On the Closure Properties of Robotic Grasping

The form{closure and force{closure properties of robotic grasping are investigated. Loosely speaking, these properties are related to the capability of the robot to inhibit motions of the workpiece in spite of externally applied forces. In this paper, form{closure is considered as a purely geometric property of a set of unilateral (contact) constraints, such as those applied on a workpiece by a mechanical xture, while force{closure is related with the capability of the particular robotic device being considered to apply forces through contacts. The concepts of partial form{ and force{closure properties are introduced and discussed, and an algorithm is proposed to obtain a synthetic geometric description of partial form{closure constraints. While the literature abounds with form{closure tests, proposed algorithms for testing force{closure are either approximate or computationally expensive. This paper proves the equivalence of force{closure analysis with the study of the equilibria of an ordinary di erential equation, to which Lyapunov's direct method is applied. This observation leads to an e cient algorithm for assessing the force{closure property of the grasp. Submitted, Int. J. of Robotics Research, Nov. 1993. Accepted, Jul. 1994.