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Advanced Theory of Constraint and Motion Analysis for Robot Mechanisms

Book Description

Advanced Theory of Constraint and Motion Analysis for Robot Mechanisms provides a complete analytical approach to the invention of new robot mechanisms and the analysis of existing designs based on a unified mathematical description of the kinematic and geometric constraints of mechanisms.

Beginning with a high level introduction to mechanisms and components, the book moves on to present a new analytical theory of terminal constraints for use in the development of new spatial mechanisms and structures. It clearly describes the application of screw theory to kinematic problems and provides tools that students, engineers and researchers can use for investigation of critical factors such as workspace, dexterity and singularity.

• Combines constraint and free motion analysis and design, offering a new approach to robot mechanism innovation and improvement.
• Clearly describes the use of screw theory in robot kinematic analysis, allowing for concise representation of motion and static forces when compared to conventional analysis methods.
• Includes worked examples to translate theory into practice and demonstrate the application of new analytical methods to critical robotics problems.

Table of Contents

  1. Cover image
  2. Title page
  3. Table of Contents
  4. Copyright
  5. Preface
  6. Chapter 1. Introduction
    1. Abstract
    2. 1.1 Review of Mechanism
    3. 1.2 Contradiction Between Calculation and Practice of Mobility of Spatial Mechanism
    4. 1.3 Possible Causes for Contradiction between the Calculated DOF and the Actual One
    5. 1.4 Contents of the Book
    6. References
  7. Chapter 2. A Brief Introduction to Screw Theory
    1. Abstract
    2. 2.1 Plücker Vector
    3. 2.2 Rigid Body’s Motion Expression
    4. 2.3 Screw Expression of Motion and Force
    5. 2.4 Reciprocal Product of Screws and its Geometric Meaning
    6. 2.5 Linear Combinations of Screws and Principal Screws of a Screw System
    7. 2.6 Identification of Principal Screws of a Screw System
    8. 2.7 Conclusions
    9. References
  8. Chapter 3. Twists and Wrenches of a Kinematic Chain
    1. Abstract
    2. 3.1 Free Motions and the Constraints of a Kinematic Pair
    3. 3.2 Twists of Kinematic Chains
    4. 3.3 Theory of Reciprocal Screws
    5. 3.4 Conclusions
    6. References
  9. Chapter 4. Free Motion of the End Effector of a Robot Mechanism
    1. Abstract
    2. 4.1 Free Motion Space and Constraint Space of Kinematic Chain
    3. 4.2 General Steps to Analyze the Degree of Freedom of the End Effector
    4. 4.3 Application of the Analytical Theory of the Degree of Freedom of the End Effector
    5. 4.4 The Equivalent Substitutions for Hybrid Kinematic Chains
    6. 4.5 Conclusions
    7. References
  10. Chapter 5. Workspace of the End Effector of a Robot Mechanism
    1. Abstract
    2. 5.1 Workspace Based on Mobility Analysis
    3. 5.2 Symmetrical Characteristics of the Workspace for Spatial Parallel Mechanisms with Symmetric Structure
    4. 5.3 Applications of the Symmetrical Workspace Theorem
    5. 5.4 Conclusions
    6. References
  11. Chapter 6. Singularity Analysis of the End Effector of a Mechanism within Its Workspace
    1. Abstract
    2. 6.1 Static Equilibrium Equations of the Parallel Manipulators
    3. 6.2 Symmetry of Singularity Distribution within the Reachable Workspace
    4. 6.3 Applications and Discussion
    5. 6.4 Conclusions
    6. References
  12. Chapter 7. Kinematics with Four Points′ Cartesian Coordinates for Spatial Parallel Manipulator
    1. Abstract
    2. 7.1 Kinematics Model for Spatial Parallel Manipulators with Four Points′ Cartesian Coordinates
    3. 7.2 Forward Kinematics of Spatial Parallel Manipulators
    4. 7.3 Conclusions
    5. References
  13. Chapter 8. Kinematics and Statics of Manipulators
    1. Abstract
    2. 8.1 Key Problems in Kinematics and Statics Analysis
    3. 8.2 Kinematics and Statics of Series Manipulators
    4. 8.3 Kinematics and Statics of Parallel Manipulators
    5. 8.4 Conclusions
    6. References
  14. Chapter 9. Fundamental Factors to Investigating the Motions and Actuations of a Mechanism
    1. Abstract
    2. 9.1 The Basic Steps for Calculating the DOF of the Mechanism with a Prescribed End Effector
    3. 9.2 Actuation Schemes to Control of the Mechanism
    4. 9.3 Conclusions
    5. References
  15. Chapter 10. Motion Characteristics of a Robotic Mechanism
    1. Abstract
    2. 10.1 Problems Existing in the Traditional Theories of DOF
    3. 10.2 Theory of DOF for the Mechanism with an End Effector
    4. 10.3 Proof of the Theory
    5. 10.4 Applications and Discussions
    6. 10.5 Conclusions
    7. References
  16. Chapter 11. Mechanism Theory and Application of Deployable Structures Based on Scissor-Like Elements
    1. Abstract
    2. 11.1 Deployable Structures
    3. 11.2 Brief Review of Reciprocal Screw Theory Based on Exponential Production
    4. 11.3 Mechanism Theory of a Deployable Structure Unit
    5. 11.4 Applications of Deployable Structure Units
    6. 11.5 Conclusions
    7. References
  17. Chapter 12. Structure Synthesis of Spatial Mechanisms
    1. Abstract
    2. 12.1 General Process of Mechanism Synthesis
    3. 12.2 Analysis of Structure Synthesis
    4. 12.3 Conclusion
    5. References
  18. Chapter 13. Workspace Synthesis of Spatial Mechanisms
    1. Abstract
    2. 13.1 Theorem of Dexterous Workspace of Spatial Parallel Manipulator
    3. 13.2 Optimum Design of Spatial Manipulators Aiming at a Desired Dexterous Workspace
    4. 13.3 Conclusions
    5. References
  19. Chapter 14. Kinematic Synthesis of Spatial Mechanisms
    1. Abstract
    2. 14.1 Kinematic Synthesis of a Spatial Parallel Manipulator With Three Pure Rotational Degrees of Freedom (DOFs)
    3. 14.2 Kinematics of a Spatial Parallel Manipulator With Two Rotational and One Translational DOF
    4. 14.3 Kinematic of the Suspension Mechanism with Invariable Orientation Parameters
    5. 14.4 Conclusions
    6. References
  20. Index