Lenarcic / Lenarcic Advances in Robot Kinematics: Motion in Man and Machine

Motion in Man and Machine
1. Auflage 2010
ISBN: 978-90-481-9262-5
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 551 Seiten

The ?rst International Meeting of Advances in Robot Kinematics, ARK, occurred in September 1988, by invitation to Ljubljana, Slovenia, of a group of 20 int- nationally recognized researchers, representing six different countries from three continents. There were 22 lectures and approximately 150 attendees. This success of bringing together excellent research and the international community, led to the formation of a Scienti?c Committee and the decision to repeat the event biannually. The meeting was made open to all individuals with a critical peer review process of submitted papers. The meetings have since been continuously supported by the Jozef ? Stefan Institute and since 1992 have come under patronage of the Inter- tionalFederationforthePromotionofMechanismandMachineScience(IFToMM). Springer published the ?rst book of the series in 1991 and since 1994 Kluwer and Springer have published a book of the presented papers every two years. The papers in this book present the latest topics and methods in the kinem- ics, control and design of robotic manipulators. They consider the full range of - botic systems, including serial, parallel and cable driven manipulators, both planar and spatial. The systems range from being less than fully mobile to kinematically redundant to overconstrained. The meeting included recent advances in emerging areas such as the design and control of humanoids and humanoid subsystems, the analysis, modeling and simulation of human body motion, the mobility analysis of protein molecules and the development of systems which integrate man and - chine.

Jadran Lenarcic has been Professor at the Faculty of Electrical Engineering, University of Ljubljana, Slovenia, since 1988. He is Director of the J. Stefan Institute of Automatics, Biocybernetics and Robotics since 2005. He is a member of the executive committee of the International Federation for the Theory of Machines and Mechanisms, member of the Board of the European Robotics network, and memebr of the Executive Board of the European Association of Research and Technology Organisations. He is regular member of the Slovenian Academy of Engineering Science.

Autoren/Hrsg.

Lenarcic, Jadran

Inhaltsverzeichnis

1;Table of Contents;6
2;Preface;12
3;PART 1;14
3.1;Calibration and Validation of a Rigid Body Kinematic Model of Flexure Hinges;15
3.1.1;1 Introduction;15
3.1.2;2 Rigid Body Kinematic Models of Flexure Hinges;17
3.1.2.1;2.1 Leaf Spring Model;17
3.1.2.2;2.2 Kimball–Tsai Method;18
3.1.2.3;2.3 Modified Kimball–Tsai Method;18
3.1.3;3 Flexure Hinge Test Bench;19
3.1.4;4 Parameter Calibration of a Flexure Hinge;19
3.1.5;5 Validation and Model Comparison;20
3.1.6;6 Conclusion and Outlook;21
3.1.7;Acknowledgements;22
3.1.8;References;22
3.2;Dynamic Jacobian Inverses of Mobile Manipulator Kinematics;23
3.2.1;1 Introduction;23
3.2.2;2 Basic Concepts;24
3.2.2.1;2.1 Kinematics;24
3.2.2.2;2.2 Jacobian;25
3.2.2.3;2.3 Adjoint Jacobian;25
3.2.2.4;2.4 Regular and Singular Configurations;25
