Numerically Controlled Machining of Freeform Curves Using Biarc Approximation

• Published in: International journal of advanced manufacturing technology 2001-01, Vol.17 (11), p.783-790
• Main Authors: Tseng, Y.-J., Chen, Y.-D., Liu, C.-C.
• Format: Article
• Language: English
• Subjects: Approximation; Curvature; Cutting tool paths; Free form; Machine tools; Machining; Mathematical analysis; Segments; Smoothness
• ISSN: 0268-3768; 1433-3015
• DOI: 10.1007/s001700170104

To machine a shape incorporating freeform curves, the free-form curves must be approximated and represented in a form suitable for numerically controlled (NC) tool-path generation. Instead of the commonly used line segment approximation, a new method using biarc approximation is presented here. The purpose is to reduce sudden changes in tool movement and increase continuity and smoothness. A biarc can be described as two consecutive circular arcs with an identical tangent at the connecting point. Therefore, tangent continuity can be maintained. Furthermore, curvature continuity can be improved if the difference between the two curvatures is minimised. In this research, biarc segments are used to approximate the freeform curves by controlling the largest deviation distance between the curves and the biarcs. The test results show that the biarc approximation method generates fewer tool-path segments than the traditional line approximation. The definitions of the biarcs are used to generate NC tool paths. A new tool-path generation method is developed for processing rough cutting and finish cutting paths. Example parts modelled with B-spline curves are tested and machined.