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# Reciprocity-Based Singular Value Decomposition for Inverse Kinematic Analysis of the Metamorphic Multifingered Hand

[+] Author and Article Information
Lei Cui

King’s College London, University of London, Strand, London WC2R 2LS UK;  The Robotics Instute Carnegie Mellon University 5000 Forbes Avenue, Pittsburgh, PA 15213, USAleicui@cmu.edu

Jian S. Dai

Chair of Mechanisms and Robotics, Centre for Advanced Mechanisms and Robotics, Tianjin University, Tianjin; Centre for Robotics Research, King’s College London,  University of London, Strand, London WC2R 2LS UKjian.dai@kcl.ac.uk

J. Mechanisms Robotics 4(3), 034502 (Jul 03, 2012) (6 pages) doi:10.1115/1.4006187 History: Received April 21, 2010; Revised December 29, 2011; Published July 03, 2012; Online July 03, 2012

## Abstract

With a new type of multifingered hands that raise a new philosophy in the construction and study of a multifingered hand, this paper is a follow-on study of the kinematics of the metamorphic multifingered hand based on finger constraint equations. The finger constraint equations lead to a comprehensive mathematical model of the hand with a reconfigurable palm which integrates all finger motions with the additional palm motion. Singular values of the partitioned Jacobian matrix in their analytical form are derived and applied to obtaining analytical solution to inverse kinematics of a complete robotic hand. The paper for the first time solves this integrated motion and the multifingered hand model with the singular value decomposition and extra degrees of freedom are examined with the singular value analysis to avoid the singularities. The work identifies finger displacement and velocity with effect from the articulated palm and presents a new way of analyzing a multifingered robotic hand.

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## Figures

Figure 1

Screws related to joints of the multifingered hand

Figure 2

The geometric arrangement of the palm

Figure 3

Local reference frame of finger f1

Figure 4

(a) Singular value σ 11 in the case of θ 1,2  = 0.52, (b) singular value σ 11 in the case of θ 1,2  = 0.86, and (c) singular value σ 11 in the case of θ 1,2  = 2.618

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