When grasping an object using three-fingered end-effectors, a certain geometrical entity can be created based on the grasping points and a definition of an auxiliary point. This geometric configuration is referred to as the invariant configuration of the three-fingered grasp. This article exploits the geometric properties of such configuration using screw theory and inner product spaces. The results are shown to present themselves as an elegant and efficient framework in calculating the friction forces between the fingers and the grasped object and / or in defining the instantaneous motion of the finger-tips in accomplishing the desired motion of the grasped object.
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