Solution of kinematic equations for robot manipulators

  • C. Y. Ho
  • K. W. Copeland


The paper derives kinematic equations of a general robot manipulator presented in the form of an open kinematic chain. Kinematic modelling is based on placing Cartesian-type local coordinate systems on segments of the manipulator and on calculation of their mutual transformations. Equations are written in a form suitable for programming on a digital computer. The given mathematical apparatus represents the basis of a complex mathematical modelling of a robot manipulator and is outstanding for its simplicity, efficiency, and engineering usefulness.

  • \(\overrightarrow{v}\) — a three-dimensional-vector

  • v — a general vector

  • A — a matrix


Coordinate Frame Robot Manipulator Kinematic Chain Revolute Joint Orientation Vector 
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  1. [1]
    R. Paul, B. Shimano, and G. Mayer, “Kinematic Control Equations for Simple Manipulators,” IEEE Transactions on Systems, Man, and Cybernetics, Vol. SMC-11, pp. 449–455, June 1981.Google Scholar
  2. [2]
    J.Denavit and R.S. Hartenburg, “A Kinematic Notation for Lower-Pair Mechanisms Based on Matrices,” J. Appl. Mech., pp. 215–221, June 1955.Google Scholar

Copyright information

© Crane Russak & Company Inc 1984

Authors and Affiliations

  • C. Y. Ho
    • 1
  • K. W. Copeland
    • 1
  1. 1.University of Missouri-RollaRollaUSA

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