Advertisement

Toolpath Interpolation and Smoothing for Computer Numerical Control Machining of Freeform Surfaces: A Review

  • Wen-Bin Zhong
  • Xi-Chun LuoEmail author
  • Wen-Long Chang
  • Yu-Kui Cai
  • Fei Ding
  • Hai-Tao Liu
  • Ya-Zhou Sun
Open Access
Review Special Issue on Improving Productivity Through Automation and Computing

Abstract

Driven by the ever increasing demand in function integration, more and more next generation high value-added products, such as head-up displays, solar concentrators and intra-ocular-lens, etc., are designed to possess freeform (i.e., non-rotational symmetric) surfaces. The toolpath, composed of high density of short linear and circular segments, is generally used in computer numerical control (CNC) systems to machine those products. However, the discontinuity between toolpath segments leads to high-frequency fluctuation of feedrate and acceleration, which will decrease the machining efficiency and product surface finish. Driven by the ever-increasing need for high-speed high-precision machining of those products, many novel toolpath interpolation and smoothing approaches have been proposed in both academia and industry, aiming to alleviate the issues caused by the conventional toolpath representation and interpolation methods. This paper provides a comprehensive review of the state-of-the-art toolpath interpolation and smoothing approaches with systematic classifications. The advantages and disadvantages of these approaches are discussed. Possible future research directions are also offered.

Keywords

Computer numerical control (CNC) toolpath interpolation smoothing freeform surface 

Notes

Acknowledgements

The authors acknowledge the support from the UK Engineering and Physical Sciences Research Council (EPSRC) under the program (No. EP/K018345/1) and the International Cooperation Program of China (No. 2015DFA70630).

