Manipulation of the grasped object is defined as the ability of the mechanical end-effector to create an instantaneous motion of the object with respect to a fixed reference frame (e.g., palm reference frame). This class of manipulation is usually referred to as the fine manipulation whereas a collection of all these instantaneous motions of the object is referred to as the gross manipulation. This paper presents a new method where for a given desired twist of the grasped object, the instantaneous motions of the fingertips can be determined. The results of the paper are divided into two parts. First, for the case where the motion of the object is created through motions of the fingertip in off-tangent planes to the object at the contact points. Second, where a class of motion of the grasped object is achieved through motions of the fingertips which are restricted to the tangent planes. The method of this paper utilizes screw geometry, inner product spaces and information regarding grasp configuration. The method is also illustrated through examples.

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