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Index

adaptation, interactive, 199, 200 interactive software, 199,200

AFNOR,42 AFRI,42 'almost certain' convergence, 31 arm, range, 144

work space, 140-4 Armstrong's equations, 57-9

method, 253-4 aspect, manipulator, 138-49

elbow-high, 140 elbow-low, 140

attitude see orientation

Bezier surfaces, 98, 99 binary coding in training and

trajectory restitution, 208-10 first-order, 208 second-order, 209

bracket measurement, 45, 46 B-spline surfaces, 98, 99

CAD, applied to robotics, 116-17 programming data bases, 126

CAD/CAM, and general modelling, 81 and robotics, 82 software, 81-2 systems, 85

CATIA system, 85, 111 central inertia tensor, 12 closed-loop arm compensation, 28 computer-aided design see CAD computer-assisted training (CAT), 156 computer control of robot, 233-5 computer-integrated manufacture, 82 computer simulation, 116 et seq

use in constraint analysis, 230 configuration

analysis, 222-3 errors, 9 polynomial interpolation, 223

region, 156 rigid body, 9, 10 space constraints, 212 et seq

Paul's method, 213 et seq Taylor's method, 221 et seq

Configurational Space Model (CSM), 24 configuration of rigid body, 9-10

helical method, 22-4 constraints, 108 et seq

continuous motion, 188 holonomous, 109 mechanical,109 rheonomous, 109 scleronomous, 109 use of inverse dynamic model, 230

continuous motion, constraints, 187 continuous path control, 188 et seq controllability, 75-8 control using a model, 231-5 convergence in probability, 31 coordinates, 10

Cartesian, 10 cylindrical, 10 operational, 10 spherical, 10

265

Coons surface, 100-2 Corio lis and centrifugal forces, 250-1 cube, measuring, 44

D'Alembert's principle, 55-6 damping in mechanical structure, 74 data base, CAD, 126

representation of operation, 128 deformation, modelling, 177

elastic, 178-9 degrees of freedom (DOF), 9

elementary particle, 9 rigid body, 9

Denavit-Hartemberg method, 117-18 direct models, 59-60 direct motion, representation of, 117-24 dynamic equations, use of, 59-60

266 Index

dynamic errors, 32-4 electro-dynamometric platform, 50-1 rule method, 48 string potentiometer method, 49

dynamic model, robot, 229 et seq dynamic performance index, 32 dynamic precision, 32-4

AFRI definition, 32 dynamics of robots, 53-79, 229-56

effect on trajectory, 219 elastic deformation in body, 60 et seq

finite element model, 67 localized parameters, 61 model approach, 67

electro-dynamometric platform, 50-1 energy dissipation in body, 60 et seq equations of motion, 54 et seq error compensation, 231

evaluation, 31 walking movement, 200, 201

error, geometrical, 176 positioning and orienting, 175

error measurement convergence 'almost certain', 31 least squares, 31 probability, 31

Euclid,108 Euler angle, axis, 18-20

parameters, rotating body, 15-17 experimental assembly cell, 113 expert system, 122 extended body, definition, 244-5

facetization, 103 finite element model, 67-8 fixed reference trihedron, 9 flexion in robots, 78-9 fluid actuator, 72-4

double action hydraulics, 73 force capacity

direct proboem, 158 inverse problem, 170

force-torque relationship, 159 Fourier transforms in modelling, 202

GDP system, 85, 106-8 gearing, use of cables, tapes and belts,

69-74 gears, 72 geometrical elements, 84-108

constraints on, 84 lines, 89 et seq points, 85 et seq

surfaces, 96 geometrical modelling, 81

mechanisms and objects, 112 production processes, 83 systems, 84

graphics simulation, 82 biped locomotion, 193, 197 programming, 197

gravitational forces, 246 gravity, effect on, 229

motor torque, 165 gripper orientation, 149-51

handicapped person, dynamic model, 198 adaptation software, 199 teleprocessing system, 199

helical method, configuration, 22-4

ideal control of robot, 232 inertia, effect of, 247 inertial errors, 235 inverse dynamic model, 230 inverse model, 59 inverse motion, simulation, 124-6 inverse problem, closed-loop solution,

254 ISO,42 isometric projection, 88

JIRA,42 Jordan's canonic form, 75-8 joystick, manipulator for

programming, 203 JPL robot, 239

Khalil's method, 225 kinematic loop, 119

simulation, 123 specification, 123

knowledge model, 175, 181

Lagrange function, 56-8 modelling, 235

complete rule, 243-51 simplification of rule, 237 simplified dynamic mode, 235-43

