Energy efficient trajectories of industrial machine tools with parallel kinematics

Mechanisms with parallel kinematics are receiving growing attention in industrial applications including flexible machine tools, due to superior positioning and faster performance as compared to series kinematic schemes. In addition to a precise contour forming by a PKM-based machine, its redundant degrees of freedom (DOFs) can be used to improve its energy efficiency. A new approach of tool trajectory planning is proposed in this paper which utilizes redundant DOFs to so position the tool relative to the workpiece during the contour forming that non-regenerative drives involved in the cutting process primarily stay in motoring mode. This excludes energy losses on nonregenerative breaking and significantly improves energy efficiency of milling operation. As the proposed approach reduces the order of the optimization problem, its solution included in the paper is obtained partially analytically and partially numerically. The solution is independent of inaccuracies of dynamic modeling and ensures high accuracy contour forming and stable drive operation. The paper findings are supported by experimental results obtained with the help of an industrial PKM-based machine KIM-1000.