Skip to main content
SpringerLink
Log in

Adaptable geometric patterns for five-axis machining: a survey

  • ORIGINAL ARTICLE
  • Published:
The International Journal of Advanced Manufacturing Technology Aims and scope Submit manuscript

Abstract

The paper presents a survey of five-axis computer numerical controlled (CNC) machining optimization methods employing adaptable geometric patterns. First, the survey introduces evolution of CNC interpolators from the simplest Taylor series-based routines to sophisticated procedures based on constraint minimization from dynamic systems control theory. Furthermore, a variety of methods based on spline interpolation, NURBS interpolation and Farouki’s Pythagorean–hodograph curves is presented and analyzed. Next, the survey deals with techniques to optimize the positions and orientations of the tool in a particular neighborhood of the part surface. The most important application of these techniques is cutting by a flat-end or a fillet mill while avoiding local overcuts or undercuts due to the curvature interference and rear gouging. This section is supplemented by detection of global interference using visibility cone schemes and their recent modifications and improvements. Solutions offered by solid modeling are presented as well. Finally, adaptable geometric patterns employed for tool path generation are considered and analyzed. The adaptation is performed using certain criteria of the tool path quality, such as kinematics error, scallops, possible undercuts or overcuts, and the continuity of the path. Also covered are complex pocket milling employing geometric patterns capable of following the boundary, such as the offset methods, regional milling, the potential path methods, and clustering. The chapter also presents tool path optimization based on the adaptable curvilinear grids connecting the cutter location points. Finally, navigation approaches and the shortest-path schemes are considered, along with the adaptive space-filling curve algorithms and their combinations with grid generation.

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. The NURBS++ package, http://libnurbs.sourceforge.net/index.shtml.

  2. NURBS Toolbox, http://www.aria.uklinux.net/nurbs.php3.

  3. NIST/IGES, http://www.nist.gov/iges/.

  4. SLC file format, http://www-rp.me.vt.edu/bohn/rp/SLC.html. Info Page: CAD/CAM, http://www.cs.cmu.edu/People/unsal/research/rapid/cadcam.html.

  5. CAD Importer File Formats, http://www.actify.com/v2/products/Importers/formats.htm.

  6. Makino. GE FANUC, NURBS Interpolation, http://www.makino.com/about/article/2-1-2008/GE_Fanuc

  7. Makino. Interpolating Curves http://www.makino.com/about/article/2-1-2008/Interpolating_Curves

  8. Aigner M, Šír Z, Jüttler B (2007) Evolution-based least-squares fitting using Pythagorean hodograph spline curves. Comput Aided Geom Des 24:310–322

    MATH  Google Scholar 

  9. Alt H, Godau M (1995) Computing the Fréchet distance between two polygonal curves. Int. J. Comput. Geom. Appl. 5:75–91

    MathSciNet  MATH  Google Scholar 

  10. Alt H, Knauer C, Wenk C (2001) Matching polygonal curves with respect to the Fréchet distance, Lecture Notes in Computer Science, 18th Annual Symposium on Theoretical Aspects of Computer Science Dresden, Germany, pp. 63–74, February 15–17

  11. Altintas Y, Merdol SD (2007) Virtual high performance milling. CIRP Ann-Manufacturing Technology 56(1):81–84

    Google Scholar 

  12. Altintas Y, Erkorkmaz K (2003) Feedrate optimization for spline interpolation in high speed machine tools. CIRP ann 52(1):297–302

    Google Scholar 

  13. Anderson RO (1978) Detecting and eliminating collisions in NC machining. Computer-Aided Design 10(4):231–237

    Google Scholar 

  14. Anotaipaiboon W, Makhanov SS (2005) Tool path generation for five-axis NC machining using adaptive space-filling curves. Int. J. Prod. Res. 43(8):1643–1665

    MATH  Google Scholar 

  15. Arkin EM, Fekete SP, Mitchell JSB (2000) Approximation algorithms for lawn mowing and milling. Computational Geometry: Theory and Applications 17(1–2):25–50

    MathSciNet  MATH  Google Scholar 

  16. Bahr B, Xiao X, Krishnan K (2001) A real time scheme of cubic parametric curve interpolations for CNC systems. Comput. Ind. 45:309–317

    Google Scholar 

  17. Balasubramaniam M, Sarma SE, Marciniak K (2003) Collision free finishing tool paths from visibility data. Comput Aided Des 35(4):359–374

    Google Scholar 

  18. Bao HP, Yim H (1992) Tool path determination for end milling of non-convex shaped polygons. NAMRI Transactions, 151–158

  19. Belogay E, Cabrelli C, Molter U, Shonkwiler R (1997) Calculating the Hausdorff distance between curves. Inf. Process. Lett. 64:17–22

    MathSciNet  Google Scholar 

  20. Bieterman MB, Sandstrom DR (2003) A curvilinear tool-path method for pocket machining. J. Mater. Process. Technol. 125(4):709–715

    Google Scholar 

  21. Blasquez I, Poiraudeau J-F (2004) Undo facilities for the extended z-buffer in NC machining simulation. Comput. Ind. 53(2):193–204

    Google Scholar 

  22. Brackbill JU, Saltzman JS (1982) Adaptive zoning for singular problems in two dimensions. J Comput Phys 46:342–368

    MathSciNet  MATH  Google Scholar 

  23. Bohez ELJ, Makhanov SS, Sonthipermpoon K (2000) Adaptive nonlinear tool path optimization for 5-axis machining. Int. J. Prod. Res. 38(17):4329–4343

    MATH  Google Scholar 

  24. Kim BH, Choi KB (2002) Machining efficiency comparison direction-parallel path with contour parallel path. Comput. Aided Des 34:89–95

