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Singularity Traces of Planar Linkages That Include Prismatic and Revolute Joints

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

University of Dayton, Dayton, OH

Charles W. Wampler

General Motors R&D Center, Warren, MI

Paper No. DETC2015-47390, pp. V05BT08A080; 11 pages
  • ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 5B: 39th Mechanisms and Robotics Conference
  • Boston, Massachusetts, USA, August 2–5, 2015
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5713-7
  • Copyright © 2015 by ASME and General Motors


This paper presents a general method to construct a singularity trace for single degree-of-freedom, closed-loop linkages that include prismatic, in addition to, revolute joints. The singularity trace has been introduced in the literature as a plot that reveals the gross motion characteristics of a linkage relative to a designated input joint and design parameter. Previously, singularity traces were restricted to mechanisms composed of only rigid bodies and revolute joints. The motion characteristics identified on the plot include changes in the number of solutions to the forward kinematic position analysis (geometric inversions), singularities, and changes in the number of branches. To illustrate the adaptation of the general method to include prismatic joints, basic slider-crank and inverted slider-crank linkages are explored. Singularity traces are then constructed for more complex Assur IV/3 linkages containing multiple prismatic joints. These Assur linkages are of interest as they form an architecture that is commonly used for mechanisms capable of approximating a shape change defined by a general set of closed curves.

Copyright © 2015 by ASME and General Motors
Topics: Linkages



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