The non-uniform rational B-spine (NURBS) curve interpolation is a key technology of the advanced computer numerical control (CNC) system. NURBS curve interpolation can realize a high-speed and high-precision machining, and it can also avoid some inevitable deficiencies of the linear and circular interpolation functions which are generally used in traditional NC system. Before the interpolation, some calculation tasks are finished, which will decrease the amount of calculation during interpolation and increase the interpolation efficiency. Further, an adaptive NURBS curve interpolation with real-time and flexible S-shaped curve acceleration/deceleration (ACC/DEC) control method is added to the interpolation algorithms. The NC machining simulation conducted with the MATLAB software and the NURBS curve interpolation experiments performed on the 4-axis polishing machine tool demonstrate the validity and correctness of the adaptive real-time NURBS curve interpolation algorithm in the CNC system.

非均匀有理B脊线（NURBS）曲线插值是高级计算机数控（CNC）系统的一项关键技术。NURBS曲线插补可以实现高速，高精度的加工，并且还可以避免传统数控系统中通常使用的线性和圆弧插补功能的某些不可避免的缺陷。在插值之前，要完成一些计算任务，这将减少插值期间的计算量并提高插值效率。此外，将具有实时和灵活的S形曲线加/减速（ACC / DEC）控制方法的自适应NURBS曲线插值添加到插值算法中。