A smooth spiral tool path for high speed machining of 2D pockets

We introduce a new algorithm for generating a spiral tool path for high-speed machining of pockets without islands. The pocket may be an arbitrary simply-connected 2D shape bounded by straight-line segments and circular arcs. The tool path is generated by interpolating growing disks placed on the medial axis of the pocket. It starts inside the pocket and spirals out to the pocket boundary. The tool path is guaranteed to be free of self-intersections and allows machining of the pocket without tool retractions. The start point of the spiral may be chosen freely by the user anywhere within the pocket. Most importantly, the spiral tool path complies with a user-specified maximum cutting width. The output of our algorithm is a G1G1-continuous spiral path. However, in a post-processing step, a properly adapted variant of the recent “PowerApx” package [Heimlich M, Held M. Biarc approximation, simplification and smoothing of polygonal curves by means of Voronoi-based tolerance bands. International Journal of Computational Geometry & Applications 2008;18(3):221–50] can be used to boost the tool path to C2C2-continuity. Our new algorithm was implemented and tested successfully on real-world data. We conclude our paper by an analysis of sample tool paths produced by our implementation.