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| موضوع: كتاب Fundamentals of Robotic Mechanical Systems السبت 04 يناير 2014, 1:30 pm | |
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أخوانى فى الله أحضرت لكم كتاب Fundamentals of Robotic Mechanical Systems Theory , Methods , and Algorithms Third Edition Jorge Angeles
و المحتوى كما يلي :
Contents Prefac e t o th e Thir d Editio n x v Prefac e t o th e Firs t Editio n xi x 1 An Overvie w of Roboti c Mechanica l System s 1 1.1 Introduction 1 1.2 The General Architecture of Robotic Mechanical Systems . . . . 3 1.2.1 Types of Robots by Functio n 6 1.2.2 Types of Robots by Siz e 7 1.2.3 Types of Robots by Application 7 1.3 Manipulators 7 1.3.1 Robotic Arms 9 1.3.2 Robotic Hand s 10 1.4 Motion Generators 12 1.4. 1 Parallel Robots 12 1.4. 2 SCARA Systems 16 1.5 Locomotor s 17 1.5.1 Legge d Robots 17 1.5.2 Wheeled Robots 19 1.6 Swimming Robots 22 1.7 Flyin g Robots 23 1.8 Exercise s 24 2 Mathematica l Backgroun d 27 2.1 Preamble 27 2.2 Linea r Transformations 28 2.3 Rigid-Bod y Rotations 33 2.3.1 The Cross-Produc t Matrix 36 2.3.2 The Rotation Matrix 38 2.3.3 The Linea r Invariants of a 3 x 3 Matrix 4 2 2.3.4 The Linea r Invariants of a Rotation 4 3 2.3.5 Example s 4 5 2.3.6 The Euler-Rodrigue s Parameters 51 2.4 Composition of Reflections and Rotations 54Contents 2.5 Coordinate Transformations and Homogeneou s Coordinates . . . 56 2.5.1 Coordinate Transformations Between Frame s with a Common Origin 56 2.5.2 Coordinate Transformation with Origin Shift 60 2.5.3 Homogeneou s Coordinates 62 2.6 Similarity Transformations 65 2.7 Invariance Concepts 71 2.7.1 Applications to Redundant Sensing 75 2.8 Exercise s 79 Fundamental s of Rigid-Bod y Mechanic s 89 3.1 Introduction 89 3.2 General Rigid-Bod y Motion and Its Associated Screw 89 3.2.1 The Screw of a Rigid-Bod y Motion 93 3.2.2 The Pliicker Coordinates of a Lin e 95 3.2.3 The Pose of a Rigid Body 98 3.3 Rotation of a Rigid Body About a Fixe d Point 102 3.4 General Instantaneous Motion of a Rigid Body 103 3.4. 1 The Instant Screw of a Rigid-Bod y Motion 104 3.4. 2 The Twist of a Rigid Body 107 3.5 Acceleration Analysis of Rigid-Bod y Motions 110 3.6 Rigid-Bod y Motion Referred to Moving Coordinate Axe s 112 3.7 Static Analysis of Rigid Bodies 114 3.8 Dynamics of Rigid Bodies 118 3.9 Exercise s 122 Geometr y of Decouple d Seria l Robot s 129 4. 1 Introduction 129 4. 2 The Denavit-Hartenber g Notation 129 4. 3 The Geometric Model of Six-Revolut e Manipulators 138 4. 4 The Inverse Displacement Analysis of Decoupled Manipulators . 14 1 4.4. 1 The Positioning Problem 14 2 4.4. 2 The Orientation Problem 157 4. 5 Exercise s 162 Kinetostatic s of Seria l Robot s 167 5.1 Introduction 167 5.2 Velocity Analysis of Serial Manipulators 168 5.3 Jacobia n Evaluation 175 5.3.1 Evaluation of Submatrix A 175 5.3.2 Evaluation of Submatrix B 178 5.4 Singularity Analysis of Decoupled Manipulators 180 5.4. 