    Google Scholar 

  25. Bohez ELJ (2002) Compensating for systematic errors in 5-axis NC machining. Comput. Aided Des 34(5):505–520

    Google Scholar 

  26. Bohez ELJ, Minh NTH, Kiatsrithanakorn B, Natasukon P, Ruei-Yun H, Son LT (2003) The stencil buffer sweep plane algorithm for 5-axis CNC tool path verification. Comput Aided Des 35(12):1129–1142

    Google Scholar 

  27. Butler J, Haack B, Tomizuka M (1988) Reference input generation for high speed coordinated motion of a two axis system. In Symposium on Robotics, Winter Annual Meeting of the American Society of Mechanical Engineers, pp. 457–470

  28. Charakhch’yan AA, Ivanenko SA (1997) A variational form of the Winslow grid generator. J Comput Phys 136(2):385–398

    MathSciNet  Google Scholar 

  29. Chen L, Woo T (1992) Computational geometry on the sphere with application to automated machining. J. Mech. Des. 114:288–295

    Google Scholar 

  30. Chen C-CA, Juang Y-S, Lin W-Z (2002) Generation of fractal tool paths for irregular shapes of surface finishing areas. J. Mater. Process. Technol. 127(2):146–150

    Google Scholar 

  31. Chen YD, Ni J, Wu SM (1993) Real-time CNC tool path generation for machining IGES surfaces. ASME Journal of Engineering for Industry 115(4):480–486

    Article  Google Scholar 

  32. Cheng MY, Tsai MC, Kuo JC (2002) Real-time NURBS command generators for CNC servo controllers. Int. J. Mach. Tools Manuf. 42:801–803

    Google Scholar 

  33. Chiou C-J, Lee Y-S (2002) A machining potential field approach to tool path generation for multi-axis sculptured surface machining. Comput. Aided Des. 34(5):357–371

    Google Scholar 

  34. Cho I, Lee K, Kim J (1997) Generation of collision-free cutter location data in five-axis milling using the potential energy method. Int J Adv Manuf Tech 13(8):523–529

    Google Scholar 

  35. Choi BK, Jerard RB (1998) Computer aided machining—the z-map way: sculptured surface machining—theory and applications. Kluwer Academic Publishers, Dordrecht

    Google Scholar 

  36. Choi Y-K, Banerjee A (2007) Tool path generation and tolerance analysis for free-form surfaces. Int. J. Mach. Tools Manuf. 47(3–4):689–696

    Google Scholar 

  37. Constantinescu D, Croft EA (2000) Smooth and time optimal trajectory planning for industrial manipulators along specified paths. J. Robot. Syst. 17:233–249

    MATH  Google Scholar 

  38. Cox JJ, Takezaki Y, Ferguson HRP, Kohkonen KE, Mulkay EL (1994) Space-filling curves in tool-path applications. Comput. Aided Des. 26(3):215–224

    MATH  Google Scholar 

  39. De Boor C (2001) A practical guide to splines. Springer, New York

    MATH  Google Scholar 

  40. Dong J, Stori JA (2003) Optimal feed-rate scheduling for high speed contouring. ASME International Mechanical Engineering Congress. Washington, D.C. pp. 497–513, November 15–21.

  41. Dong J, Stori JA (2006a) A generalized time-optimal bi-directional scan algorithm for constrained feedrate optimization. ASME Journal of Dynamic Systems, Measurement, and Control 128:379–390

    Google Scholar 

  42. Dong J, Stori JA (2006b) A generalized time-optimal bidirectional scan algorithm for constrained feedrate optimization. Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME 128(2):379–390

    Google Scholar 

  43. Dong J, Ferreira PM, Stori JA (2007) Feed-rate optimization with jerk constraints for generating minimum-time trajectories. Int. J. Mach. Tools Manuf. 47:1941–1955

    Google Scholar 

  44. Timar SD, Farouki RT, Smith TS, Boyadjieff CL (2005) Algorithms for time-optimal control of CNC machines along curved tool paths. Robot. Comput.-Integr. Manuf 21:37–53

    Google Scholar 

  45. Dragomatz D, Mann S (1997) A classified bibliography of literature on NC milling path generation. Comput. Aided Des. 29(3):239–247

    Google Scholar 

  46. DoCarmo MP (1976) Differential geometry of curves and surfaces. Prentice-Hall, Englewood Cliffs

    Google Scholar 

  47. Elber G, Cohen E (1990) Hidden curve removal for free form surfaces. In SIGGRAPH ’90: Proceedings of the 17th annual conference on Computer graphics and interactive techniques, pp. 95–104

  48. Elber G, Cohen E (1995) Arbitrarily precise computation of gauss maps and visibility sets for freeform surfaces. In SMA ’95: Proceedings of the third ACM symposium on Solid modeling and applications, pages 271–279

  49. Elber G (1995) Freeform surface region optimization for 3-axis and 5-axis milling. Comput. Aided Des 27(6):465–70

    MATH  Google Scholar 

  50. Elber G, Zussman E (1998) Cone visibility decomposition of freeform surface. Comput. Aided Des. 30(4):315–320

    MATH  Google Scholar 

  51. Elber G, Cohen E (1999) A unified approach to verification in 5-axis freeform milling environments. Comput. Aided Des. 31(13):795–804

    MATH  Google Scholar 

  52. Erkorkmaz K, Altintas Y (2001) High speed CNC system design. Part I: jerk limited trajectory generation and quintic spline interpolation. Int. J. Mach. Tools Manuf. 41(9):1323–1345

    Google Scholar 

  53. Erkorkmaz K, Heng M (2008) A heuristic feedrate optimization strategy for NURBS toolpaths. CIRP Annals-Manufacturing Technology 57:407–410

