In current industrial applications many engineering parts having complex shapes are designed using sculptured surfaces in CAD system. Due to the lack of smooth motions and accurate machining of these surfaces using standard linear and circular motions in conventional CNC machines, new commercial CNC systems are equipped with parametric curve interpolation function. However, in some applications these surfaces can be very complex that are susceptible to gouging and due to the approximation of;​ CL‐path in CAM system and path parameter in real – time, high machining accuracy, smooth kinematic and feed‐rate profiles, are difficult to achieve. This dissertation focuses on developing algorithms that generate tool paths in NURBS form for smooth, high speed and accurate sculptured surface machining. The first part of the research identifies and eliminates gouge cutter location (CL) point from the tool path. The proposed algorithm uses global optimization technique (Particle Swarm Optimization) to check all the CC‐points along a tool‐path with high accuracy, and only gouging free CC‐points are used to generate the set of valid CL‐points. Mathematical models have been developed and implemented to cover most of the cutter shapes, used in the industry.

In the second phase of the research, all valid CL‐points along the tool‐path are used to generate CL‐path in B‐spline form. The main contribution of this part is to formulate an error function of the offset approximation and to represent it in NURBS form to globally bound the approximation errors. Based on this error function, an algorithm is proposed to generate tool‐paths in B‐spline from with;​ globally controlled accuracy, fewer control points and low function degree, compared to its contemporaries. The proposed approach thus presents an error‐ bounded method for B‐spline curve approximation to the ideal CL‐path within the accuracy. This part of research has two components, one is for 2½‐ axis (pocket) and the other one is for 3‐axis (surface) CNC machining.

The third part deals with the problem of CL‐path parameter estimation during machining in real time. Once the gouging free CL‐path in NURBS form with globally controlled accuracy is produced, it is re‐parameterized with approximate arc‐length in the off‐line stage. The main features of this work are;​ (1) sampling points and calculating their approximate arc‐lengths within error bound by decomposing the input path into Bezier curve segments, (2) fitting the NURBS curve with approximate arc‐length parameter to the sample points until the path and parameterization errors are within the tolerance, and (3) segment the curve into pieces with different feed rates if during machining the cutter trajectory errors are beyond the tolerance at highly curved regions in the NURBS tool path.