Müller / Zlatanov Singular Configurations of Mechanisms and Manipulators

1. Auflage 2019
ISBN: 978-3-030-05219-5
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 589, 236 Seiten

Reihe: CISM International Centre for Mechanical Sciences

The book introduces the main problems, key methods, and milestone results in singularity analysis of mechanisms. It provides a comprehensive and concise overview of basic results while also addressing a few advanced topics of singularities in mechanical systems and robots.

Autoren/Hrsg.

Müller, Andreas

Zlatanov, Dimiter

Inhaltsverzeichnis

1;Preface;6
2;Contents;9
3;Generalized Singularity Analysis;10
3.1;1 Introduction;10
3.2;2 The Standard View of Singularity;13
3.2.1;2.1 The Simplest Case: Serial Chain Singularity;13
3.2.2;2.2 The Serial–Parallel Duality;15
3.2.3;2.3 A Generalization: The Input–Output Equation;16
3.2.4;2.4 The Counterexamples;17
3.3;3 Singularity via Differentiable Maps;20
3.3.1;3.1 Serial Chains;20
3.3.2;3.2 Chains with Closed Loops;20
3.3.3;3.3 Regular and Singular Configurations;22
3.4;4 Singularity via Instantaneous Kinematics;23
3.4.1;4.1 Instantaneous Motions;24
3.4.2;4.2 Instantaneous Definition of Singularity;25
3.4.3;4.3 Singularity Types and Classes;26
3.4.4;4.4 Classes of Singularities;28
3.5;5 Common and Uncommon Singularities;29
3.5.1;5.1 Generic and Nongeneric Singularity Types;29
3.5.2;5.2 Parallel Mechanisms with Extendable Legs;30
3.5.3;5.3 The Isotropic Singularity of the Orthoglide;31
3.6;6 Constraint Singularities of Parallel Manipulators;35
3.6.1;6.1 Another ``Isotropic'' Configuration;35
3.6.2;6.2 Constraints, Freedoms, and Constrained Singularities;36
3.6.3;6.3 Singularities of 3-RPS Manipulators;37
3.6.4;6.4 The Simplest Constraint Singularity;39
3.6.5;6.5 Constraint Singularities as Branching Points;40
3.7;7 Conclusions;45
3.8;References;46
4;Singularity Set Computation: A Hands-On Session with the CUIK Suite;48
4.1;1 Introduction;48
4.1.1;1.1 Basic Concepts;49
4.1.2;1.2 An Illustrative Example;50
4.2;2 Singularity Set Computation with the CUIK Suite;53
4.2.1;2.1 Preparation;53
4.2.2;2.2 Dextar's Geometry;54
4.2.3;2.3 Assembly Constraints;55
4.2.4;2.4 Inverse Singularity Conditions;57
4.2.5;2.5 Forward Singularity Conditions;58
4.2.6;2.6 Computation and Output Plots;59
4.2.7;2.7 Visualizing the Output Portrait;69
4.2.8;2.8 Visualizing the Input Portrait;70
4.2.9;2.9 Workspace Boundaries and Interior Barriers;72
4.3;References;74
5;Cuspidal Robots;75
5.1;1 Introduction;75
5.1.1;1.1 Preliminaries;75
5.1.2;1.2 Brief History of Cuspidal Robots;76
5.1.3;1.3 Questions of Interest;77
5.1.4;1.4 Chapter Outline;78
5.2;2 Postures;78
5.2.1;2.1 Definition;78
5.2.2;2.2 Postures and Aspects Case 1: Non-cuspidal Robots;78
5.2.3;2.3 Postures and Aspects Case 2: Cuspidal Robots;80
5.2.4;2.4 Non-singular Change of Posture Versus Singular Change of Posture;82
5.3;3 Path Feasibility;85
5.3.1;3.1 Showing an Example;85
5.3.2;3.2 Regions of Feasible Paths for Non-cuspidal Robots;86
5.3.3;3.3 Characteristic Surfaces;88
5.3.4;3.4 Uniqueness Domains and Regions of Feasible Paths for Cuspidal Robots;91
5.4;4 Identification, Enumeration and Classification of Cuspidal and Non-cuspidal Robots;92
5.4.1;4.1 Simplifying Geometric Conditions;92
5.4.2;4.2 Identification of Cuspidal Robots and Classification;95
5.5;5 Higher-Degree-of-Freedom Robots and Parallel Robots;101
5.5.1;5.1 6-dof Serial Robots;101
5.5.2;5.2 Parallel Robots;102
5.6;6 Conclusions;105
5.7;References;106
6;Mechanism Constraints and Singularities—The Algebraic Formulation;108
6.1;1 Introduction;109
6.2;2 Parameterization of SE(3);109
6.3;3 Constraint Equations;113
6.3.1;3.1 Geometric Constraint Equations;114
6.3.2;3.2 Elimination Method;128
6.3.3;3.3 Linear Implicitization;130
6.3.4;3.4 Singularities in Serial Chains;139
6.4;4 Algebraic Basics;141
6.4.1;4.1 Ideals and Affine Varieties;141
6.4.2;4.2 Standard Bases;153
6.4.3;4.3 Elimination;156
6.4.4;4.4 Dimension, Primary Decomposition;159
6.5;5 Complete Kinematic Analysis of the TSAI Parallel Manipulator;162
6.5.1;5.1 Introduction;162
6.5.2;5.2 Manipulator Design;163
6.5.3;5.3 Deduction of Constraint Equations;164
6.5.4;5.4 Solving the System;167
6.6;6 The Manipulator's Operation Modes;171
6.7;7 Conditions for Singular Poses;174
6.7.1;7.1 Changing Operation Modes;180
6.8;8 Conclusion;185
6.9;References;185
7;Local Investigation of Mobility and Singularities of Linkages;188
7.1;1 Introduction;188
7.2;2 Kinematic Model of Single-Loop Linkages;190
7.2.1;2.1 Geometric Loop Closure Constraints and the Configuration Space;190
7.2.2;2.2 Velocity Loop Closure Constraints;192
7.3;3 Kinematic Model of Multi-loop Linkages;194
7.4;4 Phenomenology and Definitions;196
7.5;5 Local Analysis of Smooth Finite Motions;204
7.5.1;5.1 Kinematic Tangent Cone to the C-Space;205
7.5.2;5.2 Higher-Order Loop Closure Constraints;206
7.5.3;5.3 Computational Procedure;208
7.5.4;5.4 Examples;209
7.6;6 Local Analysis of Smooth Finite Motions with Certain Rank;215
7.6.1;6.1 Kinematic Tangent Cone;215
7.6.2;6.2 Higher-Order Time Derivatives of Jacobian Minors;217
7.6.3;6.3 Examples;218
7.7;7 Interlude: The Tangent Cone to a Variety;221
7.8;8 Local Analysis of the Configuration Space;225
7.8.1;8.1 Higher-Order local Approximation;225
7.8.2;8.2 Higher-Order Series Expansion of the Constraint Mapping;225
7.8.3;8.3 Examples;227
7.9;9 Local Analysis of Subvarieties of the C-Space of Points with Certain Rank;231
7.9.1;9.1 Higher-Order Local Approximation;232
7.9.2;9.2 Higher-Order Series Expansion of Jacobian Minors;232
7.9.3;9.3 Examples;232
7.10;10 Discussion;233
7.11;References;234