Stable prehension with three fingers

We study grasps by a robot hand in the absence of friction. In two dimensions, a hand with three spring-loaded fingers and five degrees of freedom can achieve an equilibrium grasp on any object described by a polygon. Furthermore, the grasp is stable, that is, at a local minimum of the potential energy function defined by the springs of the fingers. In three dimensions, the hand can grasp any cylinder. In contrast, if the degrees of freedom of the hand are restricted to correspond to a hand built by Hanafusa and Asada, stable grips on a polygon cannot in general be achieved.