Complete Solution of the Nine-Point Path Synthesis Problem for Four-Bar Linkages-Reference-Cited by-同舟云学术

Complete Solution of the Nine-Point Path Synthesis Problem for Four-Bar Linkages

Published:1992-03-01 Issue:1 Volume:114 Page:153-159
ISSN:1050-0472
Container-title:Journal of Mechanical Design
language:en
Short-container-title:

Author:

Wampler C. W.¹,Morgan A. P.¹,Sommese A. J.²

Affiliation:

1. Mathematics Department, General Motors Research Laboratories, Warren, MI 48090

2. Mathematics Department, University of Notre Dame, Notre Dame, IN 46556

Abstract

The problem of finding all four-bar linkages whose coupler curve passes through nine prescribed points has been a longstanding unsolved problem in kinematics. Using a combination of classical elimination, multihomogeneous variables, and numerical polynomial continuation, we show that there are generically 1442 nondegenerate solution along with their Roberts cognates, for a total of 4326 distinct solutions. Moreover, a computer algorithm that computes all solutions for any given nine points has been developed.

Publisher

ASME International

Subject

Computer Graphics and Computer-Aided Design,Computer Science Applications,Mechanical Engineering,Mechanics of Materials

Link

http://asmedigitalcollection.asme.org/mechanicaldesign/article-pdf/114/1/153/5507001/153_1.pdf

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