Abstract: The paper characterizes the grasp stiffness and joint stiffness for the grasping system of a multi fingered dextrous hand, and develops the expressions for the potential energy, kinetic energy and the dissipation function in a grasp. Using a Lagrangian formula, the small displacement disturbance equation for multi\|fingered grasping system is introduced and the equation is solved by modal analysis. Based on this work, an optimum grasping planning is formulated as a non linear programming problem so that the grasping system could have ideal asymptotical stability. An example for the BH 2 anthropoid hand grasping a cylinder object demonstrates the applicability and effectiveness of the method.

Key words: robots　fingers, stability, optimal planning