Elbow and elbow manipulators are optimal!

We show that the elbow manipulators and their duals are the optimal designs for 6R manipulators. The performance measures used are those of work-volume and a property defined herein called well-connected-workspace. It is shown that a 6R manipulator, M, has maximal work-volume and a well-connected-workspace if and only if M or M* (its dual) is an elbow manipulator.