Development of the Forward and Inverse Kinematic Models for the AdvancedDeburring and Chamfering System (ADACS) Industrial Robot

摘要

The kinematic model for the Advanced Deburring and Chamfering System (ADACS)robot, which determines the position and orientation of the manipulator end-effector for a given set of joint angles, is developed using the standardized Denavit-Hartenberg method as well as an alternative link transform method. The Denavit-Hartenberg notation is described and the parameters for each link are provided in table form. The transform matrix for each link is then derived using these parameters and the mathematical kinematic model is developed. The inverse kinematic model, which determines the joint value set for a given end-effector position and orientation, is developed from the kinematic model derived using the Denavit-Hartenberg method. The first three joints are solved using a geometric approach. The last three joints are solved for by algebraic and trigonometric manipulation of the rotation part of the transformation matrix. There are two problems that are dealt with when the inverse kinematic model is solved for. One is the presence of a singularity point in the manipulator. A singularity occurs when two or more joint axes line up causing an infinite number of possible solutions for any given orientation. As the singularity is approached, excessive speed occurs in joint 4 as the wrist 'rolls over'. A singularity occurs when joint 5 is zero. When a singularity occurs, joint 5 is set to 0, joint 4 is set to its previous value and joint 6 is solved for. There is also an ambiguity in the wrist. There are two solutions for the last three joints for a specific orientation.