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

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.