Lagrange multiplier, 57 least-squares convergence, 31 lines as geometrical elements, 89-96 load capacity, 164 localized deformations, 69-74 localized parameters, deformation

modes, 61-3

locomotion model logical model, 193-5 monopodal and multipodal, 229 orthesis, 192

lofting, 100

manipulator aspect, 139 equivalent mass, 174 programming, joystick, 203 range, 138 et seq

matrix notation, kinematics, 245 measurement, Peugeot method, 47 measuring bracket, 46

cube, 43 robot, 44

mechanical transmission device, load deformation, 69

mechanisms, graphs, closed and open-loop, 121

minimal time control, limitations, 212 model

construction, 179 control use of, 23 deformation, applied to, 63-5 Fourier transform, use of, 203 general theorem, use of, 251 et seq high level, 54 Lagrangian, use of, 65 static, three-dimensional, 137 et seq

Moebius mathematics, 106 motor force and necessary torques, 117 movements, analysis of, 187-227

NBS, 42 Newton's first law, 55

second law, 54 third law, 55

non-redundant mechanism work volume, 151-4

numerical simulation, 119

open-chain error compensation, 28 optimum movement, 220 orientation, rigid body, 13 orthesis, walking, 190-202

analytical methods, 194 CAD programming, 190 compensation, joystick, 200 dynamic model, 198 graphics simulation, 193, 197 hardware, model, 192 kinematic model, 191, 195 numerical simulation, 195

Index

overall model, 192 Overhauser method, 203

cubic function, 205

Paul's method, motion control, 213 et seq

performance index, 31 Peugeot dynamic, 31 Renault, 31

performance model, 137 points on geometrical elements,

85 et seq point-to-point control, 210 ct seq

motion, constant, 187 point-to-point transformation, 85

dimetric and isometric projections, 85 scaling, 86 symmetry, 87

267

polyhedra, modelling of, 104-8 precision, characteristics required, 41-2

classification, 41-2 measurement, 36-40 measuring cube, 42 measuring robot, 44 of position, 29 et seq test methods, 42 three-dimensional measuring machine, 42

probability convergence, 31 programming, actuator level, 124

object level, 124 projections, conical, 89

cylindrical, 88 dimetric, 87 isometric, 87 parallel, 88 perspective, 89

pulley block gears, 69-70

range, three-dimensional, 147-8 redundant mechanical work volume,

154-8 repeatability, 34-5

and robot operation, 35-6 static, 34

rigid body, positional errors, 24-8 closed-loop, 28 compensation, 25-8

rigid body, 12 central inertial tensor, 11 centre of inertia, 11 configuration and motion, 9-28 degrees of freedom, 9

268 Index

kinetic energy, 11 operation coordinates, 10 orientation, 9

robot, as acceleration generator, 137 as configuration generator, 137 as force generator, 137 decoupling and optimal control, 231 dynamics, 53 et seq inertial characteristics, 173 localized,181 measuring, 44 models, random error compensation, 181 optimal estimator, 184 overall, 183

robot operation and design, computer simulation, 116 et seq

robot representation, CATIA system, 115

Rodriguez-Hamilton parameters, rotating body, 17-18

rotation matrix, 13 velocity, 10-13

rotation matrix, rigid body, 12

simulators, numerical, 119 situation, 13, 19, 24, 25, 29-31, 33,

36,40,46,54,55,59,60,63,83, 84,117,119,123,124,137,151 et seq

space shuttle manipulator, 229 Space State Model (SSM), 241 static errors, 30 et seq

modelling of, 174 et seq

precision, 30 position, 34

static test bench, 45 static three-dimensional models, 137-86 string potentiometer, use of, 49 surface as geometrical element, 96

Bezier,98 complex surface, 97 cones, 96 cylinder, 96 operation on, 102-4 surface of revolution, 96

surface image generation, 146-7

Ta"it-Bryan angles, 20-2 three-dimensional measuring

machine, 44 three-dimensional modelling, 81

and CAD/CAM, 81 torque, effect on joints, 171 trajectory control, 21 et seq transition time, minimization, 188

VD!,42 VDMA,42

work space, 157 work volumes, 15 et seq

non-redundant mechanisms, 151-4 redundant mechanisms, 154-8

zone of full manipulator employment, 149