Romansy 14 pp 49-58 | Cite as

Inverse Dynamic Analysis of Parallel Manipulators with 3 or 6 Degrees of Freedom

  • Thomas Geike
  • John Mcphee
Part of the International Centre for Mechanical Sciences book series (CISM, volume 438)


An approach is presented for automatically generating inverse dynamic solutions for planar parallel manipulators with 3 DOF and spatial parallel manipulators with 6 DOF, thereby eliminating the errors and tedium associated with hand derivations. Kinematic and dynamic equations are formulated using a combination of linear graph theory, the principle of virtual work, and symbolic programming. A planar RRR manipulator and a Gough-Stewart platform are used to validate the inverse dynamic formulations, and to compare their computational efficiencies.


Multibody System Parallel Manipulator Virtual Work Inverse Dynamic Analysis Symbolic Programming 
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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  1. Dasgupta, B., and Mruthynjaya, T. (1998). A Newton-Euler Formulation for the Inverse Dynamics of the Stewart Platform Manipulator. Mechanism and Machine Theory, 33: 1135–1152.CrossRefMATHMathSciNetGoogle Scholar
  2. Ma, O., and Angeles, J. (1989) Direct Kinematics and Dynamics of a Planar 3-DOF Parallel Manipulator. In Advances in Design Automation - 1989, 3: 313–320.Google Scholar
  3. McPhee, J., Shi, P., and Piedboeuf, J.-C. (1999) Inverse Dynamics of Multibody Systems using Virtual Work and Symbolic Programming. In Proceedings of the Euromech Colloquium 404 on Advances in Computational Multibody Dynamics.Google Scholar
  4. McPhee, J. (1998) Automatic Generation of Motion Equations for Planar Mechanical Systems Using the New Set of “Branch Coordinates”. Mechanism and Machine Theory, 33: 805–823.CrossRefMATHGoogle Scholar
  5. Merlet, J.-P. (2000). Parallel Robots Dordrecht, The Netherlands: Kluwer Academic Press.CrossRefGoogle Scholar
  6. Schiehlen, W., ed. (1990) Multibody Systems Handbook. Berlin: Springer-Verlag.Google Scholar
  7. Shi, P., and McPhee, J. (2000) Dynamics of Flexible Multibody Systems using Virtual Work and Linear Graph Theory. Multibody Systems Dynamics, 4: 355–381.CrossRefMATHGoogle Scholar
  8. Shi, P., and McPhee, J. (2002) Symbolic Programming of a Graph-Theoretic Approach to Flexible Multibody Dynamics. Mechanics of Structures and Machines, 30: 123–156.CrossRefGoogle Scholar
  9. Tsai, L.-W. (2000) Solving the Inverse Dynamics of a Stewart-Gough Manipulator by the Principle of Virtual Work. Journal of Mechanical Design, 122: 3–9.CrossRefGoogle Scholar
  10. Wang, J., and Gosselin, C., (1998) A New Approach for the Dynamic Analysis of Parallel Manipulators. Multibody System Dynamics, 2: 317–334.CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Wien 2002

Authors and Affiliations

  • Thomas Geike
    • 1
  • John Mcphee
    • 2
  1. 1.Department of Mechanical EngineeringBraunschweig UniversityGermany
  2. 2.Department of Systems Design EngineeringUniversity of WaterlooCanada

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