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Some Special Cases of the Burmester Problem for Four and Five Poses

[+] Author Affiliations
Jorge Angeles, Shaoping Bai

McGill University, Montreal, QC, Canada

Paper No. DETC2005-84871, pp. 307-314; 8 pages
  • ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 7: 29th Mechanisms and Robotics Conference, Parts A and B
  • Long Beach, California, USA, September 24–28, 2005
  • Conference Sponsors: Design Engineering Division and Computers and Information in Engineering Division
  • ISBN: 0-7918-4744-6 | eISBN: 0-7918-3766-1
  • Copyright © 2005 by ASME


The Burmester problem aims at finding the geometric parameters of a planar four-bar linkage for a prescribed set of finitely separated poses. The synthesis related to the Burmester problem deals with both revolute-revolute (RR) and prismatic-revolute (PR) dyads. A PR dyad is a special case of RR dyad, i.e., a dyad with one end-point at infinity. The special nature of PR dyads warrants a special treatment, outside of the general methods of four-bar linkage synthesis, which target mainly RR dyads. In this paper, we study the synthesis of planar four-bar linkages addressing the problem of the determination of PR dyads. The conditions for the presence of PR dyads with the prescribed poses are derived. A synthesis method is developed by resorting to the parallelism condition of the displacement vectors of the circle points of PR dyads. We show that the “circle” point of a PR dyad can be determined as one common intersection of three or four circles, depending on whether four or, correspondingly, five poses are prescribed.

Copyright © 2005 by ASME



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