[Springer Tracts in Mechanical Engineering] Finite and Instantaneous Screw Theory in Robotic Mechanism ||

This book presents a finite and instantaneous screw theory for the development of robotic mechanisms. It addresses the analytical description and algebraic computation of finite motion, resulting in a generalized type synthesis approach. It then discusses the direct connection between topology and performance models, leading to an integrated performance analysis and design framework. The book then explores parameter uncertainty and multiple performance requirements for reliable, optimal design methods, and describes the error accumulation principle and parameter identification algorithm, to increase robot accuracy. It proposes a unified and generic methodology, and appliesto the invention, analysis, design, and calibration of robotic mechanisms. The book is intended for researchers, graduate students and engineers in the fields of robotic mechanism and robot design and applications. 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