Approximate Motion Synthesis of Spherical Kinematic Chains

Abstract

In this paper we present a novel dimensional synthesis technique for approximate motion synthesis of spherical kinematic chains. The methodology uses an analytic representation of the spherical RR dyad’s workspace that is parameterized by its dimensional synthesis variables. A two loop nonlinear optimization technique is then employed to minimize the distance from the dyad’s workspace to a finite number of desired orientations of the workpiece. The result is an approximate motion dimensional synthesis technique that is applicable to spherical open and closed kinematic chains. Here, we specifically address the spherical RR open and 4R closed chains however the methodology is applicable to all spherical kinematic chains. Finally, we present two examples that demonstrate the utility of the synthesis technique.