Standard Article

Robot Kinematics

  1. Dan Zhang1,
  2. Zhuming Bi1,
  3. Zhen Gao2

Published Online: 13 JUN 2008

DOI: 10.1002/9780470050118.ecse204

Wiley Encyclopedia of Computer Science and Engineering

Wiley Encyclopedia of Computer Science and Engineering

How to Cite

Zhang, D., Bi, Z. and Gao, Z. 2008. Robot Kinematics. Wiley Encyclopedia of Computer Science and Engineering. 1–12.

Author Information

  1. 1

    University of Ontario Institute of Technology, Oshawa, Ontario, Canada

  2. 2

    University of Science and Technology of China, Hefei, China

Publication History

  1. Published Online: 13 JUN 2008


In this article, kinematics of robot manipulators is presented with a systematic and general approach—Denavit-Hartenberg convention. The basic mathematical concepts are explained in detail, including translational transformation, rotational transformation, homogeneous transformation, Euler angle, direct kinematics and inverse kinematics, and so on. The relation between joint velocities and end-effector linear and angular velocities is described by the Jacobian matrix. As an example, a parallel manipulator with three degrees of freedom (DOFs) is presented. This 3DOF-parallel manipulator can be used for machine tools, and it includes two rotations and one translation along the z axis. Both direct and inverse kinematic problems are conducted based on the theory described in the beginning of the article. The case study will allow readers to better understand the knowledge of robot kinematics.


  • robot manipulator;
  • direct kinematics;
  • inverse kinematics;
  • velocities;
  • Jacobian matrix;
  • parallel manipulator