Posture, Workspace, and Manipulability of the Metamorphic Multifingered Hand With an Articulated Palm

Abstract

This paper presents a novel multifingered hand with an articulated palm that makes the hand adaptable and reconfigurable. The posture of the new multifingered hand is enhanced by the additional motion of the palm and the workspace of fingers is augmented by the palm workspace. To analyze this integrated workspace, this paper introduces finger-operation planes to relate the finger motion to the palm motion and its configuration. Normals of these operation planes are used to construct a Gauss map. Adding an additional dimension, a four-dimensional ruled surface can be generated from this map to illustrate variation of posture. With the change of palm configurations, a posture manifold can be developed from the posture ruled surfaces. The workspace analysis is developed by introducing a palm workspace-triangle. This workspace-triangle evolves into a helical workspace-triangle tube when palm inputs vary and further develops into a four-dimensional presentation. This progresses into a set of workspaces of the multifingered hand by varying the palm configuration, leading to a larger workspace of the new multifingered hand as the union of the workspaces corresponding to individual palm configuration. This paper further investigates manipulability of the multifingered hand by modeling the contact point as a hypothetical spherical joint. Based on reciprocity relationship of screw systems, the finger Jacobian matrices and the hand Jacobian matrix are established. With singular value decomposition, manipulability of each finger is explored and the hand manipulability is revealed by the diagonal nature of the Jacobian matrix of the hand.