The Space of Passive Planar Compliances Achieved by a Multi-Finger Hand

Abstract In this paper, the limitations on the space of object planar compliant behaviors that can be passively achieved by a multi-finger grasp are identified. A general planar compliance can be completely characterized by its principal stiffnesses, principal axes orientation, and center location. A set of necessary and sufficient conditions for a compliant behavior to be achieved by a passively elastic grasp with specified contact locations is identified. It is shown that the locus of compliance center locations that can be passively achieved is a finite area uniquely determined by the contact locations of the fingertips, the principal stiffnesses, and the principal axes orientations. The implications of the realization conditions are illustrated in the geometry of the grasp. A synthesis procedure to realize a compliance within the realizable region using a 3-finger grasp is also developed.