Stable Poses of 3-Dimensional Objects

This paper considers the gravitational stability of a frictionless 3-dimensional object in contact with immovable objects. Arbitrarily curved objects are considered. This paper also shows how to determine the region over which the object's center of mass can move while the object maintains a given set of contacts and remains in stable equilibrium. We present symbolic solutions for up to three contacts and discuss numerical solutions for larger numbers of contacts. This analysis has application in planning the motions of quasi-statically walking robots over uneven terrain and the manipulation of heavy objects.