Shape for Contact

Abstract

Given a desired function for an e ffector, what is its appropriate shape? This thesis addresses the problem of designing the shape of a rigid end e ffector to perform a given manipulation task. It presents three main contributions: First, it describes the contact kinematics of an eff ector as the product of both its shape and its motion, and assumes a xed motion model to explore the role of shape in satisfying a certain manipulation task. Second, it formulates that manipulation task as a set of constraints on the geometry of contact between the eff ector and the world. Third, it develops tools to transform those contact constraints into an e ector shape for general 1-DOF planar mechanisms and general 1-DOF spatial mechanisms, and discusses the generalization to mechanisms with more than one degree of freedom. We describe the case studies of designing grippers with invariant grasp geometry, grippers with improved grasp stability, and grippers with extended grasp versatility. We further showcase the techniques with the design of the fi ngers of the MLab hand, a three-fingered gripper actuated with a single motor, capable of exerting any combination of geometrically correct enveloping or fingertip grasps of spherical, cylindrical, and prismatic objects of varying size.