References

  1. [1]
    X. Jiang, P. Scott, D. Whitehouse. Freeform surface characterisation — A fresh strategy. CIRP Annals, vol. 56, no. 1, pp. 553–556, 2007. DOI:  https://doi.org/10.1016/j.cirp.2007.05.132.CrossRefGoogle Scholar
  2. [2]
    J. Chaves-Jacob, G. Poulachon, E. Duc. Optimal strategy for finishing impeller blades using 5-axis machining. The International Journal of Advanced Manufacturing Technology, vol. 58, no. 5–8, pp. 573–583, 2012. DOI:  https://doi.org/10.1007/S00170-011-3424-1.CrossRefGoogle Scholar
  3. [3]
    F. Z. Fang, X. D. Zhang, A. Weckenmann, G. X. Zhang, C. Evans. Manufacturing and measurement of freeform optics. CIRP Annals, vol. 62, no. 2, pp. 823–846, 2013. DOI:  https://doi.org/10.1016/j.cirp.2013.05.003.CrossRefGoogle Scholar
  4. [4]
    I. S. Jawahir, D. A. Puleo, J. Schoop. Cryogenic machining of biomedical implant materials for improved functional performance, life and sustainability. Procedia CIRP, vol. 46, pp. 7–14, 2016. DOI:  https://doi.org/10.1016/j.procir.2016.04.133.CrossRefGoogle Scholar
  5. [5]
    National Joint Registry. Joint Replacement Surgery: The National Joint Registry, [Online], Available: https://doi.org/www.hqip.org.uk/, March 8, 2019.
  6. [6]
    U.S. Product Data Association. Initial Graphics Exchange Specification, IGES 5.3, 1996.Google Scholar
  7. [7]
    M. J. Pratt. Introduction to ISO 10303-the STEP standard for product data exchange. Journal of Computing and Information Science in Engineering, vol. 1, no. 1, pp. 102–103, 2001. DOI:  https://doi.org/10.1115/1.1354995.CrossRefGoogle Scholar
  8. [8]
    T. R. Kramer, F. M. Proctor, E. Messina. The NIST RS274NGC Interpreter-Version 3, Technical Report NI-STIR 6556, Department of Commerce, USA, 2000.CrossRefGoogle Scholar
  9. [9]
    Automation Systems and Integration — Numerical Control of Machines — Program Format and Definitions of Address Words — Part 1: Data Format for Positioning, Line Motion and Contouring Control Systems, ISO 6983-1: 2009, December 2009.Google Scholar
  10. [10]
    Y. Zhang, X. L. Bai, X. Xu, Y. X. Liu. STEP-NC based high-level machining simulations integrated with CAD/CAPP/CAM. International Journal of Automation and Computing, vol. 9, no. 5, pp. 506–517, 2012. DOI:  https://doi.org/10.1007/s11633-012-0674-9.CrossRefGoogle Scholar
  11. [11]
    B. Venu, V. R. Komma, D. Srivastava. STEP-based feature recognition system for B-spline surface features. International Journal of Automation and Computing, vol. 15, no. 4, pp. 500–512, 2018. DOI:  https://doi.org/10.1007/s11633-018-1116-0.CrossRefGoogle Scholar
  12. [12]
    M. Y. Cheng, M. C. Tsai, J. C. Kuo. Real-time NURBS command generators for CNC servo controllers. International Journal of Machine Tools and Manufacture, vol. 42, no. 7, pp. 801–813, 2002. DOI:  https://doi.org/10.1016/S0890-6955(02)00015-9.CrossRefGoogle Scholar
  13. [13]
    K. Nakamoto, T. Ishida, N. Kitamura, Y. Takeuchi. Fabrication of microinducer by 5-axis control ultraprecision micromilling. CIRP Annals, vol. 60, no. 1, pp. 407–410, 2011. DOI:  https://doi.org/10.1016/j.cirp.2011.03.021.CrossRefGoogle Scholar
  14. [14]
    S. J. Yutkowitz. Apparatus and Method for Smooth Cornering in A Motion Control System, U.S. Patent 6922606, July 2005.Google Scholar
  15. [15]