1 Manipulator Workspace 182 5.5 Acceleration Analysis of Serial Manipulators 186 5.6 Static Analysis of Serial Manipulators 190 5.7 Planar Manipulators 192Contents xi 5.7.1 Displacement Analysis 193 5.7.2 Velocity Analysis 195 5.7.3 Acceleration Analysis 198 5.7.4 Static Analysis 199 5.8 Kinetostati c Performance Indices 201 5.8.1 Positioning Manipulators 207 5.8.2 Orienting Manipulators 210 5.8.3 Positioning and Orienting Manipulators 211 5.8.4 Computation of the Characteristic Length : Applications to Performance Evaluation 218 5.9 Exercise s 227 6 Trajector y Planning : Pick-and-Plac e Operation s 233 6.1 Introduction 233 6.2 Background on PPO 234 6.3 Polynomial Interpolation 236 6.3.1 A 3-4- 5 Interpolating Polynomial 236 6.3.2 A 4-5-6- 7 Interpolating Polynomial 24 0 6.4 Cycloidal Motion 24 3 6.5 Trajectories with Via Poses 24 5 6.6 Synthesis of PPO Usin g Cubic Splines 24 6 6.7 Exercise s 252 7 Dynamic s of Seria l Roboti c Manipulator s 257 7.1 Introduction 257 7.2 Inverse vs. Forwar d Dynamics 257 7.3 Fundamental s of Multibody System Dynamics 259 7.3.1 On Nomenclature and Basic Definitions 259 7.3.2 The Euler-Lagrang e Equation s of Serial Manipulators 260 7.3.3 Kane' s Equation s . 268 7.4 Recursive Inverse Dynamics 269 7.4. 1 Kinematic s Computations: Outward Recursions 269 7.4. 2 Dynamics Computations: Inward Recursions 275 7.5 The Natural Orthogonal Complement in Robot Dynamics . . . . 280 7.5.1 Derivation of Constraint Equation s and Twist-Shap e Relations 285 7.5.2 Noninertial Base Lin k 288 7.6 Manipulator Forwar d Dynamics 289 7.6.1 Planar Manipulators 293 7.6.2 Algorithm Complexit y 306 7.6.3 Simulation 310 7.7 Incorporation of Gravity Into the Dynamics Equation s 312 7.8 The Modeling of Dissipative Force s 313 7.9 Exercise s 316xii Contents 8 Specia l Topic s in Rigid-Bod y Kinematic s 323 8.1 Introduction 323 8.2 Computation of Angular Velocity from Point-Velocit y Data . . . 324 8.2.1 A Robust Formulatio n 330 8.3 Computation of Angular Acceleration from Point-Acceleratio n Data 331 8.3.1 A Robust Formulatio n 337 8.4 Exercise s 339 9 Geometr y of Genera l Seria l Robot s 34 3 9.1 Introduction 34 3 9.2 The IDP of General Six-Revolut e Manipulators 34 4 9.2.1 Preliminaries 34 5 9.2.2 Derivation of the Fundamenta l Closure Equation s . . . . 34 9 9.3 The Univariate-Polynomia l Approach 357 9.3.1 The Raghavan-Rot h Procedure 357 9.3.2 The Li-Woernle-Hille r Procedure 364 9.4 The Bivariate-Equatio n Approach 367 9.4. 1 Numerical Conditioning of the Solutions 369 9.5 Implementation of the Solution Method 370 9.6 Computation of the R,emaining Join t Angles 371 9.6.1 The Raghavan-Rot h Procedure 372 9.6.2 The Li-Woernle-Hille r Procedure 373 9.6.3 The Bivariate-Equatio n Approach 374 9.7 Example s 375 9.8 Exercise s 384 10 Kinematic s of Alternativ e Roboti c Mechanica l Systems 387 10.1 Introduction 387 10.2 Kinematic s of Parallel Manipulators 388 10.2.1 Velocity and Acceleration Analyses of Parallel Manipulators 40 1 10.3 Multifingered Hand s 40 8 10.4 Walking Machines 41 3 10.5 Rolling Robots 41 6 10.5.1 Robots with Conventional Wheels 41 7 10.5.2 Robots with Omnidirectional Wheels 42 2 10.6 Exercise s 42 6 11 Trajector y Planning : Continuous-Pat h Operation s 42 9 11.1 Introduction 42 9 11.2 Curve Geometry 430 11.3 Parametric Path Representation 43 5 11.4 Parametric Splines in Trajectory Planning 44 9 11.5 Continuous-Pat h Tracking 45 4 11.6 Exercise s 46 3Contents xiii 12 Dynamic s of Comple x Roboti c Mechanica l System s 46 9 12.1 Introduction 46 9 12.2 Classification of Robotic Mechanical Systems with Regard to Dynamics 470 12.3 The Structure of the Dynamics Models of Holonomi c Systems . . 