Robot Kinematics—A Compact Analytic Inverse Solution for Velocities

There are, it seems, several notions, widely but not universally accepted, that hamper the full velocity determination of serial robot arms: (a) that certain generally based rules must be rigorously followed to establish a configuration pattern for any particular robot; (b) that, when things get difficult, there is no alternative to numerical methods; (c) that little can be gained from carefully examining the relevance of certain fundamentals of kinematic geometry. The more usual serial arms can, however, be analyzed elegantly, but only when elementary screw theory is recognized as being both essential and ubiquitous. Then, with the aid of the coordinate transformation for screws, the inverse velocity problem can be simply formulated analytically. Certain other matters, such as closure determination and proximity to special configurations, are touched upon.