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Using a Singularity Locus to Exhibit the Number of Geometric Inversions, Transitions and Circuits of a Linkage

[+] Author Affiliations
David H. Myszka, Andrew P. Murray

University of Dayton, Dayton, OH

James P. Schmiedeler

University of Notre Dame, Notre Dame, IN

Paper No. DETC2010-28188, pp. 771-781; 11 pages
  • ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 2: 34th Annual Mechanisms and Robotics Conference, Parts A and B
  • Montreal, Quebec, Canada, August 15–18, 2010
  • Conference Sponsors: Design Engineering Division and Computers in Engineering Division
  • ISBN: 978-0-7918-4410-6 | eISBN: 978-0-7918-3881-5
  • Copyright © 2010 by ASME


The identification of motion characteristics and assembly circuits is fundamental in creating a workable mechanism. A circuit defect prevents a mechanism from moving between desired positions. This paper extends the established methods for analyzing multi-degree-of-freedom platforms to gain insight on single-actuated linkages. Specifically, from a plot of the singularity locus projected onto the input joint space, the number of singularities, number of geometric inversions and circuit regimes are revealed. The input/output motion of the linkage can be inferred from the locus. The methodology to produce the singularity locus is general and does not rely on geometric insights of a particular mechanism. By using the locus, desired operational features can be readily identified, such as a fully rotatable crank. Unique motion characteristics, such as a greater than 360° non-rotatable crank, can be also be detected. Further, it is observed that transition linkages serve as bounds between the regions of circuit change.

Copyright © 2010 by ASME
Topics: Linkages , Circuits



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