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El. knyga: Mechanisms: Kinematic Analysis and Applications in Robotics

(Professor, Department of Mechanical Engineering, Tecnologico Nacional de Mexico, Celaya, Mexico), (Design Engineer, ZKW Mexico, Mexico)
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Theory of mechanisms is an applied science of mechanics that studies the relationship between geometry, mobility, topology, and relative motion between rigid bodies connected by geometric forms. Recently, knowledge in kinematics and mechanisms has considerably increased, causing a renovation in the methods of kinematic analysis. With the progress of the algebras of kinematics and the mathematical methods used in the optimal solution of polynomial equations, it has become possible to formulate and elegantly solve problems.

Mechanisms: Kinematic Analysis and Applications in Robotics provides an updated approach to kinematic analysis methods and a review of the mobility criteria most used in planar and spatial mechanisms. Applications in the kinematic analysis of robot manipulators complement the material presented in the book, growing in importance when one recognizes that kinematics is a basic area in the control and modeling of robot manipulators.

  • Presents an organized review of general mathematical methods and classical concepts of the theory of mechanisms
  • Introduces methods approaching time derivatives of arbitrary vectors employing general approaches based on the vector angular velocity concept introduced by Kane and Levinson
  • Proposes a strategic approach not only in acceleration analysis but also to jerk analysis in an easy to understand and systematic way
  • Explains kinematic analysis of serial and parallel manipulators by means of the theory of screws

PART 1: INTRODUCTION
1.Overview of kinematics and its algebras
2. Overview of mechanisms and robot manipulators

PART 2: MATHEMATICAL BACKGROUND
3. Linear algebra
4. The Lie algebra se(3) of the Euclidean group SE(3)
5. Polynomial
6. Vector derivative

PART 3: GEOMETRY OF MECHANISMS
7. Generalities
8. Mobility of mechanisms

PART 4: DISPLACEMENT
9. Closed kinematic chains
10. Open kinematic chains

PART 5: VELOCITY
11. Angular velocity
12. Vectorial method
13. Graphical method
14. Analytical method

PART 6: ACCELERATION
15. Angular acceleration
16. Vectorial method
17. Analytical method

PART 7: ROBOTICS
18. Fundamentals of screw theory
19. Robot manipulators

APPENDIX A: Maple Sheets

Jaime Gallardo-Alvarado received his Ph.D. degree from the Tecnológico Nacional de México in La Laguna. He is a member of the National System of Researchers of Mexico, and is currently a professor in the Department of Mechanical Engineering at the Tecnológico Nacional de México in Celaya. His areas of interest include kinematics and dynamics of rigid bodies, Lie algebras, screw theory, and robot kinematics. Dr. Gallardo-Alvarado is author of the book Kinematic Analysis of Parallel Manipulators by Algebraic Screw Theory” and has published more than 70 research papers in scientific journals. José Gallardo-Razo received his B.Sc. degree from the Tecnológico Nacional de México in Celaya. He is currently a Design Engineer in ZKW Mexico. His areas of interest cover kinematics, dynamics and control of robot manipulators, mechanical design, and CAD-CAE-CAM.
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