KINEMATIC DEXTERITY OF ROBOTIC MECHANISMS

In this article we develop a mathematical theory for optimizing the ki nematic dexterity of robotic mechanisms and obtain a collection of ana lytical tools for robot design. The performance criteria we consider a re workspace volume and dexterity; by the latter we mean the ability t o move and apply forces in arbitrary directions as easily as possible. Clearly, dexterity and workspace volume are intrinsic to a mechanism so that any mathematical formulation of these properties must necessar ily be independent of the particular coordinate representation of the kinematics. By regarding the forward kinematics of a mechanism as defi ning a mapping between Riemannian manifolds, we apply the coordinate-f ree language of differential geometry to define natural measures of ki nematic dexterity and workspace volume. This approach takes into accou nt the geometric and topological structures of the joint and workspace s. We show that the functional associated with harmonic mapping theory provides a natural measure of the kinematic dexterity of a mechanism. Optimal designs among the basic classes of mechanisms are determined as extrema of this measure. We also examine the qualitative connection s between kinematic dexterity and workspace volume.