Iterative coordinate transformation procedure for one class of robots

A necessary feature of robot systems is a capability to process robot paths in terms of Cartesian coordinates. However, the so-called articulated robot arms which represent the more advanced systems operate in terms of their revolute and sliding joint coordinates, and these do not lend themselves easily to translation into Cartesian equivalents. As a rule, the direct (joint-to-Cartesian space) coordinate transformation can be solved for in closed form. As for the inverse (Cartesian-to-joint) transformation, for some rather common arm designs practical solutions cannot be found in closed form. An iterative procedure for one such class of articulated robots is presented. The procedure produces an exact solution for the wrist tip position coordinates and an approximate solution for the wrist orientation coordinates. The convergence characteristics of the procedure are discussed.