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.

Key Features

  • 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


Researchers, engineers and graduate students working on engineering design, robotics and automation

Table of Contents


Chapter 1. Introduction


1.1 Review of Mechanism

1.2 Contradiction Between Calculation and Practice of Mobility of Spatial Mechanism

1.3 Possible Causes for Contradiction between the Calculated DOF and the Actual One

1.4 Contents of the Book


Chapter 2. A Brief Introduction to Screw Theory


2.1 Plücker Vector

2.2 Rigid Body’s Motion Expression

2.3 Screw Expression of Motion and Force

2.4 Reciprocal Product of Screws and its Geometric Meaning

2.5 Linear Combinations of Screws and Principal Screws of a Screw System

2.6 Identification of Principal Screws of a Screw System

2.7 Conclusions


Chapter 3. Twists and Wrenches of a Kinematic Chain


3.1 Free Motions and the Constraints of a Kinematic Pair

3.2 Twists of Kinematic Chains

3.3 Theory of Reciprocal Screws

3.4 Conclusions


Chapter 4. Free Motion of the End Effector of a Robot Mechanism


4.1 Free Motion Space and Constraint Space of Kinematic Chain

4.2 General Steps to Analyze the Degree of Freedom of the End Effector

4.3 Application of the Analytical Theory of the Degree of Freedom of the End Effector

4.4 The Equivalent Substitutions for Hybrid Kinematic Chains

4.5 Conclusions


Chapter 5. Workspace of the End Effector of a Robot Mechanism


5.1 Workspace Based on Mobility Analysis

5.2 Symmetrical Characteristics of the Workspace for Spatial Parallel Mechanisms with Symmetric Structure

5.3 Applications of the Symmetrical Workspace Theorem

5.4 Conclusions


Chapter 6. Singularity Analysis of the End Effector of a Mechanism within Its Workspace


6.1 Static Equilibrium Equa


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© 2014
Academic Press
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About the authors

Jingshan Zhao

Jingshan Zhao is a leading machine design, mechanical systems and robotics researcher at China’s prestigious Tsinghua University. He has received numerous awards for doctoral excellence in China over the past decade, including the New Century Excellent Talents in University Award in 2009 from the Education Ministry of China. He has contributed to more than 40 articles in international journals, is an editorial board member of the Journal of Machinery and Automation, and is the regional editor for Asia of The Open Mechanical Engineering Journal.