Finite and Instantaneous Screw Theory in Robotic Mechanism (Springer Tracts in Mechanical Engineering)

Preface
Contents
1 Introduction
	1.1 Classification of Robotic Mechanism
		1.1.1 Open-loop Robotic Mechanism
		1.1.2 Closed-loop Robotic Mechanism
		1.1.3 Hybrid Robotic Mechanism
	1.2 Synthesis, Analysis, Design and Calibration of Robotic Mechanism
	1.3 Screw Theory in Robotic Mechanism
		1.3.1 Instantaneous Screw
		1.3.2 Finite Screw
		1.3.3 Relation Between Finite and Instantaneous Screws
	1.4 Scope and Organization of This Book
	References
2 Finite and Instantaneous Screw Theory
	2.1 Introduction
	2.2 Finite Screw
		2.2.1 Quasi-vector Derived from Dual Quaternion
		2.2.2 Screw Triangle Product
		2.2.3 Algebraic Structure of Finite Screw
	2.3 Instantaneous Screw
		2.3.1 Instantaneous Screw in Vector Form
		2.3.2 Algebraic Structure of Instantaneous Screw
		2.3.3 Twist and Wrench with Reciprocal Product
		2.3.4 Classification of Twist Spaces and Wrench Spaces
	2.4 Differential Mapping Between the Screws
		2.4.1 One-DoF Motion
		2.4.2 Multi-DoF Motion
	2.5 Discussion on the Algebraic Structures of FIS
	2.6 Conclusion
	References
3 Topology and Performance Modeling of Robotic Mechanism
	3.1 Introduction
	3.2 FIS Based Topology and Performance Modeling
	3.3 FIS Based Finite and Instantaneous Motion Modeling
		3.3.1 The Finite Motion Modeling
		3.3.2 The Instantaneous Motion Modeling
	3.4 Example
		3.4.1 Typical Open-loop Mechanism
		3.4.2 Typical Closed-loop Mechanism
	3.5 Integrated Framework for Type Synthesis and Performance Analysis
	3.6 Conclusion
	References
4 Type Synthesis Method and Procedure of Robotic Mechanism
	4.1 Introduction
	4.2 General Procedure of Finite Screw Based Type Synthesis
	4.3 The Commonly Used Motion Pattern
		4.3.1 One-DoF Motion Pattern
		4.3.2 Multi-DoF Motion Pattern
	4.4 Limb Synthesis
		4.4.1 Standard Limb Structure
		4.4.2 Derivative Limb Structure
		4.4.3 Composition Algorithms Among Joint Motions
		4.4.4 Equivalent Groups of Joints
	4.5 Assembly Condition and Actuation Arrangement
		4.5.1 Assembly Condition
		4.5.2 Non-redundant Actuation Arrangement
		4.5.3 Intersection Algorithms Among Limb Motion
	4.6 Type Synthesis of Robotic Mechanism
	4.7 Conclusion
	References
5 Type Synthesis of Mechanisms with Invariable Rotation Axes
	5.1 Introduction
	5.2 Mechanism with Invariable Rotation Axes
		5.2.1 Mechanism with One Invariable Rotation Axis
		5.2.2 Mechanism with Two Invariable Rotation Axes
	5.3 Examples with One Invariable Rotation Axis
		5.3.1 Open-loop Mechanisms with Schoenfiles Motion
		5.3.2 Open-loop Mechanisms with Planar Motion
	5.4 Examples with Two Invariable Rotation Axes
		5.4.1 Single Closed-loop Mechanisms with Double-Schoenfiles Motion
		5.4.2 Closed-loop Mechanisms with Tricept Motion
	5.5 Conclusion
	References
6 Type Synthesis of Mechanism with Variable Rotation Axes
	6.1 Introduction
	6.2 Mechanism with Variable Rotation Axes
		6.2.1 Mechanism with One Variable Rotation Axis
		6.2.2 Mechanism with One Invariable and One Variable Rotation Axes
		6.2.3 Mechanism with Two Variable Rotation Axes
	6.3 Example with One Variable Rotation Axis