47 1 12.4 Dynamics of Parallel Manipulators 47 4 12.5 Dynamics of Rolling Robots 48 4 12.5.1 Robots with Conventional Wheels 48 5 12.5.2 Robots with Omnidirectional Wheels 49 3 12.6 Exercise s 502 A Kinematic s of Rotations : A Summar y 507 B Numerica l Equation-Solvin g 513 B.l The Overdetermined Linea r Case 514 B.1.1 The Numerical Solution of an Overdetermined System of Linea r Equation s 515 B.2 The Underdetermine d Linea r Case 519 B.2.1 The Numerical Solution of an Underdetermine d System of Linea r Equation s 520 B.3 Nonlinear-Equatio n Solving: The Determined Case 521 B.3.1 The Newton-Raphso n Method 522 B.4 Overdetermined Nonlinear Systems of Equation s 524 B.4. 1 The Newton-Gaus s Method 525 B.4. 2 Convergence Criterion 525 Reference s 529 Inde x 54 3 Index ABB-IR B 1000 robot, 164 , 229 acatastatic systems, 47 1 acceleration analysis of parallel manipulators, 40 3 of rigid bodies, 110 of serial manipulators, 186 affine transformation, 29, 62 Agile Eye, 12 AI, see artificial intelligence algorithm definition, 24 angle of rotation, 38 angular acceleration computation, 331 invariant-rat e relations, 110 matrix , 110 vector, 110 angular velocity dyad, 121, 259 invariant-rat e relations, 108, 508- 511 matrix , 102 vector, 102 Appendix A, 507 Appendix B, 513 arc-welding , 430 operation, 44 4 path-tracking , 45 9 architecture of a kinematic chain, 131 manipulator, 129 articulated-bod y method, 290 artificial intelligence, 4 , 24 axia l component of a vector, 31 axia l vector of a 3 x 3 matrix , 4 2 base frame, 139 basis of a vector space, 31 Bezout' s method, 400 bivariate-equatio n approach, 345 , 357, 367 C, 25 C++ , 25 Canadarm, see Canadarm2 Canadarm2, 5, 6 canonical form of a rotation, 4 1 Carausius morosus, 17, 534 Cartesian coordinates of a manipulator, 129 also, see Cartesian variables Cartesian decomposition, 4 2 Cartesian variables of a manipulator, 138 caster wheel, 417 , 48 5 catastatic system, 47 1 Cayley' s Theorem, 81 Cayley-Hamilto n theorem, 36 change of basis, 65 characteristic equation , 33, 36 of a manipulator, 145 , 367 characteristic length, 206, 211, 216 characteristic polynomial, 33 of a manipulator, 184 , 344 , 364 , 367, 390, 40 1 Chasles' Theorem, see Mozzi-Chasles ' Theorem Chebyshev norm, 206, 45 9 Cholesky-decompositio n algorithm, 290, 309 closure equations , 139 compatibility conditions for acceleration, 332 for velocity, 326 composite rigid-bod y method, 29054 4 INDEX composition of reflections and rotations, 54 condition number, 205, 369 configuration of a manipulator, 129 constraint wrenches, 167 continuous path, 234 , 34 5 operations, 42 9 tracking, 45 4 control vector, 280, 310 coordinate transformation, 56-6 5 Coriolis acceleration, 113 and centrifugal forces, 283, 284 , 290 Couette flow, 314 Coulomb dissipation function, 315 friction, 261, 315 CP, see continuous path cross-produc t matrix , 36 curvature, 43 1 derivative w. r. t. a parameter, 43 8 derivative w. r. t. the arc length, 43 1 parametric representation, 43 6 time-derivative , 43 3 cycloidal motion, 24 3 Darboux vector, 43 3 time-derivative , 43 4 decoupled manipulators, 133, 138 decoupled robots, 129 Delta Robot, 14 Delta robot, 14 delta-arra y (A-array) , 427 , 49 3 Denavit-Hartenber g frames, 131 notation, 129 parameters, 133, 134 rotation matrix , 134 vector joining two frame origins, 135 determined system, 521 dexterity , 24 measures, see kinetostatic performance indices DEXTRE , 5 dextrou s hands, see