    Google Scholar 

  54. Farin GE (1999) NURBS: from projective geometry to practical use. A. K. Peters, Natick

    MATH  Google Scholar 

  55. Farouki RT (1994) The conformal map z→z2 of the hodograph plane. Comput. Aided Geom. Des. 11:363–390

    MathSciNet  MATH  Google Scholar 

  56. Farouki RT, Sakkalis T (1994) Pythagorean-hodograph space curves. Adv. Comput. Math. 2(1):41–66

    MathSciNet  MATH  Google Scholar 

  57. Farouki RT, Neff CA (1995) Hermite interpolation by Pythagorean hodograph quintics. Math Comput 64(212):1589–1609

    MathSciNet  MATH  Google Scholar 

  58. Farouki R, Saitou K, Tsai Y-F (1998) Least-square tool path approximation with Pythagorean-hodograph curves for high-speed CNC machining. In Cripps R (ed) Proceedings of the IMA Mathematics of Surfaces VIII Conference, Information Geometers Press, p. 245–264.

  59. Farouki RT, Manjunathaiah J, Jee S (1998) Design of rational cam profiles with Pythagorean–hodograph curves. Mech Mach Theory 33(6):669–682

    MATH  Google Scholar 

  60. Farouki RT, Manjunathaiah J, Yang GF (1999) G codes for the specification of Pythagorean-hodograph tool paths and associated feedrate functions on open-architecture CNC machines. Int. J. Mach. Tools Manuf. 39:123–142

    Google Scholar 

  61. Farouki RT, Tsai Y-F, Wilson CS (2000) Physical constraints on feedrates and feed accelerations along curved tool paths. Comput Aided Geom Des 17(4):337–359

    MathSciNet  MATH  Google Scholar 

  62. Farouki RT, Tsai Y-F, Yuan G-F (1999) Contour machining of free-form surfaces with real-time PH curve CNC interpolators. Comput Aided Geom Des 16(1):61–76

    MathSciNet  MATH  Google Scholar 

  63. Farouki RT, Sakkalis T, Vaserstein L (2009) Non-existence of rational arc-length parametrizations for curves in Rn. J. Comput. Appl. Math 228(1):494–497

    MathSciNet  MATH  Google Scholar 

  64. Feng H-Y, Li H (2002) Constant scallop height tool path generation for three axis sculptured machining. Comput. Aided Des 34:647–654

    Google Scholar 

  65. Feng H-Y, Teng Z (2005) Iso-planar piecewise linear NC tool path generation from discrete measured data points. Comput. Aided Des. 37:55–64

    Google Scholar 

  66. Fleisig RV, Spence AD (2001) A constant feed and reduced angular acceleration interpolation algorithm for multi-axis machining. Comput. Aided Des. 33:1–15

    Google Scholar 

  67. Flutter A, Todd J (2001) A machining strategy for tool making. Comput. Aided Des. 33(13):1009–1022

    Google Scholar 

  68. Gani EA, Kruth JP, Vanherck P, Lauwers B (1997) A geometrical model of the cut in five-axis milling accounting for the influence of tool orientation. Int J Adv Manuf Tech 13(10):677–684

    Google Scholar 

  69. Garcia-Alonso A, Serrano N, Flaquer J (1994) Solving the collision detection problem. IEEE Comput. Graph. Appl. 14(3):36–43

    Google Scholar 

  70. Gian R, Lin T, Lin AC (2003) Planning of tool orientation for five-axis cavity machining. Int J Adv Manuf Tech 22(1–2):150–160

    Google Scholar 

  71. Goldstein BL, Kemmerer SJ, Parks CH (1998) A brief history of early product data exchange standards-NISTIR 6221

  72. Gray PJ, Bedi S, Ismail F (2003) Rolling ball method for 5-axis surface machining. Comput. Aided Des. 35(4):347–357

    Google Scholar 

  73. Gray PJ, Bedi S, Ismail F (2005) Arc-intersect method for 5-axis tool positioning. Comput. Aided Des. 37(7):663–674

    Google Scholar 

  74. Gray PJ, Ismail F, Bedi S (2007) Arc-intersect method for 311/22-axis tool paths on a 5-axis machine. Int. J. Mach. Tools Manuf. 47(1):182–190

    Google Scholar 

  75. Griffiths JG (1994) Tool path based on Hilbert’s curve. Comput. Aided Des. 26(11):839–844

    Google Scholar 

  76. Hansen A, Arbab F (1992) An algorithm for generating NC tool paths for arbitrarily shaped pockets with islands. ACM Trans. Graph 11(2):152–182

    MATH  Google Scholar 

  77. Hatna A, Grieve B (2000) Cartesian machining versus parametric machining: a comparative study. Int. J. Prod. Res. 38(13):3043–3065

    Google Scholar 

  78. Held M (1991) A geometry-based investigation of the tool path generation for zigzag pocket machining. Vis. Comput 7(5–6):296–308

    Google Scholar 

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

    MATH  Google Scholar 

  80. Held M, Klosowski J, Mitchell JSB (1995) Evaluation of collision detection methods for virtual reality fly-throughs. In proceedings Seventh Canadian Conference on Computational Geometry, 205–210

  81. Held M, Luk´acs G, Andor L (1994) Pocket machining based on contour-parallel tool paths generated by means of proximity maps. Comput. Aided Des. 26(3):189–203

    MATH  Google Scholar 

  82. Hook TV (1986) Real-time shaded nc milling display. In SIGGRAPH ’86: Proceedings of the 13th annual conference on computer graphics and interactive techniques, 15–20

