This paper deals with several of the basic concepts in the kinematics of mechanical hands. Several different types of finger contacts are modeled and used in a number synthesis of three-fingered hands. Screw theory is used to show which finger configurations allow complete immobilization of the gripped object relative to the fingers, and also allow for the manipulation of the object by the fingers while maintaining the grasp. Shown in this paper is how to determine the forces applied by the fingers on the object, and also how to compute the velocities of the fingers and the object. The analysis developed in this paper is shown to lead to a hand with three fingers, each with three turning joints, and having friction contacts with an object at three separate points.

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