		6.3.1 Single Closed-loop Mechanism with 1R1T Motion
		6.3.2 Closed-loop Mechanism with 3T1R Motion
	6.4 Example with One Invariable and One Variable Rotation Axes
		6.4.1 Open-loop Mechanism with 3T2R Motion
		6.4.2 Closed-loop Mechanism with Exechon Motion
	6.5 Example with Two Variable Rotation Axes
		6.5.1 Single Closed-loop Mechanisms with 2R Motion
		6.5.2 Closed-loop Mechanisms with Z3 Motion
	6.6 Conclusion
	References
7 Kinematic Modeling and Analysis of Robotic Mechanism
	7.1 Introduction
	7.2 Displacement Modeling
		7.2.1 Forward Kinematics Modeling
		7.2.2 Inverse Kinematics Modeling
	7.3 Workspace Analysis
		7.3.1 Sub-three-dimensional Orientation Space
		7.3.2 Sub-three-dimensional Position Space
		7.3.3 Workspace Regardless of Initial Pose
	7.4 Velocity Analysis
		7.4.1 Jacobian Matrix of Open-loop Mechanism
		7.4.2 Jacobian Matrix of Closed-loop Mechanism
	7.5 Example
		7.5.1 Typical Open-loop Mechanism
		7.5.2 Typical Closed-loop Mechanism
	7.6 Conclusion
	References
8 Static Modeling and Analysis of Robotic Mechanism
	8.1 Introduction
	8.2 Twist and Wrench Analysis
		8.2.1 Open-loop Mechanism
		8.2.2 Closed-loop Mechanism
	8.3 Stiffness Modeling
		8.3.1 m-DoF Virtual Spring
		8.3.2 Open-loop Mechanism
		8.3.3 Closed-loop Mechanism
	8.4 Example
		8.4.1 Typical Open-loop Mechanism
		8.4.2 Typical Closed-loop Mechanism
	8.5 Conclusion
	References
9 Dynamic Modeling and Analysis of Robotic Mechanism
	9.1 Introduction
	9.2 Velocity Modeling
		9.2.1 Open-loop Mechanism
		9.2.2 Closed-loop Mechanism
	9.3 Acceleration Modeling
		9.3.1 Open-loop Mechanism
		9.3.2 Closed-loop Mechanism
	9.4 Dynamic Modeling
		9.4.1 Wrench Analysis
		9.4.2 Dynamic Modeling
	9.5 Example
		9.5.1 Typical Open-loop Mechanism
		9.5.2 Typical Closed-loop Mechanism
	9.6 Conclusion
	References
10 Optimal Design of Robotic Mechanism
	10.1 Introduction
	10.2 Parameter Uncertainty
		10.2.1 Statistical Objective
		10.2.2 Probabilistic Constraint
	10.3 Multi-objective Optimization
		10.3.1 Performance Index
		10.3.2 Response Surface Method Model
		10.3.3 Pareto-based Optimization
	10.4 Procedure of Multi-objective Optimization with Parameter Uncertainty
	10.5 Example
		10.5.1 Typical Open-loop Mechanism
		10.5.2 Typical Closed-loop Mechanism
	10.6 Conclusion
	References
11 Synthesis, Analysis, and Design of Typical Robotic Mechanism
	11.1 Introduction
	11.2 1T2R Mechanism with Invariable Rotation Axes
		11.2.1 Type Synthesis
		11.2.2 Performance Modeling
		11.2.3 Optimal Design
	11.3 2R Mechanism with Variable Rotation Axes
		11.3.1 Type Synthesis
		11.3.2 Performance Modeling
		11.3.3 Optimal Design
	11.4 Conclusion
	References
12 Kinematic Calibration of Robotic Mechanism
	12.1 Introduction
	12.2 Error Modeling
		12.2.1 Joint
		12.2.2 Open-loop Mechanism
		12.2.3 Closed-loop Mechanism
	12.3 Error Identification
		12.3.1 Redundant Error Analysis
		12.3.2 Error Identification Algorithm
	12.4 Example
		12.4.1 Typical Open-loop Mechanism
		12.4.2 Typical Closed-loop Mechanism
	12.5 Conclusion
	References
Appendix A Differentiation of Finite Screw Considering Both Motion Parameters and Screw Axis
References
Appendix B Quasi-differential Function