An Algorithm to Generate Compact Dual NURBS Tool Path with Equal Distance for 5-Axis NC Machining

A new algorithm is proposed to generate compact dual NURBS tool paths with equal distance (DNTPED) for 5-axis NC machining. The DNTPED has significant advantages over conventional linear tool path in the NC machining of free-form surface since it reduces the tangency discontinuities along the tool path. The discontinuities, the inherent character of the linear interpolation, are the important sources of practical feed-speed fluctuation of the machine tool. The new algorithm is proposed to generate DNTPED based on the theories of rational motion. Here the rational rigid movement of a cutter is represented by a B-spline curve in dual quaternion space. DNTPED is obtained directly from the B-spline dual quaternion curve with the help of the blossom form of the B-spline curve. Comparing with the existing method, the DNTPED consists of less data and each NURBS can be treated as one curve, not as a collection of bezier segments.