  83. Hornung C, Lellek W, Rehwald P, Straßer W (1985) An area oriented analytical visibility method for displaying parametrically defined tensor-product surfaces. Comput Aided Geom Des 2(1–3):197–205

    MATH  Google Scholar 

  84. Ho S, Sarma S, Adachi Y (2001) Real-time interference analysis between a tool and an environment. Comput. Aided Des 33(13):935–47

    Google Scholar 

  85. Hosseinkhani Y, Akbaria J, Vafaeesefat A (2007) Penetration–elimination method for five-axis CNC machining of sculptured surfaces. Int. J. Mach. Tools Manuf. 47:1625–1635

    Google Scholar 

  86. Hsueh Y-W, Hsueh M-H, Lien H-C (2007) Automatic selection of cutter orientation for preventing the collision problem on a five-axis machining. Int J Adv Manuf Tech 33(9–10):994–1000

    Google Scholar 

  87. Hu J, Xiao L, Wang Y, Wu Z (2006) An optimal feed rate model and solution algorithm for a high-speed machine of small line blocks with look-ahead. Int J Adv Manuf Tech 28(9):930–935

    Google Scholar 

  88. Huang Y, Oliver JH (1995) Integrated simulation, error assessment, and tool path correction for five-axis NC machining. J. Manuf. Syst. 14(5):331–334

    Google Scholar 

  89. Huang J-T, Yang DCH (1992) A generalized interpolator for command generation of parametric curves in computer controlled machines. Proceedings of the Japan/USA Symposium on Flexible Automation, ASME 1:393–399

    Google Scholar 

  90. Ilushin O, Elber G, Halperinc D, Weinc R, Kim MC (2005) Precise global collision detection in multi-axis NC-machining. Comput. Aided Des. 37:909–920

    Google Scholar 

  91. Ivanenko SA (1988) Generation of non-degenerate meshes. USSR Computational Mathematics and Mathematical Physcics 28:141–146

    MathSciNet  MATH  Google Scholar 

  92. Ivanenko SA (1999) Harmonic mappings. In: Thompson JF, Soni BK, Weatherill NP (eds) Handbook of grid generation 8. CRC, New York, pp 1–43

    Google Scholar 

  93. Jeong J, Kim K (1999) Generating tool paths for free-form pocket machining using z-buffer-based Voronoi diagrams. Int J Adv Manuf Tech 15(3):182–187

    Google Scholar 

  94. Jeong J, Kim K (1999) Generation of tool paths for machining free-form pockets with islands using distance maps. Int J Adv Manuf Tech 15(5):311–316

    Google Scholar 

  95. Jerard RB, Drysdale RL (1989) Methods for geometric modeling, simulation and spatial verification of NC machining programs. In: Wozny MJ, Turner JU, Pegna J (eds) Product modeling for computer-aided design and manufacturing. Elsevier/North-Holland, New York

    Google Scholar 

  96. Jun C-S, Cha K, Lee Y-S (2003) Optimizing tool orientations for 5-axis machining by configuration-space search method. Comput. Aided Des. 35(6):549–566

    Google Scholar 

  97. Juttler B (2001) Hermite interpolation by Pythagorean hodograph curves of degree seven. Math Comput 70(235):1089–1111

    MathSciNet  Google Scholar 

  98. Kang J-K, Suh S-H (1997) Machinability and set-up orientation for five-axis numerically controlled machining of free surfaces. Int J Adv Manuf Tech 13(5):311–325

    Google Scholar 

  99. Kim H-C, Lee S-G, Yang M-Y (2006) An optimized contour parallel tool path for 2D milling with flat end mill. Int J Adv Manuf Tech 31:567–573

    Google Scholar 

  100. Kim SJ, Lee D-Y, Kim H-C, Lee S-G, Yang M-Y (2006) CL surface deformation approach for a 5-axis tool path generation. Int J Adv Manuf Tech 28(5–6):509–517

    Google Scholar 

  101. Kiritsis D (1994) High precision interpolation algorithm for 3D parametric curve generation. Comput. Aided Des. 26(11):850–856

    MATH  Google Scholar 

  102. Ko TJ, Kim HS, Park SH (2005) Machineability in NURBS interpolator considering constant material removal rate. Int. J. Mach. Tools Manuf. 45(6):665–671

    Google Scholar 

  103. Kondo M (1994) Decomposition of complex geometry for a manufacturing application. Comput. Aided Des. 26(3):244–252

    MATH  Google Scholar 

  104. Koren Y (1976) Interpolator for a computer numerical control system. IEEE Trans Comput 25(1):32–37

    MATH  Google Scholar 

  105. Korosec M. (2009) Feed rate optimization in free form machining using NURBS approximation, Computers & Industrial Engineering

  106. Kiswanto G, Lauwers B, Kruth J-P (2007) Gouging elimination through tool lifting in tool path generation for five-axis milling based on faceted models. Int J Adv Manuf Tech 32(3–4):293–309

    Google Scholar 

  107. Krishnan KK, Kappen J, Bahr B (2001) Calculation of variable federate and spindle speed for NURBS based CNC machining. Transactions of NAMRI/SME 24:429–435

    Google Scholar 

  108. Kruth J-P, Klewais P (1994) Optimization and dynamic adaptation of the cutter inclination during five-axis milling of sculptured surfaces. CIRP ann 43(1):443–448

    Google Scholar 

  109. Lai W, Faddis T, Sorem R (2000) Incremental algorithms for finding the offset distance and minimum passage width in a pocket machining toolpath using the Voronoi technique. Material Processing Technology 100:30–35

    Google Scholar 

  110. Lai Y-L, Wu JS-S, Hung J-P, Chen J-H (2006) A simple method for invalid loops removal of planar offset curves. Int J Adv Manuf Tech 27(11–12):1153–1162

