The concept of a dextrous workspace, the space in which a manipulator hand can reach any point and rotate fully about any axis through that pont, is introduced. It is shown that the extrous workspace is bounded by surfaces generated by the algorithm presented in another paper. It is also demonstrated that classes of manipulator geometries possessing dextrous workspaces do exist.
A new theory and a resulting algorithm for tracing the bounding surfaces of mechanical manipulator workspaces is presented. The natures of the numerous singular configurations and means of accommodating them within the algorithm are also studied. In order to sort surfaces of interest from the large number of possible solutions, a numerically implementable labelling technique is also presented. The algorithm is applicable to all practicable manipulator configurations with three, or more, degrees of freedom.