multifingered hands dextrou s manipulation, 10 dextrou s workspace, 201 DH , see Denavit-Hartenber g dialytic elimination, 185, 230 DIESTRO inverse kinematics, 379 Jacobian , 227 manipulator, 217, 379 differentiation with respect to vectors, 36, 37 direct kinematic problem of parallel manipulators, 388 displacement equation s of a manipulator, 139 dissipation function, 261, 314 duality, 167 dynamic systems, 1 dynamics of holonomic systems, 47 0 of multibody systems, 259 of parallel manipulators, 47 4 of rigid bodies, 118 of robotic mechanical systems, 470 of rolling robots, 48 4 of serial manipulators, 257 EE, see end-effecto r elastodynamic, 168 end-effector , 131 Euclidean norm, 38 Euler angles, 42 , 81, 87 equatio n (for graphs), 47 4 equatio n (in mechanics), 120 parameters, see Euler-Rodrigue s parameters Euler' s formula for graphs, see Euler equatio n for graphs theorem, 36 Euler-Lagrang e equations , 258, 260INDEX 54 5 derived with the NOC, 282, 47 2 Euler-Rodrigue s parameters, 51 Fanu c Arc Mate inverse displacement, 375 Fanu c Arc Mate 120iB, 165 Fanu c Robot Arc Mate characteristic length, 226 DH parameters, 225 KCI , 226 feasible twists, 167 Firs t La w of Thermodynamics, 191 flight simulator, 389 floating-poin t operation, 24,189 , 289, 515 flop, see floating-point operation forward dynamics algorithm complexity , 306 of serial manipulators, 257, 289 fractal, 524 Frenet , see Frenet-Serre t Frenet-Serre t formulas, 43 1 frame, 43 0 vectors, 43 1 friction forces, 313 Frobeniu s norm, 204 fuzz y logic, 24 genealogy of robotic mechanical systems, 1, 4 general architecture of a manipulator, 4 generalize d coordinates, 260, 261, 470 generaUze d forces, 260, 261, 490 generalize d inertia matrix , 262, 49 8 Cholesky decomposition, 291 factoring, 291 time-rat e of change, 298 generalize d speeds, 261, 47 1 Ginger, see Segway gluing operation, 43 9 grasping matrix , 410 gravity terms, 312 wrench, 281 hand-ey e calibration, 76 Hex a robot, 15 higher kinematic pair, 130 holonomic systems, 469 , 47 0 homogeneous coordinates, 56 homotopy, 34 5 IDP, see inverse displacement problem ilonators, 20 inertia tensor, 118 inertia dyad, 120, 259 input, 1, 280 instant screw axis , 104 instrument calibration, 75 intelligent machines, 2, 24 intelligent robots, 2 invariance, 71 inverse displacement problem of a general 6R manipulator, 34 4 inverse dynamics of serial manipulators, 257 recursive, 269 inverse kinematics problem of parallel manipulators, 390 inverse vs. forward dynamics, 257 inward recursions, 275, 278 ISA, see instant screw axi s isomorphism, 33 isotropic manipulator, 206 matrix , 203, 206 isotropy, 209 iteration, 24 , 45 8 Jacobia n matrix , 167 condition number, 205 evaluation, 175 invertibility, 201 transfer formula, 173 joint, 130 coordinates, 129, 133 parameters, 133 variables, 133 Kane' s equations , 26854 6 INDEX KCI , see kinematic conditioning index kernel of a linear transformation, 29 Kinemate , 108 kinematic chain, 129 conditioning index , 204 constraints, 281 constraints for serial manipulators, 285 pair, 130 kinematic chain architecture of a , 131 kinetostatic performance indices, 201 kinetostatics, 167 least-squar e error, 525 least-squar e solution, 525 Le e vs. Li , 34 5 Lee' s manipulator, 376 Lee' s procedure, 373 left hand, 15 legged robots, 17 L i vs. Lee , see Le e vs. L i