    S. S. Yeh, P. L. Hsu. Adaptive-feedrate interpolation for parametric curves with a confined chord error. Computer-Aided Design, vol. 34, no. 3, pp. 229–237, 2002. DOI:  https://doi.org/10.1016/S0010-4485(01)00082-3.CrossRefGoogle Scholar
  16. [16]
    L. Piegl, W. Tiller, The NURBS Book, 2nd ed., New York, USA: Springer-Verlag, 1996.zbMATHGoogle Scholar
  17. [17]
    Y. F. Tsai, R. T. Farouki, B. Feldman. Performance analysis of CNC interpolators for time-dependent feedrates along PH curves. Computer Aided Geometric Design, vol. 18, no. 3, pp. 245–265, 2001. DOI:  https://doi.org/10.1016/S0167-8396(01)00029-2.MathSciNetzbMATHCrossRefGoogle Scholar
  18. [18]
    C. Brecher, S. Lange, M. Merz, F. Niehaus, C. Wenzel, M. Winterschladen, M. Weck. NURBS based ultra-precision free-form machining. CIRP Annals, vol. 55, no. 1, pp. 547–550, 2006. DOI:  https://doi.org/10.1016/S0007-8506(07)60479-X.CrossRefGoogle Scholar
  19. [19]
    A. Vijayaraghavan, A. Sodemann, A. Hoover, J. Rhett Mayor, D. Dornfeld. Trajectory generation in high-speed, high-precision micromilling using subdivision curves. International Journal of Machine Tools and Manufacture, vol. 50, no. 4, pp. 394–403, 2010. DOI:  https://doi.org/10.1016/j.ijmachtools.2009.10.010.CrossRefGoogle Scholar
  20. [20]
    Z. Q. Yin, Y. F. Dai, S. Y. Li, C. L. Guan, G. P. Tie. Fabrication of off-axis aspheric surfaces using a slow tool servo. International Journal of Machine Tools and Manufacture, vol. 51, no. 5, pp. 404–410, 2011. DOI:  https://doi.org/10.1016/j.ijmachtools.2011.01.008.CrossRefGoogle Scholar
  21. [21]
    X. S. Wang, X. Q. Fu, C. L. Li, M. Kang. Tool path generation for slow tool servo turning of complex optical surfaces. The International Journal of Advanced Manufacturing Technology, vol. 79, no. 1–4, pp. 437–448, 2015. DOI:  https://doi.org/10.1007/s00170-015-6846-3.CrossRefGoogle Scholar
  22. [22]
    L. Lu, J. Han, C. Fan, L. Xia. A predictive feedrate schedule method for sculpture surface machining and corresponding B-spline-based irredundant PVT commands generating method. The International Journal of Advanced Manufacturing Technology, vol. 98, no. 5–8, pp. 1763–1782, 2018. DOI:  https://doi.org/10.1007/s00170-018-2180-x.CrossRefGoogle Scholar
  23. [23]
    W. B. Zhong, X. C. Luo, W. L. Chang, F. Ding, Y. K. Cai. A real-time interpolator for parametric curves. International Journal of Machine Tools and Manufacture, vol. 125, pp. 133–145, 2018. DOI:  https://doi.org/10.1016/j.ijmachtools.2017.11.010.CrossRefGoogle Scholar
  24. [24]
    FANUC Corporation. FANUC Series 30i/31i/32i/35i-MODEL B, [Online], Available: https://doi.org/www.fanuc.co.jp/en/product/cnc/fs_30i-b.html, March 8, 2019.
  25. [25]
    Siemens AG. SIEMENS SINUMERIK 840D sl Brochure, [Online], Available: https://doi.org/www.industry.usa.siemens.com/drives/us/en/cnc/systems-and-products/Documents/Brochure-SINUMERIK-840D-sl.pdf, March 8, 2019.
  26. [26]
    HEIDENHAIN Corporation. HEIDENHAN iTNC 530 Brochure, [Online], Available: https://doi.org/www.heidenhain.de/fileadmin/pdb/media/img/895822-25_iTNC530_Design7_en.pdf, March 8, 2019.
  27. [27]
    Delta Tau Data Systems Inc. Power PMAC User’s Manual, [Online], Available: https://doi.org/www.deltatau.com/manuals/, March 8, 2019.
  28. [28]
    Aerotech Inc. Automation 3200 Brochure, [Online], Available: https://doi.org/www.aerotech.co.uk/product-catalog/motion-controller/a3200.aspx, March 8, 2019.
  29. [29]
