The synthesis of stable grasps in the plane

This paper addresses the problem of synthesizing stable grasps on arbitrary planar polygons. Each finger is a virtual spring whose stiffness and compression can be programmed. The contacts between the finger tips and the object are point contacts without friction. We prove that all force-closure grasps can be made stable, and it costs O(n) time to synthesize a set of n virtual springs such that a given force-closure grasp is stable. We can also choose the compliance center and the stiffness matrix of the grasp, and so choose the compliant behavior of the grasped object about its equilibrium. The planning and execution of grasps and assembly operations become easier and less sensitive to errors.