A smooth tool path planning method on NURBS surface based on the shortest boundary geodesic map

To fill the development gap between computer-aided design (CAD) and computer-aided manufacturing (CAM) on non-uniform rational b-spline (NURBS), a general tool path planning method on NURBS surface is proposed in this study. The generated tool path is composed of a series of closed paths which are derived by mapping the contours of a shortest boundary geodesic map (SBGM) from parameter space to 3D Euclidean space. SBGM that is created in parameter space depicts the shortest boundary geodesic distance (SBG) from internal points on NURBS surface to surface boundaries. It is calculated in discrete form firstly and then reconstructed by using a bicubic smoothing spline algorithm to improve the smoothness of the generated tool path. The tool path interval is deduced according to the requirement of residual scallop height constraint and determined conveniently based on the SBG difference of the two adjacent paths. It is confirmed that the proposed tool path planning method can be applied on all kinds of NURBS surface without the requirements of any other post-processing procedures. Typical case studies and experiments are presented to verify the effectiveness of the proposed method. Comparing with other traditional approaches, the proposed tool path planning method has excellent performance in improving the smoothness and reducing the total length of tool path.