3.2.2.5;2.5 Continuation Method;26
3.2.3;3 Dynamic Inverses;27
3.2.4;4 Example Jacobian Inverses;29
3.2.4.1;4.1 Right Inverses;28
3.2.4.2;4.2 Non-Right Inverses;29
3.2.4.2.1;4.2.1 Adjoint Jacobian;29
3.2.4.2.2;4.2.2 Adjugate DexterityMatrix Inverse;29
3.2.4.2.3;4.2.3 Singularity Robust Inverse;30
3.2.5;5 Computer Simulations;30
3.2.6;6 Conclusions;32
3.2.7;Acknowledgements;32
3.2.8;References;32
3.3;A Robust Forward Kinematics Analysis of 3-RPR Planar Platforms;34
3.3.1;1 Introduction;34
3.3.2;2 Cayley–Menger Determinants and Bilateration;36
3.3.3;3 Distance-Based Coordinate-Free Formulation;37
3.3.4;4 Numerical Example;39
3.3.5;5 Conclusions;41
3.3.6;Appendix;42
3.3.7;References;43
3.4;Hierarchical Decomposition and Kinematic Abstraction with Virtual Articulations;44
3.4.1;1 Introduction;44
3.4.2;2 Hierarchical Linkages;45
3.4.3;3 Structure Abstraction;47
3.4.4;4 Decomposition Algorithms;48
3.4.5;5 Scaling Results;51
3.4.6;6 Conclusions;53
3.4.7;Acknowledgements;53
3.5;Researching into Non-Singular Transitions in the Joint Space;55
3.5.1;1 Introduction;55
3.5.2;2 Kinematic Problems;56
3.5.2.1;2.1 Case Study;57
3.5.3;3 Locus of Cusp Points;58
3.5.4;4 Non-Singular Transitions in the Joint Space;59
3.5.5;5 Conclusions;61
3.5.6;Acknowledgements;62
3.5.7;References;62
3.6;MARIONET, A Family of Modular Wire-DrivenParallel Robots;63
3.6.1;1 Introduction;63
3.6.2;2 Actuation Scheme;64
3.6.3;3 The MARIONET family;65
3.6.3.1;3.1 MARIONET-REHAB;66
3.6.3.2;3.2 MARIONET-CRANE;67
3.6.3.3;3.3 MARIONET-ASSIST and MARIONET-VR;68
3.6.4;4 Lessons Learned;68
3.6.4.1;4.1 Improving the DRM;68
3.6.4.2;4.2 Kinematics;69
3.6.4.3;4.3 Singularity;69
3.6.5;5 Conclusion;70
3.6.6;References;70
3.7;Using Cosserat Point Theory for EstimatingKinematics and Soft-Tissue Deformation DuringGait Analysis;72
3.7.1;1 Introduction;72
3.7.2;2 Motion and Deformation of a Tetrahedron;73
3.7.3;3 Experimental Setup;75
3.7.4;4 Results;75
3.7.4.1;4.1 Group 1 Results (Rigid Tetrahedra);77
3.7.4.2;4.2 Group 2 Results (Deformable Tetrahedra);77
3.7.5;5 Conclusions;78
3.7.6;Acknowledgements;78
3.7.7;References;78
4;PART 2;80
4.1;Mechanical Generators of 2-DoF Translation along a Ruled Surface;81
4.1.1;1 Introduction;81
4.1.2;2 2-DoF Translation along a Ruled Helicoid;82
4.1.3;3 Mechanical Generators of 2-DoF Translation along a Ruled Helicoid;85
4.1.4;4 Mechanical Generators of 2-DoF Translation along a RevoluteHyperboloid;87
4.1.5;5 Conclusions;88
4.1.6;Acknowledgements;88
4.1.7;References;88
4.2;Worm-Like Robotic Locomotion in Flexible Environment;89
4.2.1;1 Introduction;89
4.2.2;2 Contact Compliance Analysis;90
4.2.3;3 Structural Compliance Analysis;91
4.2.3.1;3.1 Model of Intestines;92
4.2.3.2;3.2 Superposition Principle;94
4.2.4;4 Two-Cell Robot Example;94
4.2.4.1;4.1 Analysis;95
4.2.4.2;4.2 Approximate Closed-Form Solution;95
4.2.4.3;4.3 Comparison to Exact Solution;95
4.2.5;5 Conclusions;96
4.2.6;References;96
4.3;Actuation Strategy Based on the Acceleration Model for the 3-PRPR Redundant Planar Parallel Manipulator;98
4.3.1;1 Introduction;98
4.3.2;2 Acceleration Model Formulation;99
4.3.3;3 Motion Planning;101
4.3.4;4 Numerical Examples;102
4.3.5;5 Conclusions;105
