Towards construction of 3D frictional form-closure grasps: a formulation

This paper addresses the problem of computing n-finger form-closure grasps of polyhedral objects. Given grasping points of m fingers not in form-closure, we propose a sufficient and necessary condition for other n-m fingers to achieve an n-finger form-closure grasp with the m fingers. Based on this condition, it is demonstrated that the problem of computing grasping points of the n-m fingers can be formulated as an existence problem of a solution for a set of linear inequalities. Several sufficient conditions are also presented to guarantee the form-closure property of the n-finger grasp