onto an un-machined parent part due to the differing heights of the parent part that could result in the change of depositing parameters. A test part was designed as shown in Fig. 4(a), which consists of bosses, pockets, holes and a step. The part geometry was first interpreted. The manufacturability analysis showed that there was no internal feature and no special tooling needed. However, a number of overhangs exist, leading to an amount of support material that was required in different building directions. Using the current orientation in Fig. 4(a) or changing the orientation by using plane A, B, C or D as the base surface, building overhanging features became unavoidable. Hence, the volume of support material required and the resulting build times were calculated by using (2). As a result, building the part by using plane A as the base surface was considered to be the proper orientation. However, it was also noted that more than 10% of the total material was used to build the support structure. Subsequently, the part was decomposed by removing the four bosses from plane D (as shown in Fig.4(b)) and the result was fed back to the part orientation module. The final orientation was then determined namely, additively manufacture the part by using plane D as the base surface, in which case no support material was needed. As a finishing operation was required in order to obtain a high surface quality, the CAD model was modified and the building directions of the parent part and four child parts were determined. The next step was to apply the precedence constraints and then the manufacturing operations were arranged in the following order: (i) deposit the parent part; (ii) measure the parent part; (iii) machine the parent part; (iv) rotate the parent part by which plane D becomes the top surface; (v) deposit child parts on the top of the machined parent part; (vi) measure the child parts; (vii) finish machine the test part and (viii) measure the complete test part" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002359_s00170-010-2783-3-Figure11-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002359_s00170-010-2783-3-Figure11-1.png", + "caption": "Fig. 11 Meshing of a steel die and b bimetallic die", + "texts": [ + " Due to the symmetry of the die, one half of the die has been considered. 4.2 Meshing and boundary conditions ANSYS simulation software has been applied to carry out finite element heat transfer analysis to study the transient thermal response of both the conventional steel die and the bimetallic die. This software is capable of simulating both the steady state and transient behavior when subjected to different heat loads. In this simulation, transient thermal analysis has been used as the temperature of the die changes with time for given heat loads. Figure 11a and b show the meshing of the dies that was done for the model with quadrilateral elements (automatic mesh method). There are 39,881 nodes and 23,459 elements for steel die where as the bimetallic die is meshed with 40,194 nodes and 23,653 elements that are automatically created depending on the physical structure. Fine relevance center and medium smoothing has been applied in the meshing. Boundary conditions have been set to use the heat flux as heat input on the cavity surface and convection film coefficient in the cooling channels that carry out heat from the die and the casting" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002189_ijrapidm.2010.036116-Figure18-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002189_ijrapidm.2010.036116-Figure18-1.png", + "caption": "Figure 18 Simultaneous five-axis deposition (see online version for colours)", + "texts": [ + " This approach is suitable for the component geometries in which the volume of undercut is substantially smaller than the volume of the final component, say, 10%. Manufacture of extremely complex components like geometries with substantial undercuts would require 5-axis deposition. A simpler version of this is an indexed 5-axis HLM in which the deposition is planar but the substrate is oriented so as to eliminate undercuts. An example of this kind is shown in Figure 17. More complex contours such as the one shown in Figure 18 will require simultaneous 5-axis deposition as the slice will no longer be planar. In addition to the existing 3-axis HLM, a 5-axis HLM machine is being built by integrating a Hermle C30U 5-axis CNC machining centre and a Fronius TPS 2700 CMT. CMT stands for cold metal transfer, an improved version of pulsed synergic welding with considerably low power consumption and hence the heat input. A generic HLM facility by integrating both these 3-axis and 5-axis HLM machines through a pallet system is shown in Figure 19" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002745_robio.2010.5723320-Figure15-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002745_robio.2010.5723320-Figure15-1.png", + "caption": "Fig. 15 Model of robot", + "texts": [ + " 12 Chasing target [Task 3] Going through environment with many obstacles In this task, we place several obstacles in different color, shape, and size. In this environment, we conduct an experiment in which the robot avoids these obstacles. Fig. 13 shows the experiment environment in task 3. Fig. 13 Avoiding multiple objects Fig. 14 shows the developed mobile robot. This robot has two active wheels. We employ Logicool Qcam Pro 9000 as the CCD camera. Fig. 14 Mobile robot In this paper, we employ tau-margin for avoiding the mobile robot. We model the mobile robot as shown Fig. 15. The robot has two wheels and impellent force of each wheel is controlled independently. Fig. 16 shows the coordinate system of the camera. Equation (6)-(9) shows the controller. [Task1 and Task3] C ob L T x kkT + \u2212 \u2212 \u2212= 11 21 \u03c4 (6) C ob R T x kkT + \u2212 \u2212 \u2212 \u2212= 11 21 \u03c4 (7) 21 , kk : Proportional gain [Task2] ( ) CT ob L Txk x kkT +\u2212\u2212 \u2212 \u2212 \u2212= 321 11 \u03c4 (8) CT ob R Txk x kkT +\u2212 \u2212 \u2212 \u2212 \u2212= 321 11 \u03c4 (9) 321 ,, kkk : Proportional gain RL TT , denote impellent force of each wheel, CT denotes the constant torque, obx denotes the center of the detected object on the coordinate of the camera" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001199_biorob.2008.4762786-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001199_biorob.2008.4762786-Figure2-1.png", + "caption": "Fig. 2. Human model", + "texts": [ + "00 \u00a92008 IEEE 187 In this section, we consider evaluation indexes of the sitto-stand movement for setting the parameters of the support system. Especially, this paper focuses on the stabilizing of the user\u2019s posture and the reduction of the burdens of the user\u2019s muscles. In order to evaluate them quantitatively, a human body of the user is modeled, and the evaluation indexes of burdens and stability in the sit-to-stand movement are introduced. The human body of the user is modeled as rigid body linkages on the sagittal plane as shown in Fig. 2. The human model has revolute joints and the seven degrees of freedom. Let the joint angles be \u03b8i(i = 1, \u00b7\u00b7\u00b7, 7) according to a notation of Denavit-Hartenberg. A base coordinate frame O\u2212 xyz is set as shown in Fig. 2. The mass, the inertia tensor and the center of gravity (COG) of the linkage are calculated by using the regression equations and the length of the linkage is used as the measured value of the user. In order to reduce redundancy of degrees of freedom of the human model of the user as much as possible, joints of the user\u2019s body are constrained with keeping the natural motion of the sit-to stand. \u03b81 is fixed so that the heel is contacted with floor surface. The wrist joint angle \u03b87 is set so that the link of the hand is horizontal" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002762_1077546312458820-Figure8-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002762_1077546312458820-Figure8-1.png", + "caption": "Figure 8. (a) Experimental rotor. (b) Rotor casing with vibration sensors and analyzer.", + "texts": [ + " By comparison of Figures 6(b) and 7, it can be seen that the low speed (<60Hz) synchronous responses corresponding to station 1, 7 and 12 before balancing (Figure 6(b)) are lower than those seen in after balancing (Figure 7). However at first bending critical speed the synchronous response after balancing is much lower than that before balancing. This will enable the rotor to pass first bending critical speed. This trend is also seen in the experimental results in the following section. The stepped carbon steel experimental rotor (see Figure 8(a)) is 1270mm in length, with two discs at either ends. The rotor is housed inside a casing as shown in Figure 8(b), which is maintained at negative pressure with respect to atmosphere to avoid drag on the system. The lateral vibrations of the rotor are measured by five eddy current displacement sensors located along the length of rotor. These sensors are mounted on the casing and measure the absolute vibration of the rotor in terms of zero to peak amplitude. The sensitivity of the eddy current displacement sensor used is 8mV/mm. The phase angle is measured relative to a reference signal which is generated by the key phasor sensor located at the bottom of the test rig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002519_bf01111855-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002519_bf01111855-Figure5-1.png", + "caption": "Fig. 5. Effect of pore size, rp, on electrode volume, k, (k, CA0 forzero order) = 10 - u mol/cm2/s, U= = 0-45 x 10 -3 em/s, Case II0.", + "texts": [ + "5 to 25 #m, when total electrode thickness is of the order of 3 times that for the zero-order case at 80 % conversion (106 cc as opposed to 34 cc approximately). The total catalyst volume under firstorder conditions is about 26.5 cc. This represents about 560 g for a metal the density of platinum and as such is only marginally acceptable for an implantable fuel cell. For the zero-order case under the same conditions about 8.9 cc of catalyst would be required. Effect of pore size on volume (ks = 10 -11 moll cm2/s, Um= 0.45 x 10 -3) Fig. 5 shows the relationship between pore size and electrode volume. At large rp values (10 -4 cm) catalyst volumes and weights become unacceptably high. As a practical lower limit of electrode thickness (pore length) is perhaps 25 #m, giving a total practical electrode volume of 26 cc for the zero-order case calculated for a biporous 15 #m membrane, with U m = 0.45 x 10 -3 , there is little point in attempting to construct electrodes with rp less than about 10-5 cm in this case. However, in the first-order case, the greater catalyst weight required necessitates an increase in k,, which would be best carried out by increasing k s ", + " In addition, the diffusion case alone is shown, together with the first-order case for the largest practical value of Um (0\"451 10 -a cm/s). This plot is analogous to Fig. 2, as both represent variations in k,, one at constant ks, the other at constant rp. It can be seen that increase in ks beyond the value of 10 -11 mol/cm2/s only marginally reduces area for all cases, though an order of magnitude reduction in k~ (from 10-~1 to 10 -12 ) approximately doubles the membrane area required for the cases with Um in the practical range. In the same way, Fig. 5 may be used to show the variation in catalyst volume with ks at constant rp. It can be seen that reducing ks by an order of magnitude at rp = 10 .5 (equivalent to increasing rp to 10 -4 cm at ks = 10 -11) results in catalyst volumes of 75 cc for the zero-order case and 180 cc for the first-order case. These represent weights of 1-6 and 3.8 kg, respectively, for a catalyst metal of the density of platinum,* and are thus entirely unacceptable for implantable use. These considerations suggest that ks = 10- ~ is the lowest practical limit in the zero-order case, with a slightly higher value (k s CAo ~ 3 X 10 -11) for the first-order case to keep the total catalyst weight at a reasonable level" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003257_1.3617043-Figure24-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003257_1.3617043-Figure24-1.png", + "caption": "Fig. 24 Instrumentation locations", + "texts": [ + " 23 (reference [4]) shows the degree of agreement that can be expected between the steady-state computed values and experimentally measured values. Compar ison wi th Experimental Data Fig. 18 essentially represents the conditions for a particular experimental run made with the SA-2 rig in April, 1964. During this run two capacitance probes measured absolute x-y shaft motion in the same plane; a third probe measured the absolute motion of a fixed shoe; a fourth probe measured the absolute motion of a spring-loaded shoe. Both shoe probes looked at corner-mounted buttons located at the shoe leading edge (Fig. 24). In formulating the physical data for the dynamics program (lie following items had to be approximated: 1 T h e unbalance force was estimated to be 340 milligrams with an uncertainty of \u00b1 5 0 milligrams. The effect of the unbalance force is to change the orbit amplitude. 2 The unbalance moment was known to be small. The estimate of 0.002 in-lb could be in error up to 15 percent. The effect of the unbalance moment is to change the amount of conical motion in the shaft orbit . 3 The maehined-in clearance c was taken as 1" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001411_iccas.2008.4694526-Figure11-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001411_iccas.2008.4694526-Figure11-1.png", + "caption": "Fig. 11 NRL two fin vehicle showing wing mean position at, (a) -30\u00b0 which produces a positive lift force, and (b) +30\u00b0 which produces a negative lift force.", + "texts": [ + " Similarly, if the vehicle is very far above desired depth, the maximum negative lift gait is 100% used for both fins. And if the vehicle is within some predetermined range of desired depth the output kinematics is calculated as a combination of the optimal positive lift, forward thrust, and negative lift gaits. An alternate to the WGC method of fuzzy logic PID control has also been investigated in which control over fin lift force is achieved through biasing the fin mean bulk rotation position (\u03a6mean) up or down (Fig. 11). This propulsion control method entirely decouples lift from thrust, simplifying the controller design. The effectiveness of this MBAB method was suggested by the results of the CFD studies [2] illustrated in Fig. 3 where we see lift increase as the fin stroke is biased downwards. Control over horizontal plane motion is still achieved through combining the preprogrammed forward and reverse gaits for the left and right fins as in Eq. (9). \u03b8 \u03c8 \u03c8 uuu uuuu uuuu zBIASBULK yxHORIZRIGHT yxHORIZLEFT += \u2212\u2212= ++= _ _ _ (9) The final step in modeling the vehicle control law progression, for both the WGC and MBAB methods, is determining how each gait or combination of gaits maps to a force vector generated by each fin" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000691_tac.1979.1101989-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000691_tac.1979.1101989-Figure5-1.png", + "caption": "Fig. 5. The error variables e , and ez versus time.", + "texts": [ + " The state variable filters had an input gain of 50. The initial estimate of parameters a and fi, compared to the correct values ac and Bc, were al = 100 a f = 2 a2= 100 a;= 10 Dl =50 /3f= -1 = 50 &= -2. Three consecutive runs were made in simulating the above data. In each run, the value of the adaptive gains were chosen as G=kZ; the value of k was changed in each run according to Run 1- - .k=10 Run2-*-k=100 Run3-.-k=1000. Figs. 1 - 4 plot the estimates of each variable versus time with the consecutive run of each variable plotted together. Fig. 5 is a plot of el and e, versus I for k = 1OOO. These curves are similar for smaller k. It is seen that the convergence is nonoscillatory and rapid. The monotone increase in convergence speed with increasing k is apparent. No numerical difficulties were encountered. A check of the same system using double precision calculation reveals virtually no difference in behavior. 296 IBEB T R A N S A ~ O N S ON AUTOMATIC CONTROL, VOL ~ 0 2 4 , NO. 2, APRIL 1979 The results of a more extensive evaluation of the adaptive observer are reported in [20]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003153_1.3555028-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003153_1.3555028-Figure5-1.png", + "caption": "Fig. 5\u2014Effect of Speed on Operating Characteristics.", + "texts": [ + " The seal chosen as a base operates at a speed of 2000 rpm, a shear modulus of 180,000 psi (about the value for nylon), a fluid viscosity of 1 X 10~5 lb sec/in2 (SAE 10 oil), a surface tension (including wetting angles) of 1.5 X 10~4 lb/in (SAE 10 oil), a radius of 1 inch, a thickness of 0.1 inches, a width of 0.05 inches, a spring load of 10 pounds, a hydrostatic load fraction of 0.5, and a wave amplitude of 5 microinches with 2 waves around the face. Sealed pressure is plotted as a function of wetted fraction and clearance. A wetted fraction of /3 = 1 is the limit of sealing. Because of the approximations used, we can probably assume that the seal leaks when /? approaches 1. The effect of speed is shown in Figure 5. Since viscosity and speed only occur- together in die equations, the dependence of operating parameters on viscosity is the same as that for speed. As speed increases, both wetted fraction and clearance increase for a given sealed pressure. The effect of shear modulus is shown in Figure 6. As shear modulus decreases, the wetted fraction and clearance both increase for a given sealed pressure. 706 / O C T O B E R 1969 Transactions of the AS ME Downloaded From: http://tribology.asmedigitalcollection" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003169_0369-5816(65)90020-7-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003169_0369-5816(65)90020-7-Figure3-1.png", + "caption": "Fig. 3. Deformation pattern.", + "texts": [], + "surrounding_texts": [ + "The r e s u l t s a r e : Qs = Us(~b - ~b0) , (3a) Mq~ = \u00bdUsA(dp -q50)2 + M s , (3b) Ndp = \u00bdPA - Us(q50 - qS) co t q5 . (3c) E q s . (3) d e t e r m i n e f o r c e s and m o m e n t s in the she l l in t e r m s of the unknown h inge l oca t i on q50 and the l i m i t p r e s s u r e p . N~b is equa l to i t s un - d i s t u r b e d va lue \u00bdPA at the h inge c i r c l e , q5 = qS0, and d e c r e a s e s t o w a r d the i n t e r i o r of the p l a s t i c zone . At the n o z z l e junc t ion N~ > 0 s i n c e eq. (7) ( d i s c u s s e d subsequen t ly ) i s s a t i s f i ed . F o r a l l c a s e s in the r a n g e of p a r a m e t e r s c o n s i d e r e d that have been checked N~ > 0. Since N o = (~0 T and N~ >0, all stress points in the plastic zone lie on the NO/(~oT = 1 plane of the yield surface. For the nozzle, the well known equilibrium equations are dQ c NO dX + a - = p ' (4a) d / ~ X dX - Q c = 0 - (4b) The ax ia l c o o r d i n a t e X is m e a s u r e d a long the n o z z l e beg inn ing at the junc t ion . R e f e r r i n g to f ig . 3, the hoop f o r c e f o r X < X 0 is equa l to i t s fu l ly p l a s t i c va lue ~0 t. Making th i s subs t i t u t i on and w r i t i n g U c = (1)-trot/a) , a so lu t ion to eqs . (4) i s g iven by" + ] + }, + { + "image_filename": "designv11_7_0001544_6.2008-4506-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001544_6.2008-4506-Figure2-1.png", + "caption": "Figure 2. Pre-test photo of non-contacting finger seal inner diameter.", + "texts": [ + " The forward finger element, also referred to as the high pressure finger element, is a washer made of thin sheet stock with multiple curved slots machined around the inner diameter (i.d.) to form the fingers. The aft finger element, or the low pressure finger element, is essentially the same as the forward finger element except that each finger has an axial extension at the seal inner diameter that forms a lift pad concentric to the rotor. The lift pad has a circumferential groove to insure low pressure on all edges of the lift pad. This can be seen in Fig. 2. The forward and American Institute of Aeronautics and Astronautics 3 aft finger elements are oriented to each other such that the fingers of each element block the slots in the other element. The fingers act as cantilever beams, flexing in response to rotor dynamic motion and radial growth of the rotor due to centrifugal and thermal forces. This compliant feature permits operation at clearances much smaller than fixed clearance seals resulting in lower leakage rates. Geometric features on the lift pad id or on the rotor od generate a hydrodynamic lift force during shaft rotation allowing the seal to ride on a thin film of air rather than rubbing against the rotor" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003061_j.ymssp.2012.09.012-Figure9-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003061_j.ymssp.2012.09.012-Figure9-1.png", + "caption": "Fig. 9. Meshing plane: maximum of the meshing force signal with additional pitch errors on the single pinion and gear teeth.", + "texts": [ + " 4 were presented in Cartesian \u2018\u2018pinion teeth gear teeth\u2019\u2019 meshing plane coordinates. Visible are the meshing force variations caused by the different pitch errors of pinion and gear teeth and thus the meshing quality in terms of best/worst contact tooth pair could be determined. If the measured acceleration signal of the gear case was used instead of the simulated meshing force, changes in the acceleration similar to the changes shown in Fig. 8 would be observed, reflecting dynamic overload and allowing for the assessment of meshing quality. Fig. 9 presents a similar case but with additionally introduced emphasised pitch errors on the single pinion and the single gear tooth. These imperfections are introducing periodic deformations into the signal visible on the signal spectrum as a modulation of the meshing frequency by the rotational frequencies of both shafts. Observation of the maximum values of the signal on the local meshing plane reveals that the same pitch error caused the structure seen in Fig. 8 but with the addition of a characteristic \u2018\u2018cross\u2019\u2019 pattern caused by the contacts between the badly manufactured pinion and the gear teeth", + " When the signal changes are relatively small, the squared signal envelope may be used to create the local plane instead of the signal itself, emphasising changes in the signal and making them more observable. In this paper the envelope of the filtered signal was calculated using the absolute value of the Hilbert Transform (HT). Before the application of the HT the signals were filtered around the third (biggest) meshing harmonic with the passband close to the meshing frequency. The same simulation as in Fig. 9 was used for comparison. As before the maximum values of the squared envelope for each tooth pair contact were shown on the local plane allowing for comparison of the results (Fig. 10). The tooth fatigue cracks were modelled as a 5% and 10% tooth stiffness reduction on one of the pinion teeth. The single revolution of the synchronously averaged time signal shown in Fig. 11 demonstrates the difficulties with diagnosing the early stages of fatigue defects. Visible are subtle changes in the structure of amplitude and frequency of the signal that are well masked with pitch errors" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001424_0094-114x(75)90076-2-Figure6-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001424_0094-114x(75)90076-2-Figure6-1.png", + "caption": "Figure 6.", + "texts": [ + " Expression (10) shows that the law 93h(9,o) of motion transmission depends not only on the angle A~ of axis misalignment but on the component angles Aa and A/3. It is also useful to note that, with At] = 0 and Aa # 0 and with axes zo and zh disposed in parallel planes and skew, tg \u00a2l..