Stability Analysis of 3-D Grasps by a Multifingered Hand with Rolling Contact

This paper discusses stability of 3-D grasp considering rolling contact using potential energy approach. The synthesis of stable grasps is made by three-dimensional virtual spring which is fixed at the center of the fingertip. One spring is parallel to the normal and the others are parallel to the tangent plane at the contact. The kinematics of rolling contact equations (velocity and acceleration) between the object and finger are derived. Then, the stiffness matrix of the grasp is established. The derived stiffness matrix has six terms. The first three terms are due to stiffness of the three virtual springs respectively as well as remaining terms imply rotational stiffness which are influenced by curvatures, initial contact forces and contact position. The inverse problem, which is to determine the spring stiffness from the positive definiteness of stiffness matrix of the grasp system, can be also derived. Finally, some numerical examples are presented to illustrate the nature of the equations