An Analytical Inverse Kinematics Solution Method for Robotic Manipulators

Abstract

Abstract In this study, an inverse kinematic solution approach applicable to six degree-of-freedom industrial robotic manipulators is introduced. The approach is based on a previously introduced kinematic classification of industrial robotic manipulators by Balkan et al. (1999), and depending on the kinematic structure, either an analytical or a semi-analytical inverse kinematic solution is obtained. The semi-analytical method is named as the parametrized joint variable (PJV) method. Compact forward kinematic equations obtained by utilizing the properties of exponential rotation matrices. In the inverse kinematic solutions of the industrial robots surveyed in the previous study, most of the simplified compact equations can be solved analytically and the remaining few of them can be solved semi-analytically through a numerical solution of a single univariate equation. In these solutions, the singularities and the multiple configurations of the manipulators can be determined easily. By the method employed in this study, the kinematic and inverse kinematic analysis of any manipulator or designed-to-be manipulator can be performed and using the solutions obtained, the inverse kinematics can also be computerized by means of short and fast algorithms. As an example for the demonstration of the applicability of the presented method to manipulators with closed-chains, ABB IRB2000 industrial robot is selected which has a four-bar mechanism for the actuation of the third link, and its compact forward kinematic equations are given as well as the inverse kinematic solution.