Fast and precision NURBS interpolator for CNC systems

This paper presents a performance evaluation of a NURBS interpolator that uses not Taylor's expansion method but the recursive characteristics of NURBS. Taylor's expansion has mostly been used for NURBS interpolation. However, it is very complicated and gives an indispensable truncation error. A fast and precision NURBS interpolator replacing Taylor's expansion is presented for CNC systems in robots and CNC machine tools. The presented interpolation algorithm uses the recursive equation of the NURBS formula rather than Taylor's expansion. A simulation study is conducted to demonstrate the advantages of this proposed interpolator compared with those using Taylor's equation. The feedrate error and calculation time are simulated in the performance evaluation. The recursive method of NURBS interpolation is faster and more accurate than Taylor's expansion.