__._Lo\" tg q~3h = COS Aa (24) angle of rotation is defined by the equation [ tg ~0to ~_ Aq~3h =q~3h-q~lo=arctg\\cosAa ] ~Plo. (25) A~3hm~x = --- [arc tg (co--~Aa) -- 45\"]; (26) Link 2 is able to participate in two rotary and two sliding motions relative to link 3. To compose the matrix of transformation of $3 to S2, use the auxiliary coordinate system S, (Fig. 6(a)). Note that the rotation through angle A8 is followed by the spring deformation variation (Fig. 6(b)). On the basis of Fig. 6(a) constructions attain the expression for the matrix M23 = M2.M.3, and the transformation of & to So through $2 is where Mo2M=dVM = Ib,, bl2 b,3 6.11 Ib2, b= b23 b2, I [b,, b32 b33 ?1 Io 0 0 b . = cos ~o cos A8 ; b12 = cos ~,o sin A8 sin AT - sin \u00a2,o cos a y ; b13 = cos ~O~o sin A8 cos A T + sin ~O,o sin Ay; b14 = X2 (\u00b0') COS ~Olo + y2 (%) sin ~O,o + x, (\u00b0') cos ~010; b2, = sin ~o cos A8 ; b22 = sin ~1o sin A8 sin Ay + cos ~o cos Ay; b23 = sin ~0,o sin A8 cos Ay - c o s ~p~o sin AT; b24 = x2 ~\u00b03) sin q~,o - y2 \u00a2\u00b0; cos ~,o + x(\u00b0=) sin ~O,o; b31 = - s in A8; b32 = cos A8 sin Ay; b33 = COS A\u00a2$ COS A T ; b34 = -72 (03)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002316_j.cirp.2011.03.060-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002316_j.cirp.2011.03.060-Figure3-1.png", + "caption": "Fig. 3. Comparison of a vectorial deviation and a deviation in normal direction.", + "texts": [ + " Since the distance of each individual grid point relative to the gear\u2019s rotary/ symmetry axis varies, the deviations between original points and rotated points differ over the entire flank (see Figs. 2b and 4). The deviations of the individual grid points depend on the chosen definition of deviation type (see Sections 3.2\u20133.4) [7]. The deviation between a nominal point and a \u2018measured\u2019 point can be evaluated in different ways. The simplest calculation is the vectorial (or Euclidean) distance deuclid between both points (see Fig. 3). But, the positioning uncertainty of the measuring device directly affects this deviation [8,9]. Therefore, it will mostly be used for geometry measurements, where the normal direction of a datum point is unknown. Fig. 4 shows the resulting deviations of one bevel gear tooth (grey grid: ideal surface; black grid: evaluated actual surface, based[()TD$FIG] on single point \u2018measurements\u2019). The \u2018measured\u2019 surface appears to be tilted to the ideal surface, with higher deviations at the topland and at the outer end of the tooth (heel) resulting from the simulation of \u2018measurement\u2019 points (Fig. 2). Another, more common method to calculate geometrical deviations requires the knowledge of all normal directions Ndatum at the nominal points (Fig. 3), which is fulfilled in most applications of gear metrology. It projects the vectorial deviation to the normal direction at the \u2018measured\u2019 point. The scalar product dproj = Deuclid Ndatum is in all cases smaller than or equal to the vectorial deviation deuclid. Table 1 compares the vectorial deviations of Fig. 4 at the flank corner points with the corresponding deviations in normal directions. The general appearance of the \u2018measured\u2019 surface remains tilted, but with smaller deviation values. A further but uncommon approach is to calculate angular deviations (in radians) related to a certain reference diameter (rpitch) or related to the local diameters of the datum points. Fig. 5 compares vectorial deviation and angular deviation. The main reason to take this unusual definition into account and to compare it with the common versions is the calculation of tooth thickness deviations in accordance with the standards, i.e. as an angular [()TD$FIG] [()TD$FIG] A. Guenther / CIRP Annals - Manufacturing Technology 60 (2011) 551\u2013554 553 deviation. Consequently (and following the basic concept of the projected deviation dproj in Fig. 3), the datum point Pdatum together with its tangential plane (defined by normal direction Ndatum) is rotated by an angle w such that the \u2018measured\u2019 point Pmeas coincides with the rotated tangential plane. Table 1 shows the result of this calculation, applied to the same nominal points of Section 3.1. The form deviation pattern referred to the pitch radius constantly amounts to 10 mm at both flanks (3rd column). If the individual grid points are referenced to the local radius, the deviation pattern again appears tilted, but at even smaller deviations (4th column, Table 1)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001860_tmech.2010.2057440-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001860_tmech.2010.2057440-Figure1-1.png", + "caption": "Fig. 1. Rigid body equipped with n accelerometers moving in space.", + "texts": [ + " In order to compare the robustness of the proposed method with that of other existing CA methods, a simple experiment was performed, which is described and discussed in Section IV. Let us begin by reviewing the existing methods, with emphasis on the CA class. Few researchers have worked on the theory behind accelerometer arrays. Despite the many specific case studied in the literature, the model of a generic array of n uniaxial accelerometers was written down only recently [27]. Let us rewrite it here as an introduction to the main matter of this paper. Consider a rigid body moving in space, to which we attach n uniaxial accelerometers, as depicted in Fig. 1. The ith accelerometer is located at point Pi , its sensitive direction being represented by the unit vector ei . Notice that this assembly is completely general, since any multiaxial accelerometer may be represented by multiple uniaxial accelerometers located at a common point. Let O and B be two reference points on the ground and on the rigid body, respectively. Moreover, let b and pi represent the positions of B and Pi , with respect to O, respectively, while ri \u2261 pi \u2212 b remains attached to the rigid body" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000805_tmag.2007.893297-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000805_tmag.2007.893297-Figure2-1.png", + "caption": "Fig. 2. Forces exerted in mover at outlet edge. (a) Entry interval (entrance end). (b) Ejection interval (exit end).", + "texts": [ + " However, if the mover goes through the boundary between the active part and the inactive part of the armature at stationary discontinuous armature PM-LSM, the attractive force produced between the armature\u2019s core and mover\u2019s permanent magnet fluctuates highly. The attractive force produced at the entry interval operates in the same direction as the mover. That is, the mover is accelerated by the force that pulls the mover into the armature area. On the other hand, the attractive force generated at the ejection interval operates in the opposite direction to the mover. In other words, the mover becomes decelerated by the force, which pulls back the mover to the armature area. Fig. 2 shows forces exerted in the mover at the outlet edge. Due to the effect of the force that operates at the outlet edge, it has become a problem that the velocity of the mover is different from that of the velocity command during reacceleration and deceleration when the mover changes from freewheeling to reacceleration and deceleration. To examine the cogging force generated at each outlet edge, an analytical result obtained by 3-D numerical analysis was used and examined. The general-purpose electromagnetic field analysis software (JMAG-Studio) was used for 3-D numerical 0018-9464/$25" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000143_ac00277a023-Figure6-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000143_ac00277a023-Figure6-1.png", + "caption": "Figure 6. Schematic of CO, sensor: (a) bulk electrolyte, (b) pH glass tlp, (c) electrolyte film, (d) gas-permeable membrane, (e) sample solution, (f) magnetic Teflon stir bar.", + "texts": [ + " In contrast, a very large potential response to high concentrations of the aliphatic carboxylic acids was observed using the microporous Teflon membrane. The potential response to low concentrations of these acids was very small and the response times were excessively long, averaging 1 h for a 2-fold concentration increase a t 5 X 10\" M concentrations. Mechanistic Implications. Interference with the Orion Model 95-02 carbon dioxide electrode is defied as a potential response which results upon passage of a neutral species other than carbon dioxide across the gas-permeable membrane (Figure 6). The corresponding pH change in the aqueous sodium bicarbonate film is sensed by an inner pH glass electrode. The magnitude of the interference by a compound, HI, expressed as a selectivity coefficient, kij'&HI, is defined by the following equation (10): M and 4 X 10-3 M. &&,HI = (H+)z/(H+)i (1) Subscripts 1 and 2 refer to the hydrogen ion activities in the film upon electrode equilibration with the same nominal concentrations of COz and HI in separate sample solutions. The potential response of the COz sensor to an acidified aqueous solution of carbon dioxide reflects the following hydrolysis reaction in the film: C02 + H20 HC03- + H+ Interference by a compound, HI, initially reflects the titration of bicarbonate ion in the film" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001982_s0022112010000364-Figure6-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001982_s0022112010000364-Figure6-1.png", + "caption": "Figure 6. Second-order pressure and stress contours for purely translational motion. (a) The hydrodynamic pressure disturbance in the absence of intermolecular effects, \u039e = \u03a5 = 0, and the influences of intermolecular effects, with \u039e = \u03a5 =0.5, on (b) the hydrodynamic pressure, (c) van der Waals stress, (d ) electric stress and (e) hydromolecular pressure perturbations. The dotted line represents a circle of spatial unit radius.", + "texts": [], + "surrounding_texts": [ + "The compliance of the substrate couples the hydrodynamic field described by the Reynolds equation (2.11) with the substrate responses (A 19), (A 20) or (A 21), and with the intermolecular stress distributions (2.15) and (2.17). Such coupling effect breaks the intrinsic symmetry of the Stokes equations (2.2)\u2013(2.4) and renders the problems (2.2)\u2013(2.4) and (2.11)\u2013(2.12) nonlinear. To second order in \u03b7, (2.11) becomes r2 \u22022P1 \u2202r2 + [ r + 3r3 h0(r) ] \u2202P1 \u2202r + \u22022P1 \u2202\u03d52 = 18 5 r3(6 + r2) h5 0(r) H0 cos \u03d5 + 48 5 r h3 0(r) \u2202H0 \u2202\u03d5 sin \u03d5 + 12 5 r2(r2 \u2212 4) h4 0(r) \u2202H0 \u2202r cos \u03d5. (5.1) Equation (5.1) is subject to boundary conditions (2.12). The case of a thin compressible layer (A 19) is addressed in detail in this section. To leading order in \u03b7, (A 19) yields the normal surface deformation H0 = P0 + \u03a0vdW 0 + \u03a0el 0 = 6r cos\u03d5 5h2 0(r) \u2212 \u03a5 h3 0(r) + \u039ee\u2212\u03ba[h0(r)\u22121]. (5.2) Substituting this expression into the second-order balance Reynolds equation (5.1), we obtain r2 \u22022P1 \u2202r2 + [ r + 3r3 h0(r) ] \u2202P1 \u2202r + \u22022P1 \u2202\u03d52 = 72 25 r4(20 + r2) h7 0(r) cos2 \u03d5 + { 18 5 \u03a5 r3(r2 \u2212 14) h8 0(r) + 12 5 \u039e\u03bar3(4 \u2212 r2)e\u2212\u03ba[h0(r)\u22121] h4 0(r) + 18 5 \u039er3(6 + r2)e\u2212\u03ba[h0(r)\u22121] h5 0(r) } cos \u03d5 \u2212 288 25 r2 h5 0(r) . (5.3) A particular integral of the form P1 = f (r) cos2 \u03d5 + [\u03a5 \u03c5(r) + \u039e\u03be (r, \u03ba)] cos\u03d5 + g(r) (5.4) is substituted into (5.3), which yields the linear system of ordinary differential equations L2f = 72 25 r4(20 + r2) h7 0(r) , (5.5) L1\u03c5 = 18 5 r3(r2 \u2212 14) h8 0(r) , (5.6) L1\u03be = 12 5 \u03bar3(4 \u2212 r2)e\u2212\u03ba[h0(r)\u22121] h4 0(r) + 18 5 r3(6 + r2)e\u2212\u03ba[h0(r)\u22121] h5 0(r) , (5.7) L0g + 2f = \u2212288 25 r2 h5 0(r) , (5.8) with Ln a differential operator given by Ln = r2 d2 dr2 + [ r + 3r3 h0(r) ] d dr \u2212 n2, with n = 0, 1, 2. (5.9) For r 1, f = O(r2), g = O(1), \u03c5 = O(r) and \u03be =O(r). Similarly, for r 1, f =O(r\u22128), g = O(r\u22128), \u03c5 = O(r\u221211) and \u03be = O(e\u2212\u03bar2 /r3). Therefore, the boundary conditions of (5.5)\u2013(5.8) are f = \u03c5 = \u03be = 0 and g\u2032 = 0 for r = 0, and vanishing values of f , g, \u03c5 and \u03be for large r . Figure 5 shows the solutions to (5.5)\u2013(5.8), which need to be obtained numerically. Nonetheless, for later use, the auxiliary function \u03c3 =2g + f is defined by combining (5.5) and (5.8). It can be shown that the resulting differential equation has the exact solution \u03c3 = 2g + f = 18 125 (14 \u2212 5r2) h5 0(r) , with \u222b \u221e 0 \u03c3r dr = 48 125 . (5.10) The dimensionless hydromolecular pressure perturbation is given by P 1 = P1 + \u03a0vdW 1 + \u03a0el 1 = f (r) cos2 \u03d5 + { \u03a5 [ \u03c5(r) + 18r 5h6 0(r) ] + \u039e [ \u03be (r, \u03ba) \u2212 6r\u03bae\u2212\u03ba[h0(r)\u22121] 5h2 0(r) ]} cos\u03d5 + g(r) \u2212 3\u03a5 2 h7 0(r) \u2212 \u03ba\u039e 2e\u22122\u03ba[h0(r)\u22121] + \u039e\u03a5 { e\u2212\u03ba[h0(r)\u22121] h3 0(r) [ 3 h0(r) + \u03ba ]} , (5.11) where we use (3.2), (3.3), (5.2) and (5.4). Because P 1 decays sufficiently rapidly for large r , the calculation of the force and torque perturbations thereby is not a singular perturbation problem, in which the required indefinite integrals of the hydromolecular pressure perturbation are convergent for large r . Figures 6 and 7 show the contours of the first perturbations of the hydrodynamic pressure (5.4), the hydromolecular pressure (5.11) and the intermolecular stresses (3.2) and (3.3), non-dimensionalized with \u00b5Ua1/2/\u03b43/2, to illustrate the rotational effects. The substrate compliance decreases and increases the hydrodynamic overpressure and underpressure levels respectively, which breaks the antisymmetry of the leadingorder hydrodynamic pressure contours and induces a lift force, and drag-force and drift-force perturbations. Note that the corkscrew rotation actively affects the pressure component of the drag force, as observed by comparing the projection along the x-axis of the contours in figures 6 and 7 and superposing them onto those shown in figure 4. The shear-stress perturbations can be obtained by differentiating the second term of the expansion of (2.13) and (2.14) in powers of \u03b70, which yields \u03c4rz1 = \u2202vr1 \u2202z \u2223\u2223\u2223 z=h0(r) = [ 12r(4 \u2212 r2) 25h5 0(r) + h0(r) 2 df (r) dr ] cos2 \u03d5 + { \u03a5 h5 0(r) \u2212 \u039ee\u2212\u03ba[h0(r)\u22121] h2 0(r) } 2 cos(\u03d5 \u2212 \u03b3 ) V(\u03c9, \u03b2) + { 2\u039e (4 \u2212 r2)e\u2212\u03ba[h0(r)\u22121] 5h3 0(r) + 2\u03a5 (r2 \u2212 4) 5h6 0(r) + h0(r) 2 [ \u03a5 d\u03c5(r) dr + \u039e \u2202\u03be (r, \u03ba) \u2202r ]} cos \u03d5 \u2212 12r cos \u03d5 cos(\u03d5 \u2212 \u03b3 ) 5h4 0(r)V(\u03c9, \u03b2) + h0(r) 2 dg(r) dr , (5.12) and \u03c4\u03d5z1 = \u2202v\u03b81 \u2202z \u2223\u2223\u2223 z=h0(r) = \u2212 [ 48r 25h4 0(r) + h0(r)f (r) r ] sin\u03d5 cos\u03d5 + { 8\u03a5 5h5 0(r) \u2212 8\u039ee\u2212\u03ba[h0(r)\u22121] 5h2 0(r) \u2212 [\u03a5 \u03c5(r) + \u039e\u03be (r, \u03ba)]h0(r) 2r } sin \u03d5 + [ \u039ee\u2212\u03ba[h0(r)\u22121] h2 0(r) \u2212 \u03a5 h5 0(r) ] 2 sin(\u03d5 \u2212 \u03b3 ) V(\u03c9, \u03b2) + 12r cos\u03d5 sin(\u03d5 \u2212 \u03b3 ) 5h4 0(r)V(\u03c9, \u03b2) , (5.13) where we use (5.2) and (5.4). The values of the forces obtained from the analytical integration of (5.11)\u2013(5.13) are compared in what follows to the numerical solution of the problem (2.11), (2.12) and (A 19), which was integrated by using a second-order finite-differences numerical scheme. In this investigation, torques are not calculated since they are found to be of O(\u03b5\u03b70), which correspond to higher-order effects that are not considered here. 5.1. Lift force Integrating the asymptotic expansion of the hydromolecular pressure (5.11) over the vertical projection of the inner element of the surface of the sphere in cylindrical coordinates, dSz = \u2212a2\u03b5r dr d\u03d5ez , and using expressions (5.10), the elastohydromolecular lift force Fz = \u00b5UV(\u03c9, \u03b2)a \u03b51/2 \u222b \u221e 0 \u222b 2\u03c0 0 P 1 r d r d\u03d5 = \u03c0\u00b5UV(\u03c9, \u03b2)a \u03b51/2 { \u2212\u03a5 + 2\u039e \u03ba + \u03b70 [ 48 125 \u2212 (\u03a5 \u2212 \u039e )2 ] + O ( \u03b73 0, \u03b7 3 0\u03a5 2, \u03b73 0\u039e 2, \u03b73 0\u03a5 \u039e, \u03b73 0\u03a5 2\u039e 2, \u03b73 0\u03a5 \u039e 3, \u03b73 0\u03a5 3\u039e )} (5.14) is obtained. It can be shown that the contribution of the shear stresses to the lift force is of order \u03b5\u03b70 \u03b70 (Urzay et al. 2007), which is neglected in this analysis. The lift force (5.14) is composed of two leading-order terms that represent the values (4.1) and (4.2) of the intermolecular forces on a small sphere near a rigid wall. These are the two fundamental acting forces in the DLVO theory. The lift force also includes a term 48\u03b70/125, which corresponds to the positive elastohydrodynamic lift force (Weekley et al. 2006; Urzay et al. 2007). The term \u2212(\u03a5 \u2212 \u039e )2 in the squared bracket represents a negative elastomolecular lift force that is a nonlinear superposition of intermolecular effects; this force corresponds to the disturbance of the intermolecular force on a stationary sphere induced by the soft substrate, as shown in Appendix B by the second-order term of (B 2). Higher-order terms result from a full elastohydromolecular coupling and involve combinations of the hydrodynamic and intermolecular compliances, such that the resulting dimensionless groups are proportional to even powers of the velocity; the expansion of the lift force remains kinematically irreversible to every order, in which its direction is independent of the direction of rotation and translation. To leading order in \u03b70, only the DLVO force, the origin of which is purely related to the intermolecular stresses and not hydrodynamically enhanced, acts on the particle along the z-axis; this force is kinematically irreversible, although the flow is still Stokesian in a linear sense. For non-zero \u03b70, the existence of a kinematically irreversible lift force of elastohydromolecular origin is explained in terms of the nonlinearity induced by the substrate compliance and intermolecular effects. Nonlinear effects in Stokes-type flows can be produced by small convective disturbances in the flow (Saffman 1964; Leighton & Acrivos 1985), non-Newtonian fluid behaviours (Hu & Joseph 1999) or electrokinetic effects (Bike & Prieve 1995), all of which induce kinematically irreversible forces on submerged particles and are important in certain range of rheological applications. In this model, the elastohydromolecular lift force is produced by the combined action of the intermolecular and hydrodynamic stresses on the substrate, which ultimately modify the compliant gap geometry and the hydrodynamic flow through that region as shown by the contours of the pressure and stress disturbances in figures 6 and 7. 5.1.1. Influences of rotation and of rotation-axis orientation on the lift force Rotational motions distort the magnitude and orientation of the pressure distribution in the gap and also modify the gap geometry, as observed in figure 7. To isolate the rotational effects, the lift force (5.14) is non-dimensionalized independently of the velocity scale V(\u03c9, \u03b2), and expressed as a function of the translational hydrodynamic compliance \u03b70/V(\u03c9, \u03b2) as shown in figure 8, where intermolecular effects have been neglected for illustrative purposes. As advanced in a previous study (Urzay et al. 2007), the inverse purely rolling motion (\u03c9 = \u22121, \u03b2 = \u03c0/2) completely suppresses the production of elastohydrodynamic lift force, since a local Couette flow is induced in the gap, and the hydrodynamic pressure becomes zero to every order of \u03b70. That is not the case when the intermolecular forces are not negligible, since both the leading-order intermolecular and second-order elastomolecular contributions to the lift force are present in (5.14). Similarly, the present formulation reveals that, for the same translational velocity, particle dimensions and substrate mechanical properties, the purely rolling motion (\u03c9 = 1, \u03b2 = \u03c0/2) produces a larger lift force than the corkscrew (\u03c9 = 1, \u03b2 = 0) and translational (\u03c9 = 0) motions; during the rolling motion, the fluid entrainment of the combined rotation and translation are aligned along the \u03b8 =0 axis and both effects more strongly synergize causing a larger positive overpressure peak in the gap and therefore larger substrate deformations. In this model, no negative values of the elastohydrodynamic lift force were found for any combination of rotation and translation. 5.1.2. Influences of intermolecular effects on the lift force Figure 7 shows that the intermolecular stresses produced by the electric and van der Waals forces disturb the compliant wall and modify the net normal stress acting on the sphere. The influences of these intermolecular effects on the lift force are shown in figure 9, which values are independent of \u03c9 and \u03b2 . For negative and order-unity values of \u03a5 , or more precisely \u03a5 \u2212(48/125)1/2, which correspond to order-unity and repulsive van der Waals forces, the lift force decreases with increasing \u03b70 because of the gap-distance-augmentation effect outlined in Appendix B, by which the repulsion decreases because of the increase of the substrate compliance and the effective clearance, which dominates the elastohydrodynamic force that typically increases with increasing \u03b70. For smaller but repulsive van der Waals forces, \u2212(48/125)1/2 \u03a5 < 0, the lift force is positive and increases with \u03b70. Slightly attractive van der Waals forces produce negative lift forces on the sphere up to a resuspension or lift-off hydrodynamic compliance \u03b70L, beyond which the elastohydrodynamic effect dominates and a positive lift force occurs. This increase proceeds up to a critical hydrodynamic compliance \u03b70C for the occurrence of irreversible elastohydrodynamic adhesion, in which no solution of the problem (2.11), (2.12) and (A 19) is found beyond \u03b70C at constant \u03a5 because of a loss of static mechanical equilibrium on the substrate surface. Positive and order-unity values of \u03a5 , which correspond to large and attractive van der Waals forces, enhance earlier irreversible elastohydrodynamic adhesion. The lift-off and elastohydrodynamic adhesion processes are addressed in detail in \u00a7 6, and a similar but simpler adhesion phenomenon is exemplified in AppendixB for a stationary sphere. Solvent ionization and electric repulsion augment the lift force, decrease the magnitude of the lift-off hydrodynamic compliance, and they extend the irreversible elastohydrodynamic adhesion boundary to larger \u03b70C by electrically stabilizing the substrate surface. 5.2. Drag-force and drift-force first perturbations The perturbations of the drag and drift forces on the sphere are calculated as Fx1 = \u2212\u00b5UVa\u03b70 \u222b 2\u03c0 0 \u222b \u221e 0 [ P 1 r2 cos(\u03d5 \u2212 \u03b3 ) + \u03c4rz1r cos(\u03d5 \u2212 \u03b3 ) \u2212 \u03c4\u03d5z1r sin(\u03d5 \u2212 \u03b3 ) ] dr d\u03d5 = \u03c0\u00b5Ua\u03b70 { \u039e [E(\u03ba) +J(\u03ba)\u03c9 sin\u03b2] \u2212 \u03a5 [F\u2212 G\u03c9 sin\u03b2] + O ( \u03b72 0, \u03b70\u03a5 2, \u03b70\u039e 2, \u03b70\u039e\u03a5 )} , (5.15) and Fy1 = \u2212\u00b5UVa\u03b70 \u222b 2\u03c0 0 \u222b \u221e 0 [ P 1 r2 sin(\u03d5 \u2212 \u03b3 ) + \u03c4rz1r sin(\u03d5 \u2212 \u03b3 ) + \u03c4\u03d5z1r cos(\u03d5 \u2212 \u03b3 ) ] dr d\u03d5 = \u2212\u03c0\u00b5Ua\u03b70 { \u03c9 cos \u03b2 [\u03a5 G + \u039eJ(\u03ba)] + O ( \u03b72 0, \u03b70\u03a5 2, \u03b70\u039e 2, \u03b70\u039e\u03a5 )} (5.16) where the electric force coefficients E(\u03ba) and J(\u03ba) are given by E(\u03ba) = 2 \u2212 6\u03ba 5 + (6\u03ba \u2212 4) \u03ba 5 e\u03baEi(\u2212\u03ba) \u2212 1 2 \u222b \u221e 0 \u03be (r, \u03ba)r2 dr, J(\u03ba) = \u22122 \u2212 6\u03ba 5 \u2212 \u03ba 5 (6\u03ba + 16)e\u03baEi(\u2212\u03ba) + 1 2 \u222b \u221e 0 \u03be (r, \u03ba)r2 dr, \u23ab\u23aa\u23aa\u23ac \u23aa\u23aa\u23ad (5.17) which are shown in figure 10, and with the van der Waals force coefficients F and G given by F = 17 25 + 1 2 \u222b \u221e 0 \u03c5(r)r2 dr = 0.9905 and G = 8 25 \u2212 1 2 \u222b \u221e 0 \u03c5(r)r2 dr = 0.0095. (5.18) The drag-force and drift-force perturbations are composed of two terms of O(\u03b70\u03a5 ) and O(\u03b70\u039e ): the van der Waals and electric drag/drift forces. These are representative of the forces induced by mixed elastohydromolecular effects. Higher-order terms involve combinations of the hydrodynamic and intermolecular compliances, such that the resulting dimensionless groups are proportional to odd powers of the velocity; the expansions of the drag and drift force remain kinematically reversible to every order, in which their direction changes under gliding direction reversal. Note that if the intermolecular effects are negligible, \u03a5 = \u039e =0, the substrate-deformation effects on the drag and drift forces become of O(\u03b72 0) for \u03b70 1, which cannot be analytically captured by solely retaining the order O(\u03b70) terms in the expansions (5.15) and (5.16). 5.2.1. Influences of rotation and rotation-axis orientation on the drag-force disturbance Figure 11 shows the effects of the rotation \u03c9 and the azimuthal orientation \u03b2 of the rotation axis on the disturbance of the drag force, obtained by numerical integration of (2.11), (2.12) and (A 19), in the absence of intermolecular forces, \u03a5 = \u039e = 0. The substrate compliance reduces the leading-order drag force (4.6) because of a decrease in the hydromolecular pressure and viscous shear stresses in the deformed gap region. The inverse purely rolling motion (\u03c9 = \u22121, \u03b2 = \u03c0/2) completely suppresses the elastohydrodynamic drag-force disturbance, since no deformation is produced in this case. For the same translational velocity, particle dimensions and substrate mechanical properties, the purely rolling motion (\u03c9 =1, \u03b2 = \u03c0/2) produces a larger drag-force reduction than the corkscrew (\u03c9 =1, \u03b2 = 0) and translational (\u03c9 = 0) motions. For \u03b70 =O(1), the elastohydrodynamic drag-force disturbance produced by surface-deformation effects is approximately 6 ln(1/\u03b5) times smaller than the leading-order force (4.6), which, as a maximum, represents a 5 %\u2013 10 % drag reduction for \u03b5 =0.1. It must be emphasized that the rotational and translational motions are nonlinearly coupled as in the corkscrew motion, for which rotation about an axis parallel to the translation axis induces an additional drag reduction; this nonlinear effect departs from the decoupled behaviour of the rotational and translational motions observed in the leading-order drag force (4.6), which is typical of linear viscous flows. In this model, no negative values of the elastohydrodynamic drag-force disturbance were found for any combination of rotation and translation. 5.2.2. Influences of the intermolecular effects on the drag-force disturbance The influences of the intermolecular effects on the drag-force disturbance on the sphere are shown in figure 12. For negative values of \u03a5 , which correspond to repulsive van der Waals forces, the drag-force disturbance increases with \u03b70, which results in an additional drag reduction to that solely produced by substrate-deformation effects. Slightly attractive van der Waals forces, \u03a5 1, produce a drag increase on the sphere up to a critical compliance, beyond which the elastohydrodynamic effect dominates and a drag reduction occurs. Positive and order-unity values of \u03a5 , which correspond to large and attractive van der Waals forces enhance irreversible elastohydrodynamic adhesion. Electric repulsion augments the drag-reduction trend and extends the elastohydrodynamic adhesion boundary to larger \u03b70. 