    F. C. Wang, D. C. H. Yang. Nearly arc-length parameterized quintic-spline interpolation for precision machining. Computer Aided Geometric Design, vol. 25, no. 5, pp. 281–288, 1993. DOI:  https://doi.org/10.1016/0010-4485(93)90085-3.zbMATHCrossRefGoogle Scholar
  30. [30]
    F. C. Wang, P. K. Wright, B. A. Barsky, D. C. H. Yang. Approximately Arc-length parametrized C3 quintic interpolatory splines. Journal of Mechanical Design, vol. 121, no. 3, pp. 430–439, 1999. DOI:  https://doi.org/10.1115/1.2829479.CrossRefGoogle Scholar
  31. [31]
    R. V Fleisig, A. D. Spence. A constant feed and reduced angular acceleration interpolation algorithm for multi-axis machining. Journal of Mechanical Design, vol. 33, no. 1, pp. 1–15, 2001. DOI:  https://doi.org/10.1016/S0010-4485(00)00049-X.Google Scholar
  32. [32]
    R. T. Farouki, S. Shah. Real-time CNC interpolators for Pythagorean-hodograph curves. Computer Aided Geometric Design, vol. 13, no. 7, pp. 583–600, 1996. DOI:  https://doi.org/10.1016/0167-8396(95)00047-X.zbMATHCrossRefGoogle Scholar
  33. [33]
    R. T. Farouki, M. Al-Kandari, T. Sakkalis. Hermite interpolation by rotation-invariant spatial pythagorean-hodograph curves. Advances in Computational Mathematics, vol. 17, no. 4, pp. 369–383, 2002. DOI:  https://doi.org/10.1023/A:1016280811626.MathSciNetzbMATHCrossRefGoogle Scholar
  34. [34]
    K. Erkorkmaz, Y. Altintas. Quintic spline interpolation with minimal feed fluctuation. Journal of Manufacturing Science and Engineering, vol. 127, no. 2, pp. 339–349, 2005. DOI:  https://doi.org/10.1115/1.1830493.CrossRefGoogle Scholar
  35. [35]
    K. Erkorkmaz, M. Heng. A heuristic feedrate optimization strategy for NURBS toolpaths. CIRP Annals, vol. 57, no. 1, pp. 407–410, 2008. DOI:  https://doi.org/10.1016/j.cirp.2008.03.039.CrossRefGoogle Scholar
  36. [36]
    M. Heng, K. Erkorkmaz. Design of a NURBS interpolator with minimal feed fluctuation and continuous feed modulation capability. International Journal of Machine Tools and Manufacture, vol. 50, no. 3, pp. 281–293, 2010. DOI:  https://doi.org/10.1016/j.ijmachtools.2009.11.005.CrossRefGoogle Scholar
  37. [37]
    K. Erkorkmaz, S. E. Layegh, I. Lazoglu, H. Erdim. Feedrate optimization for freeform milling considering constraints from the feed drive system and process mechanics. CIRP Annals, vol. 62, no. 1, pp. 395–398, 2013. DOI:  https://doi.org/10.1016/j.cirp.2013.03.084.CrossRefGoogle Scholar
  38. [38]
    W. T. Lei, M. P. Sung, L. Y. Lin, J. J. Huang. Fast realtime NURBS path interpolation for CNC machine tools. International Journal of Machine Tools and Manufacture, vol. 47, no. 10, pp. 1530–1541, 2007. DOI:  https://doi.org/10.1016/j.ijmachtools.2006.11.011.CrossRefGoogle Scholar
  39. [39]
    Y. Koren, C. C. Lo, M. Shpitalni. CNC interpolators: Algorithms and analysis. Manufacturing Science and Engineering, vol. 64, pp. 83–92, 1993.Google Scholar
  40. [40]
    M. Shpitalni, Y. Koren, C. C. Lo. Realtime curve interpolators. Computer-aided Design, vol. 26, no. 11, pp. 832–838, 1994. DOI:  https://doi.org/10.1016/0010-4485(94)90097-3.zbMATHCrossRefGoogle Scholar
  41. [41]
    T. Otsuki, H. Kozai, Y. Wakinotani. Free-form Curve Interpolation Method and Apparatus, U.S. Patent 5815401, September 1998.Google Scholar
  42. [42]
