Automatic Kinematic Modelling of Robot Manipulators and Symbolic Generation of their Inverse Kinematics Solutions

  • Dan Halperin
Conference paper


The increasing use of robot simulation systems has raised the need for a full kinematic treatment for a large number of different types of robots. Usually this is done either by supplying a general iterative inverse procedure, a time-consuming method not guaranteed to converge, or by carrying out a special analysis for each type. In this paper we present a software system whose input is an elementary geometric description of a robot. The system automatically builds the Denavit-Hartenberg model out of the input, while retaining information of how to interface between the built model and the elementary description. It then derives the equations of the inverse kinematics and subsequently solves them symbolically in closed form (if possible). The solution is accurate, efficient in on-line use, gives all possible solutions for every input frame of the end-effector and is thus suitable for use in robot simulation. Our software package was incorporated into the ROBCAD* simulation system where it has been successfully modelling and solving a myriad of kinematic structures of robots and other mechanisms.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [AU]
    A.V. Aho, J.D. Ulmann, Principles of Compiler Design, Addison-Wesley, 1977.Google Scholar
  2. [BR]
    O. Bottema, B. Roth., Theoretical Kinematics, North Holland Publishing Company, 1979.Google Scholar
  3. [Cr]
    J.J. Craig., Introduction to Robotics Addison Wesley, 1986.Google Scholar
  4. [DH]
    J. Denavit, R.S. Hartenberg, A Kinematic Notation for Lower Pair Mechanisms Based on Matrices, ASME J. of Applied Mechanics, June 1955, pp. 215–221.Google Scholar
  5. [GBF]
    A. A. Goldenberg, B. Benhabib, R. G. Fenton, A Complete Generalized Solution to the Inverse Kinematics of Robots, IEEE J. of Robotics and Automation, Vol. RA-1, No. 1, March 1985, pp. 14–20.Google Scholar
  6. [GK]
    K. C. Gupta, K. Kazerounian, Improved Numerical Solutions of Inverse Kinematics of Robots, Proc. IEEE International Conference on Robotics and Automation, 1985, pp. 743–748.Google Scholar
  7. [Ha]
    D. Halperin, Kinematic Modelling of Robot Manipulators and Automatic Generation of their Inverse Kinematics Solutions M.Sc. Thesis, Tel-aviv University, August 1986. In Hebrew (forthcoming in English).Google Scholar
  8. [Ho]
    J. Holland, ROBCAD Reference Manual, Robcad Ltd., Herzlia, 1986.Google Scholar
  9. [HMC]
    L.G. Herrera-Bendezu, E. Mu and J.T. Cain, Symbolic Computation of Robot Manipulator Kinematics, Proc. IEEE International Conference on Robotics and Automation, 1988, pp. 993–998.Google Scholar
  10. [Le]
    C.S.G. Lee, Robot Arm Kinematics, IEEE Tutorial on Robotics, 1983, pp. 47–65.Google Scholar
  11. Lu] V.J. Lumelsky, Iterative Coordinate Transformation Procedure for One Class of Robots, IEEE Trans. on Systems Man and Cybernetics Vol. SMC-14, No. 3, May 1984, pp. 500505.Google Scholar
  12. [Pa]
    R.P. Paul, Robot Manipulators, Mathematics, Programming and Control, The MIT Press, 1981.Google Scholar
  13. [Pi]
    D.L. Pieper, The Kinematics of Manipulators Under Computer Control, Ph.D. Thesis, Stanford University, 1969.Google Scholar
  14. [PSM]
    R.P. Paul, B. Shimano, G.E. Mayer, Kinematic Control Equations for Simple Manipulators, IEEE Trans. on Systems Man and Cybernetics, Vol. SMC-11, No. 6, June 1981, pp. 456–460.Google Scholar
  15. [Sh]
    B.E. Shimano, The Kinematic Design and Force Control of Computer-Controlled Ma-nipulators, Ph.D. Thesis, Stanford University, 1978.Google Scholar
  16. [So]
    D.M.Y. Sommerville, Analytical Geometry of Three Dimensions, Cambridge University Press, 1959.Google Scholar
  17. [UDH]
    J.J. Uicker Jr., J. Denavit, R.S. Hartenberg, An Iterative Method for the Displacement Analysis of Spatial Mechanisms, Trans. of the ASME, J. of Applied Mechanics Vol. 31, June 1964, pp. 309–314.Google Scholar

Copyright information

© Springer-Verlag Wien 1991

Authors and Affiliations

  • Dan Halperin
    • 1
  1. 1.Department of Computer ScienceTel-Aviv UniversityIsrael

Personalised recommendations