A Framework for Closed-Form Displacement Analysis of Planar Mechanisms

[+] Author and Article Information
A. N. Almadi, A. K. Dhingra, D. Kohli

Department of Mechanical Engineering, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53201

J. Mech. Des 121(3), 392-401 (Sep 01, 1999) (10 pages) doi:10.1115/1.2829474 History: Received October 01, 1997; Revised May 01, 1999; Online December 11, 2007


This paper presents a closed-form approach, based on the theory of resultants, to the displacement analysis problem of planar n-link mechanisms. The successive elimination procedure presented herein generalizes the Sylvester’s dialytic eliminant for the case when p equations (p ≥ 3) are to be solved in p unknowns. Conditions under which the method of successive elimination can be used to reduce p equations (in p unknowns) into a univariate polynomial, devoid of extraneous roots, are presented. This univariate polynomial corresponds to the I/O polynomial of the mechanism. A comprehensive treatment is also presented on some of the problems associated with the conversion of transcendental loop-closure equations, into an algebraic form, using tangent half-angle substitutions. It is shown how trigonometric manipulations in conjunction with tangent half-angle substitutions can lead to non-trivial extraneous roots in the solution process. Theoretical conditions for identifying and eliminating these extraneous roots are presented. The computational procedure is illustrated through the displacement analysis of a 10-link 1-DOF mechanism with 4 independent loops.

Copyright © 1999 by The American Society of Mechanical Engineers
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