Cartesian Stiffness Optimization for Serial Arm Robots

Abstract

Recently, serial arm robots drew attention of the machining industry due to their high dexterity, large workspace and ability to conduct various tasks, with a reduced capital cost compared to machine tools. However, their poor and varying rigidity, and low precision, are the main factors impeding their application to hard material machining operations. Proper development of stiffness and dynamic models is crucial to predict and compensate the tool deflections under cutting forces. However, this is only part of the solution, and there is a need for Cartesian stiffness enhancement. This can be achieved by utilizing the functionally redundant degree of freedom (DoF) around the tool axis that is available when employing a 6-DoF serial arm robot for 5-axis machining operations. In this paper, the stiffness of a serial arm robot was optimized to minimize the possible deflections during a milling operation. The machining table surface with a fixed height was divided into a mesh of evenly spaced points with the tool alignment perpendicular to its surface. The functionally redundant degree of freedom was varied sequentially, and robot configurations achieving the desired poses were determined through inverse kinematics for each scenario. The inverse of Cartesian stiffness matrix, (the Cartesian Compliance matrix) of the robot was then computed for every configuration, and the one having the optimum Cartesian compliance parameter in an arbitrary direction was selected. Consequently, a map of the optimum Cartesian compliance parameter over the surface of the machining table was obtained which can be used for static deflection compensation and, potentially for chatter avoidance in robotic milling operations. The work suggests that a significant increase in the stiffness of the robot can be obtained by using this method.