5.2.3. Influences of the intermolecular effects on the drift-force disturbance Substrate-deformation effects are found to play a very weak role on the drift force. For a stationary rotating sphere near a soft substrate, \u03c9 \u2192 \u221e, U \u2192 0, this can be explained in terms of the mutual cancellation of the two following effects: a hydrodynamic overpressure decrease in the gap region, which increases the drift, and the loss of traction due to the viscous shear-stress decrease in the same region, which reduces the drift force; both effects are found to be of the same magnitude in the range of hydrodynamic compliances \u03b70 studied in this analysis, which yields a negligibly small drift disturbances with respect to the leading-order force (4.7). Nonetheless, (5.16) predicts a drift reduction and increase due to electric repulsion and van der Waals forces, respectively, both of which actively modify the shear stress distribution in the gap and the viscous-traction efficiency." + ] + }, + { + "image_filename": "designv11_7_0001663_1.3438383-Figure13-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001663_1.3438383-Figure13-1.png", + "caption": "Fig. 13 Force and moment sign convention at ith rotor station", + "texts": [ + " Acknowledgment The research described herein was conducted at the University of Virginia under NASA Research Grant NGR 47-005-050 with W. J. Anderson, Chief of Bearings Branch, Fluid System Com ponents Division, NASA Lewis Research Center, as technical manager. The authors wish to express their appreciation to Mr. Anderson for his assistance and support in the development of this work. A P P E N D I X A flexible rotor shaft may be represented as a series of stations such as the isolated disk shown in Fig. 13. The equation for ex ternal loading due to transverse loads and moments may be derived for each station by application of energy methods. The total kinetic, potential, and dissipative energy for the i th rotor station are expressed as follows [6, 10]: Kinetic Energy Ti = j fyn( (x \u2014 eco sin (cot + (p)2 + (y + eco cos (cot + ; = {&(& + 2/2) + CIbi2 + i2 + 2co(vu - uv)) + Q(yx - xy) + Ce(6V + &\u00bb*)}i (20) The equation of motion of the isolated station are easily derived from Lagrange's equation dt\\dq) &T i>V dD 1 (_ \u2014 dq dq dq generalized force|, (21) These equations applied to the foregoing energy terms would then represent the total force balance on the system with the exception of the flexible shaft influence" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003511_6.2011-6547-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003511_6.2011-6547-Figure4-1.png", + "caption": "Figure 4. Quadrotor manipulating a single DOF cart.", + "texts": [], + "surrounding_texts": [ + "The contact force developed in this system, Fpush is given by Fpush = mB x (20) where Fpush is the contact force on the cart from the UAV. The Lagrangian equation of motion in the actuated direction is Fsin = (mB +mQ) x+mQ(r sin ) +mQ _ 2cos ; (21) where Fsin is the vehicle thrust portion applied onto the cart in the positive xC direction. Using Eqs. (21) and (20), we obtain that Fpush = mB mB +mQ (Fsin mQr _ 2cos mQr sin ): (22) The type of manipulation, whether prehensile or nonprehensile, determines the range of the force that is permissible without the loss of contact stability. Nonprehensile contact provides only positive x direction forces, as we have defined x. Prehensile contact, however, has a positive and negative force region. In section F, we discuss our endeffector design and how prehensile manipulation is achieved through magnetic force. For a magnetic cart surface, the UAV can simply reverse direction by pitching away from the cart and having a negative angle. In this configuration the Quadrotor can pull the cart in a negative x direction, allowing for cart position control. The maximum negative force that keeps the contact stable is FMagnetic and, ideally there is no maximum positive force limit that would violate the contact stability. Therefore the range of force that is available for manipulation is min(FMagnetic; FPush;MIN ) to FPush;MAX . Example prehensile and nonprehensile force range plots are given in figure-5.A and in figure-5.B, respectively. The above discussions imply that for contact stability we have FMIN < Fpush < F < FMAX (23) where FMIN and FMAX are defined by the type of manipulation. Violating Eq. (23) leads to breaking of contact and may lead to chattering or prolonged undocking. C. 1-D Manipulation Using Two UAVs In figure-6, two Quadrotors with end-effectors of length r are used as an interface to induce a force onto the cart. When the Quadrotor pitches into the cart (increase in 1;2), a portion of the UAV thrust force F1;2 is transferred to the cart through the body attached end-effector. x is the cart\u2019s horizontal position and y1;2 is the left and right contact points along y axis. Note that the contact points are allowed to slip on the flat surface of the cart. However, slipping friction effects have not been included in the model. With the above assumptions, the complete equations of motion can be determined by the Lagrangian method, and are represented in matrix form as Eqs. (24)-(28). 6 of 16 American Institute of Aeronautics and Astronautics D ow nl oa de d by P U R D U E U N IV E R SI T Y o n Ju ly 8 , 2 01 6 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /6 .2 01 1- 65 47 sinMAX MAXF MagneticF 0 StableUnstable sinMAX MAXF PushF 0 StableUnstable PushF A B Figure 5. A. Prehensile force range. B. Nonprehensile force range. 1 DOF Constrained 1 Qm g 1 Qm 1F 1y x 1C Bm 2 Qm g 2 Qm 2F 2y 2C D ow nl oa de d by P U R D U E U N IV E R SI T Y o n Ju ly 8 , 2 01 6 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /6 .2 01 1- 65 47 H X +C _X +G = B 26664 F1 F2 1 2 37775 ; (24) where F and are the system inputs and X = h x y1 y2 1 2 iT is the state vector. The body-axis torque the Quadrotor can achieve is given by while F is the vehicle thrust force. Matrices B, C, G, and H are defined in Eqs. (25) through (28) where mQ and mB is the mass of the each Quadrotor and cart, respectively. B = 2666664 sin 1 sin 2 0 0 cos 1 0 0 0 0 cos 2 0 0 r 0 1 0 0 r 0 1 3777775 (25) C = 266666666664 0 0 0 mQr _ 1cos 1 mQr _ 2cos 2 0 0 0 mQr _ 1sin 1 0 0 0 0 0 mQr _ 2sin 2 0 0 _y1sine 1mQr + _xmQrcos 1 0 0 0 0 0 _y2rmQsin 2 _xrmQcos 2 377777777775 (26) G = 2666664 0 mQg mQg mQgrcos 1 mQgrcos 2 3777775 (27) H = 2666664 mB +mQ 0 0 mQrsin 1 mQrsin 2 0 mQ 0 mQrcos 1 0 0 0 mQ 0 mQrsin mQrcos 1 mQrcos 1 0 mQr 2 + I 0 mQrsin 2 0 mQrcos 2 0 mQr 2 + I 3777775 (28)" + ] + }, + { + "image_filename": "designv11_7_0001557_j.triboint.2008.01.009-Figure11-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001557_j.triboint.2008.01.009-Figure11-1.png", + "caption": "Fig. 11. Fatigue test machine for 6206 ball bearings.", + "texts": [ + " To further verify the influence of tangential force on dent initiated flaking, a fatigue test was conducted using traction oil, which has a high tangential force coefficient (traction coefficient), and a general industrial multi-purpose lubrication oil. In order to prevent differences in dent formation caused by the type of lubrication oil, the bearings with dents formed by the common condition listed in Table 3 were washed thoroughly and tested with each type of lubrication oil mentioned earlier. Fig. 11 shows the test machine used to form dents and conduct fatigue testing. This cantilevered-type test machine is such that radial load is applied directly to the test bearing. Fatigue testing was conducted with a deep groove ball bearing (bearing no. 6206) under radial loading of 6.2 kN at a rotating speed of 3000min 1. It is well known that in a clean lubrication environment, there is a relationship between RCF life and the lubricant film parameter (L \u00bc hmin/s, where hmin is the minimum lubricant film thickness and s the Rq roughness of the contacting surfaces) [33\u201335]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001656_00368791011064446-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001656_00368791011064446-Figure1-1.png", + "caption": "Figure 1 Configuration of the problem", + "texts": [ + " (2007b) have proposed the analysis for a magnetic fluid-based squeeze film between rough porous truncated conical plates. Deheri et al. (2004) investigated the performance of a magnetic fluid-based squeeze film for a longitudinally rough slider bearing. In this paper, it was found that the negatively skewed roughness increased the load carrying capacity of the bearing. Here, we seek to study and analyze the performance of magnetic fluidbased squeeze film between longitudinally rough conical plates. The configuration of the bearing which is infinite in the Y-direction is shown in Figure 1. Squeeze film velocity dh0/dt in theZ-direction.ThemagneticfieldMisoblique to the lowerplate. The lubricant film is considered to be isoviscous and incompressible and the flow is laminar. Under the usual assumptions of the hydromagnetic lubrication, the concerned Reynold\u2019s equation (Prakash and Vij, 1973; Deheri et al., 2004; Patel and Deheri, 2007) governing the film pressure p in the present case is obtained as: 1 x d dx xh3 d dx p 2 0:5m0mM2 \u00bc 12m : h0 sin2v \u00f01\u00de where: M2 \u00bc a2 2 x2sin2v; \u00f02\u00de a is dimensionof thebearing, h isfilm thickness,v is semi-vertical angle of cone, m is fluid viscosity, m represents the magnetic susceptibility, m0 stands for permeability of the free space and : h0 \u00bc dh0=dt" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001840_ecce.2009.5316379-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001840_ecce.2009.5316379-Figure1-1.png", + "caption": "Fig. 1. Rotor structure of the tested flux-barrier type SynRM", + "texts": [ + " In addition the proposed method not only maximizes the driving efficiency but also realizes high-precision torque control performance. Installation is easy. By inputting motor parameters into the controller, the maximum efficiency drive can be carried out immediately, without any steps for adjustment. All motor parameters used in the controller are measured from off-line tests. Simulation and experimental results on a 1.1kW flux barrier type SynRM demonstrate the validity of the proposed method. II. D- AND Q-AXIS INDUCTANCES OF THE TESTED MACHINE Fig. 1 shows the rotor structure of the tested SynRM (1.1kW, 178V, 6.3A, 4P, max. 2200r/min). Magnetic saturation at the surface of the rotor core is induced by the presence of both d- and q-axis magnetic fluxes. The marks (circles, squares, etc.) in Fig. 2 are the d- and q-axis inductances, Ld and Lq, measured by a standstill off-line test [6]. Fig. 2 shows that the self-axis inductance varies with the other-axis current. Equations (1) and (2) are approximate equations for Ld and Lq. 288978-1-4244-2893-9/09/$25" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001535_6.2008-7162-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001535_6.2008-7162-Figure3-1.png", + "caption": "Figure 3. Free body diagram of (a) satellite without moving fuel and (b) moving fuel", + "texts": [ + " The generic pendulum setup is also presented in figure 2 along with additional parameters and coordinates frames to be able to describe the motion of the fuel with respect to the satellite. The parameters in the 3 of 24 American Institute of Aeronautics and Astronautics figure are defined as: (O,Xb, Yb, Zb) Body fixed reference frame (A,Xf , Yf , Zf ) Fuel fixed reference frame (E,XI , YI , ZI) Inertial reference frame ~L Pendulum direction vector \u2016L\u2016 = constant ~b Location of pendulum base with respect to the body fixed reference frame The equations of motion are derived using a two-body approach (see figure 3). Both bodies, the satellite with fixed part of the fuel and the free moving fuel (pendulum), are considered to be rigid. The orientation of each body with respect to the inertial space is described using a set of Euler angles (or quaternions) and the two bodies are connected with each other via the base of the pendulum (point p). Since the bodies are rigid we have the following relations: Is \u2202~\u03c9s \u2202t \u2223 \u2223 I = \u2211 ~Tb,ext ms \u22022~rO \u2202t2 \u2223 \u2223 \u2223 I = \u2211 ~Fb,ext If \u2202~\u03c9f \u2202t \u2223 \u2223 \u2223 I = \u2211 ~Tf,ext mf \u22022~rA \u2202t2 \u2223 \u2223 \u2223 I = \u2211 ~Ff,ext (5) which can be rewritten to: Is \u2202~\u03c9s \u2202t \u2223 \u2223 S + ~\u03c9s \u00d7 (Is~\u03c9s) = ~Tfs + ~Tds + ~Tc +~b \u00d7 ~Ffs ms~aO = ~Ffs + ~Fds + ~Fe + ~Fgs If \u2202~\u03c9f \u2202t \u2223 \u2223 \u2223 F + ~\u03c9f \u00d7 (If~\u03c9f ) = ~Tsf + ~Tdf + ~L \u00d7 ~Fsf mf~aA = ~Fsf + ~Fdf + ~Fgf (6) The connection between the bodies is included in the equations of motion via forces (Ffs, Fsf = \u2212Fsf ) and the moments (Tfs, Tsf = \u2212Tfs)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002340_j.triboint.2011.10.017-Figure7-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002340_j.triboint.2011.10.017-Figure7-1.png", + "caption": "Fig. 7. Pad showing inlet and outlet film thickness.", + "texts": [ + " The area A6 is affected by hot oil carry-over. (3) The heat flux values for the elemental nodes of the bottom surface of the pad are obtained from the solution of the energy equation. (4) Radiation heat transfer from the pad is not considered. To view results for deformation the current load system functions of plot results, counter plot nodal solution and displacement vector are chosen. Fig. 6 shows two different pad tilt positions 1 & 2 and corresponding film shapes for which torques are calculated. Referring to Fig. 7 we have the initial value of a\u00bc hi ho 1 \u00f014\u00de For the case under consideration the value of hi is constant and ho is varied by 20%, 15%, 10%, 7%, 5%, 2%, 1%, 0.5%. The corresponding values of \u2018a\u2019 are calculated using the formula in Eqs. (15) and (16). The mean film thickness at the center of the pad is constant so that the load is kept constant a0 \u00bc \u00f0aho\u00fehoDho\u00de ho hoDho \u00f015\u00de a0 \u00bc \u00f0a\u00feDho\u00de 1 Dho \u00f016\u00de where Dho\u00bc% of ho increased at leading edge. The angular stiffnesses of the film pertaining to the 2\u20131 pair are calculated as follows: For each variation of ho, the following values are calculated" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002046_s00170-009-2065-0-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002046_s00170-009-2065-0-Figure1-1.png", + "caption": "Fig. 1 Classification of the microstereolithography (\u03bc SL) processes[1]. a Vector-by-vector method. b Integral method", + "texts": [ + "eywords Projection microstereolithography (P\u03bcSL) . Segmented cross-section .Microstructure arrays Microstereolithography (\u03bcSL), which is derived from conventional stereolithography (SL), is a useful technology to fabricate a 3-D microstructure having a complex and high-aspect ratio [1]. As is shown in Fig. 1, this can be classified into two methods; the vector-by-vector (or scanning) method using the scan path of a cross-section with a focused laser beam spot [2], and the integral (or projection) method using the projected cross-sectional image on the resin surface [3]. Commercial photocurable resins, blended resin for improving the curing characteristics and mechanical properties [4, 5], and bio-compatible materials such as polyethylene glycol (PEG) and polypropylene fumarate (PPF) [6, 7] are used as the fabrication materials in the \u03bcSL research area" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001050_vppc.2007.4544122-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001050_vppc.2007.4544122-Figure1-1.png", + "caption": "Fig. 1. Elementary forces acting on a vehicle. T R", + "texts": [ + " The net force (F - Fw), accelerates the vehicle (or R Wheel radius. decelerates when Fw exceeds F). Jv Shaft inertia moment. 2) Motor ratings and transmission. The power required to Jw Wheel inertia moment. drive a vehicle has to compensate the road load Fw, i.e., 4 Wheel slip. B. Dynamics Analysis vju (7) Based on principles of vehicle mechanics and aerodynamics, The mechanical equation (in the motor referential) used to one can assess both the driving power and energy necessary to describe each wheel drive is expressed by ensure vehicle operation (Fig. 1) [6], [7], [8]. T =LVVheel =_-F (10) The rolling resistance force Fro is produced by the tire L flatteing attherodway cntact urface i.e.,The vehicle global inertia moment in the motor referential Fro~=imgcosuo (2) is given by I _ (11) Fi(x) ax1+\u00b1a2x2x3 JV= 2m i2 (I-) F(X) = f2 (x) b,x2 + b2x1x3 + b3x3 Lf3(x)i 3 3 If the adhesion coefficient of the road surface is high, then C1X3 2C2X1X2 3C3X2 - __ ? is usually low and can be neglected. Rs PLq III. NONLINEAR MODEL OF THE PMSM Ld Ld The control objective are first the control of the stator - Rs b PLd 7P'f currents through the control of the Iq current in order to l Lq 2 Lq 3 Lq produce the required torque for the motor motion and second TB 3p(Ld-TL 3pAf to control the angle between the phase motor e" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000208_robot.2005.1570615-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000208_robot.2005.1570615-Figure2-1.png", + "caption": "Fig. 2", + "texts": [], + "surrounding_texts": [ + "The essence of the tentacle model is a 3-dimensional backbone curve C that is parametrically described by a vector ( ) 3R\u2208sr and an associated frame ( ) 33\u00d7\u2208\u03c6 Rs whose columns create the frame bases (Fig. 4). The independent parameter s is related to the arclength from the origin of the curve C, a variable parameter, where (Fig. 3b) ( )\u2211 = \u2206+= N i ii lll 1 0 (1) or ull += 0 (2) where 0l represents the length of the N elements of the arm in the initial position and \u2211 = \u2206= N i ilu 1 (3) determines the control variable of the arm length. position vector, ( )srr = (4) when [ ].l,s 0\u2208 For a dynamic motion, the time variable will be introduced, ( )t,srr = . The position vector on curve C is given by ( ) ( ) ( ) ( )[ ]Tt,szt,syt,sxt,sr = (5) where ( ) ( ) ( )\u222b \u2032\u2032\u2032\u03b8= s 0 sdt,sqcost,ssint,sx (6) ( ) ( ) ( )\u222b \u2032\u2032\u2032\u03b8= s 0 sdt,sqcost,scost,sy (7) ( ) ( )\u222b \u2032\u2032= s 0 sdt,sqsint,sz (8) with [ ].s,0s \u2208\u2032 We can adopt the following interpretation [2, 6]: at any point s the relations (6)-(8) determine the current position and ( )s\u03a6 determines the robot\u2019s orientation, and the robot\u2019s shape is defined by the behaviour of functions ( )s\u03b8 and ( )sq . The robot \u201cgrows\u201d from the origin by integrating to get ( )t,sr , [ ]ul,s +\u2208 00 . The velocity components are ( )\u222b \u2032\u03b8\u2032\u2032\u03b8\u2032+\u03b8\u2032\u2032\u2032\u2212= s 0 x sdcosqcossinqsinqv && (9) ( )\u222b \u2032\u03b8\u2032\u2032\u03b8\u2032\u2212\u03b8\u2032\u2032\u2032\u2212= s 0 y sdcosqcoscosqsinqv && (10) \u222b \u2032\u2032= s 0 z sdqcosqv & (11) uvu &= (12) For an element dm, kinetic and gravitational potential energy will be ( )2222 2 1 uzyx vvvvdmdT +++= (13) zgdmdV \u22c5\u22c5= (14) where dsdm \u03c1= (15) From (13)-(15) we obtain ( )\u222b \u222b \u239c \u239c \u239c \u239d \u239b + \u239f \u239f \u23a0 \u239e \u239c \u239c \u239d \u239b \u2032\u03b8\u2032\u2032\u03b8\u2032+\u03b8\u2032\u2032\u2212\u03c1= l 0 2s 0 sdcosqcossinqsinq 2 1T && ( ) + \u239f \u239f \u23a0 \u239e \u239c \u239c \u239d \u239b \u2032\u03b8\u2032\u2032\u03b8\u2032\u2212\u03b8\u2032\u2032\u2032\u2212+ \u222b 2s 0 sdsinqcoscosqsinq && + dsudssdqcosq ls \u222b\u222b + \u239f\u239f \u239f \u23a0 \u239e \u239f \u239f \u23a0 \u239e \u239c \u239c \u239d \u239b \u2032\u2032\u2032 0 2 2 0 2 1 && \u03c1 (16) \u222b \u222b \u2032\u2032\u03c1= l 0 s 0 dssdqsingV (17) The elastic potential energy will be approximated by two components, one determined by the bending of the element ( )\u2211 = \u03b8+= N i iieb qdkV 1 22 2 4 (18) and the other is given by the axial tension/compression energy component 2 2 1 kuVea = (19) where we assumed that each element has a constant curvature and a uniform equivalent elasticity coefficient k, assumed constant on all the length of the arm. The total elastic potential energy will be eaebe VVV += (20) We will consider ( ) ( )t,sF,t,sF q\u03b8 the distributed forces on the length that determine motion and orientation in the \u03b8 - plane, q - plane and ( )tFu , the force that determines axial motion, assumed constant along the length of the arm." + ] + }, + { + "image_filename": "designv11_7_0003869_s00419-012-0608-6-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003869_s00419-012-0608-6-Figure1-1.png", + "caption": "Fig. 1 The geometrical model of the gear (a) and the cyclic symmetry sector of the system (b)", + "texts": [ + " Procedures of identifying frequencies of natural oscillations and corresponding deformed normal modes of rotating systems at both low and high speeds are presented. Additionally, a Campbell diagram was plotted for analysed system. Some introductory studies that deal with problems discussed in the paper are presented in the Ref. [7]. This paper can be considered as a continuation of authors research involved in the vibration analysis of continuous systems [8,9]. Discussion of problems in this paper can be very useful for engineers\u2013analysts who perform dynamic calculations of the rotating mechanical systems. The analysis of the gear model shown in Fig. 1 is an object of consideration. Such design is commonly used in high-speed gearboxes, among others, in aerospace industry. The model of the gear teeth is simplified down to regular cylinder of the diameter assumed as equal to the pitch diameter dz of the rimmed gear. The other geometrical dimensions of the system (diameters: d0, dp, dk, dw1, dw2; thickness: h p, hz, hb, hs ; lengths: lb, lc, ld , ls, lw) are defined as shown in Fig. 1. The gear model is composed of annular plate with geared rim installed on the hollow stepped shaft. The plate features some discontinuities in a form of holes distributed over predetermined diameter (see Fig. 1). The problem of natural oscillations of the system was solved by the finite elements method. The first step in the finite element analysis is to discretize the continuous model by elaboration a discrete model of the physical structure to be analysed. In this work, the research is focused on the natural mode shapes and corresponding natural frequencies of the system under study, so a damping and a forcing function are neglected. It leads to the differential equations of motion of the analysed system that can be written in the following form [3] Mu\u0308 + Ku = 0 (1) where M is a global inertia matrix, K is a global stiffness matrix, and u is nodal displacement vector", + " The frequencies of natural oscillations of the system are obtained by solving the following eigenvalue problem ( K \u2212 \u03c92M ) u\u0304 = 0 (3) where \u03c9 is natural frequency and u\u0304 is corresponding eigenvector, which is determined by the relation (3). Tetrahedral, 10-node (solid92), isotropic, element of 3 df in each node was adopted for the calculations. As mentioned earlier, in the geometrical model of the gear, the geometry of the teeth is omitted. It allows us to reduce the system\u2019s FE model size. The simplified geometrical model of the system consists of five sectors (see Fig. 1) that have the cyclic symmetry feature. Each of these segments is meshed by using standard procedures of the ANSYS software. The 3-D solid mesh is elaborated and as mentioned earlier, the ten-node tetrahedral element (solid92) with three degrees of freedom in each node is used to realize each sector. During the mesh generation process, it is assumed that the maximum length of each element\u2019s side needs to be no more than 2.7 [mm]. The developed FE model is displayed in Fig. 2, and it consists of 19,620 elements and 36,188 nodes, respectively", + " This problem is even worse if the angular speed of the gear is varying. The problem of influence of the angular speed on the flexural gear models deformation is analysed. For the purpose of identification of these modes, an algorithm of tagging oscillation modes, which determines the correspondence between vibration of the circular disc versus disc with holes, is used. For this purpose, an auxiliary model of annular plate in the form shown in Fig. 3b is used. The geometrical dimensions of the auxiliary model were taken from the gear geometry (shown in Fig. 1). They are as follows: addendum circle diameter dz , rim mounting diameter dp, root circle diameter dw2, and thickness h p and hz (see Table 1). Dynamic analysis is performed for the auxiliary model cases rotating at predetermined angular speed, where diameter of though holes d01 (see Fig. 3b) varies as seen in Table 2. Findings are compared to each other both quantitatively and qualitatively. This method makes it possible to investigate deformations of nodal lines associated with nodal diameters and circles due to through holes and then determine correspondence between oscillation modes of solid circular disc and a plate with holes" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002492_detc2011-48306-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002492_detc2011-48306-Figure5-1.png", + "caption": "Figure 5: The PCB and the positioning of the flex print and the flex print terminal", + "texts": [ + " The usefulness of formal or semi-formal modeling (such as SysML) is explained to be not useful in the conceptual design phase due to the rate at which models change, and due to decreased communication effectiveness caused by a lack of visual representation of the structure of the product by different engineers [28]. \u2018The ESD protection issue\u2019 scenario: Due to a requirement for better temperature sensing, a change of the design