Complete swept volume generation, Part I: Swept volume of a piecewise C1-continuous cutter at five-axis milling via Gauss map

CAD Computer Aided Design

Volumn 43, Issue 4, 2011, Pages 427-441

  Lee, Seok Won ^a   Nestler, Andreas ^a  

^a DRESDEN UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Envelope; Gauss map; Geometric modeling; Multi axis machining; NC verification; Swept volume

Indexed keywords

ENVELOPE; GAUSS MAPS; GEOMETRIC MODELING; MULTI-AXIS MACHINING; NC VERIFICATION; SWEPT VOLUME;

CUTTING; FITS AND TOLERANCES; GAUSSIAN DISTRIBUTION; GEOMETRY; MACHINE TOOLS; MILLING (MACHINING); SPHERES; VECTOR SPACES;

CUTTING TOOLS;

EID: 79952364018     PISSN: 00104485     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cad.2010.12.010     Document Type: Article

References (47)

1. B. Jacobs The expanding role of simulation Tooling & Production 71 7 2005 28 31
2. (ACM) Computational geometry impact task force. Application challenges to computational geometry. Technical report TR-521-96. CS Department, Princeton University, April 1996. Also available at: http://people.csail.mit.edu/seth/ pubs/taskforce/techrep.html.
3. Y. Huang, J.H. Oliver, and Milling N.C. Error assessment and tool path correction Computer graphics proceedings, annual conference series ACM SIGGRAPH 1986 ACM Press 287 294
4. van Hook T. Real time shaded NC milling display. In: SIGGRAPH'86, vol. 20, Number 4. 1986.
5. Müller H, Surmann T, Stautner M, Albersmann F, Weinert K. Online sculpting and visualization of multi-dexel volumes. In: 8th ACM symposium on solid modeling and applications. 2003. p. 25861.
6. J. Weld, and M. Leu Geometric representation of swept volume with application to polyhedral objects International Journal of Robotics Research 9 5 1990
7. K. Abdel-Malek, and H.J. Yeh Geometric representation of the swept volume using the jacobian rank deficiency conditions Computer-Aided Design 29 6 1997 457 468 (Pubitemid 127419682)
8. J. Lee, S. Hong, and M. Kim Polygonal boundary approximation for a 2D general sweep based on envelope and Boolean operations The Visual Computer 16 2002
9. Kim YJ, Varadhan G, Lin MC, Manocha D. Fast swept volume approximation of complex polyhedral models. In: ACM symposium on solid modeling and applications. 2003.
10. K. Abdel-Malek, D. Blackmore, and K. Joy Swept volumes: foundations, perspectives and applications International Journal of Shape Modeling 2004
11. Spatial Corp. Broomfield (CO, USA) http://www.spatial.com/products/3d- acis-modeling, cited in March 2010.
12. Siemens PLM Software, Plano (TX, USA) http://www.siemens.com/plm, cited in March 2010.
13. W.P. Wang, and K.K. Wang Geometric modeling for swept volume of moving solids IEEE Computer Graphics and Applications 6 12 1986 8 17 (Pubitemid 17517272)
14. R.R. Martin, and P.C. Stephenson Sweeping of three-dimensional objects Computer Aided Design 22 4 1990 223 234 (Pubitemid 20708213)
15. M. Husty, A. Karger, H. Sachs, and W. Steinhiper Kinematik und Robotik 1997 Springer-Verlag Berlin (Heidelberg, NY)
16. E. Kreyszig Differential geometry 1991 Dover Publications
17. C.J. Chiou, and Y.S. Lee Swept surface determination for five-axis numerical control machining International Journal of Machine Tools & Manufacture 42 2002 1497 1507
18. C.J. Chiou, and Y.S. Lee A shape-generating approach for multi-axis machining G-buffer models Computer-aided Design 31 1999 761 776
19. I.H. Kral Numerical control programming in APT 1986 Prentice-Hall Englewood Cliffs (NJ)
20. J.C.J. Chiou, and Y.S. Lee Optimal tool orientation for five-axis tool-end machining by swept envelope approach Journal of Manufacturing Science and Engineering 127 4 2005 810 818 (Pubitemid 41680970)