    Google Scholar 

  111. Langeron JM, Duc E, Lartigue C, Bourdet P (2004) A new format for 5-axis tool path computation, using B-spline curves. Comput. Aided Des. 36(12):1219–1229

    Google Scholar 

  112. Lauwers B, Dejonghe P, Kruth JP (2003) Optimal and collision free tool posture in five-axis machining through the tight integration of tool path generation and machine simulation. Comput. Aided Des. 35(5):421–432

    Google Scholar 

  113. Lee Y-S, Chang T-C (1995) 2-phase approach to global tool interference avoidance in 5-axis machining. Comput. Aided Des 27(10):715–29

    MATH  Google Scholar 

  114. Lee Y-S (1997) Admissible tool orientation control of gouging avoidance for 5-axis complex surface machining. Comput. Aided Des. 29(7):507–521

    Google Scholar 

  115. Lee Y-S, Ji H (1997) Surface interrogation and machining strip evaluation for 5-axis CNC die and mold machining. Int. J. Prod. Res. 35(1):225–252

    MATH  Google Scholar 

  116. Lee JN, Lee RS (2007) Interference-free toolpath generation using enveloping element for five-axis machining of spatial cam. J. Mater. Process. Technol. 187–188:10–13

    Google Scholar 

  117. Lee E (2003) Contour offset approach to spiral toolpath generation with constant scallop height. Comput. Aided Des. 35:511–518

    Google Scholar 

  118. Lei WT, Sung MP, Lin LY, Huang JJ (2007) Fast real-time NURBS path interpolation for CNC machine tools. Int. J. Mach. Tools Manuf. 47:1530–1541

    Google Scholar 

  119. Li F, Wang XC, Ghosh SK, Kong DZ, Lai TQ, Wu XT (1995) Tool-path generation for machining sculptured surface. J. Mater. Process. Technol. 48(1–4):811–816

    Google Scholar 

  120. Li SX, Jerard RB (1994) 5-axis machining of sculptured surfaces with a flat-end cutter. Comput. Aided Des. 26(3):165–178

    MATH  Google Scholar 

  121. Li Z, Chen W (2006) A global cutter positioning method for multi axis machining of sculptured surfaces. Int. J. Mach. Tools Manuf. 46(12–13):1428–1434

    Google Scholar 

  122. Lin R-S, Koren Y (1996) Efficient tool-path planning for machining free-form surfaces. ASME Journal of Engineering for Industry 118(1):20–28

    Google Scholar 

  123. Lindstrom P, Turk G (2000) Image-driven simplification. ACM Trans. Graph 19(3):204–241

    Google Scholar 

  124. Liu X, Ahmad F, Yamazaki K, Mori M (2005) Adaptive interpolation scheme for NURBS curves with the integration of machining dynamics. Int. J. Mach. Tools Manuf. 45:433–444

    Google Scholar 

  125. Liang H, Hong H, Svoboda J (2002) A combined 3D linear and circular interpolation technique for multi-axis CNC machining. ASME Journal of Manufacturing Science and Engineering 124:305–312

    Google Scholar 

  126. Lo CC (1997) Feedback interpolator for CNC machine tool. ASME. Journal of Manufacturing Science and Engineering 119(4):587–592

    Google Scholar 

  127. Lo CC (1999) Efficient cutter-path planning for five-axis surface machining with a flat-end cutter. Comput. Aided Des. 31(9):557–566

    MATH  Google Scholar 

  128. Lo CC (1999) Real-time generation and control of cutter path for 5-axis CNC machining. Int. J. Mach. Tools Manuf. 39(3):471–488

    Google Scholar 

  129. Lo CC (2000) CNC machine tool surface interpolator for ball-end milling of free-form surfaces. Int. J. Mach. Tools Manuf. 40(3):307–326

    Google Scholar 

  130. De Lacalle LNL, Lamikiz A, Salgado MA, Herranz S, Rivero A (2002) Process planning for reliable high-speed machining of moulds. Int. J. Prod. Res. 40(12):2789–2809

    Google Scholar 

  131. Loney GC, Ozsoy TM (1987) NC machining of free form surfaces. Comput Aided Des 9(2):85–90

    Google Scholar 

  132. Ma W, But W-C, He P (2004) NURBS-based adaptive slicing for efficient rapid prototyping. Comput. Aided Des. 36(13):1309–1325

    Google Scholar 

  133. Makhanov SS (1999) An application of variational grid generation techniques to the tool-path optimization of industrial milling robots. Comput. Math. Math. Phys. 39(9):1524–1535

    MATH  Google Scholar 

  134. Makhanov SS, Batanov D, Bohez E, Sonthipaumpoon K, Anotaipaiboon W, Tabucanon M (2002) On the tool-path optimization of a milling robot. Computers and Industrial Engineering 43(3):455–472

    Google Scholar 

  135. Makhanov SS, Ivanenko SA (2003) Grid generation as applied to optimize cutting operations of the five-axis milling machine. Appl. Numer. Math. 46(3–4):331–351

    MATH  Google Scholar 

  136. Makhanov SS, Munlin M (2007) Optimal sequencing of rotation angles for five-axis machining. Int J Adv Manuf Tech 35(10):41–54

    Google Scholar 

  137. Makhanov SS (2007) Optimization and correction of the tool path of the five-axis milling machine: Part 1. Spatial optimization, Mathematics and Computers in Simulation 75(5–6):210–230

    MathSciNet  MATH  Google Scholar 

  138. Makhanov SS (2007) Optimization and correction of the tool path of the five-axis milling machine: Part 2: rotations and setup. Math. Comput. Simul. 75(5–6):231–250

