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Optimal Kinematic Design of 6R Manipulators

A fundamental theorem for the kinematic design of robot manipulators is formulated and proved. Roughly speaking, the theorem states that a manipulator having six revolute joints is optimal if and only if the manipulator or its kine matic inverse is an elbow manipulator. By "optimal" we mean a manipulator that has the properties of (i) maximal work-volume subject to a constraint on its length and (ii) well-connected workspace—that is, the ability to reach all positions in its workspace in each configuration. The notion of work-volume we use is that derived from the translation- invariant volume form on the group of rigid motions. This notion of volume is intermediate between those of "reach able" and "dextrous" workspace and appears to be more natural in that it leads to simple analytical results.