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TECHNICAL BRIEFS

Use of Resultants and the Bernshtein Formula in the Dimensional Synthesis of Linkage Components

[+] Author and Article Information
Chuen-Sen Lin

Mechanical Engineering, Department, University of Alaska, Fairbanks, Fairbanks, AL 99775

Bao-Ping Jia

Department of Mathematics, University of Alaska, Fairbanks, Fairbanks, AL 99775

J. Mech. Des 116(4), 1171-1172 (Dec 01, 1994) (2 pages) doi:10.1115/1.2919503 History: Received November 01, 1992; Revised January 01, 1994; Online June 02, 2008

Abstract

The applications of resultants and the Bernshtein formula for the dimensional synthesis of linkage components for finite precision positions are discussed. The closed-form solutions, which are derived from systems of polynomials in multiple unknowns by applying resultant theory, are in forms of polynomial equations of a single unknown. For the case of two compatibility equations, the closed form solution is a sixth degree solution polynomial. For the case of three compatibility equations, the solution is a fifty-fourth degree solution polynomial. For each case, the Bernshtein formula is applied to calculate the number of solutions of the system of polynomial equations. The calculated numbers of solutions match the degrees of the solution polynomials for both cases.

Copyright © 1994 by The American Society of Mechanical Engineers
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