PLANAR MOTION SYNTHESIS USING AN APPROXIMATE BI-INVARIANT METRIC

In this paper we present a technique for using a bi-invariant metric i n the image space of spherical displacements for designing planar mech anisms for n ( > 5) position rigid body guidance. The goal is to perfo rm the dimensional synthesis of the mechanism such that the distance b etween the position and orientation of the guided body to each of the n goal positions is minimized. Rather than measure these distances in the plane, we introduce an approximating sphere and identify rotations which are equivalent to the planar displacements to a specified toler ance. We then measure distances between the rigid body and the goal po sitions using a bi-invariant metric on the image space of spherical di splacements. The optimal linkage is obtained by minimizing this distan ce for each of the n goal positions.