Abstract
This paper deals with the real-time NURBS interpolation method in which the interpolation error between the ideal curve and the interpolated curve is compensated within the machine basic length unit (BLU). Parametric curve interpolation methods are based on the Taylor series expansion of curve parameters and an approximation. This approach enables effective feed command generation following the target curve. However, the interpolation error caused by the curve segmentation cannot be controlled.
In this research, a two-stage interpolation method that compensates for interpolation errors within machine BLU is proposed. The interpolation result was filtered by an acceleration/jerk limitation equation. Through this two-stage interpolation, both the interpolation error condition and the motion dynamics can be satisfied.
Using computer simulations in which interpolation results are revaluated by a numerical iteration method, it is shown that the two-stage interpolation algorithm can interpolate target curves precisely with geometric and dynamic contentment. The proposed algorithm was implemented in the CNC simulator system and an experimental run was conducted to identify the real-time adaptation.
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References
Cheng M, Tsai M, Kuo J (2002) Real-time NURBS command generators for CNC servo controllers. Int J Mach Tools Manuf 42:801–813
Yang D, Kong T (1994) Parametric interpolator versus linear interpolator for precision CNC machining. Comput Aided Des 26(3): 225–234
Hillaire R, Marchetti L, Wright PK (1998) Geometry for precision manufacturing on an open architecture machine tool. Proceedings of the ASME MED 8:605–610
Zhang G, Greenway R (1998) Development and implementation of a NURBS curve motion interpolator. Robot Comput Integr Manuf 14:27–36
Yeh S, Hsu P(1999) The speed-controlled interpolator for machining parametric curves. Comput Aided Des 31:349–357
Bahr B, Xiao X, Krishnan K (2001) A real-time scheme of cubic parametric curve interpolations for CNC systems. Comput Ind 45:309–317
Tseng Y, Chen Y, Liu C (2001) Numerically controlled machining of freeform curves using biarc approximation. Int J Adv Manuf Technol 17:783–790
Farouki RT, Shah S (1996) Real-time CNC-interpolators for Pythagorean-hodograph curves. Comput Aided Geom Des 13:583–600
Xu H, Tam H, Tse P (2001) Variable feedrate CNC interpolation for planar implicit curves. Int J Adv Manuf Technol 18:794–800
Zhiming X, Jincheng C, Zhengjin F (2002) Performance evaluation of real-time interpolation algorithm for NURBS curves. Int J Adv Manuf Technol 20:270–276
Yeh S, Hsu P (2002) Adaptive-feedrate interpolation for parametric curves with a confined chord error. Comput Aided Des 34:229–237
Y. Altintas (2000) Manufacturing Automation. Cambridge University Press, New York
Piegl L, Tiller W (1995) The NURBS Book. Springer, Berlin Heidelberg New York
Yang M, Park J (2002) A study on an open architecture CNC system with a NURBS interpolator for WEDM. Int J Adv Manuf Technol 19:664–668
Zelinski P (1999) Understanding NURBS interpolation. http://www.mmsonline.com. Cited July 1999
Otsuki T, Kozai H, Wakinotani Y (1999) Free curve interpolation apparatus and interpolation method. US Patent 5,936,864, 10 Aug 1999
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Park, J., Nam, S. & Yang, M. Development of a real-time trajectory generator for NURBS interpolation based on the two-stage interpolation method. Int J Adv Manuf Technol 26, 359–365 (2005). https://doi.org/10.1007/s00170-003-1998-y
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DOI: https://doi.org/10.1007/s00170-003-1998-y