An Adaptive Real-time NURBS Interpolator for CNC Machine Tools

This paper presents a real-time interpolation method along non-uniform rational B-spline (NURBS) curves which have been used by CNC systems. The development of NURBS interpolator promises modern manufacturing system to machine arbitrary geometries with great relief of the data-flow bottleneck. In this interpolation algorithm, an Adams-Bashforth method is used as a predictor to predict the next trajectory point on the NURBS curve and an adaptive corrector is proposed so that a specified deviation between the command feedrate and the desired feedrate is met. The convergent condition for the algorithm is presented and demonstrated. Both simulation and experimental results for the NURBS interpolation are employed to verify the feasibility of the algorithm and comparison with first and second order of Taylor's expansion method is provided to reveal the accuracy of this proposed algorithm.