High accuracy spline interpolation for 5-axis machining

This article presents a new algorithm for simultaneous 5-axis spline interpolation. The algorithm basically merges two concepts: (1) the interpolation of the toolpath with Pythagorean Hodograph (PH) curves and (2) the analytic solution of the inverse kinematic problem using the template equation method. The first method allows one to obtain a analytic relation between the arclength and the parameter of the toolpath curve. This one enables one to control the velocity of the tool on the workpiece. The second method allows one to determine the analytic solution of the parameterized inverse kinematic problem that permits us to introduce arbitrary number of geometric parameters. A natural selection of the possible parameters can be the parameters of tool geometry and the workpiece placement. This way, the off-line generated inverse solutions—that transform the cutter contact curve into axis values—can be online compensated, as soon as the exact parameter values are become known. Based on these two approaches, a robust and fast method for the simultaneous 5-axis spline interpolation is developed. The result of this new algorithm is time-dependent axis splines which represent the given toolpath with high accuracy.