Research Papers

Singularity Traces of Single Degree-of-Freedom Planar Linkages That Include Prismatic and Revolute Joints

[+] Author and Article Information
Saleh M. Almestiri, Andrew P. Murray, David H. Myszka

Department of Mechanical and Aerospace Engineering,
University of Dayton,
Dayton, OH 45469

Charles W. Wampler

General Motors R&D Center,
Warren, MI 48090
e-mail: almestiris2@udayton.edu

Manuscript received September 12, 2015; final manuscript received December 13, 2015; published online May 4, 2016. Assoc. Editor: James Schmiedeler.

J. Mechanisms Robotics 8(5), 051003 (May 04, 2016) (3 pages) Paper No: JMR-15-1255; doi: 10.1115/1.4032410 History: Received September 12, 2015; Revised December 13, 2015

This paper extends the general method to construct a singularity trace for single degree-of-freedom (DOF), closed-loop linkages to include prismatic along with 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 a design parameter. The motion characteristics identified on the plot include a number of possible geometric inversions (GIs), circuits, and singularities at any given value for the input link and the design parameter. An inverted slider–crank and an Assur IV/3 linkage are utilized to illustrate the adaptation of the general method to include prismatic joints.

Copyright © 2016 by ASME
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Wampler, C. W. , 1999, “ Solving the Kinematics of Planar Mechanisms,” ASME J. Mech. Des., 121(3), pp. 387–391. [CrossRef]
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Myszka, D. H. , Murray, A. P. , and Wampler, C. W. , 2013, “ Computing the Branches, Singularity Trace, and Critical Points of Single Degree-of-Freedom, Closed-Loop Linkages,” ASME J. Mech. Rob., 6(1), p. 011006. [CrossRef]
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Grahic Jump Location
Fig. 1

Inverted slider–crank linkage position vector loop

Grahic Jump Location
Fig. 2

The inverted slider–crank singularity trace. Circular markers denote the critical points. Both circuits within the gray zones exhibit a fully rotatable crank.

Grahic Jump Location
Fig. 3

Motion curve at various lengths of a1 from the second zone. Singularity points are identified with x-shaped markers.

Grahic Jump Location
Fig. 4

Assur IV/3 linkage position vector loop

Grahic Jump Location
Fig. 5

The singularity trace for Assur IV/3 with respect to a1. Circular markers denote the critical points. The zones shaded in gray contain at least one circuit with a fully rotatable crank.



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