Abstract:

An algebraic solution for five precision points path synthesis of Stephenson-Ⅲ planar six-bar linkage was presented. The Stephenson-Ⅲ planar six-bar linkage is decomposed into two parts: a dyad and a four-bar linkage. To synthesize the two parts, the dyad first then the four-bar linkage, the kinematic constraint equations are formulated based on displacement matrix. The equations are solved with the Groebner-Sylvester (GS) hybrid approach in which a high degree univariate equation together with all its closed form solution is obtained finally. A numerical example was provided to validate the algorithm and the solutions are verified by Solidworks and SAM. The method given in this article can also be used to solve other types of synthesis problem concerning planar six-bar linkage.

Key words: path synthesis, planar six-bar linkage, algebraic method, Groebner basis, Sylvester resultant