4.3.6;References;105
4.4;Kinematics and Design of a 5-DOF Parallel Robot Used in Minimally Invasive Surgery;106
4.4.1;1 Introduction;106
4.4.2;2 The Surgical Parallel Robot;107
4.4.3;3 The Geometric Model;108
4.4.4;4 Kinematics;110
4.4.5;5 Singularity Analysis;110
4.4.6;6 Design of PARASURG 5M;111
4.4.7;7 Conclusions;113
4.4.8;References;113
4.5;Main Theorem on Sch¨onflies-Singular Planar Stewart Gough Platforms;114
4.5.1;1 Introduction;114
4.5.1.1;1.1 Notation;115
4.5.1.2;1.2 Related Work;115
4.5.2;2 Main Theorem for the General Case;116
4.5.3;3 Main Theorem for the Special Case;118
4.5.4;4 Conclusion;121
4.5.5;References;122
4.6;A Novel Actuation Module for Wearable Robots;124
4.6.1;1 Introduction;124
4.6.2;2 Design of the Actuation Scheme;126
4.6.3;3 Embodiments of the Reversing Mechanism;128
4.6.4;4 Features of the Actuation Module;130
4.6.5;5 Conclusions;132
4.6.6;References;132
4.7;Parallel Robot with Antagonistic Dielectric Elastomer Actuation for Human-Machine Interaction;133
4.7.1;1 Introduction;133
4.7.2;2 The Manipulator Concept;135
4.7.3;3 Static Analysis of the Manipulator Concept;136
4.7.4;4 Dielectric Elastomer vs. Traditional Actuation;141
4.7.5;5 Conclusions;141
4.7.6;References;142
4.8;Using Redundancy in Serial Planar Mechanisms to Improve Output-Space Tracking Accuracy;143
4.8.1;1 Introduction;143
4.8.2;2 Speed-Ratio Control for Non-Redundant Manipulators;144
4.8.3;3 Speed-Ratio Control for Three-DOF, Planar Manipulators;146
4.8.4;4 Examples;147
4.8.5;5 Conclusions;150
4.8.6;References;150
5;PART 3;151
5.1;Combining Structural and Kinematic Analysis Using Interval Analysis for a Wire-Driven Manipulator;152
5.1.1;1 Introduction;152
5.1.2;2 Related Work;153
5.1.3;3 Structural Analysis Overview;154
5.1.4;4 The Proposed Algorithm;154
5.1.4.1;4.1 Criteria for Workspace Delineation;154
5.1.4.2;4.2 Structural Analysis Using Interval Analysis;155
5.1.4.3;4.3 Algorithm;155
5.1.4.4;4.4 Remarks;156
5.1.5;5 Examples;157
5.1.5.1;5.1 A 2-DOF Planar Robot with a 3-Bar Truss;157
5.1.5.2;5.2 A 2-DOF Planar Robot with a 9-Bar Truss;158
5.1.6;6 Conclusions;160
5.1.7;References;161
5.2;Multiple-Point Kinematic Control of a Humanoid Robot;162
5.2.1;1 Introduction;162
5.2.2;2 Kinematic Modelling;163
5.2.2.1;2.1 Hierarchical Model of Humanoid Robot;164
5.2.2.2;2.2 Virtual Joints;165
5.2.2.3;2.3 Augmented Jacobian;166
5.2.2.4;2.4 Center-of-Mass Jacobian;167
5.2.2.5;2.5 Conflicting Tasks;169
5.2.3;3 Simulations in VR;169
5.2.3.1;3.1 Standing up from a Sitting Position;170
5.2.3.2;3.2 Collision Avoidance;170
5.2.3.3;3.3 More Complex Tasks;171
5.2.4;4 Conclusions and Future Work;172
5.2.5;References;173
5.3;Optimum Design of a Pan-Tilt Drive for Parallel Robots;174
5.3.1;1 Introduction;174
5.3.2;2 Kinematics of the Pan-Tilt Mechanism;176
5.3.3;3 Optimization of the Pan-Tilt Mechanism;177
5.3.3.1;3.1 Minimization of the Transmission Defect;178
5.3.4;4 Conclusions;180
5.3.5;Appendix;181
5.3.6;References;181
5.4;LQP-Based Controller Design for Humanoid Whole-Body Motion;182
5.4.1;1 Introduction;182
5.4.2;2 Modelling;183
5.4.2.1;2.1 Whole-Body Dynamics;183
5.4.2.2;2.2 Contact Model;184
5.4.2.3;2.3 Task Description and Control;184