    R. T. Farouki, Y. F. Tsai. Exact taylor series coefficients for variable-feedrate CNC curve interpolators. Computer-Aided Design, vol. 33, no. 2, pp. 155–165, 2001. DOI:  https://doi.org/10.1016/S0010-4485(00)00085-3.CrossRefGoogle Scholar
  43. [43]
    S. S. Yeh, P. L. Hsu. The speed-controlled interpolator for machining parametric curves. Computer-aided Design, vol. 31, no. 5, pp. 349–357, 1999. DOI:  https://doi.org/10.1016/S0010-4485(99)00035-4.zbMATHCrossRefGoogle Scholar
  44. [44]
    H. Zhao, L. M. Zhu, H. Ding. A parametric interpolator with minimal feed fluctuation for CNC machine tools using arc-length compensation and feedback correction. International Journal of Machine Tools and Manufacture, vol. 75, pp. 1–8, 2013. DOI:  https://doi.org/10.1016/j.ijmachtools.2013.08.002.CrossRefGoogle Scholar
  45. [45]
    M. Chen, W. S. Zhao, X. C. Xi. Augmented Taylor’s expansion method for B-spline curve interpolation for CNC machine tools. International Journal of Machine Tools and Manufacture, vol. 94, pp. 109–119, 2015. DOI:  https://doi.org/10.1016/j.ijmachtools.2015.04.013.CrossRefGoogle Scholar
  46. [46]
    Wikipedia. Heun’s Method, [Online], Available: https://doi.org/en.wikipedia.org/wiki/Heun%27s_method, May 20, 2019.
  47. [47]
    J. E. Bobrow. Optimal robot plant planning using the minimum-time criterion. IEEE Journal on Robotics and Automation, vol. 4, no. 4, pp. 443–450, 1988. DOI:  https://doi.org/10.1109/56.811.CrossRefGoogle Scholar
  48. [48]
    G. Pardo-Castellote, R. H. Jr. Cannon. Proximate time-optimal algorithm for on-line path parameterization and modification. In Proceedings of IEEE International Conference on Robotics and Automation, IEEE, Minneapolis, USA, pp. 1539–1546, 1996. DOI:  https://doi.org/10.1109/ROBOT.1996.506923.Google Scholar
  49. [49]
    D. Verscheure, B. Demeulenaere, J. Swevers, J. De Schutter, M. Diehl. Time-optimal path tracking for robots: A convex optimization approach. IEEE Transactions on Automatic Control, vol. 54, no. 10, pp. 2318–2327, 2009. DOI:  https://doi.org/10.1109/TAC.2009.2028959.MathSciNetzbMATHCrossRefGoogle Scholar
  50. [50]
    S. D. Timar, R. T. Farouki, T. S. Smith, C. L. Boyadjieff. Algorithms for time-optimal control of CNC machines along curved tool paths. Robotics and Computer-Integrated Manufacturing, vol. 21, no. 1, pp. 37–53, 2005. DOI:  https://doi.org/10.1016/j.rcim.2004.05.004.CrossRefGoogle Scholar
  51. [51]
    S. D. Timar, R. T. Farouki. Time-optimal traversal of curved paths by Cartesian CNC machines under both constant and speed-dependent axis acceleration bounds. Robotics and Computer-integrated Manufacturing, vol. 23, no. 5, pp. 563–579, 2007. DOI:  https://doi.org/10.1016/j.rcim.2006.07.002.CrossRefGoogle Scholar
  52. [52]
    J. Dong, J. A. Stori. Optimal feed-rate scheduling for highspeed contouring. Journal of Manufacturing Science and Engineering, vol. 129, no. 1, pp. 63–76, 2004. DOI:  https://doi.org/10.1115/1.2280549.CrossRefGoogle Scholar
  53. [53]
    J. Dong, J. A. Stori. A generalized time-optimal bidirectional scan algorithm for constrained feed-rate optimization. Journal of Dynamic Systems, Measurement, and Control, vol. 128, no. 2, pp. 379–390, 2006. DOI:  https://doi.org/10.1115/1.2194078.CrossRefGoogle Scholar
  54. [54]
    J. Y. Dong, P. M. Ferreira, J. A. Stori. Feed-rate optimization with jerk constraints for generating minimum-time trajectories. International Journal of Machine Tools and Manufacture, vol. 47, no. 12–13, pp. 1941–1955, 2007. DOI:  https://doi.org/10.1016/j.ijmachtools.2007.03.006.CrossRefGoogle Scholar
