Polynomial Inverse Kinematic Solution of the Jaco Robot

This article presents a polynomial solution to the inverse kinematic problem of the 6R serial Jaco robot. The solution is specifically tailored to the Jaco robot, which is not wrist-partitioned. The derivation of the univariate 16-degree polynomial is presented, starting from the direct kinematic equations providing the position and orientation of the end-effector as a function of the joint variables. Upon calculation of the roots of the polynomial, all joint variables are obtained by backsubstitution, leading to a unique set of joint variables for each of the roots. Also, it is shown that for certain configurations, the 16-degree polynomial contains only terms of even powers while all terms are not zero in general. Two numerical examples are given to demonstrate the effectiveness of the solution process.