A General Stability Test for MultiplyContacted Objects in a Potential Field , withExample Applications to Planar

This paper develops a general test for determining the stability of an object, B, in frictionless contact with bodies A1; : : : ;Ak, in the presence of gravity, or any other force arising from a potential eld. For a small number of contacts, the stability of B depends on the surface normals and surface curvatures of the contacting bodies. For a su ciently large number of contacts, the surface normals alone determine the stability of B. In addition, the stability test includes as a parameter the location of B's center of mass. We use this feature of the test to study in detail the stability of planar objects in the presence of gravity. Using the stability test, we nd the set of center of mass locations which keep B in stable equilibrium for a given contact geometry. In a companion paper, we present an extension of this work to threedimensional objects. This extension has applications in areas such as grasping, xturing, and robot locomotion.