Parallel Robotic Machine Tools (eBook)

Parallel Robotic Machine Tools 1
1 Introduction 11
1.1 The History of Parallel Robots 11
1.2 Introduction of Conventional Machine Tools 15
1.3 Parallel Robot-based Machine Tools 19
1.4 Scope and Organization of this Book 26
2 Kinematics of Mechanisms 29
2.1 Preamble 29
2.2 Position and Orientation of Rigid Body 29
2.2.1 Rotation Matrix 29
2.2.2 Euler Angles 32
2.3 Homogeneous Transformation 34
2.4 Denavit–Hartenberg Representation 37
2.5 Jacobian Matrix 38
2.6 Conclusions 41
3 Architectures of Parallel Robotic Machine 42
3.1 Preamble 42
3.2 Fundamentals of Mechanisms 42
3.2.1 Basic Kinematic Elements of Mechanisms 42
3.2.1.1 Prismatic Joint (P, also called sliders) 43
3.2.1.2 Revolute Joint (R, also called pin joint or hinge joint) 43
3.2.1.3 Hooke Joint (H, also called universal joint, Cardan joint or Hardy-Spicer joint) 44
3.2.1.4 Spherical Joint (S, also called ball-in-socket joint) 44
3.2.2 Classification of Mechanisms 45
3.3 Graph Representation of Kinematic Structures 47
3.4 Design Criteria 47
3.5 Case Study: Five Degrees of Freedom Parallel Robotic Machine 49
3.5.1 Serial Mechanisms 50
3.5.2 Parallel Mechanisms 50
3.5.3 Hybrid Mechanisms 56
3.6 Redundancy 57
3.7 Conclusions 57
4 Planar Parallel Robotic Machine Design 59
4.1 Preamble 59
4.2 Planar Two Degrees of Freedom Parallel Robotic Machine 65
4.3 Planar Three Degrees of Freedom Parallel Robotic Machine 69
4.4 Conclusions 76
5 Spatial Parallel Robotic Machines with Prismatic Actuators 77
5.1 Preamble 77
5.2 Six Degrees of Freedom Parallel Robotic Machine with Prismatic Actuators 78
5.2.1 Geometric Modeling and Inverse Kinematics 78
5.2.2 Global Velocity Equation 80
5.2.3 Stiffness Model 81
5.3 General Kinematic Model of n Degrees of Freedom Parallel Mechanisms with a Passive Constraining Leg and Prismatic Actuators 84
5.3.1 Geometric Modeling and Lumped Compliance Model 84
5.3.1.1 Geometric Modeling 84
5.3.1.2 Lumped Models for Joint and Link Compliances 88
5.3.2 Inverse Kinematics 89
5.3.3 Jacobian Matrices 90
5.3.3.1 Rigid Mechanisms 90
5.3.3.2 Compliant Model 90
5.3.3.3 Global Velocity Equation 91
5.3.4 Kinetostatic Model for the Mechanism with Rigid Links 92
5.3.5 Kinetostatic Model for the Mechanismwith Flexible Links 94
5.3.6 Examples 95
5.3.6.1 5-dof Parallel Mechanism 95
5.3.6.2 4-dof Parallel Mechanism 96
5.3.6.3 3-dof Parallel Mechanism 97
5.4 Conclusions 99
6 Spatial Parallel Robotic Machines with Revolute Actuators 101
6.1 Preamble 101
6.2 Six Degrees of Freedom Parallel Robotic Machine with Revolute Actuators 101
6.2.1 Geometric Modeling 101
6.2.2 Global Velocity Equation 103
6.2.2.1 Rigid Model 103
6.2.2.2 Compliant Model 103
6.2.3 Stiffness Model 104
6.3 General Kinematic Model of n Degrees of Freedom Parallel Mechanisms with a Passive Constraining Leg and Revolute Actuators 109
6.3.1 Geometric Modeling and Lumped Compliance Model 109
6.3.2 Inverse Kinematics 110
6.3.2.1 Solution for the Case of Mechanisms with Rigid Links 110
6.3.2.2 Solutions for the Mechanisms with Flexible Links 112
6.3.3 Jacobian Matrices 114
6.3.3.1 Rigid Mechanisms 114
6.3.3.2 Compliant Model 114
6.3.3.3 Global Velocity Equations 114
6.3.4 Kinetostatic Model for the Mechanism with Rigid Links 117
6.3.5 Kinetostatic Model for the Mechanismwith Flexible Links 117
6.3.6 Examples 119
6.3.6.1 5-dof Parallel Mechanism 119
6.3.6.2 4-dof Parallel Mechanism 119
6.3.6.3 3-dof Parallel Mechanism 121
6.4 Conclusions 123
7 Reconfigurable Parallel Kinematic Machine Tools 124
7.1 Preamble 124
7.2 Theoretical Design 125
7.3 Kinematics Model 127
7.4 Case Study 129
7.5 Conclusions 132
8 Performance Evaluation of Parallel Robotic Machines 133
8.1 Preamble 133
8.2 Global Stiffness Evaluation 133
8.2.1 Case Study: A Novel Three Degrees of Freedom Parallel Manipulator 133
8.2.2 Kinematic Modeling 135
8.2.3 The Global Stiffness Evaluation 137
8.3 Optimal Calibration Method 139
8.4 Conclusions 144
9 Design Optimization of Parallel Robotic Machines 145
9.1 Preamble 145
9.2 Optimization Objective and Criteria 146
9.3 Basic Theory of Evolutionary Algorithms 147
9.4 Single-Objective Optimization 152
9.4.1 Objective of Global Stiffness 152
9.4.2 Spatial Six-Degree-of-Freedom Mechanism with Prismatic Actuators 153
9.4.3 Spatial Six-Degree-of-Freedom Mechanism with Revolute Actuators 155
9.4.4 Spatial Five-Degree-of-Freedom Mechanism with Prismatic Actuators 157
9.4.5 Spatial Five-Degree-of-Freedom Mechanism with Revolute Actuators 159
9.4.6 Spatial Four-Degree-of-Freedom Mechanism with Prismatic Actuators 162
9.4.7 Spatial Four-Degree-of-Freedom Mechanism with Revolute Actuators 164
9.4.8 Spatial Three-Degree-of-Freedom Mechanism with Prismatic Actuators 166
9.4.9 Spatial Three-Degree-of-Freedom Mechanism with Revolute Actuators 167
9.4.10 The Tricept Machine Tool Family 169
9.5 Multiobjective Optimization 172
9.5.1 Case Study 1: Three Degrees of Freedom Parallel Manipulator – Two Translations and One Rotation 172
9.5.1.1 Structure Description 172
9.5.1.2 Optimization 176
9.5.2 Case Study 2: Tripod Compliant ParallelMicromanipulator 185
9.5.2.1 Structure Description 185
9.5.2.2 Performance Indices Optimization 186
9.6 Conclusions 191
10 Integrated Environment for Design and Analysis of Parallel Robotic Machine 192
10.1 Preamble 192
10.2 Case Study 193
10.3 Conclusions 208
References 209
Index 217