  55. [55]
    T. Yong, R. Narayanaswami. A parametric interpolator with confined chord errors, acceleration and deceleration for NC machining. Computer-aided Design, vol. 35, no. 13, pp. 1249–1259, 2003. DOI:  https://doi.org/10.1016/S0010-4485(03)00043-5.CrossRefGoogle Scholar
  56. [56]
    J. X. Guo, K. Zhang, Q. Zhang, X. S. Gao. Efficient time-optimal feedrate planning under dynamic constraints for a high-order CNC servo system. Computer-aided Design, vol. 45, no. 12, pp. 1538–1546, 2013. DOI:  https://doi.org/10.1016/j.cad.2013.07.002.CrossRefGoogle Scholar
  57. [57]
    Z. Y. Jia, D. N. Song, J. W. Ma, G. Q. Hu, W. W. Su. A NURBS interpolator with constant speed at feedrate-sensitive regions under drive and contour-error constraints. International Journal of Machine Tools and Manufacture, vol. 116, pp. 1–17, 2017. DOI:  https://doi.org/10.1016/j.ijmachtools.2016.12.007.CrossRefGoogle Scholar
  58. [58]
    S. H. Suh, S. K. Kang, D. H. Chung, I. Stroud. Theory and Design of CNC Systems, London, UK: Springer, 2008. DOI:  https://doi.org/10.1007/978-1-84800-336-1.zbMATHCrossRefGoogle Scholar
  59. [59]
    M. Annoni, A. Bardine, S. Campanelli, P. Foglia, C. A. Prete. A real-time configurable NURBS interpolator with bounded acceleration, jerk and chord error. Computeraided Design, vol. 44, no. 6, pp. 509–521, 2012. DOI:  https://doi.org/10.1016/j.cad.2012.01.009.Google Scholar
  60. [60]
    X. Beudaert, S. Lavernhe, C. Tournier. Feedrate interpolation with axis jerk constraints on 5-axis NURBS and G1 tool path. International Journal of Machine Tools and Manufacture, vol. 57, pp. 73–82, 2012. DOI:  https://doi.org/10.1016/j.ijmachtools.2012.02.005.CrossRefGoogle Scholar
  61. [61]
    Y. A. Jin, Y. He, J. Z. Fu. A look-ahead and adaptive speed control algorithm for parametric interpolation. The International Journal of Advanced Manufacturing Technology, vol. 69, no. 9–12, pp. 2613–2620, 2013. DOI:  https://doi.org/10.1007/s00170-013-5241-l.CrossRefGoogle Scholar
  62. [62]
    Y. A. Jin, Y. He, J. Z. Fu, Z. W. Lin, W. F. Gan. A fine-interpolation-based parametric interpolation method with a novel real-time look-ahead algorithm. Computer-aided Design, vol. 55, pp. 37–48, 2014. DOI:  https://doi.org/10.1016/j.cad.2014.05.002.CrossRefGoogle Scholar
  63. [63]
    Y. S. Wang, D. D. Yang, R. L. Gai, S. H. Wang, S. J. Sun. Design of trigonometric velocity scheduling algorithm based on pre-interpolation and look-ahead interpolation. International Journal of Machine Tools and Manufacture, vol. 96, pp. 94–105, 2015. DOI:  https://doi.org/10.1016/j.ijmachtools.2015.06.009.CrossRefGoogle Scholar
  64. [64]
    D. F. Rogers. An Introduction to NURBS: With Historical Perspective, San Francisco, USA: Elsevier, 2000.Google Scholar
  65. [65]
    SIEMENS. SINUMERIK 840D sl/828D Basic Functions Function Manual, [Online], Available: https://doi.org/cache.industry.Siemens.com/dl/files/431/109476431/att_844512/v1/FB1sl_0115_en_en-US.pdf, May 20, 2019.
  66. [66]
    Aerotech, Inc. A3200 Help File 4.09.000, [Online], Available: https://doi.org/www.aerotechmotioncontrol.com/manuals/index.aspx, May 20, 2019.
  67. [67]
