Formulation of the kinematic model of a general (6 DOF) robot manipulator using a screw operator

摘要

Abstract In general, the manipulator's end‐effector can be located in a desired position and orientation in its work‐space through angular and/or linear displacements of its joints. These joint coordinates can be obtained by solving the loop‐closure equation of the manipulator's kinematic model. The most common method for obtaining this equation is based on the point coordinates 4×4 homogeneous transformation matrix. This method uses a special set of frames which are adapted to the manipulator's configuration. Within the last few years there has been some interest in the use of screw operators (line transformations) to model the kinematic configuration of manipulators and to form the loop‐closure equation. In this article, a kinematic model of a general (6 DOF) manipulator is obtained through the application of a screw operator (dual‐unit quaternion) to represent the screw displacements of the line coordinates of the manipulator link and joint axes. The loop‐closure equation of the closed kinematic chain is obtained by introducing a hypothetical link/joint at the manipulator's end‐effector location. The resultant non‐linear loop‐closure equation is then solved for the joint coordinates using a numerical technique. The method is illustrated with an example.