Determination of unstable singularities in parallel robots with N arms

John F. O'Brien, Farhad Jafari, John T. Wen

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


Parallel mechanisms frequently possess an unstable type of singularity that has no counterpart in serial mechanisms. When the mechanism is at or near this type of singularity, it loses the ability to counteract external forces in certain directions. The determination of unstable singular configurations in parallel robots is challenging, and in the past, has been tackled by exhaustive numerical searches of the mechanism workspace using an accurate analytical model of the mechanism kinematics. This paper considers the singularity-determination problem from a geometric perspective for n-legged spatial parallel mechanisms. By using the constraints on the passive joint velocities, a necessary condition for an unstable singularity is derived.

Original languageEnglish (US)
Pages (from-to)160-167
Number of pages8
JournalIEEE Transactions on Robotics
Issue number1
StatePublished - Feb 2006
Externally publishedYes

Bibliographical note

Funding Information:
Manuscript received January 21, 2005; revised May 26, 2005. This paper was recommended for publication by Associate Editor J. P. Merlet and Editor I. Walker upon evaluation of the reviewers’ comments. This work was supported in part by the Missile Defense Agency and the Army Research Office under Grants DAAD19-02-1-0102 and DAAD19-00-1-0153, in part by a Wyoming EPSCoR NASA Seed Grant, and in part by the State of Wyoming. The work of J. Wen was supported in part by the Center for Automation Technologies and Systems under a block grant from the New York State Office of Science, Technology, and Academic Research (NYSTAR), in part by the National Science Foundation under Grant IIS-9820709, and in part by the China NSFC Two-Bases Project under Grant 60440420130. This paper was presented in part at the IEEE International Conference on Robotics and Automation, Barcelona, Spain, May 2005.


  • Actuator singularity
  • Parallel robots
  • Platform mechanism
  • Self-motion
  • Unstable singularity


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