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


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
Your Session has timed out. Please sign back in to continue.






Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In