A Dexterity Measure for the Kinematic Control of a Multifinger, Multifreedom Robot Hand

Abstract

This work examines the properties of the manifold gener ated as the configuration space of the linkage used for each finger of the Salisbury hand. We begin with an exhaustive catalog of design types for the finger based on an analysis of its branch loci. We then study the condi tions under which the forward kinematic map becomes singular. These singularities define a submanifold that partitions the linkage's configuration space into a number of open sheets, each of which maps diffeomorphically onto a corresponding open region in the finger's reach able work space. Next we consider the determinant func tion of the finger's Jacobian matrix. The stationary points of this function reveal those configurations where the Jacobian determinant is a maximum. The Jacobian deter minant can be thought of as an oriented volume in the tangent space to the finger's work space, and the orienta tion of this volume reveals the most favorable direction(s) for effecting tip motion or, reciprocally, for applying tip forces. From this we establish a simple criterion that can be used to find the optimal grasp configuration(s) for a given finite displacement of the workpiece.