Numeric implementation of drop and tilt method of 5-axis tool positioning for machining of triangulated surfaces

  • Ravinder Kumar Duvedi
  • Sanjeev Bedi
  • Ajay Batish
  • Stephen Mann


In this paper, we present an algorithm to find a gouge-free, multipoint of contact tool path for machining a triangulated surface. The algorithm is based on a proven 3-axis method of dropping a generalized radiused end mill on to a triangulated surface to find a gouge-free tool position. This algorithm is wrapped within the bisection algorithm to find a gouge-free 5-axis tool position that touches the triangulated part at two or more points. Our algorithm does not require solving systems of nonlinear equations and has been tested on several parts.


CNC Machining 5-axis machining Multi-point machining STL 


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  1. 1.
    Bedi S, Ismail F, Mahjoob MJ, Chen Y Toroidal versus ball nose and flat bottom end mills. Int J Adv Manuf 13:326–32Google Scholar
  2. 2.
    Yaua HT, Chuanga CM, Lee YS (2004) Numerical control machining of triangulated sculptured surfaces in a stereo lithography format with a generalized cutter. Int J Prod Res 42(13): 2573–98CrossRefGoogle Scholar
  3. 3.
    Patel K, Bolanos GS, Bassi R, Bedi S (2011) Optimal tool shape selection based on surface geometry for three-axis CNC machining. Int J Adv Manuf Technol 57:655–70CrossRefGoogle Scholar
  4. 4.
    Lasemi A, Xue D, Gu P (2010) Recent development in CNC machining of freeform surfaces: A state-of-the-art review. Comput-Aided Des 42:641–54CrossRefGoogle Scholar
  5. 5.
    Rao N, Ismail F, Bedi S (1997) Tool path planning for five-axis machining using the principal axis method. Int J Mach Tools Manuf 37(7):1025–40CrossRefGoogle Scholar
  6. 6.
    Bedi S, Gravelle S, Chen Y (1997) Principal curvature alignment technique for machining complex surfaces. J manuf Sci Eng 119(4B):756–765CrossRefGoogle Scholar
  7. 7.
    Rao N, Bedi S, Buchal R (1996) Implementation of the principal-axis method for machining of complex surfaces. Int J Adv Manuf Technol 11(4):249–257CrossRefGoogle Scholar
  8. 8.
    Warkentin A, Ismail F, Bedi S (2000) Multi-point tool positioning strategy for 5-axis machining of sculptured surfaces. Comput Aided Geom Des 17(1):83–100CrossRefMathSciNetGoogle Scholar
  9. 9.
    He Y, Chen Z Optimising tool positioning for achieving multi-point contact based on symmetrical error distribution curve in sculptured surface machining, The International Journal of Advanced Manufacturing Technology (2014) 1–8. doi:10.1007/s00170-014-5862-z
  10. 10.
    Warkentin A, Ismail F, Bedi S (2000) Comparison between multi-point and other 5-axis tool positioning strategies. Int J Mach Tools Manuf 40(2):185–208CrossRefGoogle Scholar
  11. 11.
    Duvedi RK, Bedi S, Batish A, Mann S (2014) A multipoint method for 5-axis machining of triangulated surface models. Comput-Aided Des 52:17–26CrossRefGoogle Scholar
  12. 12.
    Lauwers B, Kiswanto G, Kruth JP (2003) Development of a five-axis milling tool path generation algorithm based on faceted models. CIRP Ann—Manuf Technol 52(1):85–8CrossRefGoogle Scholar
  13. 13.
    Duvedi R, Batish A, Bedi S, Mann S Scallop height of 5-axis machining of large triangles with a flat end mill, Computer-Aided Design and Applications to appearGoogle Scholar
  14. 14.
    Li C, Mann S, Bedi S (2005) Error measurements for flank milling. Comput-Aided Des 37(14):1459–1468CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London 2015

Authors and Affiliations

  • Ravinder Kumar Duvedi
    • 1
  • Sanjeev Bedi
    • 2
  • Ajay Batish
    • 1
  • Stephen Mann
    • 2
  1. 1.Thapar UniversityPatialaIndia
  2. 2.University of WaterlooWaterlooCanada

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