Stability Analysis of Planar Grasp with 2D-Virtual Spring Model

We analyze stability of planar grasp using a 2D virtual spring model. A 2D virtual spring model is widely used to explore frictionless grasp, but the direction of contact force has not been studied for a grasped object displaced by external disturbance. Finger displacement is restricted to the normal at initial contact. We introduce a 2D spring model for a frictionless case. The direction of contact force is explicitly formulated. Using potential energy, we analyze stability of frictionless grasp and show that the 1D-spring model is a special case of our proposed 2D-spring model. Frictional grasp stability is also studied using rolling contact. Numerical examples of 2-fingered grasp demonstrate the effects of parameters such as spring stiffness and contact force. It is shown that an optimum force exists for stabilizing frictionless grasp. It is proved that friction enhances grasp stability from the relationship between frictionless and frictional stiffness matrices. Stiffness conditions for stabilizing 3-fingered grasp is clarified.