    MathSciNet  MATH  Google Scholar 

  139. Anotaipaiboon W, Makhanov SS (2008) Curvilinear space-filling curves for five-axis machining. Comput. Aided Des. 40(3):350–367

    Google Scholar 

  140. Mani K, Kulkarni P, Dutta D (1999) Region-based adaptive slicing. Comput. Aided Des. 31(5):317–333

    MATH  Google Scholar 

  141. Marciniak K (1987) Influence of surface shape in admissible tool positions in 5-axis face milling. Comput. Aided Des. 19(5):233–236

    MATH  Google Scholar 

  142. Meek DS, Walton DJ (1997) Geometric Hermite interpolation with Tschirnhausen cubics. J. Comput. Appl. Math 81:299–309

    MathSciNet  MATH  Google Scholar 

  143. Tikhon M, Ko TJ, Lee SH, Kim HS (2004) NURBS interpolator for constant material removal rate in open NC machine tools. Int. J. Mach. Tools Manuf. 44:237–245

    Google Scholar 

  144. Monreal M, Rodr´ıguez CA (2003) Influence of tool path strategy on the cycle time of high-speed milling. Comput. Aided Des. 35(4):395–401

    Google Scholar 

  145. Moon HP, Farouki RT, Choi HI (2001) Construction and shape analysis of PH quintic Hermite interpolants. Comput Aided Geom Des 18(2):93–115

    MathSciNet  MATH  Google Scholar 

  146. Morishige K, Takeuchi Y (1995) 5 axis control rough cutting of an impeller with an efficiency and accuracy. Proceedings 1997 IEEE International Conference on Robotics and Automatics, 1241–1247

  147. Morishige K, Takeuchi Y, Kase K (1999) Tool path generation using C-space for 5-axis control machining. Journal of Manufacturing Science and Engineering 121(1):144–149

    Google Scholar 

  148. Muller M, Erds G, Xirouchakis PC (2004) High accuracy spline interpolation for 5-axis machining. Comput. Aided Des. 36(13):1379–1393

    Google Scholar 

  149. Munlin M, Makhanov SS, Bohez ELJ (2004) Optimization of rotations of a five-axis milling machine near stationary points. Comput. Aided Des. 36(12):1117–1128

    Google Scholar 

  150. My CA, Bohez ELJ, Makhanov SS (2005) Critical point analysis of 3D vector field for 5-axis tool path optimization. In Proceedings of the 4th Asian Conference on Industrial Automation and Robotics, ACIAR 2005, 11–13 May 2005, Bangkok, Thailand, 11

  151. My CA, Makhanov SS, Munlin M, Bohez ELJ, Phien HN, Tabucanon MT (2005) On 5-axis freeform surface machining optimization: vector field clustering approach. International Journal of CAD/CAM 5:1–14

    Google Scholar 

  152. Nam S-H, Yang M-Y (2004) A study on a generalized parametric interpolator with real-time jerk-limited acceleration. Comput. Aided Des. 36:27–36

    Google Scholar 

  153. Narayanaswami R, Choi Y (2001) NC machining of freeform pockets with arbitrary wall geometry using a grid-based navigation approach. Int J Adv Manuf Tech 18(10):708–716

    Google Scholar 

  154. Naylor B, Amanatides J, Thibault W (1990) Merging BSP trees yields polyhedral set operations. In SIGGRAPH ’90: Proceedings of the 17th annual conference on Computer graphics and interactive techniques, pages 115–124

  155. Noborio H, Fukuda S, Arimoto S (1989) Fast interference check method using octree representation. Adv Robot 3(3):193–212

    Google Scholar 

  156. Park SC, Choi BK (2000) Tool-path planning for direction parallel area milling. Comput. Aided Des. 32(1):17–25

    MathSciNet  Google Scholar 

  157. Park SC, Chung YC (2002) Offset tool-path linking for pocket machining. Comput. Aided Des. 34(4):299–308

    Google Scholar 

  158. Park SC, Chung YC, Choi BK (2003) Contour-parallel offset machining without tool-retractions. Comput. Aided Des. 35(9):841–849

    Google Scholar 

  159. Park S, Kim SH, Cho H (2006) Kernel software for efficiently building, reconfiguring, and distributing an open CNC controller. Int J Adv Manuf Tech 27:788–796

    Google Scholar 

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

    Google Scholar 

  161. Piegl L, Tiller W (1995) The NURBS book. Springer, London

    MATH  Google Scholar 

  162. Pi J, Red E, Jensen G (1998) Grind-free tool path generation for five-axis surface machining. Computer Integrated Manufacturing Systems 11(4):337–350

    Google Scholar 

  163. Piazzi A, Visioli A (1998) Global minimum-time trajectory planning of mechanical manipulators using interval analysis. Int. J. control 71(4):631–652

    MathSciNet  MATH  Google Scholar 

  164. Pottmann H, Wallner J, Glaeser G, Ravani B (1999) Geometric criteria for gouge-free three-axis milling of sculptured surfaces. ASME J. Mech. Des 121(2):241–248

    Google Scholar 

  165. Pottmann H, Ravani B (2000) Singularities of motions constrained by contacting surfaces. Mech Mach Theory 35(7):963–984

    MathSciNet  MATH  Google Scholar 

  166. Pateloup V, Chanal H, Duc E, Ray P (2006) HSM-adapted tool path calculation for pocketing. Mach. Sci. Technol 10(2):181–196

    Google Scholar 

  167. Radzevich SP, Goodman ED (2002) Computation of optimal workpiece orientation for multi-axis NC machining of sculptured part surfaces. ASME J. Mech. Des 124(2):201–212

