A simplified inverse kinematic model calculation method for all 6R type manipulators

An inverse kinematic model of a manipulator - equipped with an end effector - is a function which allows to calculate a manipulator configuration corresponding to a given end effector location (position and orientation). In this paper, we consider the case of 6R type manipulators having a single open kinematic chain structure and six revolute joints R. The first method, which brought back the determination of this model to the computation of the roots of a polynomial equation whose degree - equal to sixteen - is minimal, was proposed in 1988 by Lee and Liang. Nevertheless, Lee and Liang's technique was extremely complicated and necessitated divisions which prevent it from being used in any case. Here, we present a simplified method for this calculation, which does not involve any division; as a consequence it works in any case. We present also an example of a particular, but non academic, manipulator for which we actually obtain sixteen different real configurations corresponding to a particular given end effector location; this result demonstrates that the degree of the previous polynomial equation cannot be reduced.