    J. Huang, X. Du, L. M. Zhu. Real-time local smoothing for five-axis linear toolpath considering smoothing error constraints. International Journal of Machine Tools and Manufacture, vol. 124, pp. 67–79, 2018. DOI:  https://doi.org/10.1016/j.ijmachtools.2017.10.001.CrossRefGoogle Scholar
  68. [68]
    J. X. Yang, A. Yuen. An analytical local corner smoothing algorithm for five-axis CNC machining. International Journal of Machine Tools and Manufacture, vol. 123, pp. 22–35, 2017. DOI:  https://doi.org/10.1016/j.ijmachtools.2017.07.007.CrossRefGoogle Scholar
  69. [69]
    S. J. Sun, H. Lin, L. M. Zheng, J. G. Yu, Y. Hu. A realtime and look-ahead interpolation methodology with dynamic B-spline transition scheme for CNC machining of short line segments. The International Journal of Advanced Manufacturing Technology, vol. 84, no. 5–8, pp. 1359–1370, 2016. DOI:  https://doi.org/10.1007/s00170-015-7776-9.Google Scholar
  70. [70]
    J. Shi, Q. Z. Bi, L. M. Zhu, Y. H. Wang. Corner rounding of linear five-axis tool path by dual PH curves blending. International Journal of Machine Tools and Manufacture, vol. 88, pp. 223–236, 2015. DOI:  https://doi.org/10.1016/j.ijmachtools.2014.09.007.CrossRefGoogle Scholar
  71. [71]
    Q. Z. Bi, J. Shi, Y. H. Wang, L. M. Zhu, H. Ding. Analytical curvature-continuous dual-Bézier corner transition for five-axis linear tool path. International Journal of Machine Tools and Manufacture, vol. 91, pp. 96–108, 2015. DOI:  https://doi.org/10.1016/j.ijmachtools.2015.02.002.CrossRefGoogle Scholar
  72. [72]
    S. Tulsyan, Y. Altintas. Local toolpath smoothing for five-axis machine tools. International Journal of Machine Tools and Manufacture, vol. 96, pp. 15–26, 2015. DOI:  https://doi.org/10.1016/j.ijmachtools.2015.04.014.CrossRefGoogle Scholar
  73. [73]
    B. Sencer, K. Ishizaki, E. Shamoto. A curvature optimal sharp corner smoothing algorithm for high-speed feed motion generation of NC systems along linear tool paths. The International Journal of Advanced Manufacturing Technology, vol. 76, no. 9–12, pp. 1977–1992, 2015. DOI:  https://doi.org/10.1007/s00170-014-6386-2.CrossRefGoogle Scholar
  74. [74]
    H. Zhao, L. M. Zhu, H. Ding. A real-time look-ahead interpolation methodology with curvature-continuous B-spline transition scheme for CNC machining of short line segments. International Journal of Machine Tools and Manufacture, vol. 65, pp. 88–98, 2013. DOI:  https://doi.org/10.1016/j.ijmachtools.2012.10.005.CrossRefGoogle Scholar
  75. [75]
    X. Beudaert, S. Lavernhe, C. Tournier. 5-axis local corner rounding of linear tool path discontinuities. International Journal of Machine Tools and Manufacture, vol. 73, pp. 9–16, 2013. DOI:  https://doi.org/10.1016/j.ijmachtools.2013.05.008.CrossRefGoogle Scholar
  76. [76]
    V. Pateloup, E. Duc, P. Ray. Bspline approximation of circle arc and straight line for pocket machining. Computer-aided Design, vol. 42, no. 9, pp. 817–827, 2010. DOI:  https://doi.org/10.1016/j.cad.2010.05.003.CrossRefGoogle Scholar
  77. [77]
    FANUC Corporation. FANUC Series 30i-LB Operator’s Manual, [Online], Available: https://doi.org/www.fanuc.co.jp/en/product/cnc/fs_30i-b.html, May 20, 2019.
  78. [78]
    Z. Y. Yang, L. Y. Shen, C. M. Yuan, X. S. Gao. Curve fitting and optimal interpolation for CNC machining under confined error using quadratic B-splines. Computer-aided Design, vol. 66, pp. 62–72, 2015. DOI:  https://doi.org/10.1016/j.cad.2015.04.010.MathSciNetCrossRefGoogle Scholar
