A constant feed and reduced angular acceleration interpolation algorithm for multi-axis machining

Multi-axis tool paths are currently generated as a set of discrete data points consisting of a position vector, representing the tool tip, and an orientation unit vector, representing the tool axis. The CNC interpolator must convert these points into continuous machine tool axis motions. To achieve the highest quality parts, a constant feed and reduced angular acceleration must be maintained throughout the motion. This paper presents a new algorithm for off-line interpolation of the data points, followed by real-time axis command generation. The splines produced by the algorithm are C2 continuous, and independent of machine tool kinematics. Hence the motions produced will be the same on any five-axis machine tool, hexapod, or robotic arm. Three splines are computed: position, orientation, and reparameterization. The position spline is a near arc-length parameterized quintic polynomial spline. The paper introduces a near arc-length parameterized quintic spherical Bézier spline as the orientation spline. Coordinated motion is accomplished with an orientation reparameterization spline. The proposed algorithm is demonstrated using a practical example.