is necessary. Discussing the proposed solution with the electronic engineers, it becomes apparent that this type of solution is prone to electrostatic discharges and that mitigations have to be made for the electronics not to be damaged in such a case. The proposed design is shown in Figure 5. For easier handling of the small thermo sensor, it is placed on a flex print which can easily be connected to the PCB compared to five ordinary wires. Due to the stiffness of the flex print, the location and orientation of the terminal is important and this fitting is made in corporation between the electronics Downloaded From: http://proceedings.asmedigitalcollection.asme.org/pdfaccess.ashx?url=/data/conferences/idetc/cie2011/70722/ on 07/13/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use 9 Copyright \u00a9 2011 by ASME and the mechanical engineer. Figure 5 shows the PCB connector placement and the position of the flex print. Discussion on solutions: In this particular case, the orientation and location of the terminal on the PCB, and the placement of the connector on the flex print is a clear dependency between electronics and mechanical models. In order to reach a solution, both electronics and mechanical engineers had to have several discussions during a number of design iterations. From Table 2, three solutions have been identified which should aid in overcoming this challenge related to information transfer across domains: a) Controlling the design through requirements management; b) Simulation of phenomena incorporating model elements from different domains; c) Integration of models through model transformations" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002727_piee.1967.0214-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002727_piee.1967.0214-Figure2-1.png", + "caption": "Fig. 2 Schematic arrangement of generator windings", + "texts": [ + " A comprehensive mathematical model has been given,10 mainly in its relationship to accurate generator representation and its solution by analogue computer, but no corresponding account appears to have been devoted to the application of digital methods of analysis to this form of model and those that may be developed from it. The purpose of the present paper is therefore to document investigations that have been carried out in the application of digital-computer methods of dynamic-performance evaluations of large turbogenerator units. It seeks to describe the 1116 2.2 Generator equations 2.2.1 Equations in the d and qaxes The direct- and quadrature-axis equations used for the generator are derived from the schematic layout of the 3-phase windings shown in Fig. 2, and their algebraic signs correspond PROC. IEE, Vol. 114, No. 8, AUGUST 1967 1o generator action. They are subject to the following assumptions: (a) A current in any winding is assumed to set up an m.m.f. wave which is sinusoidally distributed in space around the air gap. (b) The effects of hysteresis are neglected. (c) It is assumed that a component of m.m.f. acting along the direct axis produces a sinusoidally distributed flux wave in that axis only, and that, similarly, a quadratureaxis m.m" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002900_icma.2013.6617997-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002900_icma.2013.6617997-Figure4-1.png", + "caption": "Fig. 4 Finite element model of flexspline", + "texts": [ + " We considered that the two sides of one gear respectively corresponded to angel i\u03d5 and 1i\u03d5 + , so the tangential force and radius force acting on this gear tooth was as follows ( )1 1 max 2 cos 2 2 i i g t R t d f b q d \u03d5 \u03d5 \u03c0 \u03d5 \u03d5 \u03d5 \u03d5 + \u2212\u239b \u239e = \u239c \u239f \u239d \u23a0 \u222b (5) \u03b1tantr ff = (6) We got an approximation of the meshing range size according to the wave generator outer circle figure and the flexspline inner circle figure, so the 2\u03d5 was set to 40\u00b0. We made the forces shown in equation (5) and (6) to act on every node of flexspline, and then the whole model of flexspline in ANSYS is shown as Fig. 4. In order to decrease the scale of solution and improve the computational speed and precision, we selected the precondition conjugate gradient method in ANSYS, and set the size of solution step enough large. In harmonic reducer, flexspline is the weakest link, so we mainly analyse the deformation and stress of flexspline with different loads in this article. Because the deformation and stress of flexspline were caused by both the stretching effect of wave generator and the meshing force between flexspline and circular spline, we firstly solved the deformation and stress of flexspline only with the action of wave generator (without load), then we made the mesh force which could simulate the load on the output of the reducer to act on the teeth of flexspline for further solution and analysis (with load)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001473_j.jbiomech.2009.08.025-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001473_j.jbiomech.2009.08.025-Figure3-1.png", + "caption": "Fig. 3. Schematic diagram of the impact model.", + "texts": [ + " Theoretical equations based on impact dynamic theory related to these kinetic factors can be used to numerically investigate the factors affecting ball behavior by simulating ball behavior. The side-foot kick should be analyzed three-dimensionally and the theoretical equations of both the ball velocity and rotation should be derived. Asai et al. (2002) conducted finite-element model simulations during ball impact for curve kick and reported that the coefficient of friction had a relatively smaller effect on the ball rotation than Nomenclature For the following terms, x, y, and z in the subscripts represent each component of the coordinate system for the impact model shown in Fig. 3. Rax, Raz ankle joint reaction force Tay ankle joint torque Ffx, Ffz ball reaction force ti contact time between the foot and the ball Vf0x, Vf0z foot velocity immediately before impact Vf1x, Vf1z foot velocity immediately after impact of0y foot angular velocity immediately before impact of1y foot angular velocity immediately after impact Vb1x, Vb1z ball velocity immediately after impact ob1y ball angular velocity immediately after impact mf mass of the foot Ify moment of inertia of the foot mb mass of the ball Iby moment of inertia of the ball kz distance from the COM of the foot to the ankle lx distance from the COM of the foot to the medial aspect rb radius of the ball (=0", + " The determination coefficients and p-values for these cubic regression surfaces were computed and statistical significance was set at po0.05. To eliminate the influence of inter-trial variance in the foot velocity immediately before impact, the measurement values of the ball velocity and rotation were normalized to the foot velocity immediately before impact. For simplicity, the ball was assumed to be hit by the vertical medial aspect and launched horizontally, as shown by the impact model in Fig. 3. Because the ball and foot movements in the vertical direction were not considered, gravity was neglected here. Furthermore, the ankle joint reaction force was assumed to have only a horizontal component and the ankle joint torque was assumed to act only about the vertical axis. Based on these assumptions, the following eight equations were obtained for ball impact. The impulse\u2013momentum relationship for the foot is expressed as Z ti 0 Raxdt\u00fe Z ti 0 Ffxdt\u00bcmf \u00f0Vf1x Vf0x\u00de \u00f02\u00de Z ti 0 Razdt\u00fe Z ti 0 Ffzdt\u00bcmf \u00f0Vf1z Vf0z\u00de \u00f03\u00de The angular impulse\u2013momentum relationship for the foot is expressed as Z ti 0 Taydt\u00fekz Z ti 0 Raxdt\u00fe lz Z ti 0 Ffxdt lx Z ti 0 Ffzdt\u00bc Ify\u00f0of1y of0y\u00de \u00f04\u00de The impulse\u2013momentum relationship for the ball is expressed as Z ti 0 Ffxdt\u00bcmbVb1x \u00f05\u00de Z ti 0 Ffzdt\u00bcmbVb1z \u00f06\u00de The angular impulse\u2013momentum relationship for the ball is expressed as \u00f0rb db\u00de\u00f0 Z ti 0 Ffzdt\u00de \u00bc Ibyob1y \u00f07\u00de The coefficient of restitution is expressed as e\u00bc Vb1x \u00f0Vf1x\u00fe lzof1y\u00de \u00f0Vf0x\u00fe lzof0y\u00de \u00f08\u00de The degree of slip on the contact point is expressed as Vb1z rbob1y \u00bc cs\u00f0Vf1z lxof1y\u00de \u00f09\u00de where Vb1z rbob1y and Vf1z lxof1y in Eq" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001527_tmag.2007.916702-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001527_tmag.2007.916702-Figure1-1.png", + "caption": "Fig. 1. Linear resonant actuator driven by dc brush motor.", + "texts": [ + " We also presented the dynamic analysis method for this LRA employing the 3-D finite element method in the previous paper [4]; however, it was found that the calculated current waveform was pretty different from the measured one because the contact resistance between brush and commutator was not taken into account in the computation. It is difficult to assume the appropriate contact resistance of the dc brush motor on operation. In this paper, the effects of the contact resistance on the dynamic oscillation characteristics of the LRA are quantitatively clarified. The usefulness of the use of appropriate contact resistance is clarified through the comparison with the measured results. Fig. 1 shows a prototype of an LRA driven by a dc brush motor. It mainly consists of the dc brush motor, a couple of four-pole permanent magnets, a resonance spring, and a shaft. Digital Object Identifier 10.1109/TMAG.2007.916702 The rotor is directly connected to the shaft of the dc brush motor, and the armature is connected to the resonance spring. The operating principle of this actuator is that the armature moves linearly in the direction of axis as the attractive and repulsive force acts on the armature according to the rotation of the rotor" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002010_1.4002342-Figure7-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002010_1.4002342-Figure7-1.png", + "caption": "Fig. 7 Simple turnout and cross-sections", + "texts": [ + " In this section, numerical examples re presented in order to demonstrate the use of the numerical rocedure presented in this investigation and the effect of wheel nd tongue rail profiles on the location of contact point in turnout ection is discussed. Three different wheel profiles are considered n this example, as shown in Fig. 6. That is i conical wheel rofile, ii arc wheel profile, and iii severely worn arc wheel rofile obtained by measurement. The track gauge is assumed to e 1067 mm narrow gauge . The stock rail profile is assumed to e 50 kg N of Japan Industrial Standard JIS while the tongue ail is JIS 70 S. The wheel and rail contact on the point section of simple turnout is considered, as shown in Fig. 7, and the tongue ail cross-section profiles available from the drawing at points A to are given in this figure as well. In order to discuss the accuracy of derivatives of rail crossection profiles obtained using a direct interpolation along the rack, the first order derivatives obtained using the interpolation nd the three-layer spline are compared in Fig. 8. In this figure, ail cross-sections at the middle of sections A and B and sections and C are shown. As can be observed from these figures, the rst derivatives obtained using the direct interpolation and the ayer spline are in good agreement even around regions, where ournal of Computational and Nonlinear Dynamics om: http://computationalnonlinear", + " Due to severe wear on the wheel tread, the flange angle becomes very steep and this leads to an unwanted flange contact with the side of the tongue rail in all the sections. Furthermore, nearly conformal contact is observed in sections A \u2013 B and no tread contact on wheel center is observed in sections B \u2013 D due to the concave tread wear. That is, the wheel is still in contact with stock rail at the flange-like part of outside of the wheel. Since the stock rail is being separated from the tongue rail as the wheel travel farther, as shown in Fig. 7, the contact on the stock rail is forced to be lost and then the wheel drops on the tongue rail with severe impact. In the worst case, the wheel can be guided to a wrong direction. Using the procedure developed in this investigation, the effect of wheel and rail wear on the turnout negotiation can be clearly demonstrated from a wheel/rail contact geometry point of view and such an analysis can be systematically performed by updating rail profiles obtained using automated profile interpolation procedures" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003197_ias.2011.6074331-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003197_ias.2011.6074331-Figure3-1.png", + "caption": "Fig. 3. Principle of the suspension force generation in the proposed IWBLM.", + "texts": [ + " The stator core is classified into three sections as the section a, the section-13 and the section-yo In the section-a, the there phase three-wire windings Nua, Nva and Nwa are wound; in the section-13, Nup, Nvp and Nwp are wound; in the section-y, Nuy, Nvy and Nwy are wound. All these windings are short pitch and simple. Each section is controlled by separate general-use 3- phase inverters. In this example, the number of the slots, the poles, and sections has been decided respectively, but there are various cases. III. PRINCIPLE OF SUSPENSION FORCE GENERATION The suspension force is regulated to suspend the rotor of BELM. Fig. 3 shows the principle of the suspension force generation in the proposed IWBLM. The suspension force is generated by unbalanced flux density in air-gap with controlled d-axis currents ida, id(l and idy in each section. For example, in section-a the field-strengthening control is done and then the air-gap flux density is increased; in the section-13 and section-y the field-weakening control is done and then the air-gap flux density is decreased. By the net vector sum in three sections, thus the suspension force is generated in the x positive direction", + " Thus F is shown as (6) By the equations (2), (5) and (6), the force components Fa, F J3 and Fy in three-axis coordinate are deri ved as (7) Equation (7) shows the force transformation from two-axis coordinate to three-axis coordinate [10]. The inverse relation can be written as (8) The force can be mutually transformed between two-axis and three-axis coordinates. 978-1-4244-9500-9/11/$26.00 \u00a9 2011 IEEE B. Relationship between d-axis currents and suspension force From the principle of suspension force generation as described in Fig. 3, the electromagnetic forces are generated along the a-, 13- and y- axes, respectively when the rotor is positioned at 0Jt=00. However, the directions of electromagnetic force are changed in accordance with the rotor angular position. The electromagnetic forces when the rotor is positioned at any angle, OJ{ are defined as Fa(w/), FB(w/) and Fy(w/) in the sections a, 13 and y, respectively. Here, as an example, let us consider the electromagnetic forces when the rotor is positioned at 00. The electromagnetic force F a(w/) in the section-a is generated along the a-axis, F a(O) is generated in the direction of 00 when the d-axis current ida is positive (field-strengthening control)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003156_robio.2013.6739739-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003156_robio.2013.6739739-Figure5-1.png", + "caption": "Fig. 5. Bezier Path update", + "texts": [ + " The optimal path Lo can be represented as )(min LLo VL l\u03a9\u2208 = (18) where \u2126l is the set of paths in \u2126f satisfying L m DD T> , or else, it is equivalent to \u2126f; TD is a given threshold. E. Bezier Path Update As mentioned above, the sensing information changes in real-time with the mobile manipulator moving along the planned path. Whenever the mobile manipulator thinks its path passes through any an infeasible region, it has to update the path based on the present position and velocity. An example of path update is shown in Fig. 5. At the beginning, the ultrasonic sensors can only detect infeasible region 1, and path 1 is chosen as an optimal path, however, when the mobile manipulator is at point Pu, infeasible region 2 is detected, so the mobile manipulator plan its path again and choose the path 2 to move. When the mobile manipulator finally arrives at the grasp circle, its arm grasps the object based on the inverse kinematics. To testify the proposed approach, several simulation experiments have been carried out. The mobile manipulator parameters are given as follows" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001971_j.snb.2010.11.015-Figure10-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001971_j.snb.2010.11.015-Figure10-1.png", + "caption": "Fig. 10. Inverting op-amp configuration used to invert the output signal of ureaCCCII+.", + "texts": [ + " 8 shows the output voltage decreasing as the urea concentration increases. This outcome is due to the nature of a urea based ISFET biosensor in which the output signal is an indirect measurement of urea [7,13,14]. In order to obtain the correct signal trend for the instrumentation amplifier stage, additional circuitry was added between diode, D1 and Y3-node of the CCII+3 to invert the output signal of the urea-CCCII+. The additional circuitry consists of a simple high input impedance voltage follower and an inverting amplifier as shown in Fig. 10. 458 P. Pookaiyaudom et al. / Sensors and A p m m t c t w a t With the circuit modification, observed output signals can be roperly recorded and the ratio of response can be obtained, which ake the sensors versatile and have the potential for real-time easurement. In order to verify the performance of the system, itrated concentrations of both urea and creatinine were prepared overing values in the normal physiological range [3]. The concenration value used for urea were 2 mM, 4 mM, 8 mM and 10 mM, hile the concentration for creatinine were 40 M, 80 M, 100 M nd 150 M" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001468_j.optlastec.2009.02.005-Figure8-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001468_j.optlastec.2009.02.005-Figure8-1.png", + "caption": "Fig. 8. Boundary conditions.", + "texts": [ + " (1)): rCP @T @t \u00fe v @T @x \u00bc @ @x k @T @x . (1) In Eq. (1) T is the temperature, Cp and k are respectively the specific heat and the conductivity of the metal. meshed geometry. 0 20 40 60 80 100 120 140 160 180 200 220 240 0.0 ordinate (mm) Te m pe ra tu re (\u00b0 C ) Calculated Temperature Measured Temperature 10.08.06.02.0 4.0 40 60 80 100 120 140 160 180 200 220 240 260 280 M ea su re d Te m pe ra tu re (\u00b0 C ) Fig. 10. Measured temperatures for hybrid and laser welding process. The boundary conditions (Fig. 8) are: Temperature at the limit of the melt pool: this temperature value is comprised between Liquidus and the Solidus ones, but it is not exactly known. So it has been chosen in order that the measured and the calculated temperatures agree. For the boundaries 1, 2 and 3: global heat transfer between the considered system and the surrounding media (Eq. (2)): k\u00f0T\u00de ~rT ~n \u00bc h \u00f0T1 T\u00de. (2) In this equation h is the transfer coefficient combining convection and radiation heat transfer and TN is the ambient temperature" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002687_21573698-1303444-Figure7-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002687_21573698-1303444-Figure7-1.png", + "caption": "Fig. 7 Effect of spine angle on the periods of rotation of a model diatom with 4, 12, and 24 spines compared with the minimal inscribing spheroid.", + "texts": [ + " For a diatom with short spines relative to the body dimensions, the spheroid axis ratio will depend more heavily on the ratio of body height to diameter (the spines will have less influence over the shape of the spheroid). If the spines are long relative to the body, then spine angle becomes more important in governing the axis ratio of the spheroid. [19] Spine length was fixed at 1.80 \u00a3 1025 m, and spine angle was varied for three spine densities (4, 12, and 24 spines per cell). Results from these models suggest that spine angle affects the period of rotation only at small angles (,308) and that the effect becomes more pronounced as spine number increases (Fig. 7). For this range of angles, and for angles approaching 90o, the period of rotation of a cell with spines cannot be approximated well by Jeffery\u2019s theory for spheroids. The poorest agreement between the modeled cell and the minimal inscribing spheroid was observed when angles were at their most extreme, 0 and 908 (Fig. 7). [20] The average period of rotation of the modeled disk was slightly lower than that obtained in Goldsmith and Mason\u2019s (1962) laboratory experiments (6.5 and 7.6 s, respectively). For reference, the predicted period of rotation for a spheroid with the same height and diameter is T \u00bc 11 s (Jeffery 1922). Sharp edges on modeled and manufactured cylinders and disks reduce their periods of rotation relative to smoother spheroids of comparable aspect ratios (Karp-Boss and Jumars 1998). [21] The fit of our numerical results to Jeffery orbits of spheroids and to experimental results for disks indicates that the underlying computational approach is sound" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003102_j.rcim.2013.03.002-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003102_j.rcim.2013.03.002-Figure4-1.png", + "caption": "Fig. 4. Vectors to determine the orientation of the moving platform.", + "texts": [ + " The forward kinematics problem, also referred as direct kinematics problem, consists on determining the position and orientation of the moving platform knowing the magnitude of the input strokes. In this particular case, the strokes di are known and px, py, pz, \u03b1, \u03b2 and \u03b3 are to be determined. This work approaches the forward kinematics problem by analyzing the orientation and the position of the platform independently. Since the di strokes magnitudes are given, therefore the three points in space that define the platform (see Fig. 4) plane are known and can be written as ei \u00bc aC\u03c8 i aS\u03c8 i di 2 64 3 75 f or i\u00bc 1; 2 and 3 \u00f06\u00de where ei is the vector that describes the position of point Bi relative to frame G. Consider that the vectors v1 and v2 that lie on the platform plane UV are defined as follows v1 \u00bc e2\u2212e1 and v2 \u00bc e3\u2212e1 \u00f07\u00de Hence, the cross product of v1 and v2 results in a vector that is normal to the platform plane, namely n\u00bc v1 v2 \u00bc nx; ny; nz h iT \u00f08\u00de where the unit vector n\u0302 can be obtained as follows n\u0302\u00bc n=jnj \u00bc n\u0302x; n\u0302y; n\u0302z h iT \u00f09\u00de and vector n\u0302 can be further expressed as n\u0302x; n\u0302y; n\u0302z h iT \u00bc GRH \u22c5 0 0 1 T \u00f010\u00de where n\u0302x \u00bc C\u03b3S\u03b2C\u03b1\u00fe S\u03b3S\u03b1 \u00f011a\u00de n\u0302y \u00bc S\u03b3S\u03b2C\u03b1\u2212C\u03b3S\u03b1 \u00f011b\u00de n\u0302z \u00bc C\u03b2C\u03b1 \u00f011c\u00de In order to obtain a closed-form solution for determining \u03b1, this paper proposes the following geometric method" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000500_14356007.a19_177.pub2-Figure7-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000500_14356007.a19_177.pub2-Figure7-1.png", + "caption": "Figure 7. Schematic view of a frame and plate electrolyzer A) Anode plate; B) Cross-sectional view a) Tantalum foil; b) Platinum foil strip anodes; c) Anode channel; d) Supporting plate; e) Graphite cathode block; f ) Cathode channel; g) Cooling channel; h) Spacer; i) Diaphragm; j) Anolyte inlet; k) Anolyte outlet", + "texts": [ + " High anodic current density with minimum heating of the electrolyte 3. Effective dissipation of heat through heat exchangers with large surface areas 4. Small anolyte gap to minimize voltage losses 5. Dimensionally stable anode constructionwith minimum use of platinum The first successful industrial realization was the Degussa\u2013Wei\u00dfenstein cell [119]. A further development is a bipolar electrolyzer [120\u2013122] with ion-exchange membranes [123], which is reviewed in [124], [125]. A bipolar electrode plate (see Fig. 7) is the basic element in the filter-press electrolysis cell, which consists of 26 electrodes [124], [126]. The characteristic feature is the large number of vertical, parallel anolyte channels (9 3 mm). The anodes are ribbonlike platinum foils on a carrier, which is cooled from behind. Anolyte and catholyte are separated by a microporous polymer diaphragm or, in a more recent development, by a cationexchange membrane [127]. The electrolytic conditions for the production of crystalline peroxodisulfate salts are determined by the solubilities of the starting materials and products in the electrolytes, and these in turn are dependent on the proton activity" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003102_j.rcim.2013.03.002-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003102_j.rcim.2013.03.002-Figure1-1.png", + "caption": "Fig. 1. CAD model of the 3-CUP parallel mechanism.", + "texts": [ + " Lower mobility PMs are typically used in more specific tasks instead of general purpose tasks; however there is a certain loss of flexibility due to the reduction in DOF of the manipulator. The 3-CUP (where C, U, and P denote cylindrical, universal, and prismatic joint, respectively) PM analyzed in this paper consists of a moving platform and a fixed base connected by three identical legs that are evenly distributed on the fixed base. This robotic architecture was proposed by Rodriguez-Leal and Dai [7] based on Artiomimetics. For convenience of the reader, a CAD model of the 3-CUP manipulator is shown in Fig. 1. The mobility of the 3-CUP PM has been studied by Rodriguez-Leal et al. [8] where it was determined that the moving platform has 3 DOF: i.e. one