Constraint Singularities as C-Space Singularities

  • Dimiter Zlatanov
  • Ilian A. Bonev
  • Clément M. Gosselin


This paper examines the phenomenon of constraint singularity of a parallel mechanism, as defined in a recent publication. We focus our attention on the fact that constraint singularities are always singular points of the configuration space of the kinematic chain. As such, they separate distinct configuration space regions and may allow transitions between dramatically different operation modes. All this is exemplified by a multi-operational parallel mechanism that can undergo a variety of transformations when passing through singular configurations.


Mixed Mode Parallel Mechanism Kinematic Chain Orientation Mode Constraint Singularity 
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  1. Appleberry, W.T., 1992, “Anti-rotation positioning mechanism,” US Patent 5, 156, 062.Google Scholar
  2. Bonev, I.A., Zlatanov, D. and Gosselin, C.M., 2002, “Advantages of the Modified Euler Angles in the Design and Analysis of PKMs,” Parallel Kinematics Seminar,Chemnitz, Germany, April 23–25.Google Scholar
  3. Di Gregorio, R., and Parenti-Castelli, V., 1998, “A Translational 3-DOF Parallel Manipulator,” Advances in, Robot Kinematics: Analysis and Control, J. Lenarcic and M.L. Husty (eds.), Kluwer Academic Publishers, pp. 49–58.Google Scholar
  4. Di Gregorio, R., 2001, “Statics and Singularity of the 3-UPU Wrist,” Proceedings of the IEEE/ASME International Conference on Advanced Intelligent Mechatronics, Como, Italy, pp. 470–475, July 8–12.Google Scholar
  5. Hunt, K. H., 1973, “Constant-velocity shaft couplings: a general theory,” Transactions of the ASME, Journal of Engineering for Industry, Vol. 95B, pp. 455–464. Hunt, K.H., 1978, Kinematic Geometry of Mechanisms, Oxford University Press.Google Scholar
  6. Karouia, M., and Hervé, J.M., 2000, “A Three-DOF Tripod For Generating Spherical Rotation,” Advances in Robot Kinematics, J. Lenarcic and M.M. Stanisic (eds.), Kluwer Academic Publishers, pp. 395–4020.Google Scholar
  7. Park, F.C., and Kim, J.W., 1999, “Singularity analysis of closed-loop kinematic chains,” ASME Journal of Mechanical Design, Vol. 121, pp. 32–38.CrossRefGoogle Scholar
  8. Tsai, L-W., 1996, “Kinematics of a Three-DOF Platform With Three Extensible Limbs,” Recent Advances in Robot Kinematics, J. Lenarcic and V. Parenti-Castelli (eds.), Kluwer Academic Publishers, pp. 401–410.Google Scholar
  9. Zlatanov, D., Benhabib, B. and Fenton, R.G., 1994, “Singularity Analysis of Mechanism and Robots Via a Velocity-Equation Model of the Instantaneous Kinematics,” Proceedings of the IEEE International Conference on Robotics and Automation, San Diego, CA, pp. 986–991.Google Scholar
  10. Zlatanov, D., 1998, “Generalized Singularity Analysis of Mechanisms,” Ph.D. thesis, University of Toronto.Google Scholar
  11. Zlatanov, D., Bonev, I.A., Gosselin, C.M., 2002, “Constraint Singularities of Parallel Mechanisms,” accepted for publication, Proceedings of the IEEE International Conference on Robotics and Automation, Washington, DC, May 12–15.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2002

Authors and Affiliations

  • Dimiter Zlatanov
    • 1
  • Ilian A. Bonev
    • 1
  • Clément M. Gosselin
    • 1
  1. 1.Laboratoire de robotiqueUniversité LavalQuébecCanada

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