IJAT Vol.16 No.3 pp. 349-355
doi: 10.20965/ijat.2022.p0349


Reverse Engineering Algorithm for Cutting of Ruled Geometries by Wire

Anthony T. H. Beaucamp*,† and Yoshimi Takeuchi**

*Department of Micro-Engineering, Kyoto University
Cluster C3, Kyotodaigaku-katsura, Nishikyo-ku, Kyoto 615-8540, Japan

Corresponding author

**Department of Mechanical Engineering, Chubu University, Kasugai, Japan

July 4, 2021
October 7, 2021
May 5, 2022
ruled geometries, wire cutting, differential geometry, reverse engineering

Abrasive wire cutting (AWC) and wire electric discharge machining (WEDM) are efficient and economical processes for the fabrication of precision parts from bulk material. Operating costs and manufacturing lead times are low compared to more general methods such as 5-axis CNC milling, turning, or electro-discharge machining. In this paper, an algorithm based on differential geometry in Euclidean space is proposed for reverse engineering of ruled geometries. The algorithm can determine whether a given geometry is producible by wire cutting, and can also derive the associated wire trajectories. Implementation is demonstrated by producing complex turbine blade geometries on 4-axis wire cutting machines with an overall shape accuracy of 20–40 μm peak-to-valley.

Cite this article as:
Anthony T. H. Beaucamp and Yoshimi Takeuchi, “Reverse Engineering Algorithm for Cutting of Ruled Geometries by Wire,” Int. J. Automation Technol., Vol.16, No.3, pp. 349-355, 2022.
Data files:
  1. [1] B. Ravani and J. Wang, “Computer aided geometric design of line constructs,” J. of Mechanical Design, Vol.113, No.4, pp. 363-371, 1991.
  2. [2] H. Yan, R. Lee, and Y. Yang, “An algorithm for surface design and tool path generation in wire-cut electrical discharge machining,” Int. J. of Machine Tools and Manufacture, Vol.35, No.12, pp. 1703-1714, 1995.
  3. [3] M. Peternell, H. Pottmann, and B. Ravani, “On the computational geometry of ruled surfaces,” Computer-Aided Design, Vol.31, No.1, pp. 17-32, 1999.
  4. [4] H. Chen and H. Pottmann, “Approximation by ruled surfaces,” J. of Computational and Applied Mathematics, Vol.102, No.1, pp. 143-156, 1999.
  5. [5] H. Pottmann and S. Leopoldseder, “A concept for parametric surface fitting which avoids the parametrization problem,” Computer Aided Geometric Design, Vol.20, No.6, pp. 343-362, 2003.
  6. [6] J. Hsieh, “Modeling tool path in wire electric discharge machining using Denavit-Hartenberg notation,” Proc. of the Institution of Mechanical Engineers, Part B: J. of Engineering Manufacture, Vol.225, No.7, pp. 1063-1072, 2011.
  7. [7] S. Kobayashi and K. Nomizu, “Foundations of differential geometry,” Wiley, 1996.
  8. [8] S. Roth, “Ray casting for modeling solids,” Computer Graphics and Image Processing, Vol.18, No.2, pp. 109-144, 1982.
  9. [9] [Accessed April 21, 2022]
  10. [10] T. Surazhsky, E. Magid, O. Soldea, G. Elber, and E. Rivlin, “A comparison of gaussian and mean curvatures estimation methods on triangular meshes,” Proc. of ICRA’03 IEEE Int. Conf.: Robotics and Automation, Vol.1, pp. 1021-1026, 2003.
  11. [11] E. Savio, L. De Chiffre, and R. Schmitt, “Metrology of freeform shaped parts,” Annals of the CIRP, Vol.56, No.2, pp. 810-835, 2007.
  12. [12] T. Nakagawa, M. Sampei, and A. Hirata, “High Accuracy Control with Lateral Dimension Estimator for Wire EDM,” Procedia CIRP, Vol.95, pp. 255-261, 2020.
  13. [13] W. Griffin, Y. Wang, D. Berrios, and M. Olano, “Real-time GPU surface curvature estimation on deforming meshes and volumetric data sets,” Visualization and Computer Graphics, IEEE Trans., Vol.18, No.10, pp. 1603-1613, 2012.

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Last updated on May. 20, 2022