translation axis perpendicular to the fixed base and two rotations about two skew axes. Strictly speaking, the 3-CUP PM is a lower mobility (i.e. less than 6 DOF), 2R1T (namely, 2 rotations and 1 translation) parallel mechanism. The study of kinematics is a very crucial aspect approached by researchers in order to define possible applications of PM [9,10], which in most cases result in the solution of nonlinear equation systems [11-13]", + " The joint axis si4 is parallel to the V-axis, while the joint axis si3 is parallel to the XY plane and is perpendicular to si4. The 3- CUP PM can be considered as a non-canonical 3-PSP PM, according to [8], where it is proved that both architectures have identical mobility. The inverse kinematics problem consists in determining the actuators strokes (i.e. di) in order to configure the end-effector in a desired position and orientation. Denoting G (X, Y, Z) and H (U, V, W) as the global and platform reference frames that are located on the base and moving platform centroids, respectively (see Fig. 1), consider the loop closure equation for leg i defined in the G frame as (see Fig. 2) p\u00fe Hbi \u00bc ai \u00fe di \u00f01a\u00de where p\u00bc px py pz 2 64 3 75; bi \u00bc GRH \u22c5R\u00f0W ; \u03c7i\u00de\u22c5\u00bdbi;0;0 T ; a\u00bc aC\u03c8 i aS\u03c8 i 0 2 64 3 75 and GRH \u00bc C\u03b3C\u03b2 C\u03b3S\u03b2S\u03b1\u2212S\u03b3C\u03b1 C\u03b3S\u03b2C\u03b1 \u00fe S\u03b3S\u03b1 S\u03b3C\u03b2 S\u03b3S\u03b2S\u03b1\u00fe C\u03b3C\u03b1 S\u03b3S\u03b2C\u03b1\u2212C\u03b3S\u03b1 \u2212S\u03b2 C\u03b2S\u03b1 C\u03b2C\u03b1 2 64 3 75 \u00f01b\u00de Let GRH be the rotation matrix that defines the orientation of the platform relative to frame G and follows the X-Y-Z Euler angle convention, where \u03b1, \u03b2 and \u03b3 are their respective angular displacements [14]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003286_s00707-013-0822-5-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003286_s00707-013-0822-5-Figure2-1.png", + "caption": "Fig. 2 Scheme of the tribo-fatigue roller/shaft system", + "texts": [ + "), for example, in the critical zones of main crack initiation (direct effect in tribo-fatigue [1\u20136]). On the other hand, this model allows studying the significant change of contact boundary conditions due to volume deformation of the system\u2019s elements by non-contact forces (back effect in tribo-fatigue [1\u20136]). The latter effect will be discussed further. Consider the example of calculation of contact pressure with regard to non-contact (volume) deformation. As an object of study, let us take a roller/shaft system that is acted upon by contact FN and non-contact Fb forces (Fig. 2). This model is used in wear-fatigue tests for contact-mechanical fatigue (Fig. 1a) [33,34]. For this model, the problem of the influence of the non-contact load value on contact pressure changes will be solved. From Fig. 1a, it is seen that the surfaces of contacting bodies are bounded by the second-order surfaces; therefore, to determine the contact pressure, one could confine oneself to Hertz\u2019s theory. Yet, since during long fatigue loading the cases of contact of bodies with arbitrary-shape surfaces are most probable, it is preferable to use more general methods of numerical modeling for contact pressure calculation", + " 4 and 5 it can be seen that for the contact load predetermined by FN at the contact region edges, the numerical modeling error is the largest. At the contact load assigned by \u03b4, the error distribution practically does not differ from the one depicted in Fig. 5. In addition to the contact load, which will be set by the bodies approach \u03b4 = 2.723 \u00d7 10\u22125 m, the tensile (compressive) or bending load will also be applied to the shaft. From Table 1, it is seen that the errors at the contact load assigned by FN are somewhat less than those predetermined by \u03b4. In the coordinate system shown in Fig. 2, displacements (40) at tension-compression will be u\u0304(b1) z = \u2212 \u03bd2 E2 \u03c3 (b1) xx R2, (47) and at bending u\u0304(b2) z = \u2212 \u03bd2 2E2 \u03c3 (b2) xx R2. (48) From Fig. 6, it follows that depending on the non-contact stresses at the contact region center \u03c3a based on \u03c3 (max) a = 6.4\u00d7108 Pa, the maximum contact pressure p0 based on p(c) 0 = 3.844\u00d7109 Pa varies approximately from +17 to \u221220 % at tension-compression and approximately from +9 to \u22129 % at bending. Figure 7 illustrates that depending on the non-contact stresses at the contact region center \u03c3a based on \u03c3 (max) a = 6" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000715_3.61139-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000715_3.61139-Figure1-1.png", + "caption": "Fig. 1 Rotorcraft fuselage model.", + "texts": [ + " When in contact with the ground, the fuselage is supported by a system of springs and dampers to simulate the restraint to fuselage motion in an actual helicopter due to the landing gear system. When airborne in hovering flight the aircraft is unrestrained elastically. The rotor consists of three or more rigid blades attached to the hub by means of slender elastic beam segments. These beam segments represent the flexbeam or strap of a bearingless rotor. A schematic of the fuselage is shown in Fig. 1. The hub, mast, and landing gear are all included in the mass and inertia of the fuselage. The total fuselage mass is mf and the moments of inertia for the mass center of the fuselage are Ix and Iy, respectively, for the X and Y directions. The aircraft reference center is a distance z above the body mass center and a distance h below the hub center. For air resonance and ground resonance, in hover and on the ground, respectively, vertical translation and yaw rotation of the body are insignificant" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000278_j.jsv.2007.03.071-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000278_j.jsv.2007.03.071-Figure2-1.png", + "caption": "Fig. 2. The external torques acting on the shafts of meshing gears. The right-hand side drawing illustrates the interaction force between the gears.", + "texts": [ + " However in noisy operation, the gears lose contact, with an audible impact when the gears re-establish contact. This is known as a backlash oscillation. There are in fact two broad types of backlash oscillations. Starting from state (a) in Fig. 1, the system can pass through state (b) (freeplay) to state (c) (torque reversal) and back again. Alternatively, the system can simply oscillate between states (a) and (b). We consider a model of two meshing spur gears and the external forces acting on the two shafts, as shown schematically in Fig. 2. The X-shaft is driven by a motor torque T\u00f0t\u00de. The first harmonic of the sound generated by a noisy pump is at the same frequency as the gross rotation rate of the machine. This motivates us to seek forcing mechanisms which operate at integer multiples of the gross rotation rate. There may be ARTICLE IN PRESS J. Mason et al. / Journal of Sound and Vibration 308 (2007) 431\u2013440 433 several such mechanisms but this paper examines only two: eccentric mounting of the gears and torque ripple. Eccentricity arises when the axis of rotation is not exactly in the centre of the gear" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000077_2006-01-0358-Figure7-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000077_2006-01-0358-Figure7-1.png", + "caption": "Figure 7: FCM vs. ANSYS forced response analysis load and constraint locations. (Pockets labeled 0 - 9)", + "texts": [ + " A free-free torsion stiffness value was found through a free-free impact analysis with the ANSYS cage model giving Nm/rad 75k t \u2248 (4) The constrained cage torsion stiffness value will be used in the FCM validation analysis with ANSYS (discussed next), but in the absence of constraints, such as the DBM using the FCM, the free-free torsion stiffness in Equation (4) is used. In order to gain confidence that the results from the FCM accurately predict the response of the actual cage, a forced response analysis between the FCM and ANSYS was completed where the cage was subjected to several loads and fixed at several locations as shown in Figure 7. Table 2 contains the conditions used in the forced response comparative analysis. Forced response results for the FCM and the ANSYS cage model at pockets zero, one and two are presented in Figures 8, 9 and 10 respectively. The results for pockets zero, one and two are in very good agreement both in amplitude and frequency. Displacements in the Z direction for pocket two, shown in Figure 10, vary significantly between ANSYS and the FCM, but further review indicates the displacements are relatively small compared to the displacements in the Y direction and therefore have a small effect on the overall response" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000638_j.talanta.2008.04.035-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000638_j.talanta.2008.04.035-Figure1-1.png", + "caption": "Fig. 1. Parallel-plate chemicapacitor element: (a) top-view photograph showing square capacitor and wirebond pad and (b) cross-sectional diagram (not to scale).", + "texts": [ + " Presented herein are the results from the exposure of four chemicapacitors, each filled with a different semi-selectively MeS absorbing dielectric polymers. As chemicals sorb into the dielectric, they alter its permittivity and thereby raise or lower the capacitance of the sensor. The four polymers have functional groups of varied polarity, acidity, and dielectric constant (\u223c2\u201310). The sensor structures used in this study were fabricated using the Multi-User MEMS Process (MUMPs) [13] from MEMSCAP, Inc. (Durham, NC). Fig. 1 shows a top-view photograph and a side-view cross-section diagram of one of these structures. In the present work, two chips were used, each having multiple parallel-plate capacitor structures spaced approximately 300\u2013500 m apart, on a 2 mm \u00d7 5 mm chip [14]. The structures are made from polycrystalline silicon deposited on an insulating silicon nitride layer. Each parallel-plate capacitor is square-shaped, approximately 285 m on a side, with a 0.75 m vertical gap between the plates. The top S.V" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003858_s11661-013-1936-z-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003858_s11661-013-1936-z-Figure1-1.png", + "caption": "Fig. 1\u2014Setup for sonoprocessing (ultrasonic treatment) of solidifying alloy: (a) schematic diagram, and (b) crucible regions used for microstructure investigation.", + "texts": [ + " These objectives were achieved through metallographic studies on optical and electron microscopes. The hypereutectic Al-Si alloy B390 was used in the current study. This alloy contains ~17 pct Si, 4.5 pct Cu, 0.55 pct Mg,<1.5 pct Zn,<1.3 pct Fe, and lower levels of Mn, Ni, and Sn. Ingots of this alloy were melted in a resistance furnace set at 1023 K (750 C), and then allowed to cool down to pouring temperature. The molten alloy was poured into the crucible mold for sonoprocessing (UST). The UST of the solidifying alloy was carried out using the ultrasonic system shown in Figure 1. Ultrasonic vibrations were transferred through a horizontal guide rod and vertical guide plate to the mold, which is made of stainless steel in the form of crucible. The vibrations are, thus, transferred to the solidifying alloy through the bottom and walls of the crucible horn. The ultrasonic system provides a power of 2 KW, frequency of 19.5 kHz, and vibration amplitude of about 25 to 30 lm at the bottom of crucible. The capacity of the crucible is about 1.3 kg liquid aluminum. The mold (crucible) temperature was kept at room temperature during all experiments" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003762_robio.2012.6491146-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003762_robio.2012.6491146-Figure2-1.png", + "caption": "Fig. 2. Model of flat-footed biped robot with mechanical impedance at ankles", + "texts": [ + " We have shown that this robot achieves faster PDW than that of conventional flat-footed robots with the ankle springs using the ankle inerters. We expect that biped robots achieve fast and energy-efficient active walking by mimicking this flat-footed PDW. We have thus developed a novel biped robot that can mimic the flat-footed PDW with mechanical impedance at the ankles on level ground as shown in Fig. 1. In this paper, we show a mechanism and control method of our biped robot and its active walking performance by simulations and experiments. Fig. 2 shows a model of our biped robot. This model has flat feet that have a spring, a damper (joint damping), and an inerter at each ankle. Since this robot does not have knees, it scuffs the toe of the swing leg on the ground during the single support phase. To avoid this, we assume that the ground has footholds the same as stepping-stones. In a walking experiment, this assumption is satisfied by footholds like stepping-stones on the ground. The actuators of the robot become passive joints with damping when they are not actuated" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003592_978-3-319-06698-1_33-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003592_978-3-319-06698-1_33-Figure1-1.png", + "caption": "Fig. 1 a Vectors A, B, C , D, F , G, H locate the pivots in position j = 0 from the fixed frame coordinate system 0. b The three vector loops in position j . Note that the vector A has not been drawn in order to make the figure more clear", + "texts": [ + "eywords Kinematic synthesis \u00b7 Six-bar linkage This chapter presents the synthesis equations for a Watt I six-bar linkage, Fig. 1a, to guide a rigid body through N specified task positions. This is a generalization of the motion generation problem for four-bar linkages, see Hartenberg and Denavit [5], Erdman et al. [3], and McCarthy and Soh [6]. Our formulation yields 28 equations in 28 unknowns for the maximum number of task positions, N = 8, which has a nine-homogeneous Bezout degree of 3.43\u00d71010. M. Plecnik (B) \u00b7 J. M. McCarthy Robotics and Automation Laboratory, University of California, Irvine, CA 92697, USA e-mail: mplecnik@uci", + " Pennock and Israr [8] design an adjustable six-bar linkage for function generation. Other recent work is Shiakolas et al. [9], who used an optimization formulation to design six-bar linkages for the combination of crank angle and coupler point location. This work follows Wampler et al. [14] and formulates the loop equations of the linkage using vectors in the complex plane and their conjugates together known as isotropic coordinates. We use the polynomial continuation software Bertini to solve the system of equations [1, 11]. AWatt I six-bar linkage, Fig. 1a, can be viewed as a four-bar linkage sitting on top of another four-bar linkage. The base four-bar linkage consists of the ground link AB, the cranks AC and B DF , and the floating link C DG. The second four-bar linkage is attached to B DF , has cranks C DG and F H , and the floating link G H P . The floating link G H P is considered to be the end-effector of the system. The goal is to place a task frame attached to G H P in N positions j for j = 0, . . . , N \u2212 1. A task frame j is defined by the coordinates of its origin Pj and its orientation angle measured relative to a fixed frame. Complex coordinates are used to define these parameters, so j = (x j + iy j , ei\u03b8 j ) = (Pj , Tj ). (1) For convenience, choose the fixed frame to coincide with the first task frame, so 0 = (0, 1), Fig. 1. The coordinates of the seven pivots are identified in position j = 0 by the complex vectors A, B, C , D, F , G, H as shown in Fig. 1a. The coordinates of these vectors are 14 unknowns of the linkage synthesis problem. Following Wampler [13], we consider these vectors and their complex conjugates as separate unknowns, which yields a total of 28 unknowns. The synthesis equations are obtained from three vector loop equations for the Watt I six-bar linkage formulated in each of the specified task positions. The rotations of each joint relative to the initial configuration are defined by the pairs of complex vectors and their conjugates, (Q j , Q\u0304 j ) = (ei\u03c6 j , e\u2212i\u03c6 j ), (R j , R\u0304 j ) = (ei\u03c1 j , e\u2212i\u03c1 j ), (S j , S\u0304 j ) = (ei\u03c8 j , e\u2212i\u03c8 j ), (U j , U\u0304 j ) = (ei\u03bc j , e\u2212i\u03bc j ). (2) The overbar denotes the complex conjugate. Notice that each pair satisfies the condition that their product equals one, that is, Q j Q\u0304 j = 1, R j R\u0304 j = 1, S j S\u0304 j = 1, U jU\u0304 j = 1, j = 1, . . . , N \u2212 1. (3) This yields 4(N \u2212 1) equations in the unknown joint rotation angles. Using these rotation unit vectors, we obtain three sets of loop equations from Fig. 1b, A j = { A + Q j (C \u2212 A) + R j (G \u2212 C) \u2212 Tj G = Pj A\u0304 + Q\u0304 j (C\u0304 \u2212 A\u0304) + R\u0304 j (G\u0304 \u2212 C\u0304) \u2212 T\u0304 j G\u0304 = P\u0304j j = 1, . . . , N \u2212 1, (4) B j = { B + S j (D \u2212 B) + R j (G \u2212 D) \u2212 Tj G = Pj B\u0304 + S\u0304 j (D\u0304 \u2212 B\u0304) + R\u0304 j (G\u0304 \u2212 D\u0304) \u2212 T\u0304 j G\u0304 = P\u0304j j = 1, . . . , N \u2212 1, (5) C j = { B + S j (F \u2212 B) + U j (H \u2212 F) \u2212 Tj H = Pj B\u0304 + S\u0304 j (F\u0304 \u2212 B\u0304) + U\u0304 j (H\u0304 \u2212 F\u0304) \u2212 T\u0304 j H\u0304 = P\u0304j j = 1, . . . , N \u2212 1. (6) This is 6(N \u2212 1) equations in the pivot location and joint angle unknowns. The collection of the joint normalization conditions (3) and the three sets of loop equations A j , B j , and C j yields 10(N \u2212 1) equations in the 8N + 6 unknowns, \u3008A, A\u0304, B, B\u0304, C, C\u0304, D, D\u0304, F, F\u0304, G, G\u0304, H, H\u0304 \u3009\u3008Q j , Q\u0304 j , R j , R\u0304 j , S j , S\u0304 j , U j , U\u0304 j \u3009 j = 1, " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000237_s11249-006-9118-4-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000237_s11249-006-9118-4-Figure5-1.png", + "caption": "Figure 5. A femto slider (Panda III) used in this study.", + "texts": [ + " The length of the suspension (distance from the center of the base plate swage hole to the dimple) is 11 mm. The spring rate, pitch and roll stiffness are obtained from a static analysis, which is 10 N/m, 0.5 lNm/degree and 0.6 lNm/degree, respectively. From a modal analysis, we can obtain the resonant frequencies of the suspension assembly for 1st bending, 2nd bending, 1st torsion, 2nd torsion and sway modes are 3.2, 6.2, 6.9, 18.9 and 15.4 kHz, respectively. A femto-sized slider with 3.5 nm FH, Panda III, developed by DSI is used in the simulation studies. Figure 5(a) shows the geometry of the ABS. The gram load is 0.8 g, and the slider s crown and camber are 15 nm and 5 nm, respectively. A static air bearing analysis is conducted at a spindle speed of 10,000 rpm. The simulation results are shown in table 1. It is considered that the slider at the radial position of 22.9 mm is the worst case for the head positioning among these three cases due to the low flying height and big skew angle. This position is selected for the following simulation studies. Figure 5(b) shows the air pressure on the ABS at this position. It is assumed that the probability distributions of both the sample slider s and disk s surface heights follow the normal distributions. The surface roughness specifications are listed in table 2. Currently only the air bearing force, air shear force, contact force and friction force are taken into account. It is known that the short range forces, such as intermolecular force, electrostatic force and lubricant meniscus force, may play a significant role in flying stability of sliders with sub-5 nm FH [5\u20137]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000734_1.2990770-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000734_1.2990770-Figure2-1.png", + "caption": "FIG. 2. Schematic of the adhesive contact between an elastic-plastic sphere and a rigid flat for two cases: a without a neck and b with a neck. c Typical load-approach curve for a single load-unload cycle of an elasticplastic contact. d Uniformly distributed imaginary nonlinear springs simulating the Lennard\u2013Jones potential.", + "texts": [ + " 24 and 25, where the material hardness, H, rather than the material yield strength was used for defining S. This parameter may play a major role in cyclic loadunload of adhesive contacts. The model developed in Ref. 30 will be extended here to the case of multiple loadingunloading cycles in order to study the effect of the Tabor parameter and the plasticity parameter S on the evolution of load-approach curves and plastic deformations in the sphere. The adhesive contact between an elastic-plastic sphere and a rigid flat is shown schematically in Fig. 2. The approach, , is the distance between the summit of the original undeformed hemisphere shown by the dashed lines in Figs. 2 a and 2 b and the approaching rigid flat. This approach is the input parameter for the current contact problem. Negative values of correspond to a gap between the undeformed sphere and the rigid flat, and positive values of to an interference between them. The base of the hemisphere is fixed while its spherical surface can deform due to a pressure distribution, p r , which is given by the Lennard\u2013Jones potential [This article is copyrighted as indicated in the article", + " When the local distance h r is smaller than the interatomic distance, , the short-range repulsive forces prevail over the attraction forces and the local pressure p r becomes negative. Otherwise, when h r is larger than the attraction forces prevail and the local pressure p r is positive. The integration of p r over the sphere surface determines the external force Fe required to maintain a certain given approach, . Typical load-approach curves for a single load-unload cycle see, e.g., Ref. 30 are schematically presented in Fig. 2 c . As can be seen the external force at a certain given approach, , is different during the load and the unload stages as would be expected for elastic-plastic material. In Fig. 2 c negative values of Fe correspond to attraction and positive ones to repulsion between the sphere and the flat. Two critical values of approach, in and out, corresponding to jump-in and jump-out instabilities, respectively, are also shown in Fig. 2 c . During the loading stage the sphere starts deforming when in Fig. 2 a and a neck is formed instantaneously when = in Fig. 2 b resulting in a discontinuous increase in the attraction Fig. 2 c . This neck disappears instantaneously during the unloading stage when the approach decreases and becomes = out causing a discontinuous decrease in the attraction. A commercial FE package ANSYS 9.0 was used to solve this axisymmetric elastic-plastic contact problem. The nonlinear relation between the local pressure, p r , and the local separation, h r see Eq. 3 , was simulated by uniformly distributed imaginary nonlinear springs that connect the sphere surface to the rigid flat see Fig. 2 d . Each spring applies a pointwise force to the sphere surface according to its length change30 to simulate the Lennard\u2013Jones potential of Eq. 3 . Such modeling of surface forces by nonlinear springs allows FE simulation of adhesive contacts for various material constitutive laws e.g., hyperelastic, viscoelas- tic, and viscoplastic and is not limited to an elastic-plastic behavior only. It also provides a natural and smooth transition from repulsion to attraction contact zones compared to the segregated use of contact elements in the repulsion zone and Eq", + " Further load-unload cycles duplicated these of the second and third cycles and hence, are omitted from the figure. The hysteretic loop indicates alternating plasticity where the kinematic hardening material repeatedly undergoes plastic deformation during both the loading and unloading stages, with zero incremental plastic deformation over the entire load-unload cycle.33 This phenomenon, which is called plastic shakedown, is typical of elastic-perfectly plastic materials, or materials with kinematic hardening. The evolution of the compressive/tensile plastic strains in the axial direction x3 in Fig. 2 at the vicinity of the contact zone, for the three load-unload cycles shown in Fig. 3 is presented in Fig. 4. Figures 4 a , 4 c , and 4 e show the strains corresponding to the maximum approach, = max, during the first, second, and third loading stages, respec- tively. Similarly, Figs. 4 b , 4 d , and 4 f show the strains at the jump-out, = out, during the first, second, and third unloading stages, respectively. Since the material response is purely elastic for in during loading and for out during unloading, as can also be seen from the coinciding load-approach lines in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000002_j.1600-0498.1985.tb00801.x-Figure9-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000002_j.1600-0498.1985.tb00801.x-Figure9-1.png", + "caption": "Figure 9.", + "texts": [ + " Problem X The object KARQ moves on a frictionless plane QR. The body M is situated on the curve KQ which forms the left edge of KARQ. A force acts on M in a direction perpendicular to the base QR. The two bodies possess given initial velocities; the problem is to determine the motion of the system as M slides down KQ. Assume the base QR of KARQ lies on the u-axis of a u-z co-ordinate system. Suppose at a given instant that M is at the point C on the curve KQ. Consider the following designations (Figure 9): (uM,z) = co-ordinates of M (um,b) = co-ordinates of K in rn F e RM Rm = vertical force acting on M = angle between the normal to the curve KQ at C and the = magnitude of force of reaction exerted on M by m = magnitude of net force acting on m as a result of the force vertical exerted by M and the reaction at the base. RM and R, are the constraint forces which act on M and