Fingertip-based within-hand manipulation, also called precision manipulation, refers to the repositioning of a grasped object within the workspace of a multifingered robot hand without breaking or changing the contact type between each fingertip and the object. Given a robot hand architecture and a set of assumed contact models, this paper presents a method to perform a gross motion analysis of its precision manipulation capabilities, regardless of the particularities of the object being manipulated. In particular, the technique allows the composition of the displacement manifold of the grasped object relative to the palm of the robot hand to be determined as well as the displacements that can be controlled-useful for high-level design and classification of hand function. The effects of a fingertip contacting a body in this analysis are modeled as kinematic chains composed of passive and resistant revolute joints; what permits the introduction of a general framework for the definition and classification of nonfrictional and frictional contact types. Examples of the application of the proposed method in several architectures of multifingered hands with different contact assumptions are discussed; they illustrate how inappropriate contact conditions may lead to uncontrollable displacements of the grasped object.