On Invariant Connguration of a Three-fingered Grasp

When grasping an object using three ngered end-eeectors, a certain geometrical entity can be created based on the grasping points and a deenition of an auxiliary point. This geometric connguration is referred to as the invariant connguration of the three n-gered grasp. This paper exploits the geometric properties of such connguration using screw theory and inner product spaces. The results are shown to present themselves as an elegant and eecient framework in calculating the friction forces between the ngers and the grasped object and/or in deening the instantaneous motion of the nger-tips in accomplishing the desired motion of the grasped object.