m. R, acts on M along the normal at C and is directed away from KQ. R, acts on rn horizontally to the right. The accelerations corresponding to these forces, if reversed, constitute the \u201clost motions\u201d" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003908_1.4026876-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003908_1.4026876-Figure1-1.png", + "caption": "Fig. 1 Mechanical system", + "texts": [ + "1) satisfying Assumptions 1-3 and a nonzero, self-conjugate, set C. Step 1: Choose the parameter vectors f ij; i \u00bc 1;\u2026;p; j\u00bc 1;:::; pi; satisfying constraints 1-2. Then use the SVD to obtain the matrices Qi;Hi and Ri; i \u00bc 1;\u2026;p; satisfying Eq. (4.9). Step 2: Compute the vectors vij and wij; i \u00bc 1;\u2026;p; j\u00bc 1;:::; pi, using Eq. (4.11). Step 3: Construct the matrices J, V and W according to Eqs. (2.7), (2.8), and (4.5). Step 4: Compute the real gain controller using \u00bdFv;Fa \u00bc WJ 1V 1. Consider the four degrees of freedom mechanical system shown in Fig. 1. The equation of motion can be written by a descriptor secondorder linear system m1 0 0 0 0 m2 0 0 0 0 m3 0 0 0 0 0 0 BBBBBBBB@ 1 CCCCCCCCA \u20acx\u00f0t\u00de \u00fe b1 \u00fe b2 b2 0 0 b2 b2\u00fe b3 b3 0 0 b3 b3\u00fe b4 b4 0 0 b4 b4 0 BBBBBBBB@ 1 CCCCCCCCA _x\u00f0t\u00de \u00fe k1\u00fe k2 k2 0 0 k2 k2 \u00fe k3 k3 0 0 k3 k3 \u00fe k4 k4 0 0 k4 k4 0 BBBBBBBB@ 1 CCCCCCCCA x\u00f0t\u00de \u00bc 1 0 0 0 0 0 0 1 0 BBBBBBBB@ 1 CCCCCCCCA u\u00f0t\u00de where x\u00f0t\u00de \u00bc \u00bdx1; x2; x3; x4 T and u\u00f0t\u00de \u00bc \u00bdu1; u2 T. The characteristic polynomial of the system can be computed as: det\u00f0Po\u00f0k\u00de\u00de \u00bc det\u00f0k2M \u00fe kD\u00fe K\u00de \u00bc det m1k 2 \u00fe \u00f0b1 \u00fe b2\u00dek\u00fe k1 \u00fe k2 b2k k2 0 0 b2k k2 m2k 2 \u00fe \u00f0b2 \u00fe b3\u00dek\u00fe k2 \u00fe k3 b3k k3 0 0 b3k k3 m3k 2 \u00fe \u00f0b3 \u00fe b4\u00dek\u00fe k3 \u00fe k4 b4k k4 0 0 b4k k4 b4k\u00fe k4 0 BBB@ 1 CCCA \u00bc a8k 8 \u00fe a7k 7 \u00fe \u00fe a1k\u00fe a0 044505-6 / Vol" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003383_s12541-013-0061-7-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003383_s12541-013-0061-7-Figure5-1.png", + "caption": "Fig. 5 Overall pressures and the contour map of flow field", + "texts": [ + " The material is extruded from the inlet and moved toward the outlet through the working area of screw rotors. Due to extrusion among material, there will be a certain pressure P2 at the outlet position, and the boundary condition for the groove can be expressed as \u0394P = P2-P1 along the direction of extrusion. The inlet boundary, velocity boundary, external surface boundary and the outlet boundary of the finite element model were set as shown in Figure 4. The overall flow field contour map for pressure is shown in Figure 5. It can be seen that the pressure increases gradually from the inlet toward the outlet. The pressure obviously increasing appears at the top of screw edge region, but it is much lower at the bottom of the groove. The pressures at the right side is little higher than that of left side along the same axial section in the flow field. It also shows that the pressures experienced by the male rotor are greater than those experienced by the female rotor. As shown in Figure 5(b), the pressures at the engagement areas are higher than those in other areas which is beneficial for the material mixing. \u03b7 m\u03b3 \u00b7n 1\u2013 = \u03c4 m\u03b3 \u00b7n 1\u2013 = \u2202\u03c1 \u2202t ----- \u2202 \u03c1ux( ) \u2202x --------------- \u2202 \u03c1uy( ) \u2202y --------------- \u2202 \u03c1uz( ) \u2202z ---------------+ + + 0= \u2202 \u03c1ux( ) \u2202t --------------- \u2207 \u03c1uxu( )\u22c5+ \u2202\u03c1 \u2202x ----- \u2202\u03c4xx \u2202x --------- \u2202\u03c4yx \u2202y --------- \u2202\u03c4zx \u2202z -------- \u03c1fx+ + + += \u2202 \u03c1uy( ) \u2202t --------------- \u2207 \u03c1uyu( )\u22c5+ \u2202\u03c1 \u2202y ----- \u2202\u03c4xy \u2202x --------- \u2202\u03c4yy \u2202y --------- \u2202\u03c4zy \u2202z -------- \u03c1fy+ + + += \u2202 \u03c1uz( ) \u2202t --------------- \u2207 \u03c1uzu( )\u22c5+ \u2202\u03c1 \u2202z ----- \u2202\u03c4xz \u2202x -------- \u2202\u03c4yz \u2202y -------- \u2202\u03c4zz \u2202z -------- \u03c1fz+ + + += \u23a9 \u23aa \u23aa \u23aa \u23a8 \u23aa \u23aa \u23aa \u23a7 \u03b3 \u00b7 \u2207 Vf r( ) \u03c9 f rf\u22c5= Vm r( ) \u03c9m rm\u22c5=\u23a9 \u23a8 \u23a7 Vfx \u03c9f y y 0 \u2013( )\u22c5= Vfy \u03c9\u2013 f x x 0 \u2013( )\u22c5= Vfz 0=\u23a9 \u23aa \u23a8 \u23aa \u23a7 Vmx \u03c9\u2013 m y\u22c5= Vmy \u03c9m x\u22c5= Vmz 0=\u23a9 \u23aa \u23a8 \u23aa \u23a7 Figure 6(a) and Figure 6(b) are pressure contour maps of envisage profile area and top profile area in the engagement areas of the screw rotor groove" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000442_j.jelechem.2006.08.007-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000442_j.jelechem.2006.08.007-Figure1-1.png", + "caption": "Fig. 1. Optical paths in the fluorescence of metal supported emitting films. See text for details.", + "texts": [ + " We will present first the correction procedure, then the experimental methods, afterwards the results will be discussed and finally the conclusions will be enumerated. In the analysis of photoluminescence of solid films, it must be considered the absorption of both the excitation and emission beams by the film material in order to have quantitatively correct results. When a fluorescent film of thickness L, supported on a reflective surface, is irradiated with an excitation beam of intensity I0 (of wavelength k0) there is, in principle, reflection of both the excitation and the emitted beams. Fig. 1 illustrates a volume element in the film in this situation. The emitted intensity measured at the detector Im, at a given emission wavelength k, will have two contributions: directly emitted Ied and reflected Ier. Each of these two will in turn have two contributions: emission due to the direct excitation beam I0d and that due to the reflected beam I0r. In general absorption by the film will be present with extinction coefficients a0 at k0 and ae at k. Considering the symmetry of the problem, it can be writ- ten for the total intensity at a given wavelength dIe(k) emitted from a layer of thickness dx: dIe \u00bcu\u00f0k\u00deI0 exp a0x cosh0 \u00fe f0 exp a0\u00f02L x\u00de cosh0 ncAdx \u00f01\u00de where u(k) is the fluorescent emission relative to I0 at wavelength k, f0 is the metal reflectance at k0, nc is the chromophore concentration and A is the area covered by the excitation beam", + " 2 shows the corrected fluorescent emission spectra of a PANI film on Pt at different potentials among with the corresponding absorption spectra. These were obtained from the experimental spectra through Eq. (3), after subtracting the metal dispersion background, using the absorption spectra of Fig. 2b and the platinum reflectance spectrum (not shown); because PANI films are porous and incorporate electrolyte [28], it is assumed that its refractive index is approximately equal to that of the external medium, thus a00 \u00bc a0 and a0e \u00bc ae (see Fig. 1). The excitation wavelength was fixed at 310 nm, which falls inside de p\u2013p* absorption envelope of the benzenoid units [38]. The main characteristics of the emission spectra have been described before, including the presence of small peaks attributed to Raman dispersion of the underlying metal surface [14]. It is observed a decrease in emission intensity as the polymer film is oxidized (going from 0.1 to 0.6 V), leaving a small but not null emission when the polymer is in the emeraldine state. This behavior has been attributed to quenching by charge carriers [10\u201314]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002392_j.matdes.2012.02.002-Figure14-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002392_j.matdes.2012.02.002-Figure14-1.png", + "caption": "Fig. 14. The die for SPF of multi-sheet cylinder sandwich structure of Inconel718 superalloy 1-admitting pipe passage in bulging time; 2-die head cap; 3-die inner core; 4-die outer canister; 5-die lower cover.", + "texts": [ + " The die material should have the following properties: good mechanical properties in high temperature; good performance in rapid thermal and quench; good oxidation resistance in high temperature; good machining properties; high phase transition temperature. In consideration of these factors, heat resisting cast-steel 35Cr24NiSiNRe is used in the experiment. The mechanical properties of the material are shown in Table 5. The superplastic forming die scheme of multi-sheet cylinder sandwich structure is shown in Fig. 14. The superplastic parameters for the multi-sheet cylinder sandwich structure include forming temperature, the rate of loading pressure in forming, the final pressure, dwell time. The selection criteria are as follows: (1) The temperature in SPF process. The low flow stress and the large elongation are required in superplastic forming of multi-sheet cylinder sandwich structure. And at the same time a higher forming temperature is chosen in favor of transformation and dissolution of Laves phase produced in the laser welding process" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000702_09544070jauto469-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000702_09544070jauto469-Figure5-1.png", + "caption": "Fig. 5 Forces and moments considered to act on the piston", + "texts": [ + " [22] to study this secondary motion and to investigate the influential factors of load, speed, piston clearance, and gudgeon pin offset. Details of the former are outlined here. The piston skirt analysis links the piston dynamics with the hydrodynamic action of the lubricant surrounding the skirt. The influence of the latter adds additional components to the forces and moments governing the calculation of the piston dynamics. When the piston is free to move within the piston clearance, as shown in Fig. 5, they may be divided into four main groups: (a) the forces acting in the axial direction and arising from the reciprocating action of the piston and the gas pressure on the piston crown, namely Fpin, Fcg, FG, and also a component of MI; (b) hydrodynamic forces and moment acting against the transverse motion of the piston, namely GH, MH, and Gpin; (c) inertial forces acting in the transverse direction due to the transverse accelerations of the piston, namely Gcg and a component of MI; (d) forces acting along the connecting rod, which may be attributed to the reciprocating mass of the piston assembly, namely Frod" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003992_s00422-014-0625-3-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003992_s00422-014-0625-3-Figure1-1.png", + "caption": "Fig. 1 The seven-link bipedal walking model. The upper body, the legs and the feet are modeled as rigid sticks without flexible deformation. The mass of each part is averagely distributed among the corresponding stick. a The degree of freedom, b the mass distribution and the torsional springs at the joints", + "texts": [ + ", the angle between the two sticks connected at the joint, and \u02dc\u03b8 represents the equilibrium position, where the joint torque is zero. d is the damping coefficient. In order to alleviate the oscillatory joint motion, we add a damper to each joint. The damping coefficients are set according to the critical damping. \u03b8\u0307 is the joint angular velocity. Thus, the control parameters of the mechanical system are all the equilibrium positions and spring constants, which determine the torque and stiffness of each joint. Figure 1 shows the structure and the related variables of the biped model. In this study, we employ a simple and general torsional spring model in order to exploit the essential characteristics of variable stiffness actuators. Thus, the results of this study can be expected to be suitable for a large variety of dynamic bipedal walkers with adaptable stiffness. 2.2 Walking phases Different from most former passivity-based bipedal walking models with point feet or round feet (Taga et al. 1991; Verdaasdonk et al", + " Phase switching is triggered by foot contact information and certain joint angles. Since the bisecting mechanism equipped at the hip joint restrains the direction of the upper body, the two springs at the hip joints have the same stiffness and opposite equilibrium positions. 2.3 Walking dynamics The Lagrange\u2019s equation of the first kind is used to construct the equations of dynamics. We suppose that the x-axis is along the forward direction while the y-axis is vertical to the ground upwards, as indicated in Fig. 1. The configuration of the walker is defined by the position of the hip joint and the angle of each stick. Thus, the posture of the model can be arranged in a generalized vector: q = (xh, yh, \u03b81, \u03b82, \u03b8b, \u03b82s, \u03b81 f , \u03b82 f ) \u2032 . (2) The superscript \u2032 means the transposed matrix (the same in the following paragraphs). The positive directions of all the angles are counter-clockwise. Note that the dimension of the generalized vector in different phases may be different. When the knee joint of the swing leg is locked, the freedom of the shank is reduced and the angle \u03b82s is not included in the generalized coordinates", + "1 Appendix A: Lagrange\u2019s equations for the dynamic walker The model can be defined by the Euclidean coordinates r, which can be described by the x-coordinate and y-coordinate of the center of mass of each stick and the corresponding directions. The walker can also be described by the generalized coordinates q: q = (xh, yh, \u03b81, \u03b82, \u03b8b, \u03b82s, \u03b81 f , \u03b82 f ) \u2032 (12) We defined matrix J as follows: J = dr/dq (13) The mass matrix in rectangular coordinate r is defined as: M = diag(ml , ml , Il , mt , mt , It , mb, mb, Ib, ms, ms, Is, m f , m f , I f , m f , m f , I f ) (14) where m-components are the masses of each stick, while Icomponents are the moments of inertia, as shown in Fig. 1a. The constraint function is marked as \u03be(q), which is used to maintain foot contact with ground, the direction of the upper body and knee locking. Each component of \u03be(q) should keep zero to satisfy the constraint conditions. We can obtain the equations as following: Mq q\u0308 = Fq + \u03a6 \u2032 Fc (15) \u03be(q) = 0 (16) where \u03a6 = \u2202\u03be \u2202q . Fc is the constraint force vector. Mq is the mass matrix in the generalized coordinates: Mq = J \u2032 M J (17) Fq is the active external force in the generalized coordinates: Fq = J \u2032 F \u2212 J \u2032 M \u2202 J \u2202q q\u0307q\u0307 (18) where F is the active external force vector in the Euclidean coordinates" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003197_ias.2011.6074331-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003197_ias.2011.6074331-Figure5-1.png", + "caption": "Fig. 5. x-, y- axes and a-, \ufffd-, y- axes.", + "texts": [ + " 4 (b), there are two d-axes at wt = 40\u00b0. The d-axis rotates according to the rotor rotation so that the direction of suspension force is also varied depending on the rotor angular position. In the next section, it is discussed how the d-axis currents are regulated to generate the suspension force. IV. RADIAL POSITION CONTROL METHOD A. Coordinate transformation in two- and three-axes In order to derive the relationship between the d-axis currents and the suspension force, the axes in the coordinate are defined in this section. Fig. 5 shows x- and y- axes in two axis coordinate and also a-, \ufffd- and y- axes in three-axis coordinate. The a-axis is corresponding to the x-axis. The directions of \ufffd- and y- axes are rotated by 120\u00b0 and 240\u00b0 for the a-axis, respectively. The unit vectors of each axis are defined as follows ex and ey are unit vectors on x- and y- axes, respectively; ea, eJ3 and ey are unit vectors on a-, \ufffd- and y axes respectively. Thus the unit vectors ea, eJ3 and ey are shown as (1) using ex and ey. e a = ..3:. (e x cos 0\u00b0 + e y sin 0\u00b0) 3 e fJ = " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003305_1.4026080-Figure6-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003305_1.4026080-Figure6-1.png", + "caption": "Fig. 6 Hydraulic pipe for pressure measurement", + "texts": [ + " The test rig allows a precise measurement of several parameters such as the friction torque and the minimum film thickness, as along with the pressures and temperatures at the film/pad interface. The temperature field is determined on two opposite pads set at 180 deg to each other and is equipped with thirteen thermocouples on each one. The pressure field is measured 90 deg shifted from those pads and on two other opposite pads (also set at 180 deg to each other), by using 12 pressure transducers per pad. For hydrodynamic pressure measurement, holes of 0.3 mm were made in the bearing, with each hole being linked to a pressure transducer via a connector tube, as shown in Fig. 6. The hydraulic pressures in the tube remain static; no flow rate occurs to overcome pressure losses. Thus, the local pressure on the active surface of the pad can be measured without pressure loss. To remove the air within the tubes, a special evacuation system was created. For the temperature measurements, thin thermocouples were used (0.25 mm in diameter) in order to avoid disturbing the thrust bearing behavior. The 32 type-K thermocouples were inserted through 0.3 mm holes, flush to the film/pad interface and, thus, being in direct contact with the fluid film" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002468_1077546310372848-Figure7-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002468_1077546310372848-Figure7-1.png", + "caption": "Figure 7. OH-58 A helicopter transmission.", + "texts": [ + "sagepub.comDownloaded from The second reduction occurs through a planetary gear set. The bevel-gear output shaft is splined to a sun-gear shaft. The sun gear drives three planetary gears with a subsequent version of the transmission using four planets. A fixed ring gear meshes with the planets at the top of the drive casing. The planets are attached to the carrier. The carrier is connected to the main rotor shaft. The total reduction of the system is 17.44:1. A system schematic is presented in Figure 7. A more complete system description can be found in Lewicki and Coy (1987). A finite element transmission model was constructed for rotor dynamic analysis, consisting of 186 dof. The complete system parameters and model description are presented in Stringer (2008). The nominal torque acting at the input is 352N/m as in the first application. The model is reduced from 186 to 72 modal dof, a reduction of 62%. For brevity, only the torque response is presented in Figure 8, which shows the lateral displacement at the carrier node of the vertical output shaft" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003127_jsc.0b013e318252ddba-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003127_jsc.0b013e318252ddba-Figure2-1.png", + "caption": "Figure 2. A schematic illustrating the photosensing computerized timer,* which was set 1.5 m above the ground and 10 and 13 cm behind the ball center, which was placed on a baseball tee.", + "texts": [ + " BV just before ball\u2013bat contact was measured with a vertical computerized photosensing timer (BatMaxx 5500; Figure 1. A) Posture for the maximal voluntary isometric contraction conditioning (ISO) with the lead hand (first and third sets). B) ISO with the trailing hand (second and fourth sets). VOLUME 27 | NUMBER 1 | JANUARY 2013 | 217 Journal of Strength and Conditioning Research the TM | www.nsca.com Copyright \u00a9 National Strength and Conditioning Association Unauthorized reproduction of this article is prohibited. Technasport, MN, USA; Figure 2). This device measures the amount of time a moving object takes to intercept two laser beams running to two sensors. To measure the horizontal velocity of the barrel of the bat where the ball\u2013bat contact occurs, two sensors that received vertical laser beams from the device on top were set 10 cm (3.9 inches) and 13 cm (5.1 inches) behind the baseball tee in the pitcher-to-catcher orientation. Reliability of the corrected data can be affected by aspects of swing trajectory, such as slice angle, as well as the location of ball\u2013bat impact in the grip-to-top direction of the bat", + " It has been reported that training programs composed of normal bat swings and other exercise modes, such as swinging different type of bats (3,14), power resistance training (15), and rotational medicine ball exercises (21,22), increase the baseline BV. A similar result was found for the subjects in this study who underwent the ISO warm-up followed by normal bat swings. During the ISO warm-up, subjects performed maximum isometric contraction conditioning activity at the early phase of their bat swing as shown in Figure 2. During the preswing phase and early phase of the batting swing, trailing leg muscles (semimembranosus, biceps femoris, gluteus maximus, and vastus medialis), trunk muscles (erector spinae and abdominal obliques of both sides), and lead arm muscles (posterior deltoid and triceps) reach their peak of electromyographic activity (16). Therefore, the preswing phase and early swing phase may be the crucial period of time for force production in the batting motion. The 8-week ISO training protocol might well improve the maximal strength and rate of force development during the isometric contraction at the posture of the ISO warm-up" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003662_imece2012-89440-Figure7-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003662_imece2012-89440-Figure7-1.png", + "caption": "Fig. 7: Model validation by comparing the numerical and experimental measurements of molten pool half width", + "texts": [ + " Then four measurements, including two of the longest widths and two of the shortest widths, were discarded and the average width was calculated by using the ten remaining measurements. This procedure was performed on three different samples produced at a 10 mm/s scanning speed which resulted in a melt width equal to 0.72 mm. On the other hand, two sets of samples were prepared by changing the electron beam scanning speed to 50 mm/s and 90 mm/s. Width measurements resulted in values equal to 0.68 mm and 0.63 mm, respectively. Figure 7 compares the melt pool half width measurements of the fluid flow model with respect to the experimental analysis. As shown, the numerical and experimental results are in a good agreement. The 7 Copyright \u00a9 2012 by ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 02/01/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use minimum and maximum differences between these measurements are 0.5% and 3.6%, respectively. Therefore, the current model can be used to predict the heat distribution, fluid flow, and melt pool dimensions with an acceptable accuracy" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000084_s00170-005-0312-6-Figure13-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000084_s00170-005-0312-6-Figure13-1.png", + "caption": "Fig. 13 Determination of tilting angle of cutter at the first stageFig. 12 Illustration of collision-free zone", + "texts": [ + " Since the collision-free angle of cutter orientation acquired from the first detecting coordinate system rotates along the XL1 axis of local coordinate system, the tilting angle of the cutter can be acquired from this first detection. In order to avoid the rubbing phenomenon that the cutting speed is zero, proper tilting of the cutter can be used. Therefore, the verification method of this research is to choose a collision-free zone with the least included angle formed on \u2013YL1 axis as the tilting angle \u03b1s of the cutter, as shown in Fig. 13. As to the tilting angle finally selected, this paper shall consider it together with the yaw angle of the cutter in the second stage collision-free zone detection in the next section. 