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Tool path generation for algebraically parameterized surface

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Abstract

In CAD/CAM integrated environment, parametrically defined free-form surfaces may require to be truncated to suit the profile of an object to be machined. In such a case the truncated surface needs to be parameterized anew according to the boundaries. Bilinear Coons parameterization is a well known algebraic method which can be used for generating boundary-fitted iso-parametric curves depending on the boundary information. In this paper an iso-parametric tool path generation scheme has been presented based on Coons parameterization technique for free-form surface. The scheme has been tested on some typical surfaces. Limitations in application of this scheme have also been discussed in this paper.

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References

  • Coons, S. A. (1964). Surfaces for computer-aided design of space figures. MIT ESL, 9442-M-139.

  • Ding, S., Yang, D. C. H., & Han, Z. (2005). Boundary-conformed machining of turbine blades. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 219, 255–263.

    Article  Google Scholar 

  • Elber, G., & Cohen, E. (1994). Toolpath generation for freeform surface models. Computer-Aided Design, 26(6), 490–496.

    Article  Google Scholar 

  • Farin, G. (1988). Curves and surfaces for computer aided geometric design, A practical guide. London: Academic Press Inc.

  • Faux, I. D., & Pratt, M. J. (1979). Computational geometry for design and manufacture. Chichester: Ellis Horwood.

  • George, K. K., & Babu, N. R. (1995). On the effective tool path planning algorithms for sculptured surface manufacture. Computers & Industrial Engineering, 28(4), 823–836.

    Article  Google Scholar 

  • Hoffmann, K. A. (1989). Computational fluid dynamics for engineers. Austin: Engineering Education System.

    Google Scholar 

  • Huang, Y., & Oliver, J. H. (1994). Non-constant parameter NC tool path generation of sculptured surfaces. The International Journal of Advanced Manufacturing Technology, 9, 281–290.

    Article  Google Scholar 

  • Jung, J. Y., & Ahluwalia, R. S. (2005). NC tool path generation for 5-axis machining of free-formed surfaces. Journal of Intelligent Manufacturing, 16, 115–127.

    Article  Google Scholar 

  • Lasemi, A., Xue, D., & Gu, P. (2010). Recent development in CNC machining of freeform surfaces: A state-of-the-art review. Computer-Aided Design, 42, 641–654.

    Article  Google Scholar 

  • Li, C. L. (2007). A geometric approach to boundary-conformed tool path generation. Computer-Aided Design, 39, 941–952.

    Article  Google Scholar 

  • Li, H., & Feng, H. Y. (2002). Constant scallop-height tool path generation for three axis sculpture surface machining. Computer-Aided Design, 34, 647–654.

    Article  Google Scholar 

  • Loney, G. C., & Ozsoy, T. M. (1987). NC machining of free form surfaces. Computer Aided Design, 19(2), 85–90.

    Article  Google Scholar 

  • Marsh, D. (2005). Applied geometry for computer graphics and CAD. London: Springer.

    Google Scholar 

  • Mortenson, M. E. (1985). Geometric modeling. London: Wiley.

    Google Scholar 

  • Sarkar, S., & Dey, P. P. (2012a). Construction of 2-D parametric surfaces bounded with four irregular curves. International Journal of Computer Aided Engineering and Technology, 4(5), 474–487.

    Article  Google Scholar 

  • Sarkar, S., & Dey P. P. (2012b). A new boundary interpolation technique for parameterisation of planar surfaces with four arbitrary boundary curves. Proceedings of the IMechE, Part C: Journal of Mechanical Engineering Science, doi:10.1177/0954406212460355.

  • Smith, R. E. (1983). Three-dimensional algebraic grid generation, AIAA 6th computational fluid dynamics conference. Massachusetts: Danvers.

    Google Scholar 

  • Stoker, J. J. (1989). Differential geometry. London: Wiley.

    Google Scholar 

  • Suresh, K., & Yang, D. (1994). Constant scallop-height machining of free-form surfaces. ASME Journal of Engineering for Industry, 116(2), 253–259.

    Article  Google Scholar 

  • Thompson, J. F., Warsi, Z. U. A., & Mastin, C. W. (1985). Numerical grid generation, foundations and applications. North Holland: Elsevier Science Publishing Co, Inc.

    Google Scholar 

  • Ülker, E., Turanalp, M. E., & Halkaci, H. S. (2009). An artificial immune system approach to CNC tool path generation. Journal of Intelligent Manufacturing, 20, 67–77.

    Article  Google Scholar 

  • Wang, C. C. L., & Tang, K. (2004). Algebraic grid generation on trimmed parametric surface using non-self-overlapping Coons patch mapping. International Journal for Numerical Methods in Engineering, 60(7), 1259–1286.

    Article  Google Scholar 

  • Yamaguchi, F. (1988). Curves and surfaces in computer aided geometric design. Berlin: Springer.

    Book  Google Scholar 

  • Zhang, L. P., Nee, A. Y. C., & Fuh, J. Y. H. (2004). An efficient CC-curve tool path regeneration algorithm for sculptured surface machining. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 218, 389–402.

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, Bengal Engineering and Science University, Shibpur, Howrah, 711103, West Bengal, India

    Subhajit Sarkar & Partha Pratim Dey

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  1. Subhajit Sarkar
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  2. Partha Pratim Dey
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Correspondence to Subhajit Sarkar.

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Sarkar, S., Dey, P.P. Tool path generation for algebraically parameterized surface. J Intell Manuf 26, 415–421 (2015). https://doi.org/10.1007/s10845-013-0799-x

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  • DOI: https://doi.org/10.1007/s10845-013-0799-x

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