Smooth Geodesic Interpolation for Five-Axis Machine Tools

Abstract

The smoothness of tool trajectories would be as important as that of axis trajectories for five-axis machining. The present study proposes a geodesic interpolation for five-axis machine tools. The tool positions and orientations are fitted to geodesics, respectively, to achieve smooth accurate motions of the tool center point (TCP), smooth axis motions, and the constant velocities of the TCP position and orientation. Not only the linear and circular geodesic interpolation are proposed, but also the acceleration/deceleration and block connection schemes are considered. The method is illustrated by simulations and experiments on a five-axis machining center, and compared to the interpolator with the TCP control. The real-time implementation of geodesic interpolation is well within the scope of modern CNC systems.