3.2 Determination of collision-free zone at the second stage Upon completion of collision-free detection at the first stage, the collision-free tilting angle zone of the cutter can be acquired. In order to avoid cutter from exceeding the limitation of rotation angle of five-axis machine tool, or to increase the selectivity of cutter orientation for better cutting conditions, yaw angle of the cutter can usually be considered", + " 19, it is found that the collision-free zone is between (\u03b8A)min and (\u03b8C)max, as well as (\u03b8B)max and (\u03b8C)min. Thus, any angles within these collision-free ranges can also become the yaw angle of the cutter. The description in the previous sections shows the determination of collision-free tilting angle and yaw angle range of cutter respectively. Within these ranges, no collision will be caused between cutter and surface. Within the collision-free angle range at the first stage cutter collision detection, the tilting angle range must have the minimum cross-angle with axis YL1 as shown in Fig. 13. The clearance, rcl, is another important factor that affects the inclination angle. Because the cutter grip length Lt is much greater than the clearance, the effect of the clearance may be approximately,\u0394\u03b1s2 = rcl / Lt, as shown in Fig. 20. Hence, the tilting angle of cutter in the second coordinate system is: \u03b1s2 \u00bc \u00f0\u03b8cf \u00dedif \u0394\u03b1s2: (12) In this paper, the original tool spindle axis is considered as the original orientation to determine the cutting tool yaw angle. Since the rotation axis of machine tool is limited by space and layout of various movement axes, the change of rotating axis should be minimized as much as possible so as to prevent the rotating axis from exceeding the limit, decreasing the time of rotation, and increasing the accuracy of product" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002762_1077546312458820-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002762_1077546312458820-Figure4-1.png", + "caption": "Figure 4. Schematic of test rig.", + "texts": [ + " Rotor natural frequency Cylindrical mode Conical mode First bending Second bending Natural frequency (Hz) 7.1 17.8 155.5 471.8 at UNIV ARIZONA LIBRARY on June 21, 2014jvc.sagepub.comDownloaded from required are computed from the overall system transfer matrix, as explained in Section 2.2. The balancing methodology is explained in the flow chart Figure 3. The presented procedure is applied to a vertical rotor rig. The rig consists of a vertical mounted stepped shaft with end discs mounted with suitable bearings as shown in Figure 4. The rotor model is divided into 11 elements consisting of 12 stations with discs at stations 1 and 12. The measurement sensors are located at station 1, 4, 7, 9 and 12, to measure the rotor synchronous whirl response at different speeds. The balancing plane to balance the rotor at first bending critical is located at station 1. The properties of the rotor system with estimated bearing stiffness and damping coefficients are shown in Table 1. The data used for this simulation are from the actual experimental rig", + " For the simulation, the measurements carried out on the experimental rig discussed in section 5 are utilized. The rotor synchronous whirl responses measured at measurement stations 1, 4, 7, 9, and 12 are tabulated in Table 3. The rotor response at slow speed (at 20Hz) is taken as the measure of bow and response at 100Hz (measurement speed) is used to estimate the mass unbalance. The equivalent beam stiffness matrix [Kb] required for simulation (see equation (2)) is derived from the flexibility matrix as explained in Appendix A (equations (A1) and (A2)). For the rotor system shown in Figure 4, the equivalent beam stiffness [Kb] is given by, Kb\u00bd \u00bc 1500 2034 3095 5829 96210 2034 2672 3881 6722 30118 3095 3881 5194 7639 15486 5829 6722 7639 8826 10675 96210 30118 15486 10675 8000 2 66664 3 77775 N=m The unbalance vector Uoif g is estimated at measurement speed of 100Hz using equation (19) and results are given in Table 4. at UNIV ARIZONA LIBRARY on June 21, 2014jvc.sagepub.comDownloaded from The maximum allowable synchronous whirl responses !cr\u00f0 \u00de c at critical speed !cr are assumed for five stations and are given in Table 5" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003242_icra.2013.6630915-Figure4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003242_icra.2013.6630915-Figure4-1.png", + "caption": "Fig. 4. Platform with additional load and corresponding center of mass", + "texts": [ + " Analyzing angular accelerations for determining the inertia tensor is difficult as the orientation workspace of a cable robot is relative small. To introduce a constant acceleration on the platform, a circular path in the horizontal plane is investigated. To analyze the influence of changing loads, additional loads of about 10 kg each are put on the platform. The model of the platform with mass mp with center of mass cp and two additional loads ml, m2 with their centers of mass Cl, C2 respectively, is illustrated in figure 4. The resulting center of gravity Ctotal can be derived by the weighted average (10) depending on the mass and the position of each load. The parametrization of the circular trajectory is shown in figure 5. At the position a and an angular velocity w the translational acceleration is [cos(a)] a = r circle = -r circlew2 sinJ a) (11) where w = const. The resulting dynamic forces according to equation (8) are fdyn,x fdyn,y fdyn,z Tdyn,x Tdyn,y Tdyn,z - cos (a) - sin(a) o cp,z sin (a) -cp,z cos( a) Cp,y cos (a) - cp,x sin(a) (12) where we can identify a common force amplitude of mpr c2rclew2 For the experiment, we chose a diameter of 1" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003560_978-1-4613-4560-2_2-Figure8.15-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003560_978-1-4613-4560-2_2-Figure8.15-1.png", + "caption": "Fig. 8.15. At the instant of immersion there is electro neutrality on both sides of the interface and consequently a zero potential difference and zero field across it.", + "texts": [ + "6b); the concentration-distance profiles were analyzed at t = \u00b0 and at t -+ 00 after the interface has acquired a steady-state electrification and structure. The initial condition shall first be sketched in greater detail. At the instant of immersion, the metal is electro neutral, or uncharged, q.l( = O. Since the interface region as a whole must then be electroneutral, there must be zero excess charge on the solution side of the interface, i.e., iq.l1i = iqsi = O. Hence, there is a zero potential difference t and a zero field operating in the interphase region (Fig. 8.15). This is, of course, a too simple picture. Thus, one has ignored the fact that, even when the metal charge is zero, there is a small net orientation of water molecules and, hence, water will immediately start orienting itself in respect to the surface, which will create a dipole field (cf the asymmetric water molecule, Section 7.5.5). Such aspects can always be brought into a more refined picture. As a first step, simplicity shall have the priority. Under these conditions of zero field, there are no electrical effects and one has pure chemistry, no electrochemistry" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002220_1.4001130-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002220_1.4001130-Figure3-1.png", + "caption": "Fig. 3 Machine tool setting for pinion tooth surface finishing on CNC generator", + "texts": [ + " The six axes of CNC generator are directly driven by the servo motors and are able to implement the prescribed functions of motions. Two rotational motions are provided as the rotation of the workpiece pinion/ gear R3 and the rotation that enables the machine to change the angle between the axes of the workpiece and the tool R2 . The third rotational motion R1 is provided as the rotation of the tool about its axis, and generally it is related to the cutting process. The following coordinate systems are applied to describe the relations and motions in the CNC generator Fig. 3 : Coordinate MARCH 2010, Vol. 132 / 031001-3 6 Terms of Use: http://www.asme.org/about-asme/terms-of-use s t K a d t d m g t r r i T f p f d m t r t t T c y a T a a 0 Downloaded Fr ystems KT1 xT1 ,yT1 ,zT1 and K1 x1 ,y1 ,z1 are rigidly connected o the head cutter and the pinion, respectively. Coordinate system c xc ,yc ,zc performs the swinging base rotation about z10=zc xes with angle , and the translational motions in the X and Y irections, with respect to KT1. System K10 x10,y10,z10 is parallel o Kc xc ,yc ,zc and performs the translational motion in the Z irection" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002900_icma.2013.6617997-Figure11-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002900_icma.2013.6617997-Figure11-1.png", + "caption": "Fig. 11 Radial distribution of flexspline cylinder stress without load", + "texts": [ + " The change trend of flexspline cylinder stress is consistent with the experimental result in reference [15]. It could be found that the fluctuation increases with the heighted load, so the impact of load on the stress fluctuation cannot be ignored. But the average stress increment is less than 5% of the stress without load, so the effect of wave generator has a major contribution to the stress amplitude. And then we analysed the stress of three cross sections to study the radial distribution of flexspline cylinder stress. As Fig. 11, the stress of flexspline cylinder shows dramatic fluctuation. The amplitude is largest and most volatile at the gear circle of cylinder, and the maximum stress is 256.5MPa. The reason was that the flexspline cylinder was deformed as many prisms by wave generator which has a less curvature radius than the cylinder at the major axis, and the concentration effect appeared at the junction of those prisms [12]. So it\u2019s further translated that it\u2019s most possible that destruction of flexspline happened at gear cross section, and the impact of load on the stress of flexspline could not be ignored" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003837_s00161-012-0235-z-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003837_s00161-012-0235-z-Figure3-1.png", + "caption": "Fig. 3 Information increment and the changes of the damage index in the moving system", + "texts": [ + " In the general case h > 1, q > 1 the processes of hardening\u2013softening of the system are determined by the parameter ratio h/q and are described by more complex (S-shaped) curves. For any fixed time moment t/T\u2297 = const, let us introduce a unique characteristic of systems \u2013 the damage index \u03c9 j = \u03c9st \u2212\u03c9 t , (16) where \u03c9 t = \u03c9h or \u03c9 t = \u03c9q is the damage level of a real system, and \u03c9st is the damage level of some ideal system corresponding to that of the real system. Then, it turns out that the values of damage index (16) can belong to three characteristic classes: \u03c9 j > 0;\u03c9 j < 0 and \u03c9 j = 0 (Fig. 3). There are the same three classes are for information increment I (Fig. 3). This means the existence of dependence between \u03c9 j and I . This dependence may be formulated as a first approximation in the following way I (t) = \u2212k \u00b7 trB \u00b7 t = aS \u03c9 j (t), (17) where aS is the transition function between I and \u03c9 j . The form of function aS has not yet been found, but its sense is that it transforms damages (15) into information function (14) through damage index (16). This is just the simplest solution of problem (10). Figures 2 and 3 present the graphical illustration of Eq", + " 2, ten diagrams) is located in the common plane, whose abscissa axis is the trend of the matrix B, and the ordinate axis is its determinant det B. One can plot the graph of the function detB = (trB)2; it is the parabola in Fig. 2. Then, the time diagrams of the second-order dynamic system are located relative to this parabola, as shown in Fig. 2. It is seen that four groups (1, 2, 3, and 4) of the diagrams are available, each of which lies in the characteristic zone of the plane depending on the ratio and signs of det B and tr B. Figure 3 compares the time diagrams of system (12a) presented in Fig. 2 with the plots of the information function I (t) and the function of accumulation of the damageability \u03c9 j (t). The notations of the data groups in Fig. 3 are the same as in Fig. 2. The analysis of the data plotted in Figs. 2 and 3 yields three general conclusions. First, the left branch of the parabola plotted in the det B\u2014tr B coordinates illustrates the stab. Dynamic processes that generate a positive linear information function due to the developing of non-linear hardening of an object. Second, the right branch of the parabola plotted in the det B \u2014tr B coordinates corresponds to the unstable dynamic processes that generate a negative linear information function due to the developing of non-linear softening of an object", + " This motivates quantitative differences in the trajectories of the systems to be compared. On the other hand, the principal difference is seen in their behavior: when the entropy of the thermodynamic system attains, for example, a local maximum (equilibrium state), the mechanothermodynamic system can have no such maximum\u2014it will be in the non-equilibrium state. This is observed in the cases of converging (Fig. 7a) and diverging (Fig. 7b) processes of motion (Fig. 2) and for systems hardening and softening in time, in which new positive or negative information is generated (Fig. 3). Work [6] contains some generalizations regarding a comparative behavior of thermodynamic and mechanothermodynamic systems. Consider the example of entropy calculation for the tribo-fatigue system consisting of friction pair with the elliptic contact of the ratio between smaller b and bigger a semi-axes b/a = 0.574. One of the elements of the friction pair is loaded by non-contact bending. An example of such an element is the shaft in the roller/shaft tribo-fatigue system. Specific damage \u03c9 in (7) of elementary dW which can be presented as a ratio between current parameter \u03d5i j of mechanical state (stresses and strains) of a system and its limiting value \u03d5(lim) i j " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000723_j.ijfatigue.2008.01.003-Figure15-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000723_j.ijfatigue.2008.01.003-Figure15-1.png", + "caption": "Fig. 15. Scheme of an inclined edge crack in a half-space [9].", + "texts": [ + " Changes can also be observed ahead of the dent and at the dent\u2019s center, where a relaxation of the stress is also verified. This phenomenon can be justified based on the fact that the material in the shoulder is compressed while in the remaining sites it expands. It was found that with more cycles of over-rolling, the computation time increased considerably and small changes on the residual stress distribution were found. Stress intensity factor\u2019s (SIFs) calculation was based on a model described by Fletcher and Beynon [9], which uti- lizes the Green functions presented by Rooke et al. [8]. In this model (see Fig. 15), the Hertzian normal pressure and the fluid pressure at the crack mouth are considered. However in this work, besides considering these two parameters, the residual stress distribution obtained from the finite element analysis is also included. The Hertzian pressure moves in a range e = \u00b13b with increments of b/10. SIFs in this case are calculated using the edge Green functions (presented graphically by Rooke et al. [8]) and are given by: KPH N Hertzian load \u00bc 1ffiffiffiffiffi pa p Z l1 l2 P \u00f0x\u00deGP left N \u00f0x\u00dedx \u00fe Z l4 l3 P \u00f0x\u00deGP right N \u00f0x\u00dedx ; \u00f04\u00de where N = (I, II), H = (left, right), a is the crack length, x is a general position on the surface, P(x) is the Hertzian pressure distribution (see for instance Johnson [13]), GP N are the edge Green functions, and l1, l2, l3 and l4 are the limits of integration" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003662_imece2012-89440-Figure8-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003662_imece2012-89440-Figure8-1.png", + "caption": "Fig. 8. The effect of electron beam scanning speed on temperature distribution and melt pool width, a): temperature distribution, b): melt pool width, 1) scanning speed= 10 mm/s, 2) scanning speed= 50 mm/s, 3) scanning speed= 90 mm/s", + "texts": [ + " As shown, the numerical and experimental results are in a good agreement. The 7 Copyright \u00a9 2012 by ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 02/01/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use minimum and maximum differences between these measurements are 0.5% and 3.6%, respectively. Therefore, the current model can be used to predict the heat distribution, fluid flow, and melt pool dimensions with an acceptable accuracy. 4- RESULTS AND DISCUSSIONS Figure 8a shows the effect of the electron beam scanning speed on the heat distribution. As it is shown, by increasing the scanning speed, a high temperature area is elongated in the electron beam moving direction, while its width is reduced. Also, the maximum temperature recorded for scanning speeds of 10 mm/s, 8 Copyright \u00a9 2012 by ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 02/01/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use 50 mm/s and 90 mm/s were 2285 \u00b0K, 2268 \u00b0K and 2224 \u00b0K, respectively", + " By increasing the scanning speed, the material under the beam trace have less time to be irradiated by the electron beam, and so less energy will be absorbed by it. This results in decreasing the maximum achievable temperature in the domain. On the other hand, higher beam speed results in irradiating a longer length of material along the moving direction. So, in the model with the lowest beam scanning speed, heat is more concentrated unlike the case of the highest beam scanning speed where heat is more distributed along the scanning direction. Figure 8b shows the effect of the scanning speed on the melt pool width. The results are in accordance with temperature distribution observations. As explained earlier, a higher scanning speed is accompanied by a lower heat input, which means the same amount of energy is applied to a larger volume of material. Therefore, a smaller portion of this volume reaches the critical temperature, which is required for phase transformation. The desired critical temperature for phase transformation in this study is the melting temperature. According to the description above, by increasing the beam scanning speed, the melt width decreases. Moreover, as shown in Figure 8b, by decreasing the beam scanning speed, the melt pool will have a more symmetrical shape along the direction normal to the scanning axis. Figure 9 shows the fluid flow pattern observed in the model at 10 mm/s electron beam scanning speed. As it is shown, the melted material starts to move upwards from the melt pool center (Figures 9a and 9b), and it is directed towards its edges. The negative temperature coefficient of surface tension for Ti-6Al-4V means the surface tension value decreases by increasing the material temperature" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000823_s11044-008-9122-6-Figure5-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000823_s11044-008-9122-6-Figure5-1.png", + "caption": "Fig. 5 The six-link SSRMS", + "texts": [ + " It is pointed out here that Cyril [13] had observed artificial damping in his simulation results, which are absent using the present formulation. This can be attributed to the numerical stiffness present in the original-NOC based nonrecursive formulation proposed by Cyril [13]. The present DeNOC based recursive algorithm avoids such artificial stiffness. These aspects are elaborated in Sect. 7. 6.2 Space shuttle remote manipulator system robot Next, the 6-link Space Shuttle Remote Manipulator System (SSRMS) [13, 45] is considered, whose 2nd and 3rd links are assumed flexible due to its architecture. Figure 5 shows the SSRMS whose DH and other parameters are given in Table 2. Forced simulation is performed using the scheme outlined in Fig. 6. The joint trajectories, given by (45), are prescribed for a representative maneuver of the SSRMS, considering all links are rigid. The joint torques are then computed using the inverse dynamics algorithm, developed separately, for the SSRMS robot, considering all of its links as rigid. The joint torques thus obtained are shown in Fig. 7 \u03b8i = 0.05 [ t \u2212 5 \u03c0 sin ( \u03c0 5 t )] , for i = 1, " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003201_j.mechmachtheory.2013.04.003-Figure3-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003201_j.mechmachtheory.2013.04.003-Figure3-1.png", + "caption": "Fig. 3. Difference between variational and discretized formulations.", + "texts": [ + " As p \u2192 \u221e (or t \u2192 \u221e), we know from elementary calculus that tanh(p/L) \u2192 1 and sech(p/L) \u2192 0 which gives x L;\u221e\u00f0 \u00de \u00bc p\u2212L; y L;\u221e\u00f0 \u00de \u00bc 0 \u00f024\u00de From the above, it is clear that as time increases, the straight line or the rigid link aligns with the perturbation direction, in this case the X-axis. It has not been possible to obtain analytical solution for Eq. (11) except for a simple straight line as shown in the preceding section. Oneway to solve the problem for an arbitrary curve is to discretize the curve into finite number of straight line segments. The difference between the continuous (variational) formulation and the discretized formulation is schematically shown in Fig. 3. In Section 3.1, we demonstrated that for a straight line the motion of the trailing end with L2 metric or velocity minimization is given by the tractrix Eq. (23). As shown in the right-hand side of Fig. 3, a known perturbation is given to the 1st point (the leading end) of the initial curve. The L2 metric minimizing the motion of trailing end of the 1st segment is computed in closed-form with Eq. (23) and this is the perturbation for the leading end of the 2nd segment. Sequential iteration along the linear segments up to the other end, generates the motion of the entire discretized curve or the nth point. This approach is termed as sequential optimization and is the same as the strategy used for resolution of redundancy in hyper-redundant robots (see [14\u201318])" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003331_indin.2012.6301378-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003331_indin.2012.6301378-Figure1-1.png", + "caption": "Figure 1. Bearing defects illustration", + "texts": [], + "surrounding_texts": [ + "Bearing deterioration is commonly categorized as either single-point defects (localized defects) or general roughness reduction. General roughness reduction gradually develops in a quite long term, and is not so hazardous as localized defects, which will produce excessive vibration and ruin the bearing in a short time. So bearing fault detection and diagnosis mostly concern the single-point defects [7]. 978-1-4673-0311-8/12/$31.00 \u00a92012 IEEE 580 Single-point defects generate an excitement similar to a periodical pulse train corresponding to the passage of the rolling part over the mating part in load area. Depends on the faulted element (inner race, outer race, cage or elements), the period of this excitation varies. According to rolling bearing kinematics and certain reasonable hypothesis (no slip, etc.), the four characteristic fault frequencies, as expressed in [8], are calculated with the equations below: \u2022 Cage fault frequency: !!\"! ! ! !! !!!!!! !\"# ! (1) \u2022 Outer race fault frequency: !!\"#! !! ! !! !!!!!! !\"! ! (2) \u2022 Inner race fault frequency: !!\"#! !! ! !! !\"!!!! !\"# ! (3) \u2022 Ball fault frequency: !!\"! !! !!! !! !! !! !! ! !\"#! ! (4) Where FR is the rotation speed of the inner race (with the hypothesis: the inner race rotates, and the outer race is at rest), NB is the number of balls, DB is the ball diameter, DP is the ball pitch diameter, \u03b8 is the ball contact angle. A schematic view of rolling element bearing is given in \u201cFig.2\u201d. In the following part, two approaches are given to analyze the vibration signal from a machine: the time domain techniques used for inspection, and frequency domain techniques used for diagnosis." + ] + }, + { + "image_filename": "designv11_7_0002727_piee.1967.0214-Figure7-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002727_piee.1967.0214-Figure7-1.png", + "caption": "Fig. 7 Relationship between air-gap flux and m.m.f. a Air-gap line b Open-circuit characteristic", + "texts": [ + " One means of finding this relationship lies in the open-circuit magnetisation curve for the generator, for, at rated speed in the steady-state, v9 = XaJfd (54) 1120 calculated; but where it is less significant, as it is in cylindricalrotor machines, the open-circuit magnetisation curve provides a convenient method of deriving a general relationship between flux and magnetising force. 4.2 Variation of mutual inductance from open-circuit characteristic Given the unsaturated value of mutual inductance, its value at a point on the nonlinear portion of the flux/m.m.f. relationship may be found in the following way, with reference to Fig. 7. If 4ius is a flux level at which the flux bears a linear relationship to m.m.f. and I/JS is a flux level at which this linearity is no longer maintained: and I(JS = LadHatX (56) (57) PROC. IEE, Vol. 114, No. 8, AUGUST 1967 4 0 2 0 \\ \\ 1 1 substituted into eqn. 61, which on rearrangement gives 5 10 number of iterations 15 Fig. 8 Relationship between least-square error and number of iterations test O computed a Goldington b Belvedere therefore and then J^nrlt\\~, $us = XL ad (58) (59) For a known \\jjs, it is therefore required to find the value of I/JUS that would obtain if the magnetic-circuit characteristics were linear" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002885_s00158-012-0836-y-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002885_s00158-012-0836-y-Figure2-1.png", + "caption": "Fig. 2 Finite element model with boundary conditions", + "texts": [ + " To reduce computation time, Lanoue (2008) has demonstrated that it is possible to achieve the same level of precision as that of a full model with a 1-degree slice subjected to cyclic symmetry conditions. Furthermore, this slice can be modeled with only one element in the circumferential direction, which reduces the number of required elements, and consequently, calculation time. The software chosen for the simulations was Ansys V11. The APDL (Ansys Parametric Design Language) version allows developing a generic model with a robust mesh, despite the variation of dimensions. Brick with 20 nodes (Solid186) was the type of element used. The area shown in Fig. 2 is of great interest because it is where the fatigue failure occurs. Since the model is subjected to cyclic conditions, it becomes possible to simulate the alternating torque by using tangential forces. Other boundary conditions are also shown in Fig. 2 Following Lanoue\u2019s (2009) recommendations, the contact algorithm chosen for this study was Augmented Lagrangian. This algorithm allows for controlling maximum penetration and maximum elastic slip. Other simulation options ensuring the convergence of the model are given in Table 3. 