NURBS Interpolator with Recursive Method

재귀적 방법에 의한 NURBS 보간기

  • Published : 2005.05.01

Abstract

The purpose of this research is to find a simple and accurate NURBS interpolator for CNC systems such as robot, CMM and CNC machine tools. This paper presents a new design of NURBS interpolator for CNC system. The proposed algorithm used the recursive characteristics of NURBS equation, the previous incremental value and chord length for the sake of a constant chord length. Simulation study was conducted to see the performance of the proposed interpolator with reference-word and reference-pulse method. Consequently, an accurate and simple NURBS interpolator was possible for modem CNC systems.

Keywords

References

  1. Piegl, L., Tiller, W., 'The NURBS Book,' Springer, 1997
  2. Koren, Y., Lo, C. C., Shpitalni, M., 'CNC Interpolators: Algorithms and Analysis,' ASME Manufacturing Science and Engineering, PED-64, pp. 83-92, 1993
  3. Zhang, Q. G., Greenway, R. B., 'Development and Implementation of a NURBS Curve Motion Interpolator,' Robotics and Computer-Integrated Manufacturing, Vol. 14, No. 1, pp .27-36, 1998 https://doi.org/10.1016/S0736-5845(97)00021-5
  4. Yang, D. C. H., Kong, T., 'Parametric interpolator Verses Linear Interpolator for Precision CNC Machining,' Computer-Aided Design, Vol. 26, No. 3, pp. 225-234. 1994 https://doi.org/10.1016/0010-4485(94)90045-0
  5. Yeh, S. S., Hsu, P. L., 'The Speed-Controlled Interpolator for Machining Parametric Curves,' Computer-Aided Design, Vol. 31, No. 5, pp. 349-357. 1999 https://doi.org/10.1016/S0010-4485(99)00035-4
  6. Tikhon, M., Ko, T. J., Lee, S. H., Kim, H. S., 'NURBS Interpolator for Constant Material Removal Rate in Open NC Machine Tools,' International Journal of Machine Tools & Manufacture, Vol. 44, No. 2-3, pp. 237-245, 2004 https://doi.org/10.1016/j.ijmachtools.2003.10.020
  7. Farouki, R. T., Tsai, Y. F., 'Exact Taylor Series Coefficients for Variable-Feedrate CNC Curve Interpolators,' Computer-Aided Design, Vol. 33, No. 2, pp. 155-165, 2001 https://doi.org/10.1016/S0010-4485(00)00085-3
  8. Koren, Y., Masory, O., 'Reference-Pulse Circular Interpolators for CNC System,' ASME Journal of Engineering for Industry, Vol. 103, No. 1, pp. 131-136, 1981 https://doi.org/10.1115/1.3184454
  9. Koren, Y. Masory, O., 'Reference-Word Circular Interpolators for CNC System,' ASME J. of Engineering for Industry, Vol. 104, No. 4, pp. 400-405, 1982 https://doi.org/10.1115/1.3185849
  10. Hong, W., Yang, M., 'NURBS interpolation algorithm for CNC machines,' Journal of KSPE, Vol. 17, No. 12, pp. 115-120, 2000
  11. Kiritsis, D., 'High Precision Interpolation Algorithm For 3D Parametric Curves Generation,' Computer-Aided Design, Vol. 26, No. 11, pp. 850-856. 1994 https://doi.org/10.1016/0010-4485(94)90100-7