Structural–Parametric Synthesis of Path-Generating Mechanisms and Manipulators ^†

This paper presents a structural–parametric synthesis of the four-link and Stephenson I, Stephenson II, and Stephenson III six-link path-generating mechanisms. The four-link path-generating mechanism is formed by connecting the output point and the base using an active closing kinematic chain (CKC) with two DOFs and a negative CKC of the type RR. The six-link path-generating mechanisms are formed by connecting the output point and the base by active, passive and negative CKCs. Active CKC has active kinematic pair, passive CKC has zero DOF, and negative CKC has a negative DOF. Active and negative CKCs impose geometrical constraints on the movement of the output point, and the geometric parameters of their links are determined by least-square approximation. Geometric parameters of the passive CKC are varied to satisfy the geometrical constraints of the active and negative CKCs. The CKCs of the active, passive and negative types, connecting the output point and the base, are the structural modules from which the different types of the path-generating mechanisms are synthesized. Numerical examples of the parametric synthesis of the four-link and six-link path-generating mechanisms are presented.