5.4.3;3 LQP-Based Controller Design;185
5.4.3.1;3.1 Designing LQP;185
5.4.3.2;3.2 Performing Tasks;186
5.4.4;4 Application to the Virtual iCub;186
5.4.4.1;4.1 Managing Multi-Tasks;186
5.4.4.2;4.2 Sit-to-Stand on One Foot;187
5.4.4.3;4.3 Walking;188
5.4.5;5 Conclusion;188
5.4.6;References;189
5.5;Persistent Screw Systems;190
5.5.1;1 Introduction;190
5.5.2;2 Definition;191
5.5.3;3 Forms of Persistent Screw Systems;194
5.5.4;4 Persistent Screw Systems of Dimension 3, 4 and 5;196
5.5.5;5 Conclusions;198
5.5.6;Acknowledgements;199
5.5.7;References;199
5.6;Localisation of the Instantaneous Axis of Rotation in Human Joints;200
5.6.1;1 Introduction;200
5.6.2;2 Determination of the Instantaneous Axis of Rotation Location;201
5.6.2.1;2.1 The SCoRE Method;201
5.6.2.2;2.2 Our Method;202
5.6.3;3 Simulation;203
5.6.3.1;3.1 Experimental Protocol;203
5.6.3.2;3.2 Simulations Results;204
5.6.4;4 Experimental Study on Human Subjects;205
5.6.4.1;4.1 Protocol and Apparatus;205
5.6.4.2;4.2 Data Processing and Modelling;205
5.6.4.3;4.3 Results;206
5.6.4.4;4.4 Discussion;207
5.6.5;5 Conclusions and Future Work;207
5.6.6;References;207
5.7;A Kinematic Observation and Conjecture for Creating Stable Constructs of a Peptide Nanoparticle;208
5.7.1;1 Introduction;208
5.7.2;2 Computational Model;210
5.7.2.1;2.1 Hydrogen Bond;210
5.7.2.1.1;2.1.1 Geometry of Hydrogen Bonds;210
5.7.2.1.2;2.1.2 Energy of Hydrogen Bonds;211
5.7.2.2;2.2 Mobility Analysis;212
5.7.3;3 Design and Manipulation of a Peptide Nanoparticle;212
5.7.3.1;3.1 Computational Model of the Nanoparticle;212
5.7.3.2;3.2 Experimental Method to Build the Nanoparticle;214
5.7.4;4 Conclusions;214
5.7.5;Acknowledgements;215
5.7.6;References;215
5.8;Forward Kinematic Problem of 5-PRUR Parallel Mechanisms Using Study Parameters;216
5.8.1;1 Introduction;216
5.8.2;2 Architecture;217
5.8.3;3 FKP Formulation Using Study’s Kinematic Mapping;218
5.8.3.1;3.1 Kinematic Modeling of the Principal Limb;218
5.8.3.2;3.2 FKP Formulation of the 5-PRUR, Extension from the Principal Limb;221
5.8.4;4 Cartesian Representation of Study Parameters;224
5.8.5;5 Study Parameters Representation of the Cartesian Coordinates;224
5.8.6;6 Conclusion;225
5.8.7;References;225
6;PART 4;227
6.1;The Development of a Reconfigurable Parallel Robot with Binary Actuators;228
6.1.1;1 Introduction;228
6.1.2;2 The Fivebar Structure;229
6.1.3;3 Four Point Synthesis Approach;230
6.1.4;4 (Re-)Configuration of Binary Robots;233
6.1.4.1;4.1 Robot Components for (Re-)Configuration;233
6.1.4.2;4.2 Mechanical Calibration of Binary Robots;233
6.1.5;5 Operational Status;234
6.1.6;6 Conclusions;234
6.2;On the Design of 5R Serial Manipulators with Isotropic Positioning;236
6.2.1;1 Introduction;236
6.2.2;2 Kinematic Model;237
6.2.3;3 Isotropic Design;238
6.2.3.1;3.1 Manipulator A with Near Isotropic Positioning;238
6.2.3.2;3.2 Manipulator B with Isotropic Positioning;240
6.2.3.3;3.3 Arbitrary 5R Manipulator with Isotropic Positioning;241
6.2.4;4 Positioning and Orienting Tasks;242
6.2.5;References;243
6.3;A Virtual Mechanism Enhanced Approach for Object Tracking with Humanoid Robot Head;244
6.3.1;1 Introduction;244
6.3.2;2 Methods;246
6.3.2.1;2.1 The Perceptual Problem – Acquiring 3-D Position of Object;246
