In robot hands, precision manipulation, defined as repositioning of a grasped object within the hand workspace without breaking or changing contact, is a fundamental operation for the accomplishment of highly dexterous manipulation tasks. This paper presents a method to characterize the precision manipulation capabilities of a given robot hand regardless of the particularities of the grasped object. The technique allows determining the composition of the displacement manifold (finite motion) of the grasped object relative to the palm of the robot hand and defining the displacements that can actually be controlled by the hand actuators without depending on external factors to the hand. The approach is based on a reduction of the graph of kinematic constraints related to the hand-object system through proper manipulations of the continuous subgroups of displacements generated by the hand joints and contacts. The proposed method is demonstrated through three detailed and constructive examples of common architectures of simplified multi-fingered hands.