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Stability Analysis of a Robotic Mechanism Using Computer Albegra

  • M. Golnaraghi
  • W. Keith
  • F. C. Moon

Abstract

This paper concerns the stability analysis of a two degree of freedom lumped mass model of a robotic mechanism. The equations of motion as well as the Hamiltonian for the system are derived using the symbolic manipulation system MACSYMA. The second order, nonlinear, coupled, ordinary differential equations which govern the system are linearized about a particular operating point. We emphasize the advantage of using MACSYMA to derive this linear system. The regions of flutter and divergence instabilities in a two dimensional parameter space are determined from a quartic characteristic equation. A MACSYMA program is used to perform a root locus study of this equation. A discussion of the application of the results to the control of a mechanical robot is presented.

Keywords

Computer Algebra Spring Stiffness Divergence Instability Dimensional Parameter Space Lump Mass Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Paul, R.P. Robot manipulators: Mathematics, programming, and control. MIT Press, Cambridge, 4th ed., 1982.Google Scholar
  2. 2.
    Huseyin, K. Vibrations and stability of multiple parameter systems. Sijthoff & Noordhoff International Publishers, Alphen aan den Rijn, The Netherlands, 1978.MATHGoogle Scholar
  3. 3.
    Rand, R.H. Computer algebra in applied mathematics: An introduction to MACSYMA. Pitman Publishing, Inc., Marshfield, Mass., 1st ed., 1984.MATHGoogle Scholar
  4. 4.
    MATHLAB Group Laboratories for Computer Science MIT. MACSYMA reference manual. MIT, Cambridge, Version 10, Vol. I, 1st printing, 1982.Google Scholar

Copyright information

© Kluwer Academic Publishers 1985

Authors and Affiliations

  • M. Golnaraghi
    • 1
  • W. Keith
    • 1
  • F. C. Moon
    • 1
  1. 1.Theoretical and Applied MechanicsCornell UniversityIthacaUSA

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