6.3.2.2;2.2 The Control Problem – Virtual Mechanism Approach;247
6.3.2.3;2.3 Controller Design;249
6.3.3;3 Results;250
6.3.3.1;3.1 Object Tracking with Narrow-Angle Cameras;250
6.3.4;4 Conclusions;252
6.3.5;References;253
6.4;Tangent Space RRT with Lazy Projection:An Efficient Planning Algorithm for Constrained Motions;254
6.4.1;1 Introduction;254
6.4.2;2 Tangent Space RRT Algorithm;257
6.4.3;3 Case Study;260
6.4.3.1;3.1 Two-Arm Manipulation;260
6.4.4;4 Conclusions and Future Work;262
6.4.5;References;262
7;PART 5;264
7.1;Equilibrium Analysis of Tensegrity Structures with Elastic Ties;265
7.1.1;1 Introduction;265
7.1.2;2 Problem Formulation;267
7.1.2.1;2.1 Geometric Constraint;268
7.1.2.2;2.2 Potential Energy;268
7.1.2.3;2.3 Problem Statement;269
7.1.3;3 Solution Approach;269
7.1.4;4 Numerical Example;271
7.1.5;5 Conclusions;273
7.1.6;References;273
7.2;Singularity Analysis of Lower-Mobility Parallel Robots with an Articulated Nacelle;275
7.2.1;1 Introduction;275
7.2.2;2 Grassmann–Cayley Algebra in the Projective Space P3;276
7.2.3;3 Theory of Reciprocal Screws;276
7.2.4;4 The H4 Constraint Analysis;277
7.2.4.1;4.1 Twist System and Wrench System of the 4S Parallel Linkage;278
7.2.4.2;4.2 Constraint Wrenches of the H4 Robot;279
7.2.4.3;4.3 Actuation Wrenches and Global Wrench System of the H4 Robot;280
7.2.5;5 Singularity Analysis of the H4 Robot;280
7.2.5.1;5.1 Wrench Diagram of the H4 Robot in P3;280
7.2.5.2;5.2 Superbracket of the H4 Robot;281
7.2.5.3;5.3 Geometric Conditions for the H4 Robot Singularities;282
7.2.6;6 Conclusions;283
7.2.7;References;284
7.3;Human Motion Reconstruction and Synthesis of Human Skills;285
7.3.1;1 Introduction;285
7.3.2;2 Musculoskeletal Motion Reconstruction;286
7.3.2.1;2.1 Experimental Procedure and Musculoskeletal Model;287
7.3.2.2;2.2 Control Framework;288
7.3.2.2.1;2.2.1 Marker Space Control Formulation;288
7.3.2.2.2;2.2.2 Human Motion Control Hierarchy;290
7.3.3;3 Results and Real-Time Simulation;291
7.3.4;4 Conclusions;291
7.3.5;Acknowledgements;293
7.3.6;References;293
7.4;Overconstrained Mechanisms with Radially Reciprocating Motion;295
7.4.1;1 Introduction;295
7.4.2;2 Characteristics of the PRRP Chain;296
7.4.3;3 Construction of the Radially Reciprocating MotionMechanism;297
7.4.4;4 The New Radially Reciprocating Motion Mechanisms;299
7.4.5;5 Conclusions;301
7.4.6;References;302
7.5;Control of Bipedal TurningWhile Running;303
7.5.1;1 Introduction;303
7.5.2;2 Heuristics;304
7.5.3;3 Model;306
7.5.4;4 Control Laws;307
7.5.5;5 Results;308
7.5.6;6 Conclusion;310
7.5.7;References;310
7.6;Geometrico-Static Analysis of Under-Constrained Cable-Driven Parallel Robots;311
7.6.1;1 Introduction;311
7.6.2;2 Geometrico-Static Model;312
7.6.3;3 The Stability of Equilibrium;315
7.6.4;4 Application Example: The 33-CDPR;318
7.6.5;5 Conclusions;320
7.6.6;References;321
7.7;The Inverse Kinematics of 3-D Towing;322
7.7.1;1 Introduction;322
7.7.2;2 The Static Equilibrium Condition;323
7.7.3;3 The Inverse Kinematics Problem;324
7.7.4;4 An Analytic Algorithm Based on Dialytic Elimination;325
7.7.5;5 An Example;326
7.7.6;6 Conclusions;329
7.7.7;Acknowledgements;329
7.7.8;References;329