    Google Scholar 

  168. Radzevich SP (2005) A cutting-tool-dependent approach for partitioning of sculptured surface. Comput. Aided Des. 37(7):767–778

    Google Scholar 

  169. Rao A, Sarma R (2000) On local gouging in five-axis sculptured surface machining using flat-end tools. Comput. Aided Des. 32(7):409–420

    Google Scholar 

  170. 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):1025–1040

    Google Scholar 

  171. Red EW (2000) A dynamic optimal trajectory generator for Cartesian path following. Robotica 18:451–458

    Google Scholar 

  172. Renton D, Elbestawi MA (2000) High speed servo control of multi-axis machine tools. Int. J. Mach. Tools Manuf. 40:539–559

    Google Scholar 

  173. Roth D, Ismail F, Bedi S (2003) Mechanistic modeling of the milling process using an adaptive depth buffer. Comput. Aided Des. 35(14):1287–1303

    Google Scholar 

  174. Roy U, Xu Y (1999) Computation of a geometric model of a machined part from its NC machining programs. Comput. Aided Des. 31(6):401–411

    MATH  Google Scholar 

  175. Sata T, Kimura F, Okada N, Hosaka M (1981) A new method of NC interpolation for machining the sculptured surface. CIRP Ann 30(1):369–372

    Google Scholar 

  176. Sang-Kyu Lee S-LK (2002) Development of simulation system for machining process using enhanced Z map model. J. Mater. Process. Technol. 130–131:608–617

    Google Scholar 

  177. Sarma R, Dutta D (1997) The geometry and generation of NC tool paths. ASME J. Mech. Des. 119:253–258

    Google Scholar 

  178. Sarma R (2000) An assessment of geometric methods in trajectory synthesis for shape-creating manufacturing operations. J. Manuf. Syst. 19(1):59–72

    MathSciNet  Google Scholar 

  179. Shpitalni M, Koren Y, Lo CC (1994) Realtime curve interpolators. Comput. Aided Des 26:832–838

    MATH  Google Scholar 

  180. Sheen B-T, You C-F (2006) Tool path generation for arbitrary pockets with islands. J Intell Manuf 17:275–283

    Google Scholar 

  181. Shin K, McKay N (1986) A dynamic programming approach to trajectory planning of robotic manipulators. IEEE Transaction on Automatic Control 31:491–500

    MATH  Google Scholar 

  182. Siller H, Rodriguez CA, Ahuett H (2006) Cycle time prediction in high-speed milling operations for sculptured surface finishing. J. Mater. Process. Technol. 174(1–3):355–362

    Google Scholar 

  183. ˇS´ır Z, Feichtinger R, J¨uttler B (2006) Approximating curves and their offsets using biarcs and Pythagorean hodograph quintics. Comput. Aided Des. 38(6):608–618

    Google Scholar 

  184. ˇS´ır Z, J¨uttler B (2005) Constructing acceleration continuous tool paths using Pythagorean Hodograph curves. Mech Mach Theory 40(11):1258–1272

    Google Scholar 

  185. Sencer B, Altintas Y, Croft Y (2008) Feed optimization for five-axis CNC machine tools with drive constraints. Int. J. Mach. Tools Manuf. 48:733–745

    Google Scholar 

  186. Suh SH, Shin YS (1996) Neural network modeling for tool path planning of rough cut in complex pocket milling. J. Manuf. Syst. 15(5):295–304

    Google Scholar 

  187. Sun Y-W, Guoa D-M, Jia Z-Y (2006) Spiral cutting operation strategy for machining of sculptured surfaces by conformal map approach. J. Mater. Process. Technol. 180(1–3):74–82

    Google Scholar 

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

    Google Scholar 

  189. Takata S (1989) A cutting simulation system for machinability evaluation using a workpiece model. CIRP ann 38(1):417–420

    Google Scholar 

  190. Takeuchi Y, Shimizu H, Idemura T, Watanabe T, Ito T (1990) 5-axis control machining based on solid model. Journal of the Japan Society for Precision Engineering 56(1):111–116

    Google Scholar 

  191. Takeuchi Y, Idemura T, Sata T (1991) 5-Axis Control Machining and Grinding Based on Solid Model. CIRP Annals-Manufacturing Technology 40(1):455–458

    Google Scholar 

  192. Takeuchi Y, Watanabe T (1992) Generation of 5-axis control collision-free tool path and postprocessing for NC data. CIRP Annals-Manufacturing Technology 41(1):539–542

    Google Scholar 

  193. Tsai M-S, Nien H-W, Yau H-T (2008) Development of an integrated look-ahead dynamics-based NURBS interpolator for high precision machinery. Comput. Aided Des. 40:554–566

    Google Scholar 

  194. Tseng YJ, Joshi S (1991) Determining feasible tool-approach directions for machining Bezier curves and surfaces. Comput. Aided Des. 23(5):367–378

    MATH  Google Scholar 

  195. Tata K, Fadel G, Bagchi A, Aziz N (1998) Efficient slicing for layered manufacturing. Rapid Prototyping J 4(4):151–167

    Google Scholar 

  196. Tung ED, Tomizuka M (1993) Feedforward tracking controller design based on the identification of low frequency dynamics. J. Dyn. Syst. Meas. Control 115(3):348–356

    MATH  Google Scholar 

  197. Tang TD, Bohez ELJ, Koomsap P (2007) The sweep plane algorithm for global collision detection with workpiece geometry update for five-axis NC machining. Comput. Aided Des. 39:1012–102

    Google Scholar 

  198. Tarkiainen M, Shiller Z (1993) Time optimal motions of manipulators with actuator dynamics, in: IEEE International Conference on Robotics and Automation, vol. 2, Atlanta, GA, May 2–6, IEEE Comput. Soc. Press, Los Alamitos, CA: 725–730

