Analysis of Grasp Parameter Effects for Static Stability of Planar Grasps

Abstract

Grasp stability is an important factor for grasping and manipulation. In this paper, we discuss error analysis of grasp parameters for static grasp stability in two dimensions. Each finger is modeled by translational linear springs, and the potential energy stored in the grasp is formulated. The force and moment vector and the stiffness matrix of the grasp are derived by using the first- and second-order partial derivative of the energy. The vector and the matrix are represented by a function of grasp parameters such as contact condition (rolling contact and sliding contact), contact point, local curvature, finger spring stiffness, and so on. The partial derivatives of the vector and the matrix with respect to the grasp parameters are derived. The characteristics of the parameters’ effects are investigated by using positive definiteness of the derivatives. It is analytically shown that the stability is enhanced when the rolling contact appears, the local curvature decreases, the finger stiffness increases, and so on. The directions affecting the stability by the parameters’ deviation are also derived. The effects of the other parameters are also shown.