Stability of grasped objects: Beyond force closure

This dissertation addresses the stability and compliance of grasped objects through the derivation of the stiffness matrix associated with each grasp. A grasped object is defined to be in equilibrium if the sum of all forces acting on a body equals zero, and the sum of all moments acting on a body also equals zero. An equilibrium grasp may be stable or unstable. Force closed grasps are a well-known subset of equilibrium grasps, and have the important property of being stable. However, not all stable grasps are force closed, including many common and easily obtainable grasps. In this dissertation, a general framework is established for the determination of grasp stability. Simple, easily applicable criteria are derived to determine the stability of any grasp, including the special but important limiting case of rigid bodies. In order to analyze the stability of grasps with multiple contacts, the compliance at each contact is modeled. The model includes the effect of such parameters as curvatures of the contacting surfaces, kinematics of the grasping fingers, internal forces, and compliance of the fingers and joints on the performance of the system. The methodology also allows the grasping fingers to be modeled as either compliant or rigidly fixed in space. Expressions are then developed for the changes in contact forces as a function of the rigid body motion of the grasped object. From this, 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. A large number of examples are presented, including applications in automated fixturing. Finally, the asymmetry of Cartesian stiffness matrices in a conservative system is examined. Methods of differential geometry and properties of Lie groups are used to show that in any conservative system subjected to a non zero external load, the resulting Cartesian stiffness matrix may be asymmetric whenever the basis vector utilized are not derived from generalized coordinates, in any inertial or body-fixed reference frame. However, a reference frame is found which always generates a symmetric stiffness matrix