  199. Vafaeesefa A, El Maraghy HA (1998) Accessibility analysis in 5-axis machining of sculptured surfaces. In Proceedings of the 1998 IEEE International Conference on Robotics & Automation, pages 2464–2469

  200. Vanˇeˇcek G Jr (1991) Brep-index: a multidimensional space partitioningtree. In SMA ’91: Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications, pp. 35–44

  201. Wallner J, Pottmann H (2000) On the geometry of sculptured surface machining. In: Laurent P-J, Sablonni`ere P, Schumaker LL (eds) Curve and Surface Design. Vanderbilt University Press, Nashville

    Google Scholar 

  202. Wang F-C, Wright PK (1998) Open architecture controllers for machine tools. Part 2: a real time quintic spline interpolator. Journal of Manufacturing Science and Engineering 120(2):425–432

    Google Scholar 

  203. Wang F-C, Yang DCH (1993) Nearly arc-length parameterized quintic-spline interpolation for precision machining. Comput. Aided Des. 25(5):281–288

    MATH  Google Scholar 

  204. Wang K (2003) Solid modeling for optimizing metal removal rate of three dimensional NC end milling. J. Manuf. Syst. 7(1):57–65

    Google Scholar 

  205. Warkentin A, Ismail F, Bedi S (1998) Intersection approach to multi-point machining of sculptured surfaces. Comput Aided Geom Des 15(6):567–584

    MathSciNet  MATH  Google Scholar 

  206. 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):83–100

    MathSciNet  Google Scholar 

  207. Weck M, Meylahn A, Hardebusch C (1999) Innovative algorithms for spline-based CNC controller, production engineering research and development in Germany. Annals of the German Academic Society for Production Engineering VI(1):83–86

    Google Scholar 

  208. Weck M, Ye GH (1990) Sharp corner tracking using the IKF control strategy. CIRP ann 39(1):437–441

    Google Scholar 

  209. Woo T, Turkovich B (1990) Visibility map and its application to numerical control. CIRP anna 39(1):451–454

    Google Scholar 

  210. Woo T, Gan J (1992) Maximum intersection of spherical polygons and workpiece orientation for 4- and 5-axis machining. J. Mech. Des 114:477–485

    Google Scholar 

  211. Woo TC (1994) Visibility maps and spherical algorithms. Comput Aided Des 26(1):6–16

    MATH  Google Scholar 

  212. Wings E, Juttler B (2004) Generating tool paths on surfaces for a numerically controlled calotte cutting system. Comput. Aided Des. 36:325–331

    Google Scholar 

  213. Winslow AM (1966) Numerical solution of the quasilinear Poisson equation in a nonuniform triangle mesh. J Comput Phys 1(2):149–172

    MathSciNet  Google Scholar 

  214. Xu XJ, Bradley C, Zhang YF, Loh HT, Wong YS (2002) Tool-path generation for five-axis machining of free-form surfaces based on accessibility analysis. Int. J. Prod. Res. 40(14):3253–3274

    MATH  Google Scholar 

  215. Lee Y-S, Chang T-C (1996) Automatic cutter selection for five-axis sculptured surface machining. Int J Prod Res 34(4):977–998

    MathSciNet  MATH  Google Scholar 

  216. Yeh SS, Hsu PL (1999) The speed-controlled interpolator for machining parametric curves. Comput. Aided Des. 31:349–357

    MATH  Google Scholar 

  217. Yeung MK, Walton DJ (1994) Curve fitting with arc splines for NC tool path generation. Comput. Aided Des. 26(11):845–849

    MATH  Google Scholar 

  218. Yoon J-H (1997) Tool tip gouging avoidance and optimal tool positioningfor 5-axis sculptured surface machining. Int. J. Prod. Res. 41(10):2125–2142

    Google Scholar 

  219. You CF, Sheen BT, Lin TK (2001) Robust spiral tool-path generation for arbitrary pockets. Adv. Manuf. Technol. 17:181–188

    Google Scholar 

  220. Yoon J-H, Pottmann H, Lee Y-S (2003) Locally optimal cutting positions for 5-axis sculptured surface machining. Comput. Aided Des. 35(1):69–81

    Google Scholar 

  221. Yoon J-H (2005) Fast tool path generation by the iso-scallop height method for ball-end milling of sculptured surfaces. Int. J. Prod. Res. 43:5061–5070

    MathSciNet  Google Scholar 

  222. Young H-T, Chuang L-C, Gerschwiler K, Kamps S (2004) A five-axis rough machining approach for a centrifugal impeller. Int J Adv Manuf Tech 23(3–4):233–239

    Google Scholar 

  223. Yang DCH, Kong T (1994) Parametric interpolator versus linear interpolator for precision CNC machining. Comput Aided Des 26:225–234

    MATH  Google Scholar 

  224. Zhang QG, Greenway RB (1998) Development and implementation of a NURBS curve motion interpolator. Robot. Comput.-Integr. Manuf 14(1):27–36

    Google Scholar 

  225. Kang M, Lee S-K, Ko S-L (2002) Optimization of Cutting Conditions using Enhanced Z Map Model. CIRP Annals - Manufacturing Technology 51(1):429–432

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Sirindhorn International Institute of Technology, Thammasat University, Rangsit, Pathum Thani, 12121, Thailand

    Stanislav S. Makhanov

Authors
  1. Stanislav S. Makhanov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Stanislav S. Makhanov.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Makhanov, S.S. Adaptable geometric patterns for five-axis machining: a survey. Int J Adv Manuf Technol 47, 1167–1208 (2010). https://doi.org/10.1007/s00170-009-2244-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-009-2244-z

Keywords

Search

Navigation