Li' s manipulator, see Lee' s manipulator linear invariants, 4 2 of rotation, 4 3 linear transformations, 28 local structure of a manipulator, 133 locomotors, 17 lower kinematic pair, 130 L U decomposition, 171 machine (definitions of), 24 main gauche, see left hand maneuverability, 42 6 manipulability, 201 of decoupled manipulators, 231 manipulator angular velocity matrix , 261 architecture, 129 configuration, 129 dynamics, 257, 47 4 general architecture, 4 mass matrix , 261 posture, 129 twist, 261 wrench, 261 manipulators, 7, 129 matrix norm, 204 representation, 32 mechanical system, 2 mechatronics, 24 Mekanum wheels, 20 minimum-tim e trajectory, 283 mobile wheeled pendulums, 21 module, 35 moment of inertia, 118 moment invariants, 71 moment of a line about a point, 96 about another line, 122 momentum screw, 121 motor, 108 Mozzi-Chasles ' Theorem, 91 MSS, 5 multibody system dynamics, 259 Euler-Lagrang e equations , 268 multicubic expression , 14 1 multifingered hands, 10 multilinear expression , 14 0 multiquadrati c expression , 14 1 multiquarti c expression , 14 1 natural orthogonal complement, 259 applied to holonomic systems, 47 2 applied to parallel manipulators, 47 4 applied to planar manipulators, 293 applied to rolling robots, 485 , 49 6 Newton -Eule r algorithm, 278 -Gaus s method, 45 5 -Raphso n method, 77 equation , 120 methods, 345 , 45 5INDEX 54 7 NOC, see natural orthogonal complement nonholonomic systems, 258, 469 , 48 4 noninertial base link, 288 nonlinear system, 521 norm also, see Frobeniu s norm norm (matrix -) , 204 normal component of a vector, 31 normality condition, 526 nullspace of a linear transformation, 29 numerical conditioning, 357, 369 object-oriente d programming, 25 Odetics series of hexapods , 17 ODW, see omnidirectional wheels, see omnidirectional wheels off-line , 4 , 145 , 176 omnidirectional wheels, 20, 49 3 dynamics, 49 3 kinematics, 42 2 on-line , 24 operation point, 133 orientation problem, 157 orthogonal complement, 282 orthogonal decomposition of a vector, 31 orthogonal decoupled manipulator, 152 orthogonal projection, 29 orthogonal RRR manipulator dynamics, 294 , 297 inverse kinematics, 153, 155 recursive dynamics, 304 workspace, 159 OSU ASV, 17 OSU Hexapod , 17 output, 1 outward recursions, 269 overdetermined system, 524 Pappus-Guldinu s theorem, 231 parallel axes , theorem, 120 parallel manipulators acceleration analysis, 40 1 dynamics, 47 4 kinematics, 388 velocity analysis, 40 1 parallel robots, 12 parametric path representation, 43 5 representation of curvature, 43 6 representation of curvature derivative, 43 8 representation of torsion, 43 6 representation of torsion derivative, 43 8 splines, 44 9 path-trackin g for arc-welding , 45 9 pick-and-plac e operations, 233, 234 Pliicker coordinates of a line, 95 transfer formula, 98 planar manipulators, 192 acceleration analysis, 198 displacement analysis, 193 dynamics, 263 static analysis, 199 velocity analysis, 195 platform manipulators, 389, 398, 47 4 polar-decompositio n theorem, 202 polynomial interpolation with 3-4- 5 polynomial, 236 with 4-5-6- 7 polynomial, 24 0 pose array, 99 of a rigid body, 98 positioning problem, 14 2 posture of a manipulator, 129 PPO, see pick-and-plac e operations Principle of Virtual Work, 191 prismatic pair, 130, 179 programmable robot, 2 projection, 29 theorem, 515 Puma robot, 