[1] Zhu Hao, Liu Jingnan, Yang Ankang, et al. An adaptive generation method for free curve trajectorybased on NURBS [J]. Journal of Southeast University (English Edition), 2014, 30 (3): 296-301. [doi:10.3969/j.issn.1003-7985.2014.03.007]

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An adaptive generation method for free curve trajectorybased on NURBS()

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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

30

Issue:

2014 3

Page:

296-301

Research Field:

Automation

Publishing date:

2014-09-30

Info

Title:

An adaptive generation method for free curve trajectorybased on NURBS

Author(s):

Zhu Hao¹;  2;  Liu Jingnan¹;  Yang Ankang¹;  Wang Mulan²

¹School of Automation, Southeast University, Nanjing 210096, China
² Jiangsu Key Laboratory of Advanced Numerical Control Technology, Nanjing Institute of Technology, Nanjing 211167, China

Keywords:

free curve;  NURBS(non-uniform rational B-spline);  sigmoid function;  Adams algorithm

PACS:

TP237

DOI:

10.3969/j.issn.1003-7985.2014.03.007

Abstract:

To realize the high precision and real-time interpolation of the NURBS(non-uniform rational B-spline)curve, a kinetic model based on the modified sigmoid function is proposed. The constraints of maximum feed rate, chord error, curvature radius and interpolator cycle are discussed. This kinetic model reduces the cubic polynomial S-shape model and the trigonometry function S-shape model from 15 sections into 3 sections under the precondition of jerk, acceleration and feedrate continuity. Then an optimized Adams algorithm using the difference quotient to replace the derivative is presented to calculate the interpolator cycle parameters. The higher-order derivation in the Taylor expansion algorithm can be avoided by this algorithm. Finally, the simplified design is analyzed by reducing the times of computing the low-degree zero-value B-spline basis function and the simplified De Boor-Cox recursive algorithm is proposed. The simulation analysis indicates that by these algorithms, the feed rate is effectively controlled according to tool path. The calculated amount is decreased and the calculated speed is increased while the machining precision is ensured. The experimental results show that the target parameter can be correctly calculated and these algorithms can be applied to actual systems.

References:

[1] Zhang Liyan, Bian Yuchao, Chen Hu, et al. Implementation of a CNC NURBS curve interpolator based on control of speed and precision [J]. International Journal of Production Research, 2009, 47(6):1505-1519.
[2] Sekar M, Narayanan V N, Yang S-H. Design of jerk bounded feedrate with ripple effect for adaptive NURBS interpolator [J]. The International Journal of Advanced Manufacturing Technology, 2008, 37(5/6):545-552.
[3] Peigl L, Tiller W. The NURBS book [M]. New York: Springer, 1995.
[4] Béarée R, Olabi A. Dissociated jerk-limited trajectory applied to time-varying vibration reduction [J]. Robotics and Computer-Integrated Manufacturing, 2013, 29(2):444-453.
[5] Lai J-Y, Lin K-Y, Tseng S-J. On the development of a parametric interpolator with confined chord error, feedrate, acceleration and jerk [J]. The International Journal of Advanced Manufacturing Technology, 2008, 37(1/2):104-121.
[6] Yong T, Narayanaswami R. A parametric interpolator with confined chord errors, acceleration and deceleration for NC machining [J]. Computer-Aided Design, 2003, 35(13):1249-1259.
[7] Liu X B, Ahmad F, Yamazaki K, et al. Adaptive interpolation scheme for NURBS curves with the integration of machining dynamics [J]. International Journal of Machine Tools and Manufacture, 2005, 45(4):433-444.
[8] Du Daoshan, Liu Yadong, Yan Cunliang. An accurate adaptive parametric curve interpolator for NURBS curve interpolation [J]. The International Journal of Advanced Manufacturing Technology, 2007, 32(9/10):999-1008.
[9] Zhang Deli, Zhou Laishui. Intelligent NURBS interpolator based on the adaptive feedrate control [J]. Chinese Journal of Aeronautics, 2007, 20(5):469-474.
[10] Atkinson K, Han W M. Elementary numerical analysis [M]. Beijing: Post and Telecom Press, 2009.(in Chinese)

Memo

Memo:

Biographies: Zhu Hao(1980—), male, graduate, associate professor; Liu Jingnan(corresponding author), male, doctor, processor, liujn@seu.edu.cn.
Foundation items: The Doctoral Fund of Ministry of Education of China(No. 20090092110052), the Natural Science Foundation of Higher Education Institutions of Jiangsu Province(No. 12KJA460002), College Industrialization Project of Jiangsu Province(No. JHB2012-21).
Citation: Zhu Hao, Liu Jingnan, Yang Ankang, et al. An adaptive generation method for free curve trajectory based on NURBS[J].Journal of Southeast University(English Edition), 2014, 30(3):296-301.[doi:10.3969/j.issn.1003-7985.2014.03.007]

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