Stiffness Model Based Grasp Stability Analysis of Multi-fingered Hand with Friction

Abstract

Since the friction between a finger tip and object surface is not taken into consideration in conventional stability analyses of multi-fingered hand based on stiffness model, a significant contradiction occurs when making these results apply to a practical grasp system. For example, even though the stability is guaranteed for a grasp system without friction, there is a specific case that the grasp system becomes unstable for a small rotation of an object under frictioned model.
This paper discusses a stability of grasp system with friction by substituting two perpendicular virtual springs k_xi and k_yi going through the same contact point for each finger. The rotational center is predetermined within an object and the direction of the virtual spring k_yi is so selected that the extended line passes through the center. Stiffness matrix of grasp system is first introduced by synthesizing all virtual springs, and the stability condition is made clear by exploring the positive definite of the matrix. It is shown from this analysis that virtual spring k_yi plays an important role for generating internal force of an object in an equilibrium state while k_yi is indispensable to the stability of rotation. An evaluation function, which is specified the maximum internal force in an equilibrium state, is also introduced to keep off an excessive force to the object when in actuality determining the grasp parameters such as virtual stiffness, initial compression value of virtual spring. Finally, the validity of the analysis is confirmed through some basic experiments using two-fingered hand model which is specially designed for this study.