Cartesian compliance model for industrial robots using virtual joints

Industrial robots represent a promising, cost-saving and flexible alternative for machining applications. Due to the kinematics of a vertical articulated robot the system behavior is quite different compared to a conventional machine tool. The robot’s stiffness is not only much smaller but also position dependent in a non-linear way. This article describes the modeling of the robot structure and the identification of its parameters with focus on the analysis of the system’s stiffness. Therefore a method for the calculation of the Cartesian stiffness based on the polar stiffness and the use of the Jacobian matrix is introduced. Furthermore, so called virtual joints are used. With this method it is possible to model each joint of the robot with three degrees of freedom. Beside the gear stiffness the method allows the consideration of the tilting rigidity of the bearing and the link deformations to improve the model accuracy. Based on the results of the parameter identification and the calculation of the Cartesian stiffness the experimental model validation is done.