Iterative Generation Method of Arc Length Parameterized Curve Tool Path for Surface Machining from Short-Line Tool Path

To improve the application of the parametric curve tool path in surface machining, a method for generating arc-length parameterized toolpaths based on short-line toolpaths is proposed. The method first uses commercial CAM software to plan the short-line tool path. Then, the machining tool path with smooth continuous features is extracted. The smooth and continuous features are determined according to the chord length of the short-line tool path, and the extraction method is based on Chebyshev’s inequality of large numbers. After obtaining the smooth short-line trajectory, the iterative arc-length parameterized curve toolpath generation method is used to fit the discrete short-line toolpath. In the iterative process, the B-spline toolpath with parameterized chord length is obtained first. It is discretized according to the arc length difference information of the chord length B-spline. Finally, by continuously checking and inserting B-spline nodes, and fitting according to discrete points, the arc-length parameterized B-spline tool path is obtained. The feasibility of the method is verified with a part containing a sculpted surface, and two smooth arc-length parametric toolpaths are generated. In the end, the part is machined with the arc-length parameterized curve tool path.