Skip to main content
SpringerLink
Log in

NURBS output based tool path generation for freeform pockets

  • Original Article
  • Published:
The International Journal of Advanced Manufacturing Technology Aims and scope Submit manuscript

Abstract

A robust method is proposed to generate tool paths for NURBS-based machining of arbitrarily shaped freeform pockets with islands. Although the input and output are all of higher-degree NURBS curves, only one simple category of geometric entities, i.e., line segments, is required for initial offsetting and for detecting and removing self-intersecting loops. Furthermore, using those linear non-self-intersecting offsets as the legs of NURBS control polygons, NURBS-format tool paths can be smoothly reconstructed with G1-continuity, no overcutting, no cusps, and global error control. Since all operations involved in computing tool path curves are linear geometric calculations, the method is robust and simple. Examples with integrated rough and finish cutting tool paths of pockets demonstrate the usefulness and effectiveness of this method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Held M (1991) On the computational geometry of pocket machining. Springer, Berlin Heidelberg New York

  2. Kim K, Jeong J (1995) Tool path generation for machining free-form pockets with islands. Comput Ind Eng 28(2):399–407

    Article  Google Scholar 

  3. Chuang SH, Kao CZ (1999) One-sided arc approximation of B-spline curves for interference-free offsetting. Comput Aided Des 31(2):111–118

    Article  MATH  Google Scholar 

  4. Tseng YG, Chen YD, Liu CC (2001) Numerically controlled machining of freeform curves using biarc approximation. Int J Adv Manuf Tech 17(11):783–790

    Article  MathSciNet  Google Scholar 

  5. Hansen A, Arbab F (1992) An algorithm for generating NC tool paths for arbitrary shaped pockets with islands. ACM Trans Graph 12(2):152–182

    Article  Google Scholar 

  6. Farouki RT, Neff C (1990) Algebraic properties of plane offset curves. Comput Aided Geom Des 7:101–127

    Article  MATH  MathSciNet  Google Scholar 

  7. Klass K (1983) An offset spline approximation for plane cubic splines. Comput Aided Des 15(5):297–299

    Article  Google Scholar 

  8. Tiller W, Hanson EG (1984) Offsets of two-dimensional profiles. IEEE Comput Graph Appl 4(9):61–69

    Article  Google Scholar 

  9. Coquillart S (1987) Computing offsets of B-splines curves. Comput Aided Des 19(6):305–309

    Article  MATH  Google Scholar 

  10. Hoschek J (1988) Spline approximation of offset curves. Comput Aided Geom Des 5(1):33–40

    Article  MATH  MathSciNet  Google Scholar 

  11. Pham B (1988) Offset approximation of uniform B-splines. Comput Aided Des 20(8):471-474

    Article  MATH  Google Scholar 

  12. Elber G, Cohen E (1991) Error bounded variable distance offset operator for free form curves and surfaces. Int J Comput Geom Appl 1(1):67–78

    Article  MATH  MathSciNet  Google Scholar 

  13. Lee IK, Kim Ms, Elber G (1996) Plane curve offset based on circle approximation. Comput Aided Des 28(8):617–630

    Article  MATH  Google Scholar 

  14. Chuang SH, Shih JL (in press) A novel approach for computing C2-continuous offset of NURBS curves. Int J Adv Manuf Tech

  15. Piegl L, Tiller W (1997) The NURBS book, 2nd ed. Springer, Berlin Heidelberg New York

  16. Marsh D (1999) Applied geometry for computer graphics and CAD. Springer, Berlin Heidelberg New York

  17. Boehm W, Prautzsch H (1985) The insertion algorithm. Comput Aided Des 17(2):58–59

    Article  Google Scholar 

  18. Farin G (1993) Curves and surfaces for computer aided geometry design, a practical guide, 3rd ed. Academic, San Diego, CA

  19. Chuang SH, Lin WS (1997) Tool-path generation for pockets with freeform curves using Bézier convex hulls. Int J Adv Manuf Tech 13:109–115

    Article  Google Scholar 

  20. Piegl L, Tiller W (2002) Biarc approximation of NURBS curves. Comput Aided Des 34:807–814

    Article  Google Scholar 

  21. You CF, Sheen BT, Lin TK (2001) Robust spiral tool-path generation for arbitrary pockets. Int J Adv Manuf Tech 17(3):181–188

    Article  Google Scholar 

  22. Park SC, Choi BK (2001) Uncut free pocketing tool-paths generation using pair-wise offset algorithm. Comput Aided Des 33(10):739–746

    Article  Google Scholar 

  23. Persson H (1978) NC machining of arbitrarily shaped pockets. Comput Aided Des 10(3):169–174

    Article  Google Scholar 

  24. Choi BK, Kim BH (1997) Die-cavity pocketing via cutting simulation. Comput Aided Des 29(12):837–846

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, National Chung-Hsing University, 250 Kuo-kuang Road, Taichung, 402, Taiwan

    J.-L. Shih & S.-H. Frank Chuang

Authors
  1. J.-L. Shih
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S.-H. Frank Chuang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S.-H. Frank Chuang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shih, JL., Chuang, SH. NURBS output based tool path generation for freeform pockets. Int J Adv Manuf Technol 29, 714–721 (2006). https://doi.org/10.1007/s00170-005-2570-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-005-2570-8

Keywords

Search

Navigation