Wen-Bin Zhong, Xi-Chun Luo, Wen-Long Chang, Yu-Kui Cai, Fei Ding, Hai-Tao Liu and Ya-Zhou Sun. Toolpath Interpolation and Smoothing for Computer Numerical Control Machining of Freeform Surfaces: A Review. International Journal of Automation and Computing, vol. 17, no. 1, pp. 1-16, 2020. https://doi.org/10.1007/s11633-019-1190-y
Citation: Wen-Bin Zhong, Xi-Chun Luo, Wen-Long Chang, Yu-Kui Cai, Fei Ding, Hai-Tao Liu and Ya-Zhou Sun. Toolpath Interpolation and Smoothing for Computer Numerical Control Machining of Freeform Surfaces: A Review. International Journal of Automation and Computing, vol. 17, no. 1, pp. 1-16, 2020. https://doi.org/10.1007/s11633-019-1190-y

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

doi: 10.1007/s11633-019-1190-y
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  • Author Bio:

    Wen-Bin Zhong received the Ph. D. degree in ultra precision machining from the University of Strathclyde, UK in 2018. He is currently a research fellow at the Engineering and Physical Sciences Research Council (EPSRC) Future Metrology Hub, the University of Huddersfield, UK. His research interests include ultra precision machining technologies, computer numerical control, on-machine metrology and system integration of complex machine tools. E-mail: W.Zhong@hud.ac.uk ORCID iD: 0000-0002-6895-3428

    Xi-Chun Luo received the Ph. D. degree in ultra precision manufacturing at Harbin Institute of Technology, China in 2002. He is a professor in ultra precision manufacturing and technical director of Centre for Precision Manufacturing at the University of Strathclyde, UK. He is a Fellow of the International Society for Nanomanufacturing. His research interests include ultra precision machining brittle materials, freeform machining, precision motion control, hybrid micromachining and nanomanufacturing. E-mail: Xichun.luo@strath.ac.uk (Corresponding author) ORCID iD: 0000-0002-5024-7058

    Wen-Long Chang received the Ph. D. degree in mechanical engineering at Heriot-Watt University (2012) where he initiated a novel hybrid micromachining approach with the award of a prestigious Scottish Overseas Research Studentship. Currently he is an EPSRC and Horizon 2020 Postdoc Research Associate within the Centre for Precision Manufacturing at DMEM, University of Strathclyde, UK. His research interests include micro-precision machining technologies, short pulse laser machining, laser assisted micro machining, machine tool design and system integration. E-mail: wenlong.chang@strath.ac.uk ORCID iD: 0000-0002-1809-9104

    Yu-Kui Cai received the B. Sc. degree in mechanical engineering from Qingdao University of Science and Technology, China in 2011, the Ph. D. degree in mechanical engineering from Shandong University, China in 2016. He is a Marie Sklodowska-Curie Early Stage Research Fellow in the Centre for Precision Manufacturing at the University of Strathclyde, UK. He has already published more than 30 papers in related fields. He is a member of EUSPEN (European Society for Precision Engineering and Nanotechnology) and IMAPS (International Microelectronics Assembly & Packaging Society). His research interests lie in the area of microfluidic, micromachining and laser machining, ranging from theory to design and implementation. E-mail: Yukui.cai@strath.ac.uk ORCID iD: 0000-0003-0926-198X

    Fei Ding received the B. Sc. and M. Sc. degrees in mechanical engineering from Harbin Institute of Technology, China in 2013 and 2015, respectively. He is currently a Ph. D. degree candidate in mechanical engineering at University of Strathclyde, UK.His research interests include ultra-precision machine tool design and precision motion control. E-mail: fei.ding@strath.ac.uk

    Hai-Tao Liu received the Ph. D. degree in mechanical engineering from the Harbin Institute of Technology, China in 2010. He is currently an associate professor in the Harbin Institute of Technology, China. His research interests include micro machining technology and equipment, ultra-precision machining mechanism, machining technology and equipment, ultra-clean manufacturing, laser incremental manufacturing. E-mail: hthit@hit.edu.cn ORCID iD: 0000-0002-1619-4319

    Ya-Zhou Sun received the Ph. D. degree in ultra-precision machining from Harbin Institute of Technology, China in 2005. He is currently a professor at the School of Mechatronics Engineering, Harbin Institute of Technology, China. His research interests include ultraprecision machining technologies and ultra-precision machine design. E-mail: sunyzh@hit.edu.cn

  • Received Date: 2019-03-20
  • Accepted Date: 2019-06-12
  • Publish Online: 2019-09-26
  • Publish Date: 2020-02-06
  • 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.