7.8;A Complete Method for Workspace Boundary Determination;330
7.8.1;1 Introduction;330
7.8.2;2 Necessary Conditions;331
7.8.3;3 Singularity Classification;333
7.8.4;4 Numerical Solution;334
7.8.5;5 A Comparative Example;336
7.8.6;6 Conclusions;338
7.8.7;Acknowledgements;339
7.8.8;Referenc;339
8;PART 6;340
8.1;Inverse Kinematics of Humanoid-RobotReaching through Human Visuo-Motor Learning;341
8.1.1;1 Introduction;341
8.1.2;2 Closed Loop Motion Transfer and Data Acquisition;343
8.1.3;3 Statically Stable Inverse Kinematics Determination;344
8.1.4;4 Statically Stable Motion Generation of the Humanoid Robot;346
8.1.5;5 Conclusions;347
8.1.6;Acknowledgements;348
8.1.7;References;348
8.2;Automated Fitting of an ElastokinematicSurrogate Mechanism for Forearm Motion from MRI Measurements;349
8.2.1;1 Introduction;349
8.2.2;2 Forearm Elastokinematic Surrogate Mechanism;350
8.2.3;3 Model Parameter Fitting from MRI Measurements;353
8.2.4;4 Simulation Results;356
8.2.5;5 Conclusions;357
8.2.6;References;358
8.3;Self-Motions of 6–3 Stewart–Gough Type Parallel Manipulators;359
8.3.1;1 Introduction;359
8.3.2;2 Equations of Self-Motions;360
8.3.3;3 The Butterfly Motion;361
8.3.4;4 The General Case;362
8.3.5;5 The Four-Bar Self-Motion;363
8.3.6;6 Conclusions;366
8.3.7;Acknowledgements;366
8.3.8;References;366
8.4;Constraint Compliant Control for a Redundant Manipulator in a Cluttered Environment;367
8.4.1;1 Introduction;367
8.4.2;2 Constraint Compliant Control;369
8.4.2.1;2.1 Passive Avoidance;369
8.4.2.2;2.2 Active Avoidance in Additional Objective;370
8.4.2.3;2.3 Particular Case of the Joint Velocity Limit – Scaling;370
8.4.3;3 Implementation and Comparative Results;371
8.4.3.1;3.1 Implementation;372
8.4.3.2;3.2 Results and Analysis;373
8.4.4;4 Conclusion and Perspectives;375
8.4.5;Acknowledgements;376
8.4.6;References;376
8.5;Geometric Interpolation by Quartic Rational Spline Motions;377
8.5.1;1 Introduction;377
8.5.2;2 Geometrically Continuous Rational Spline Motions;378
8.5.3;3 Interpolation Problem;379
8.5.4;4 Construction of Quartic Rational Spline Motions;380
8.5.5;5 Conclusion;383
8.5.6;References;384
8.6;Position Level Kinematics of the Atlas Motion Platform;385
8.6.1;1 Introduction;385
8.6.2;2 Atlas Velocity Level Kinematic Model;387
8.6.3;3 Atlas Position Level Kinematic Model;388
8.6.4;4 Experimental Validation;389
8.6.5;5 Orientation Estimate for Nonconstant Velocity Inputs;391
8.6.6;6 Conclusions;391
8.6.7;References;392
8.7;An Optimum Path Planning for LARMClutched Arm;393
8.7.1;1 Introduction;393
8.7.2;2 The LARM Clutched Arm;394
8.7.3;3 Formulation for Path Planning;395
8.7.4;4 Numerical Examples;397
8.7.5;5 Conclusions;400
8.7.6;References;400
8.8;A Simple Kinematic Model of a Human Body for Virtual Environments;401
8.8.1;1 Introduction;401
8.8.2;2 Human Body Kinematics;402
8.8.2.1;2.1 Kinematic Model;403
8.8.2.2;2.2 Motion Assessment;403
8.8.2.3;2.3 Singularity Handling;404
8.8.2.4;2.4 Virtual Mirror;407
8.8.3;3 Conclusions;408
8.8.4;References;408
9;PART 7;409
9.1;On the Development of Low Mass Shaking Force Balanced Manipulators;410
9.1.1;1 Introduction;410
9.1.2;2 Force Balanced Manipulator with Three Degrees of Freedom;411
