New Notation for Serial Kinematic Chains

The description of a serial kinematic chain should be unique, unambiguous, simple to determine, easy to use and well-behaved when small changes are made in the arrangement of the elements of the chain. The notation currently in use, introduced by Denavit andHartenberg, does not satisfy all of these criteria. It involves arbitrary choices, so that more than one description may apply to a given kinematic chain. More importantly, the parameters relating the links in the chain can be very sensitive to small changes in the physical arrangement of the chain. This is particularly true of so-called ideal chains, ones that permit closed-form solution of the inverse kinematic problem, since these often involve geometries where adjacent axes are parallel, perpendicular or intersect. A new notation is proposed here that does not suffer the above-mentioned short-comings. To demonstrate some of the advantages of the new notation, it is applied to the problem of finger-printing a robot arm and to the solution of the inverse kinematic problem of near-ideal arms.