Abstract: A toolpath generation method is presented for NC machining based on vector analysis and NURBS. Given optimal cutting directions at sampled points in the parameter domain of the NURBS surface, a vector field model fitting to these scattered vectors is established according to the conversion between scalar field and gradient field. Thus, tool paths in the parameter domain can be represented as vector curves of a 2D vector field. Moreover, using NURBS as the stream function of generating gradient field, a global shape optimization of tool-paths can be easily completed by adjusting the control point array of the stream function. The example shows that the precise design method of tool paths is very useful in high- efficiency machining of complex shapes.

Key words: NURBS, Tool paths, Vector field