Stable prehension with a multi-fingered hand

We study grasps by a robot hand with three spring-loaded fingers. In two dimensions, the hand can grasp any polygon stably. That is, the grip is at a local minimum of the potential energy function defined by the springs of the fingers, ignoring friction. Surprisingly, under some conditions an equilibrium grasp on a circle is unstable even with respect to translation. In three dimensions, the hand can grasp and lift any cylindrical surface with a polygonal cross-section. In contrast we show that a hand with finger angles fixed at 120°, as proposed by Hanafusa and Asada, generally can not achieve a two-dimensional stable grip in the absence of friction.