Stability of planar grasps

It is well established that all form closed grasps are stable. However, not all stable grasps are form closed, including many common and easily obtainable grasps. This is especially true in whole arm manipulators and multi-fingered hands where, in many cases, it is difficult or impossible to effect a form closed grasp. Thus it is necessary to establish a general framework for the determination of stability for any equilibrium 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 a grasped planar 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 almost any grasped planar object, including the special but important limiting case of rigid bodies where the contact compliance is zero