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A method is introduced for locating stable grasps with articulated mechanical hands. A metric called the grasp goal function represents the `distance' to an unstable grasp for a given position, external load, and set of joint torques of the gripper. The process of locating a stable grasp is treated as an optimization problem for which the most stable grasp is found by maximizing the grasp goal function. Physical constraints, such as torque or motion limitations, are accounted for by the incorporation of potential functions in the objective function. Two-dimensional and three-dimensional simulations were undertaken for which objects were represented as polygons/polyhedral and gripper elements as ellipses/ellipsoids.