On the stability of grasped objects

A grasped object is defined to be in equilibrium if the sum of all forces and moments acting on a body equals zero. An equilibrium grasp may be stable or unstable. Force closed grasps are a well-known subset of equilibrium grasps, and they are known to be stable. However, not all stable grasps are force closed, including many common and easily obtainable grasps. In this paper, we classify the categories of equilibrium grasps and establish a general framework for the determination of the stability of a grasp. In order to analyze the stability of grasps with multiple contacts, we first model the compliance at each contact. We develop expressions for the changes in contact forces as a function of the rigid body relative motion between the fingers and the grasped object. The stability of a grasp is shown to depend on the local curvature of the contacting bodies, as well as the magnitude and arrangement of the contact forces. We then derive results providing simple criteria to determine the stability of a grasped object, including the special but important limiting case of rigid bodies where the contact compliance is zero.