A New Approach To Generating Accurate Nurbs Cutter Location Paths With Approximate Arc Length Parameter

For accurate tool trajectories with respect to predetermined NURBS cutter location paths (refer to reference paths) and good tool kinematics in NC machining, many NURBS interpolation algorithms are trying to compute appropriate cutter locations on the paths during machining. Due to the high non-linearity between each interpolating chord (connecting two adjacent cutter locations) and its corresponding path segment, the existing methods can only interpolate the reference path with approximation, resulting in actual cutter trajectory with error beyond the tolerance and large feed rate fluctuations. To address problems of the current interpolation methods in this work, a new type of tool path, NURBS cutter location path with the arc length parameter, is proposed and a new approach to generating accurate paths of this type is provided through re-parameterization of the reference paths with the arc length parameter. The main features of this approach include (1) sampling points and calculating their arc lengths by decomposing an input reference path into Bezier curve segments according to criteria, and (2) fitting a NURBS tool path with the arc length parameter to the sample points until the parameterization error is less than the tolerance. This approach is applied to a benchmark for a NURBS path with the arc length parameter, and this path is then compared with the results generated using three existing interpolation methods, in order to demonstrate the advantage of this new approach.