Dexterity of underactuated manipulators

The dexterity of a manipulator with passive joints, also known as an underactuated manipulator, differs from the dexterity of a fully actuated one, even if their mechanical structures are identical. Therefore, for fault tolerance and energy saving purposes, it is important to study the dexterity of underactuated manipulators. The purpose of this work is to quantify the dexterity of underactuated robot manipulators equipped with active and passive joints. We assume that the passive joints are locked at an arbitrary known position, and we compare the dexterity of the underactuated manipulator with that of a fully actuated redundant manipulator with identical structure. Based on this comparison we propose an optimization index to find the angles at which the passive joints should be locked to maximize the dexterity of the underactuated manipulator. We discuss three important dexterity measures: workspace volume, reachability, and manipulability. Examples obtained with a 3-link planar manipulator with an arbitrarily located passive joint are presented