     

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  • [1]
    X. Jiang, P. Scott, D. Whitehouse. Freeform surface characterisation – A fresh strategy. CIRP Annals, vol. 56, no. 1, pp. 553–556, 2007. DOI: 10.1016/j.cirp.2007.05.132.
    [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: 10.1007/s00170-011-3424-1.
    [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: 10.1016/j.cirp.2013.05.003.
    [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: 10.1016/j.procir.2016.04.133.
    [5]
    National Joint Registry. Joint Replacement Surgery: The National Joint Registry, [Online], Available: https://www.hqip.org.uk/, March 8, 2019.
    [6]
    U.S. Product Data Association. Initial Graphics Exchange Specification, IGES 5.3, 1996.
    [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: 10.1115/1.1354995.
    [8]
    T. R. Kramer, F. M. Proctor, E. Messina. The NIST RS274NGC Interpreter –Version 3, Technical Report NISTIR 6556, Department of Commerce, USA, 2000.
    [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.
    [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: 10.1007/s11633-012-0674-9.
    [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: 10.1007/s11633-018-1116-0.
    [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: 10.1016/S0890-6955(02)00015-9.
    [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: 10.1016/j.cirp.2011.03.021.
    [14]
    S. J. Yutkowitz. Apparatus and Method for Smooth Cornering in A Motion Control System, U.S. Patent 6922606, July 2005.
    [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: 10.1016/S0010-4485(01)00082-3.
    [16]
    L. Piegl, W. Tiller, The NURBS Book, 2nd ed., New York, USA: Springer-Verlag, 1996.
    [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: 10.1016/S0167-8396(01)00029-2.
    [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: 10.1016/S0007-8506(07)60479-X.
    [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: 10.1016/j.ijmachtools.2009.10.010.
    [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: 10.1016/j.ijmachtools.2011.01.008.
    [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: 10.1007/s00170-015-6846-3.
    [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: 10.1007/s00170-018-2180-x.
    [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: 10.1016/j.ijmachtools.2017.11.010.
    [24]
    FANUC Corporation. FANUC Series 30i/31i/32i/35i – MODEL B, [Online], Available: https://www.fanuc.co.jp/en/product/cnc/fs_30i-b.html, March 8, 2019.
    [25]
    Siemens AG. SIEMENS SINUMERIK 840D sl Brochure, [Online], Available: https://www.industry.usa.siemens.com/drives/us/en/cnc/systems-and-products/Documents/Brochure-SINUMERIK-840D-sl.pdf, March 8, 2019.
    [26]
    HEIDENHAIN Corporation. HEIDENHAN iTNC 530 Brochure, [Online], Available: https://www.heidenhain.de/fileadmin/pdb/media/img/895822-25_iTNC530_Design7_en.pdf, March 8, 2019.
    [27]
    Delta Tau Data Systems Inc. Power PMAC User′s Manual, [Online], Available: https://www.deltatau.com/manuals/, March 8, 2019.
    [28]
    Aerotech Inc. Automation 3200 Brochure, [Online], Available: https://www.aerotech.co.uk/product-catalog/motion-controller/a3200.aspx, March 8, 2019.
    [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: 10.1016/0010-4485(93)90085-3.
    [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: 10.1115/1.2829479.
    [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: 10.1016/S0010-4485(00)00049-X.
    [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: 10.1016/0167-8396(95)00047-X.
    [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: 10.1023/A:1016280811626.
    [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: 10.1115/1.1830493.
    [35]
    K. Erkorkmaz, M. Heng. A heuristic feedrate optimization strategy for NURBS toolpaths. CIRP Annals, vol. 57, no. 1, pp. 407–410, 2008. DOI: 10.1016/j.cirp.2008.03.039.
    [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: 10.1016/j.ijmachtools.2009.11.005.
    [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: 10.1016/j.cirp.2013.03.084.
    [38]
    W. T. Lei, M. P. Sung, L. Y. Lin, J. J. Huang. Fast real-time NURBS path interpolation for CNC machine tools. International Journal of Machine Tools and Manufacture, vol. 47, no. 10, pp. 1530–1541, 2007. DOI: 10.1016/j.ijmachtools.2006.11.011.
    [39]
    Y. Koren, C. C. Lo, M. Shpitalni. CNC interpolators: Algorithms and analysis. Manufacturing Science and Engineering, vol. 64, pp. 83–92, 1993.
    [40]
    M. Shpitalni, Y. Koren, C. C. Lo. Realtime curve interpolators. Computer-aided Design, vol. 26, no. 11, pp. 832–838, 1994. DOI: 10.1016/0010-4485(94)90097-3.
    [41]
    T. Otsuki, H. Kozai, Y. Wakinotani. Free-form Curve Interpolation Method and Apparatus, U.S. Patent 5815401, September 1998.
    [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: 10.1016/S0010-4485(00)00085-3.
    [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: 10.1016/S0010-4485(99)00035-4.
