Sensitivity Analysis of Degenerate and Non-Degenerate Planar Parallel Manipulators

  • Nicolas Binaud
  • Stéphane Caro
  • Philippe Wenger
Conference paper

Abstract

This paper deals with the sensitivity analysis of degenerate and nondegenerate planar parallel manipulators. First, the manipulators under study as well as their degeneracy conditions are presented. Then, an optimization problem is formulated in order to obtain their maximal regular dextrous workspace. Finally, the sensitivity of the pose of their moving platform to variations in the geometric parameters is analyzed.

Keywords

Sensitivity analysis Degenerate manipulators Regular dextrous workspace Dexterity 

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References

  1. 1.
    Wenger, P., Gosselin, C., and Maillé, B., 1999, “A Comparative Study of Serial and Parallel Mechanism Topologies for Machine Tool,” Int. Workshop on Parallel Kinematic Machines, Milan, Italie, pp. 23–35.Google Scholar
  2. 2.
    Wang, J., and Masory, O., 1993, “On the accuracy of a Stewart platform - Part I, The effect of manufacturing tolerances,” In: Proceedings of the IEEE International Conference on Robotics Automation, ICRA’93, Atlanta, USA, pp. 114–120.Google Scholar
  3. 3.
    Kim, H.S., and Tsai, L-W., 2003, “Design optimization of a Cartesian parallel manipulator,” ASME J. Mech. Des., 125, pp. 43–51.CrossRefGoogle Scholar
  4. 4.
    Caro, S., Bennis, F., and Wenger, P., 2005, “Tolerance Synthesis of Mechanisms: A Robust Design Approach,” ASME J. Mech. Des., 127, pp. 86–94.CrossRefGoogle Scholar
  5. 5.
    Caro, S., Wenger, P., Bennis, F., and Chablat, D., 2006, “Sensitivity Analysis of the Orthoglide, A 3-DOF Translational Parallel Kinematic Machine,” ASME J. Mech. Des., 128, pp. 392–402.CrossRefGoogle Scholar
  6. 6.
    Caro, S., Binaud, N., and Wenger, P., 2008, “Sensitivity Analysis of Planar Parallel Manipulators,” ASME Proc. of International Design Engineering Technical Conferences, New York City, August.Google Scholar
  7. 7.
    Hunt K.H., 1978, Kinematic Geometry of Mechanisms, Oxford University Press, Cambridge.MATHGoogle Scholar
  8. 8.
    Hunt K.H., 1983, “Structural Kinematics of In-Parallel Actuated Robot Arms,” J. Mechanisms, Transmissions and Automation in Design, 105(4); pp. 705–712.CrossRefGoogle Scholar
  9. 9.
    Gosselin C., Sefrioui J., and Richard M.J., 1992, “Solutions Polynomiales au problème de la cinématique des manipulateurs parallèles plans trois degrés de liberté,” Mechanism and Machine Theory, 27; pp. 107–119.CrossRefGoogle Scholar
  10. 10.
    Pennock G.R., and Kassner D.J., 1990, “Kinematic Analysis of a Planar Eight-bar Linkage: Application to a Platform-Type Robot,” ASME Proc. of the 21th Biennial Mechanisms Conf., pp. 37–43, Chicago, September.Google Scholar
  11. 11.
    Gosselin C.M., and Merlet J-P, 1994, “On the Direct Kinematics of Planar Parallel Manipulators: Special Architectures and Number of Solutions,” Mechanism and Machine Theory, 29(8); pp. 1083–1097.CrossRefGoogle Scholar
  12. 12.
    Kong X., and Gosselin C.M., 2001, “Forward Displacement Analysis of Third-Class Analytic 3-RPR Planar Parallel Manipulators,” Mechanism and Machine Theory, 36; pp. 1009–1018.MATHCrossRefGoogle Scholar
  13. 13.
    Wenger P., Chablat D., and Zein M., 2007, “Degeneracy Study of the Forward Kinematics of Planar 3-RPR Parallel Manipulators,” ASME J. Mech. Des., 129, pp. 1265–1268.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  • Nicolas Binaud
    • 1
  • Stéphane Caro
  • Philippe Wenger
  1. 1.Institut de Recherche en Communications et Cybernétique de Nantes, UMR CNRS °6597 1 rue de la NoëFrance

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