On computing optimal planar grasps

The quality of a grasp can often be measured as the magnitude within which any external wrench is resistible by "unit grasp force". In this paper, we present a numerical algorithm to compute the optimal grasp on a simple polygon, given contact forces of unit total magnitude. Forces are compared with torques over the radius of gyration of the polygon. Our analysis shows that the optimal grasps may be of a continuum. We also address a grasp optimality criterion for resisting an adversary finger located possibly anywhere on the polygon boundary. The disparity between these two grasp optimality criteria are demonstrated by simulation with results advocating that grasps should be measured task-dependently. The paper assumes non-frictional contacts.