9.1.3;3 Force Balanced Manipulator with Four Degrees of Freedom;415
9.1.4;4 Evaluation and Experiments;418
9.1.5;5 Conclusion;419
9.1.6;References;419
9.2;Singularity-Invariant Leg Rearrangements in Stewart–Gough Platforms;420
9.2.1;1 Introduction;420
9.2.2;2 Condition for Singularity Invariance;421
9.2.3;3 Point-Line Component;422
9.2.4;4 Point-Plane Component;423
9.2.5;5 Line-Line Component;423
9.2.6;6 Line-Plane Component;425
9.2.7;7 Conclusions and Future Work;426
9.2.8;References;427
9.3;Geometric Kinematics of Rigid Bodies with Point Contact;428
9.3.1;1 Introduction;428
9.3.2;2 Darboux Frame and Darboux Vector;429
9.3.3;3 Sliding Motion;430
9.3.4;4 Spin-Rolling Motion;430
9.3.5;5 Sliding-Spin-Rolling Motion;431
9.3.5.1;5.1 Derivation of Geometric Invariants of Rolling Motion;432
9.3.5.2;5.2 Derivation of Geometric Invariants of Sliding Motion;434
9.3.5.3;5.3 Geometric Velocity of Sliding-Spin-Rolling Motion;434
9.3.6;6 Conclusions;435
9.3.7;References;435
9.4;Singularity Locus of 6–4 Fully-Parallel Manipulators;436
9.4.1;1 Introduction;436
9.4.2;2 Notations and Preliminary Computations;438
9.4.3;3 New Expression of the Singularity-Locus Equation;439
9.4.4;4 Discussion;440
9.4.5;5 Conclusions;442
9.4.6;Appendix A;442
9.4.7;Appendix B;443
9.4.8;References;443
9.5;The Pre-Stereographic Model of the General Three-System of Screws;445
9.5.1;1 Introduction;445
9.5.2;2 Screws and Projective Spaces;446
9.5.2.1;2.1 Physical and Geometrical Screws;446
9.5.2.2;2.2 Models of Projective Space;446
9.5.3;3 A Model of the General Three-System;447
9.5.3.1;3.1 The Pre-Stereographic Sphere;447
9.5.3.2;3.2 The Pitch Axis;449
9.5.3.3;3.3 The Screw Axis Location;449
9.5.4;4 Possible Applications of the Pre-Stereographic Model;450
9.5.5;5 Conclusions;452
9.5.6;References;452
9.6;Difficulty of Kinematic Synthesis of Usable Constrained Planar 6R Robots;453
9.6.1;1 Introduction;453
9.6.2;2 Literature Review;454
9.6.3;3 Kinematics Equations of a Planar nR Chain;455
9.6.4;4 Synthesis of RR Constraints;456
9.6.5;5 Identification of Usable Four-bar Linkages;457
9.6.6;6 Probability of a Usable Four-bar Linkage;458
9.6.7;7 Probability of Usable Constrained 2R Robots;459
9.6.8;8 Probability of Usable Constrained 6R Robots;460
9.6.9;9 Conclusions;460
9.6.10;References;461
9.7;Stiffness Analysis of Parallel Manipulators with Preloaded Passive Joints;462
9.7.1;1 Introduction;462
9.7.2;2 Manipulator Model;463
9.7.3;3 Static Equilibrium;465
9.7.4;4 Stiffness Matrix;466
9.7.5;5 Kinetostatic Control;467
9.7.6;6 Application Example;468
9.7.7;7 Conclusions;470
9.7.8;References;471
9.8;Characterization of Parallel Manipulator AvailableWrench Set Facets;472
9.8.1;1 Introduction;472
9.8.2;2 AvailableWrench Set Definition;473
9.8.3;3 Faces and Representation of a Convex Polytope;474
9.8.4;4 The AvailableWrench Set as a System of Linear Inequalities;475
9.8.4.1;4.1 Proofs of the First and Second Assertions;476
9.8.4.2;4.2 A Finite System of Linear Inequalities;477
9.8.5;5 Hyperplane Shifting Method;478
9.8.6;6 Conclusion;479
9.8.7;References;479
10;PART 8;480
10.1;Constraint-Screw System Based Synthesis of Limb Arrangement of the 3-PUP Parallel Mechanism;481
10.1.1;1 Introduction;481
