Solution region synthesis methodology of spatial 1CS-4SS linkages for six given positions

Abstract

This paper proposes a 1CS-4SS spatial linkage and presents the solution region synthesis methodology for six specified positions. Firstly, synthesis equations of the SS dyads and the CS dyad are proposed, the discrete solutions of the CS dyad are obtained by Bertini numerical method. The 1CS-4SS spatial linkage are obtained by selecting four SS dyads on the solution curves of the SS dyad and one CS dyad on the discrete solutions of the CS dyad. We display all solutions of linkages in a plane, which is called the solution region. Secondly, The Jacobian matrix is deduced to determinate the defective linkages. The Bertini numerical method and Groebner basis method are used for position analysis of the linkages, and the analysis results from the two methods are compared and mutually verified. The feasible solution region can be obtained after eliminating defective linkages and linkages that fail to satisfy the other requirements from the solution region plane. Finally, the validity of the formulas and applicability of the proposed approach are illustrated by an example.