  79. [79]
    W. Fan, C. H. Lee, J. H. Chen. A realtime curvature-smooth interpolation scheme and motion planning for CNC machining of short line segments. International Journal of Machine Tools and Manufacture, vol. 96, pp. 27–46, 2015. DOI:  https://doi.org/10.1016/j.ijmachtools.2015.04.009.CrossRefGoogle Scholar
  80. [80]
    Y. S. Wang, D. S. Yang, Y. Z. Liu. A real-time look-ahead interpolation algorithm based on Akima curve fitting. International Journal of Machine Tools and Manufacture, vol. 85, pp. 122–130, 2014. DOI:  https://doi.org/10.1016/j.ijmachtools.2014.06.001.CrossRefGoogle Scholar
  81. [81]
    A. Yuen, K. Zhang, Y. Altintas. Smooth trajectory generation for five-axis machine tools. International Journal of Machine Tools and Manufacture, vol. 71, pp. 11–19, 2013. DOI:  https://doi.org/10.1016/j.ijmachtools.2013.04.002.CrossRefGoogle Scholar
  82. [82]
    Delta Tau Data Systems, Inc. Power PMAC User’s Manual Rev. 8, [Online], Available: https://doi.org/www.deltatau.com/manuals/, May 20, 2019.
  83. [83]
    S. Tajima, B. Sencer. Kinematic corner smoothing for high speed machine tools. International Journal of Machine Tools and Manufacture, vol. 108, pp. 27–43, 2016. DOI:  https://doi.org/10.1016/j.ijmachtools.2016.05.009.CrossRefGoogle Scholar
  84. [84]
    B. Sencer, K. Ishizaki, E. Shamoto. High speed cornering strategy with confined contour error and vibration suppression for CNC machine tools. CIRP Annals, vol. 64, no. 1, pp. 369–372, 2015. DOI:  https://doi.org/10.1016/j.cirp.2015.04.102.CrossRefGoogle Scholar
  85. [85]
    S. Tajima, B. Sencer, E. Shamoto. Accurate interpolation of machining tool-paths based on FIR filtering. Precision Engineering, vol. 52, pp. 332–344, 2018. DOI:  https://doi.org/10.1016/j.precisioneng.2018.01.016.CrossRefGoogle Scholar
  86. [86]
    S. Tajima, B. Sencer. Global tool-path smoothing for CNC machine tools with uninterrupted acceleration. International Journal of Machine Tools and Manufacture, vol. 121, pp. 81–95, 2017. DOI:  https://doi.org/10.1016/j.ijmachtools.2017.03.002.CrossRefGoogle Scholar
  87. [87]
    Y. B. Bai, J. H. Yong, C. Y. Liu, X. M. Liu, Y. Meng. Polyline approach for approximating Hausdorff distance between planar free-form curves. Computer-aided Design, vol. 43, no. 6, pp. 687–698, 2011. DOI:  https://doi.org/10.1016/j.cad.2011.02.008.CrossRefGoogle Scholar
  88. [88]
    Wikkipedia. Hausdorff Distance, [Online], Available: https://doi.org/en.wikipedia.org/wiki/Hausdorff_distance, March 17, 2019.
  89. [89]
    T. Otsuki, S. Ide, H. Shiobara. Curve Interpolating Method, U.S. Patent 7274969 B2, 2007.Google Scholar

Copyright information

© The Author(s) 2019

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.

The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

To view a copy of this licence, visit https://doi.org/creative-commons.org/licenses/by/4.0/.

Authors and Affiliations

  1. 1.Centre for Precision Manufacturing, Department of Design, Manufacture & Engineering Management (DMEM)University of StrathclydeGlasgowUK
  2. 2.Engineering and Physical Sciences Research Council (EPSRC) Future Metrology Hub, Centre for Precision TechnologiesUniversity of HuddersfieldHuddersfieldUK
  3. 3.School of Mechatronic EngineeringHarbin Institute of TechnologyHarbinChina

Personalised recommendations