    [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: 10.1016/j.ijmachtools.2013.08.002.
    [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: 10.1016/j.ijmachtools.2015.04.013.
    [46]
    Wikipedia. Heun′s Method, [Online], Available: https://en.wikipedia.org/wiki/Heun%27s_method, May 20, 2019.
    [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: 10.1109/56.811.
    [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: 10.1109/ROBOT.1996.506923.
    [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: 10.1109/TAC.2009.2028959.
    [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: 10.1016/j.rcim.2004.05.004.
    [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: 10.1016/j.rcim.2006.07.002.
    [52]
    J. Dong, J. A. Stori. Optimal feed-rate scheduling for high-speed contouring. Journal of Manufacturing Science and Engineering, vol. 129, no. 1, pp. 63–76, 2004. DOI: 10.1115/1.2280549.
    [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: 10.1115/1.2194078.
    [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: 10.1016/j.ijmachtools.2007.03.006.
    [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: 10.1016/S0010-4485(03)00043-5.
    [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: 10.1016/j.cad.2013.07.002.
    [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: 10.1016/j.ijmachtools.2016.12.007.
    [58]
    S. H. Suh, S. K. Kang, D. H. Chung, I. Stroud. Theory and Design of CNC Systems, London, UK: Springer, 2008. DOI: 10.1007/978-1-84800-336-1.
    [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. Computer-aided Design, vol. 44, no. 6, pp. 509–521, 2012. DOI: 10.1016/j.cad.2012.01.009.
    [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: 10.1016/j.ijmachtools.2012.02.005.
    [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: 10.1007/s00170-013-5241-1.
    [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: 10.1016/j.cad.2014.05.002.
    [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: 10.1016/j.ijmachtools.2015.06.009.
    [64]
    D. F. Rogers. An Introduction to NURBS: With Historical Perspective, San Francisco, USA: Elsevier, 2000.
    [65]
    SIEMENS. SINUMERIK 840D sl/828D Basic Functions Function Manual, [Online], Available: https://cache.industry.siemens.com/dl/files/431/109476431/att_844512/v1/FB1sl_0115_en_en-US.pdf, May 20, 2019.
    [66]
    Aerotech, Inc. A3200 Help File 4.09.000, [Online], Available: https://www.aerotechmotioncontrol.com/manuals/index.aspx, May 20, 2019.
    [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: 10.1016/j.ijmachtools.2017.10.001.
    [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: 10.1016/j.ijmachtools.2017.07.007.
    [69]
    S. J. Sun, H. Lin, L. M. Zheng, J. G. Yu, Y. Hu. A real-time 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: 10.1007/s00170-015-7776-9.
    [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: 10.1016/j.ijmachtools.2014.09.007.
    [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: 10.1016/j.ijmachtools.2015.02.002.
    [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: 10.1016/j.ijmachtools.2015.04.014.
    [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: 10.1007/s00170-014-6386-2.
    [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: 10.1016/j.ijmachtools.2012.10.005.
    [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: 10.1016/j.ijmachtools.2013.05.008.
    [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: 10.1016/j.cad.2010.05.003.
    [77]
    FANUC Corporation. FANUC Series 30i-LB Operator′s Manual, [Online], Available: https://www.fanuc.co.jp/en/product/cnc/fs_30i-b.html, May 20, 2019.
    [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: 10.1016/j.cad.2015.04.010.
    [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: 10.1016/j.ijmachtools.2015.04.009.
    [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: 10.1016/j.ijmachtools.2014.06.001.
    [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: 10.1016/j.ijmachtools.2013.04.002.
    [82]
    Delta Tau Data Systems, Inc. Power PMAC User′s Manual Rev. 8, [Online], Available: https://www.deltatau.com/manuals/, May 20, 2019.
    [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: 10.1016/j.ijmachtools.2016.05.009.
    [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: 10.1016/j.cirp.2015.04.102.
    [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: 10.1016/j.precisioneng.2018.01.016.
    [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: 10.1016/j.ijmachtools.2017.03.002.
    [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: 10.1016/j.cad.2011.02.008.
    [88]
    Wikkipedia. Hausdorff Distance, [Online], Available: https://en.wikipedia.org/wiki/Hausdorff_distance, March 17, 2019.
    [89]
    T. Otsuki, S. Ide, H. Shiobara. Curve Interpolating Method, U.S. Patent 7274969 B2, 2007.
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