132, 133, 150 DH parameters, 133 inverse kinematics, 14 2 workspace, 151 pure reflection, 3054 8 INDEX quaternions , 53 Raghavan and Roth' s procedure, 34 5 Raghavan-Roth' s procedure, 357 range of a linear transformation, 29, 79 Rayleigh dissipation function, see dissipation function real-time , 24 , 257 reciprocal bases, 76, 175, 48 3 reciprocal product, 117 recursion, 24 redundant sensing, 75 References, 528 reflection, 30, 346 , 352 composition with rotations, 54 regional structure of a manipulator, 133 revolute pair, 130 rheonomic systems, 47 0 robot design, 168 robotic hands, 10 robotic mechanical systems, xiii , 1 Rodrigues, see Euler-Rodrigue s vector, 81 rolling robots dynamics, 48 4 kinematics, 41 6 rotating pair, 130 rotation, 33 rotation matrix , 38 exponentia l representation, 4 0 run-time , 24 Runge-Kutt a methods, 311 RVS, xiv , 235 SARAH , 11 Schonflies-motio n generators, 16 scleronomic systems, 47 0 screw amplitude, 93 axis , 93 motion, 89 pitch, 93 Segway, 22 self-inverse , 31 serial manipulators acceleration analysis, 186 dynamics, 257 kinematics, 130 statics, 190 velocity analysis, 168 workspace, 183 service angle, 201 similarity transformations, 65 simple manipulation, 10 simulation, 310 singular-valu e decomposition, 203 singular-values , 203 singularities, 167 singularity analysis of decoupled manipulators, 180 sliding pair, 130 SPDM, 5 spherical wrist, 133, 158, 159 workspace, 160 spline(s), 24 6 interpolation of 4-5-6- 7 polynomial, 251 natural, 250 nonparametric, 247 , 44 9 parametric, 44 9 periodic, 24 7 squar e root of a matrix , 52 Star robot, 15 state of a dynamical system, 280 of parallel manipulators, 480 of serial manipulators, 280, 310 variable, 261, 280, 310 variable equations , 310 vector, 280 static analysis of rigid bodies, 114 of serial manipulators, 190 static, conservative conditions, 167 stationary point, 526 Steiner, theorem, 120 Stewart platform, see Stewart-Goug h platform Stewart-Goug h platform, xix , 390 direct kinematics, 388INDEX 54 9 leg kinematics, 390 structural design, 168 structure of mechanical systems, 9 structured environment, 3 Sutherland, Sprout & Assocs. Hexa - pod,17 Swedish wheels, 20 system, 1 telemanipulators, 5 tensors, 27, 279, 280 Titan series of quadrupeds , 17 torsion, 43 1 derivative w. r. t. a parameter, 43 8 derivative w. r. t. the arc length, 43 1 parametric representation, 43 6 time-derivative , 43 3 trace of a squar e matrix , 4 2 trajectories with via poses, 24 5 trajectory planning, 233, 42 9 truncation error, 311 Trussarm, 15 TU Munich Hand , 11 TU Munich Hexapod , 17 twist, 104 axi s coordinates, 108 of a rigid body, 107 ray coordinates, 108 transfer formula, 109 twist-shap e relations, 282 for serial manipulators, 285 unimodular group (of matrices), 97 unstructured environment, 3 vector of a 3 X 3 matrix , 4 2 vector space, 28 velocity analysis of parallel manipulators, 40 1 of rolling robots, 41 8 of serial manipulators, 168 via poses, 24 5 virtual work, see Principle of Virtual Work viscosity coefBcient, 314 viscous forces, 313 walking machines kinematics, 41 3 leg architecture, 413-41 5 walking stick, 17 weighting matrix , 525 wheeled robots, 19 workspace of positioning manipulators, 182 wrench acting on a rigid body, 115 axis , 115 pitch, 115 transfer formula, 117
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