Three dimensional biarc approximation of freeform surfaces for machining tool path generation

In typical methods for machining freeform surfaces, the machining tool paths are generated by approximating the surface curves using line segments. While the approximated shape of the surface can be produced using cutters traversing along the line segments, the final surface produced may lack smoothness and continuity due to the zigzag patterns of the line segments. To reduce the difference and increase smoothness and continuity, the arc splines can be used to approximate the freeform curves and surfaces. A biarc is composed of two consecutive circular arcs with an identical tangent at the connecting point. Since the tangents at the connecting node are the same, the C¹ continuity property can be preserved. In addition, if the difference between the curvatures at the connecting node is minimized, then the C₂ smoothness property can be enhanced. In this research, the biarc segments are used to approximate the 2D and 3D freeform curves and surfaces using the largest deviation distance between the curves and the biarcs as the approximation criterion. The tool contact points generated and biarcs can be used to generate NC tool paths for machining 2D curves and 3D curves and surfaces. The methodology presented is implemented on a personal computer. Example parts modelled with B-spline curves and surfaces are tested and discussed. The test results show that the number of tool contact points and the number of segments are fewer than the typical linear approximation methods.