2.3 Selection of fatigue criterion As mentioned before, the interference fit assembly is subjected to alternating torsional loads causing fatigue failure. Fatigue life approximations can be obtained by applying a fatigue criterion to the results of the finite element analysis" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002287_iros.2012.6385948-Figure2-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002287_iros.2012.6385948-Figure2-1.png", + "caption": "Fig. 2. Partial Dynamics: upper-limbs impedance system", + "texts": [ + " In the joint space we write \u03c4 cmd such that Hq\u0308cmd + N + G = \u03c4 cmd + JT contFcont (19) and the disturbed dynamics writes, assuming no configuration change, Hq\u0308 + N + G = \u03c4 cmd + JT contF \u2032 cont + JT e Fext, (20) where H,N and G are respectively the mass and centrifugal/Coriolis matrices, G the gravity vector, JT cont, Fcont and JT e , Fext the jacobian and efforts at the contacts with the ground and at the effector, respectively. Considering the main parts involved in the manipulation task, we isolate the partial mechanical system composed of the serial chain of bodies from the end-effector to an arbitrarily selected parent body (in this case, the chest), as shown as an example in Fig. 2, subject to the dynamics H\u0303\u00a8\u0303q + N\u0303 + G\u0303 = \u03c4\u0303 cmd + JT e Fext (21) while Eq. (19) is simply written in this problem H\u0303\u00a8\u0303qcmd + N\u0303 + G\u0303 = \u03c4\u0303 cmd (22) The a\u0303 notation denotes the selected subset of a due to the reduction of the problem dimensionality1. From these two previous equations we can derive the dynamics of the disturbance resulting from an external force at the end-effector Mex\u0308 = Fext \u2212MeJ\u0307eJ \u2020 e(x\u0307\u2212 x\u0307cmd) (23) + Ke(x des \u2212 x) + Ce(x\u0307 des \u2212 x\u0307) + Mex\u0308 des where Me \u2261 (JeH\u0303 \u22121JT e )\u22121, Ke \u2261 KpMe, Ce \u2261 KdMe, 1Note that, although the manipulation model is restricted to the upperbody dynamics, the control formulation providing input torques considers whole-body balance and manipulation" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000964_j.mechmat.2008.09.004-Figure15-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000964_j.mechmat.2008.09.004-Figure15-1.png", + "caption": "Fig. 15. Mutual arrangement of vectors d~eS N and d~S under additional loading.", + "texts": [ + "2) is valid for one plane, the vector d~eS, being the sum of components d~eS N , also satisfies this inequality or, in other words, it makes an acute angle with vector d~S. Therefore, our object now is the angle, g, between vectors d~eS N and d~S. The projections of the vector d~eS N on S1- and S3axis can be determined on the base of Eqs. (3.8), (3.12) and (3.31): d~eNS 1 \u00bc duN cos a cos b cos k~g1; d~eNS 3 \u00bc duN sin b cos k~g3: \u00f08:3\u00de Eq. (8.3) gives that d~eS N3 d~eS N1 \u00bc tan H \u00bc tan b cos a : This formula determines the angle H which the increment vector d~eS N makes with S1-axis. Angles H, d, and g are shown in Fig. 15, from which it is evident that g = p/2 + d H, and the angle g must satisfy inequality g 6 p/2 or d 6 arctan tan b cosa : It is sufficient to show that d 6 b for a \u00bc 0 \u00f08:4\u00de because 0 < cosa 6 1 for a1 6 a 6 a1. As follows from Fig. 13a, the inequality (8.4) is always fulfilled because angle b falls into the region d 6 b 6 b1 for any plane located on the endpoint of vector d~S. For the planes tangential to sphere (3.23) and for the boundary planes constituting the generator of cone (b = \u00b1b1), Drucker\u2019s postulate is automatically satisfied because the incremental strain vectors are perpendicular to these planes" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000528_6.2007-6460-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000528_6.2007-6460-Figure1-1.png", + "caption": "Figure 1. Geometric Configuration of the Smart UAV", + "texts": [ + " In the helicopter mode, control is provided by rotor-generated forces and moments while in the airplane flight mode, primary control is provided by conventional aerodynamic control surfaces. T American Institute of Aeronautics and Astronautics The Smart UAV os capable of hovering for approximately one hour at sea-level starting at its design gross weight of 1,000 Kg. In the airplane mode, it can fly at speeds greater than 500 km/h. The detailed specification of the Smart UAV is given in Table 1 and Fig. 1 shows its drawing. As given in Table 2, in helicopter mode, pitching moment is generated by applying longitudinal cyclic pitch change to the rotor blades. This is accomplished by the pitch control input. Yawing moment is generated by the application of differential longitudinal cyclic pitch change to the rotors. This is accomplished by yaw control input. Rolling moment is generated by applying differential collective pitch change to the rotors. This is accomplished by the roll control input. Motion of the collective/power stick changes engine power and rotor collective pitch to provide vertical thrust control" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002010_1.4002342-Figure9-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002010_1.4002342-Figure9-1.png", + "caption": "Fig. 9 Interpolated shapes \u201estock and tongue rails\u2026", + "texts": [ + " In this figure, ail cross-sections at the middle of sections A and B and sections and C are shown. As can be observed from these figures, the rst derivatives obtained using the direct interpolation and the ayer spline are in good agreement even around regions, where ournal of Computational and Nonlinear Dynamics om: http://computationalnonlinear.asmedigitalcollection.asme.org/ on 01/ changes in curvature are significant. The three-dimensional rail shapes obtained using the interpolation procedure is presented in Fig. 9. Using the stock and tongue rail profiles, the contact geometry in turnout section can be analyzed using the two-point contact geometry procedure discussed in Sec. 3. 4.2 Two-Point Contact Analysis on Turnout. In the numerical example, the six rail profiles along the track are used in order to discuss the contact transfer from the stock to tongue rails in APRIL 2011, Vol. 6 / 024501-3 27/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use t i t t t w i c w t c s w t d a l 0 Downloaded Fr urnout section using the three different wheel profiles, as shown n Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0002662_j.jcsr.2011.11.011-Figure6-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0002662_j.jcsr.2011.11.011-Figure6-1.png", + "caption": "Fig. 6. Generalized force-displacement curve for COMBIN39 [13].", + "texts": [ + " Therefore the values of two other translational degrees of freedom and also three rotational degrees of freedom at two nodes of the element must be identical. This is done in ANSYS software using Coupling capability. In order that each of the COMBIN39 elements be able to model the desired behavior correctly, nodal coordinate system of their nodes was rotated so that their active (not coupled) translational degree of freedom sat along the longitudinal axis of the adjacent PIPE20 elements. As shown in Fig. 6, force-displacement curve for the COMBIN39 element is defined through connection of a number of points. The points on this curve (D1, F1, etc.) represent force versus relative displacement. The main purpose of the present study is determination of coordinates of these points by means of finite element model updating. To do so, force coordinates of the points have been specified and displacement coordinates are determined after finite element model updating of the double layer grid. The number of points used to define the force-displacement curve was selected according to software restrictions, required accuracy and computational time", + " Therefore, the axial stiffness of ball joint system in respect to which the responses model of the double layer grid. are sensitive, was selected for modification in FEMU process of the double layer grid. As was seen in Subsection 4.2, in the FE model of the double layer grid, axial stiffness of each joint has been modeled via the force-displacement relationship of the spring element. In ANSYS software this relationship is defined through connection of some points whose coordinates represent force versus displacement (Fig. 6). While force coordinates of the points on the forcedisplacement curve of the ball joint system had been selected in advance, the amount of displacement between the two adjacent points was considered as updating parameters. The updating parameters vector is shown with \u03b8={\u03b81,\u03b82,\u2026,\u03b8q} with q representing number of entries in this vector (number of updating parameters). The parameters \u03b81 to \u03b8q/2 pertain to the behavior of joint in the compressive zone, and the parameters \u03b8(q/2)+1 to \u03b8q pertain to the tension zone" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003609_9780470929421.ch1-Figure1.4-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003609_9780470929421.ch1-Figure1.4-1.png", + "caption": "FIGURE 1.4 Standard exchange current dependence on \u25e6GHad at equilibrium conditions for three partial reactions. (Data adapted from Parsons and Bockris [30].)", + "texts": [ + " The term g0 3 is the Gibbs energy of activation when the Gibbs energies of the initial and final states are equal. These lead to i0,3 = pH2 exp ( \u2212 (1 \u2212 \u03b3) go kT ) [ 1 + p 1/2 H2 exp ( \u2212 g0 kT )]\u22122 G3 (1.38) G3 = 2e0 ( kT h ) exp ( \u2212 g0 3 kT ) (1.39) Equation (1.38) has the same form as (1.28) and (1.32), but if \u03b1 = \u03b2 = \u03b3 , the slopes of the branches of the plots away from the maximum are twice those for the other two reactions. Gerischer [30] reached this conclusion by similar arguments, and his result is shown in Figure 1.4, in which he assumed that the maximum was the same for the three partial reactions. Parsons [32] used the well-established experimental observation that the rate of hydrogen evolution was the greatest on Pt, which must then be at the peak of the volcano. Also, the experimental results of Frumkin Dolin and Ershler [35] and those of Azzam and Bockris [36] suggest that the exchange current is the greatest for the discharge reaction and the least for the ion+atom reaction. Parsons also used the Te\u0308mkin model [37] for a heterogeneous surface which leads to an adsorption isotherm and kinetic equations which differ from the Langmuir equations in the region of moderate adsorption" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000964_j.mechmat.2008.09.004-Figure10-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000964_j.mechmat.2008.09.004-Figure10-1.png", + "caption": "Fig. 10. Displacements of planes with ~m and ~m normal vectors.", + "texts": [ + " the increments of plastic strain components d~eS 1 on the opposite sides of S3-axis are equal in magnitude and opposite in direction, and their summation (integration) leads to mutual elimination (this is valid for components d~eS 2 as well). Consequently, we have only one nonzero strain component, eS 3, meaning that the total strain vector is directed along S3-axis. Integrating in (4.6) gives eS 3 \u00bc a0F\u00f0sS=sxz\u00de; \u00f04:7\u00de where a0 \u00bc ffiffiffi 2 p psS 3r ; F\u00f0x\u00de \u00bc arccos x x 2 ffiffiffiffiffiffiffiffiffiffiffiffiffi 1 x2 p \u00fe x2 ln 1\u00fe ffiffiffiffiffiffiffiffiffiffiffiffiffi 1 x2 p x ; \u00f04:8\u00de and 0 6 x 6 1; F\u00f01\u00de \u00bc 0; F 0\u00f01\u00de \u00bc 0; and F !1 for x! 0: 3 For simplicity, there is only one tangent plane in Fig. 10. As is well known, the hodograph of stress deviator vector~S is a straight line in the Ilyushin deviatoric stress space at proportional loading. Assuming that the stress deviator vector ~S lengthens along the line arbitrary oriented in the subspace S3, we rotate the coordinate system to align the axis S3 with the vector ~S, i.e. to obtain an analog of pure shear (when stress deviator vector possesses the only nonzero component). Eqs. (4.7) and (4.8) will determine plastic strain components, eS0 3 , in the indicated new coordinate system if we replace the shear stress sxz by the modulus j~Sj", + " Therefore, similarly to the flow theory with kinematic hardening, we can suggest that the displacement DH N is the manifest of the latent internal micro-stresses, which arise in a body at plastic flow and do not disappear after unloading. Since experiments on mono-crystals show that the Bauschinger effect is observed regularly, we can apply Eq. (6.1) on micro-level. Let us construct the loading surface, employing Eq. (6.1), for the case of pure shear. The vector ~S\u00f00;0; S0\u00de, during its elongation from point A to point A1, shifts the tangent plane (line) from its initial position, marked by B, to the position B1 (Fig. 10)3. Since it is those planes for which k = 0, i.e. planes tangential to the yield surface (sphere) in S3, that determine the transformation of the sphere (3.23), we will use Eqs. (3.28), (3.29) and (6.1) at k = 0, i.e. HN = hm. The distance covered by tangent plane oriented by the normal vector ~m, Dhm = BB1, from their initial positions, h0 \u00bc ffiffiffi 2 p sS, to those determined by current vector ~S, hm, is calculated as Dhm \u00bc S0 sin b ffiffiffi 2 p sSforb1 6 b 6 p=2 and k \u00bc 0; \u00f06:2\u00de the distance Dhm is equal to zero for 0 6 b < b1, where angle b1 is calculated by Eq", + "1) for k = 0 and Eq. (6.2) give the absolute value of distance to this plane: h m \u00bc ffiffiffi 2 p sS \u00fe Dh m \u00bc ffiffiffi 2 p sS Dhm \u00bc 2 ffiffiffi 2 p sS S0 sin b; b1 6 b 6 p=2: \u00f06:3\u00de The equation of plane (line) in S1S3-plane from the range b1 6 b 6 p/2 with distance in Eq. (6.3) has the form: S1 cos b\u00fe S3 sin b\u00fe 2 ffiffiffi 2 p sS S0 sin b \u00bc 0: \u00f06:4\u00de The envelope curve of the set of lines in Eq. (6.4) is the circle, S2 1 \u00fe \u00f0S3 S0\u00de2 \u00bc R2; R \u00bc 2 ffiffiffi 2 p sS; whose center is situated at point A1 in Fig. 10. Since the loading surface is symmetrical above S3-axis, it is clear that, in three-dimensional space, we have S2 1 \u00fe S2 2 \u00fe \u00f0S3 S0\u00de2 \u00bc 8s2 S : \u00f06:5\u00de Therefore, the loading surface (Fig. 11) consists of three parts: the cone constituted by boundary planes (b = b1) located on the endpoint of the vector ~S, the initial sphere (3.23), and the sphere determined by Eq. (6.5). The subsequent yield stress, SS, in opposite direction to the vector ~S can be calculated from Eq. (6.3) as SS = h m(b = p/2): SS \u00bc S0 2 ffiffiffi 2 p sS; \u00f06:6\u00de where S0 P ffiffiffi 2 p sS" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0001237_19346182.2008.9648483-Figure1-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0001237_19346182.2008.9648483-Figure1-1.png", + "caption": "Figure 1. Cave setup for the rowing simulator.", + "texts": [ + " Consequently, four DOF of the oar (three rotational DOF and one translational DOF along the longitudinal oar axis), as well as the user\u2019s body movement, have to be measured. Furthermore, the mechanical properties of the oar and the oar lock should be based on those of a competitive rowing boat. The acoustic and visual feedback should be synchronized with the movements in all DOF. Optical flow should provide feedback on the boat movement. The rowing simulator was integrated in an already existing Cave setup (Figure 1). This Cave comprises three large projection screens (4 3m, projectors; Projectiondesign, Fredrikstad, Norway) which surround the user. Furthermore, a closed ring of loudspeakers (112 speakers and four subwoofers; Iosono GmbH, Erfurt, Germany) surrounds the Cave. In the plane of this ring, virtual sound sources can be generated at arbitrary positions by applying the method of wave field synthesis. The measurement setup of the rowing simulator consists of a shortened, instrumented single scull boat mounted on a podium inside the cave" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0003593_b978-1-78242-074-3.00011-8-Figure11.6-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0003593_b978-1-78242-074-3.00011-8-Figure11.6-1.png", + "caption": "Figure 11.6 Schematic of the multicomponent graded structure fabrication by 3D laser cladding. Longitudinal L and transversal T [22].", + "texts": [ + "\u039cexAly+Q, where Q is the reaction thermal effect. Under the Al selection as the matrix basis, besides problems with the energy transfer from the LI to the material, another factor will appear. Aluminium has a low melting point in comparison with the refractory metal melting point (cf. 660 against 1537 C for iron), and it will more effectively remove a heat due to the higher thermal conductivity, which ultimately will require a larger laser energy input. The method of FGS fabrication used in the present study is schematically presented in Figure 11.6. The hatching distance was 2 mm, the layer depth was 1 mm, and the powder feeding rate was 10 g/min. The layers were made out of Me\u00bc (Ti, Fe, or Ni) and Al powders on a related substrate by the following strategy: the first two layers were of pure Me, the next two consisted of 70% Me+30% Al, the third couple of layers were of 50% Me+50% Al, and lastly the upper 7th and 8th layers had the ratio of 30%Me+70% Al. Each second layer was formed on the bottom layer after its turning by 90 . Argon was the carrying gas", + " The powders enumerated below were used for the experiments. The iron powder had 99.76 wt.% of Fe (TLS Co.). The alloy 2024 (TLS Co.) was used as the Al powder, which had the following chemical composition: Cu 3.8-4.9, Mg 1.2-1.8, Mn 0.30-0.9, Si 0.50, Fe 0.50, Zn 0.25, Ti 0.15, Cr 0.10 wt.%, bal. Al. The powder particles were mainly spherical with the size of 80-100 mm for 95% of them. Steel substrates of a square shape with a 50-mm width and 5-mm height were used. The FGS fabrication scheme in the Fe-Al system is shown above (see Figure 11.6). Figure 11.12a-c represents the results of optical metallography. As before, the photo series was selected in order to exhibit the characteristic microstructures from the bottom (a), middle (b), and top (c) parts of the cladded layers, that is, the parts where the weight ratios of Fe-Al in powder were 3:1, 1:1, 1:3, respectively. The bottom cladding layers (Figure 11.12a) have a fine-crystalline structure with an almost uniform morphology mainly typical of single-phase iron alloys. In themiddle layers (Figure 11", + " Diamalloy is equivalent to the Inconel 525 alloy, which was studied earlier in the DMD process [53]. It combines high strength, creep resistance, and stability to oxidation and corrosion; therefore, it is widely used in space, chemical, and naval applications. Therefore, the intermetallide phase\u2019s generation of a nickel aluminide into this superalloy matrix is an interesting task, substantially changing its mechanical properties. The FGS fabrication scheme in the Ni-Al system was shown above (Figure 11.6). The optical metallography is presented in Figure 11.17. As described earlier, the photographs are selected in order to show the characteristic microstructures based on the lower (a), middle (b-c), and upper (d) parts of the FGS after 3D laser cladding, that is, where the proportions of the powdered Ni+Al 3:1; 1:1, and 1:3 by weight ratios were comprised. Under large magnification, these layers are presented on the inserts a1 for (a); b1 for (b); c1 and c2 for (c) and d1 for (d). In the lower layers in the photo (Figure 11" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_7_0000453_0308-9126(81)90078-x-FigureI-1.png", + "original_path": "designv11-7/openalex_figure/designv11_7_0000453_0308-9126(81)90078-x-FigureI-1.png", + "caption": "Fig. I 0 Directions of B end H vectors and their components in the principal direct ions", + "texts": [], + "surrounding_texts": [ + "I 1\nn.-\"\n. / x f ~ \" \" 2 - - ~ ~ \\ H (A/rn, RMS)\no 4,50\n[3 840 z~ 1250\ni x , 6 5 o\nO.OI\nOo I I I l I 500 I000 1500 2000\nMicrostrain\nF i g l 5 R v vs strain for 4-inch x \u00bd-inch bar for strain beyond the yield point\nabout the yield point of this particular steel. For strains larger than the yield point value Rv decreased.\nNote that the maximum values of Rv (in Figure 5) were larger than in Figure 4 for all four different field strengths. Yet, conditions were apparently identical. This variability is characteristic of all tests with the rotation rig: the steel's magnetic properties clearly differ from point to point.\nTraces 1 to 8 in Figures 8 and 9 show the corresponding results for the compression face of the bar. In all cases the core magnetizing current was adjusted to give a constant field strength of 800 A/m (Rr~S). For comparison, the coercivity of the steel was about 400 A/m. A negative value of Rv means that the phase of the voltage in SCn was 180 \u00b0 relative to that for a positive value of Rv: this phase reversal enabled compression to be distinguished from tension.\nDiscussion on the results o f the b e n d i n g test\nThe results show clearly that on return to zero bending moment there was residual stress on each face of the bar, of opposite sign to the applied stress. Thus the upper face was in residual tension and the lower one in residual compression. Whether the residual tension was less than\nthe residual compression, as is suggested by the graphs (R v was 0.020 for the upper face and 0.030 for the lower face) is not known. It was not possible on this sample to reduce the noise in SCn to less than Rv = 0.005 and since the residual ratios differ by about twice this (0.030-0.020), 0.005 added to the tension reading and subtracted from the compression reading would make them about equal. From the symmetry of the bending, the residual stresses should be equal, since the yield stresses of steel are equal in compression and in tension.", + "R v vs bending moment for 4-inch x \u00bd-inch bar. Rotat ion\nrig on the compression face, two more loading (5, 7) and unloading (6, 8) cycles f rom new\nRotation of magnetic field by an anisotropic ferromagnetic material\nTheory of basic phenomena\nTests with the rotation rig on mild steel showed that when it is magnetized parallel or normal to the direction o f applied tension there is no rotation of the field strength, ie there is no flux through search coil SCn. Furthermore, the flux in the steel is parallel to the field (this was verified by use of search coils threaded through fine holes in the\nsteel). In all other directions B and H are not parallel to each other. Thus there are two orthogonal directions (sometimes known as the principal directions) such that along them B and H are parallel and are related by equations\nBI = /21H1\nB2 = /22H2\nSuppose that/22 is in the direction of maximum permeability and/21 is in the direction of minimum permeability, as shown in Figure 10. I fB exists at angle ~ to the/22 direction it can be resolved along the principal directions thus:\nBI = B sin~\nB2 = B cos~\nand so\nHI = (B//21) sin\nn 2 = (B//22) COS~\nThe resulting field is at an angle (ff + 5) to/22 where tan(~k + 5) = (/22//21) tanff\nor\n[(/22//21) - 1]tanff tan5 = (1)\n1 + (/22//21)tan2~\nIf @ = 45 \u00b0 then\n/22//21 - 1 tan~i - (2)\n/22//21 \"i\" 1\nThe effect of the B vs H loop\nIn deriving Equations 1 and 2 no assumptions were made about the values of p2 and/21 . As the B vs H loop is traversed the permeability varies with the field strength H and there is also hysteresis that causes negative values of permeability for the second and fourth quadrants of the B vs H loop.", + "In order to use the equations, B vs H loops are required for the principal directions. Suppose the flux density is always at 45 \u00b0 to the #2 direction (ie ~ = 45\u00b0). As the flux density B is varied, the components in the principal directions are B2 = B1 = 0.707 B, and the corresponding values of H (//2 and HI ) are obtained from the B vs H loops in these two directions. Corresponding values of #2/#1 are thus given by (B2/1-12 )/(Bt/HI ) = H1/1t2. Figure 11 shows B vs H loops in the principal directions for an annealed sample of mild steel that was tensioned in the #2 direction in order to make it anisotropic. The angle of rotation (8) of the magnetic field, calculated from these two loops, is shown in Figure 12a for one half of a complete cycle of magnetization. Figure 12b shows the corresponding values of the amplitude of the field. The flux through SCn is proportional to H sin~, and is shown in Figure 12c (full line).\nGoing one stage further, with AC magnetization, i fB were to vary sinusoidally (B = B sinwt), the voltage induced in SCn would be proportional to\nd d (Hsin~i) = co/~cos(u~t) ~ (HsinS).\ndt\nInstead of working out this last expression in order to compare it with the experimental voltage waveform, H sin5 was measured directly with a Hall plate. The result is shown in Figure 12c (dashed line), and has a peak value of 330 A/re. The predicted waveform has a peak value of 380 A/m. Measurements also showed that it was impossible to constrain B at 45 \u00b0 during the whole of the magnetization cycle and for this reason the errors are large if one tries to predict H sin5 from the B vs H loops. What can be said, qualitatively, is that for a fixed magnetizing current, a large ratio of#2/#1 will give a large value o f f (and hence of H sin8 averaged over a B vs H loop). The waveform of the voltage in SCn depends on the relative shapes of the B vs H loops in the principal directions. These in turn vary from one sample of steel to another even when the stress is the same and it is this variation that causes some scatter in the results and limits the accuracy of the technique.\nThe effect of stress on the B vs H loops in the principal directions for mild steel\naccurate measurements of B, and hence B vs H loops. A Hall plate was used to measure H and magnetization was done with the rotation rig.\nAt high stresses any holes could act as stress-raisers and initiate local yielding, which was a reason for not making holes, if possible. For this reason an approximate method, with equipment called the C-core rig, was devised to get B vs H loops in the principal directions for both tension and compression.\nThe C-core rig: local measurement of B vs H loops\nReference 2 describes tests in which thin steel samples had small holes drilled in them for search coils in order to get" + ] + } +] \ No newline at end of file