Abstract
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.
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References
Mohan, S., Kweon, S. H., Lee, D. M., and Yang, S. H., “Parametric NURBS Curve Interpolators: A Review,” Int. J. Precis. Eng. Manuf., Vol. 9, No. 2, pp. 84–92, 2008.
Piegl, L. and Tiller, W., “The NURBS Book, 2nd ed.,” Springer, 1997.
Koren, Y., Lo, C. C., and Shpitalni, M., “CNC interpolators: algorithms and analysis,” Manufacturing Science and Engineering, Vol. 64, pp. 83–92, 1993.
Yang, D. C. H. and Kong, T., “Parametric interpolator versus linear interpolator for precision CNC machining,” Computer-Aided Design, Vol. 26, No. 3, pp. 225–234, 1994.
Zhang, Q. G. and 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.
Farouki, R. T. and Tsai, Y. F., “Exact Taylor series coefficients for variable-feedrate CNC curve interpolators,” Computer-Aided Design, Vol. 33, No. 2, pp. 155–165, 2001.
Yeh, S. S. and Hsu, P. L., “The speed-controlled interpolator for machining parametric curves,” Computer-Aided Design, Vol. 31, No. 5, pp. 349–357, 1999.
Tikhon, M., Ko, T. J., Lee, S. H., and 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.
Yong, T. and Narayanaswami, R., “A parametric interpolator with confined chord errors, acceleration and deceleration for NC machining,” Computer-Aided Design, Vol. 35, No. 13, pp. 1249–1259, 2003.
Du, D., Liu, Y., Yan, C., and Li, C., “An accurate adaptive parametric curve interpolator for NURBS curve interpolation,” The International Journal of Advanced Manufacturing Technology, Vol. 32, No. 9–10, pp. 999–1008, 2007.
Xu, R. Z., Xie, L., Li, C. X., and Du, D. S., “Adaptive parametric interpolation scheme with limited acceleration and jerk for NC machining,” The International Journal of Advanced Manufacturing Technology, Vol. 36, No. 3–4, pp. 343–354, 2008.
Lai, J. Y., Lin, K. Y., Tseng, S. J., and Ueng, W. D., “On the development of a parametric interpolator with confined chord error, feedrate, acceleration and jerk,” The International Journal of Advanced Manufacturing Technology, Vol. 37, No. 1–2, pp. 104–121, 2008.
Seker, M., Narayanan, V. N., and Yang, S. H., “Design of jerk bounded feedrate with ripple effect for adaptive NURBS interpolator,” The International Journal of Advanced Manufacturing Technology, Vol. 37, No. 5–6, pp. 545–552, 2008.
Lin, M. T., Tsai, M. S., and Yau, H. T., “Development of a dynamic-based NURBS interpolator with real-time look ahead algorithm,” International Journal of Machine Tools & Manufacture, Vol. 47, No. 15, pp. 2246–2262, 2007.
Liu, X., Ahmad, F., Yamazaki, K., and Mori, M., “Adaptive interpolation scheme for NURBS curves with the integration of machining dynamics,” International Journal of Machine Tools & Manufacture, Vol. 45, No. 4–5, pp. 433–444, 2005.
Du, D., Liu, Y., Guo, X., Yamazaki, K., and Fujishinma, M., “An accurate adaptive NURBS curve interpolator with real-time flexible acceleration/deceleration control,” Robotics and Computer-Integrated Manufacturing, Vol. 26, No. 4, pp. 273–281, 2010.
Cheng, M. Y., Su, K. H., and Wang, S. F., “Contour error reduction for free-form contour following task of biaxial motion control systems,” Robotics and Computer-Integrated Manufacturing, Vol. 25, No. 2, pp. 323–333, 2009.
Baek, D. K., Yang, S. H., and Ko, T. J., “Precision NURBS interpolator based on recursive characteristics of NURBS,” The International Journal of Advanced Manufacturing Technology, DOI: 10.1007/s00170-012-4179-z, 2012.
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Baek, DK., Ko, TJ. & Yang, SH. Fast and precision NURBS interpolator for CNC systems. Int. J. Precis. Eng. Manuf. 13, 955–961 (2012). https://doi.org/10.1007/s12541-012-0124-1
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DOI: https://doi.org/10.1007/s12541-012-0124-1