In 5-axis surface machining, there are common problems of jagged tool paths if the Tool-axis orientation depends on local surface properties, such as the surface normal. These problems occur even if the geometry is properly built and appears to have good (G1) continuity properties. This paper analyzes the cause of the problems — the higher degree discontinuity of the geometry — and provides the general mathematical description of the symptoms (jagged tool paths). We also present a set of practical remedies to cope with the higher degree discontinuity and produce smooth 5-axis tool paths.

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