Stable region of gravity position of object grasped by virtual springs

This paper considers the stable grasp in the sense of quasi-statistics, i.e., an object is grasped by a multi-fingered robot hand, where each finger is regarded as a virtual 3D linear spring. The stability analysis is to find a condition under which the equilibrium can be restored after any small perturbations of the object's position and orientation. The paper derives a necessary and sufficient condition for the grasp to be stable in terms of relations among the stiffness parameters, the contact points, and the object's COG. By using this result, a region of the object's COG can be clarified which guarantees the stable grasp.