10.1.2;2 The PUP Limb and Its Geometry Constraints;482
10.1.3;3 Constraint Screw Systems for the 3-PUP Parallel Mechanism;483
10.1.3.1;3.1 Screw Systems Based on Torque Constraints;484
10.1.3.2;3.2 Screw Systems Including Force Constraints;484
10.1.4;4 Various Limb Arrangements of the 3-PUP Parallel Mechanism and Their Instantaneous Mobility Corresponding to the Screw Systems;485
10.1.4.1;4.1 Limb Arrangement Corresponding to Type I;485
10.1.4.2;4.2 Limb Arrangement Corresponding to Type II;486
10.1.4.3;4.3 Limb Arrangement Corresponding to Type III;486
10.1.5;5 Conclusions;487
10.1.6;References;488
10.2;On Structural Properties of Sets of Finite Displacement Screws;489
10.2.1;1 Introduction;489
10.2.2;2 Notation and Basic Geometry;490
10.2.3;3 Specification of a Finite Displacement Screw;490
10.2.4;4 Sets of Relocation Screws;491
10.2.5;5 Presence of a Nodal Line;492
10.2.6;6 Interpretation;493
10.2.7;7 Mechanism with Explicit Line Symmetry;494
10.2.8;8 Conformation with a 2-System;495
10.2.9;9 Conclusion;496
10.2.10;References;496
10.3;An Autonomous and Safe Homing Strategy for Parallel Kinematic Five-Bar Manipulators;497
10.3.1;1 Introduction;497
10.3.1.1;1.1 The Five-Bar Mechanism;498
10.3.2;2 A Strategy for Autonomous Homing;498
10.3.3;3 Analysis of the Homing Strategy Proposed;499
10.3.3.1;3.1 Segmentation into Two Phases;500
10.3.3.1.1;3.1.1 Analysis of the Second Phase;500
10.3.3.1.2;3.1.2 Analysis of the First Phase;500
10.3.3.2;3.2 Choice of Workspace Partitioning and its Restrictions;501
10.3.4;4 Generalization for the Non-Symmetric Five-Bar;503
10.3.5;5 Conclusions;503
10.3.6;References;504
10.4;Singularities of Regional Manipulators Revisited;505
10.4.1;1 Introduction;505
10.4.2;2 The Kinematic Mapping;507
10.4.3;3 Jacobian Matrices;508
10.4.4;4 The Singular Locus;510
10.4.5;5 Cusps;511
10.4.6;6 Example: Ortho-Parallel Manipulator;512
10.4.7;7 Conclusions;513
10.4.8;References;514
10.5;Robot-Based HiL Test of Joint Endoprostheses;516
10.5.1;1 Introduction;516
10.5.2;2 HiL Simulator for Testing of Endoprostheses;517
10.5.3;3 Simplified Mathematical Model of the HiL Simulator;519
10.5.4;4 Biomechanical Multibody Model;522
10.5.5;5 Conclusion;522
10.5.6;References;523
10.6;An Algorithm for Real-Time Forward Kinematics of Cable-Driven Parallel Robots;524
10.6.1;1 Introduction;524
10.6.2;2 Forward Kinematics of Cable-Driven Parallel Robots;525
10.6.3;3 Real-Time Algorithm;526
10.6.4;4 Implementation and Experimental Results;529
10.6.5;5 Conclusions;532
10.6.6;References;532
10.7;Numerical Synthesis of Overconstrained Mechanisms Based on Screw Theory;534
10.7.1;1 Introduction;534
10.7.2;2 Open Kinematical Chains with Helical Joints;535
10.7.2.1;2.1 Screw System of the Helical Joints;535
10.7.2.2;2.2 Differential Displacement of the Screw Axes;536
10.7.3;3 Single Loop Spatial Mechanisms with Helical Joints;536
10.7.3.1;3.1 Closure Condition at the Velocity Level;537
10.7.3.2;3.2 Differential Displacement of the Screw Axes;537
10.7.4;4 Synthesis of Overconstrained Spatial Mechanisms;538
10.7.5;5 Numerical Synthesis Algorithm;540
10.7.6;6 Results and Outlook;541
10.7.7;References;541
11;Author Index;542
12;Subject Index;544