Second-order stability cells of a frictionless rigid body grasped by rigid fingers

The most secure type of grasp of a frictionless workpiece is the form-closure grasp. However, task constraints may make achieving form-closure impossible or undesirable. In this case, one needs to employ a force-closure grasp. In this paper, we study the subclass of force-closure grasps known as second-order stable grasps, which typically have a small number of contacts. We derive conditions for second-order stability and represent second-order stability cells as conjunctions of equations and inequalities in the configuration variables of the system. These cells are the subsets of the system´s configuration space for which the frictionless workpiece is second-order stable. We also determine the minimum and maximum numbers of contacts necessary for second-order stability. Our results are applied to a simple planar whole-arm manipulation system to generate one of its second-order stability cells