Stability analysis of frictionless grasps with a two-dimensional spring model

In this paper we discuss the stability of frictionless planar grasps using a two-dimensional (2D) virtual spring model. In previous research, a one-dimensional (1D) spring model was widely used for frictionless grasps. However, this 1D spring model has two problems. (i) The direction of contact force was not investigated when the grasped object was displaced by an external disturbance (ii) The motion of a finger is restricted to the direction along the normal at the initial contact point. To overcome these problems, a 2D spring model is introduced. The force condition, where the contact force always acts along the normal at the contact point, is formulated Using the potential energy method, the stiffness matrix is obtained. Numerical examples demonstrate the effects of tangential spring stiffness and contact force. As a result, it is shown that an optimum contact force exists for stabilization of the grasp. Stiffness conditions of the springs for stabilization are also established.