A Kinematic Structure Based Classification of Six-DOF Industrial Robots and a Method of Inverse Kinematic Solution

Abstract

Abstract A kinematic structure based classification of six degree-of-freedom industrial robotic manipulators is introduced, and sample compact kinematic equations are given according to this classification. For the classification, one hundred industrial robots are surveyed. These robots are first classified into main groups and then into subgroups under each main group, and nine kinematic main groups, each having one to ten subgroups are obtained. The main groups are based on the end-effector rotation matrices and characterized by the twist angles. On the other hand, the subgroups are based on the wrist point positions and characterized by the link lengths and offsets. Compact kinematic equations are derived for one main group and one of its subgroups by utilizing the properties of exponential rotation matrices. In the inverse kinematic solutions, most of these simplified compact equations can be solved analytically and the remaining few of them can be solved semi-analytically through a single univariate equation. In these solutions, the singularities and the multiple configurations of the manipulators can be determined easily. Utilizing the method introduced in this study, the kinematic analysis of any manipulator or designed-to-be manipulator can be performed and using the solutions, the inverse kinematics can also be computerized by means of short and fast algorithms. As an example for, the demonstration of the presented method, Unimate 4000 industrial robot is selected which has five revolute joints and one prismatic joint and its compact forward kinematic equations are given as well as the inverse kinematic solution. To generalize the solution for the corresponding subgroup, a structural parameter related to the prismatic joint is assumed to have two different possible values leading to a closed-form or a semi-analytical solution.