Special grasping configurations with dexterous hands

Dexterous hands have the ability to grasp arbitrary parts and impart arbitrary motions to those objects. They also, in general, can be placed in special configurations where the grasp of an object is underconstrained or overconstrained. It is also possible to obtain special configurations where there are not enough or there are redundant degrees of freedom for moving an object, or where the hand mechanism is in a singular configuration. All of these special configurations are revealed through the examination of linear Jacobian matrix relationships describing a grasp. Formulations are presented for determining what useful manipulations can be performed, given these circumstances.