An inverse kinematic solution algorithm for robots with two-by-two intersecting axes at the end effector

One of the most important features of an advanced control system for articulated robots is the capability of transforming the work space coordinates, which naturally characterize any robot task, into the joint coordinates, on which control actions are developed (Inverse Kinematic Problem). While simple kinematical structures allow for closed form solutions, there is a class of robots for which this is not true. If the three axes of revolution at the end effector intersect two-by-two an exact solution seems not to exist. The goal of the paper is to establish a fairly different solution algorithm, as compared to the trigonometric approach, which yields solutions in the above case. The algorithm is shown to be convergent along any trajectory. It proves very fast since it is based only on direct kinematics. Numerical examples are finally developed.