Complete Solution of the Nine-Point Path Synthesis Problem for Four-Bar Linkages
- 1 March 1992
- journal article
- Published by ASME International in Journal of Mechanical Design
- Vol. 114 (1) , 153-159
- https://doi.org/10.1115/1.2916909
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.Keywords
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