21. Du S. Simulation and tool path optimization for the hexapod milling machine. Dissertation. Universitt Dortmund, Shaker Verlag; 2004.
22. S. Du, T. Surmann, O. Webber, and K. Weinert Formulating swept profiles for five-axis tool motions International Journal of Machine Tools & Manufacture 45 2005 849 861 (Pubitemid 40259563)
23. K. Weinert, S. Du, P. Damm, and M. Stautner Swept volume generation for the simulation of machining processes International Journal of Machine Tools & Manufacture 44 2004 617 628
24. A.P. Boresi, and R.A. Schmidt Engineering mechanics: statics & dynamics 1 ed. 2000 Thomson Press
25. V.C. Boltyanskii Envelopes Popular lectures in mathematics vol. 12 1964 MacMillan Press
26. OPEN CASCADE SAS (EURIWARE group). Guyancourt. France, http://www.opencascade.org/, cited in March 2010.
27. D. Blackmore, M. Leu, and L. Wang Sweep-envelope differential equation algorithm and its application to NC machining verification Computer-Aided Design 29 9 1997 629 637 (Pubitemid 127431543)
28. Wang L, Leu MC, Blackmore D. Generating swept solids for NC verification using the SEDE method. In: ACM symposium on solid modeling and applications, proceedings of the fourth ACM symposium on solid modeling and applications. 1997. p. 36475.
29. Blackmore D, Leu MC. A differential equation approach to swept volumes. In: Proc. of rensselaer's 2nd international conference on computer integrated manufacturing. 1990. p. 1439.
30. K. Sheltami, S. Bedi, and F. Ismail Swept volumes of toroidal cutters using generating curves International Journal of Machine Tools and Manufacture 38 7 1998 855 870 (Pubitemid 128428599)
31. Roth D, Bedi S, Ismail F. Generation of swept volumes of toroidal endmills in five-axis motion using space curves. In: ACM symposium on solid and physical modeling. 1999. p. 30611.
32. D. Roth, S. Bedi, F. Ismail, and S. Mann Surface swept by a toroidal cutter during a 5-axis machining Computer-Aided Design 33 1 2001 57 63 (Pubitemid 32077179)
33. Y.C. Chung, J.W. Park, H.Y. Shin, and B.K. Choi Modeling the surface swept by a generalized cutter for NC-verification Computer Aided Design 30 8 1998 587 593
34. S. Mann, and S. Bedi Generation of the imprint method to general surfaces of revolution for NC machining Computer-Aided Design 34 5 2002 373 378 (Pubitemid 34065020)
35. Pottmann H, Peternell M. Envelopescomputational theory and applications. In: Falcidieno B (editor), Spring conference on computer graphics 2000. Comenius University; 2000. p. 323. Proceedings of the conference in Budmerice. 2000.
36. M. Dohm, and S. Zube The implicit equation of a canal surface Journal of Symbolic Computation 44 2009 111 130
37. E. Aras Generating cutter swept envelopes in five-axis milling by two-parameter families of spheres Computer Aided Design 41 2 2009 95 105
38. H. Gong, and N. Wang Analytical calculation of the envelope surface for generic milling tools directly from CL-data based on the moving frame method Computer-Aided Design 41 2009 848 855
39. J. Rossignac, J.J. Kim, S.C. Song, K.C. Suh, and C.B. Joung Boundary of the volume swept by a free-form solid in screw motion Computer-Aided Design 39 2007 745 755 (Pubitemid 47094758)
40. J. Rossignac, and J.J. Kim Computing and visualizing pose-interpolating 3D motions Computer Aided Design 33 2001 279 291 (Pubitemid 32262996)
41. Kim B, Rossignac J. Collision prediction for polyhedra under screw motions. In: Proc. of the ACM SM'03. 2003. p. 410.
42. S.W. Lee, and A. Nestler Complete swept volume generationpart II: NC simulation of self-penetration via comprehensive analysis of envelope profiles Computer Aided Design 43 4 2011 442 456
43. K.F. Gauss General investigations of curved surfaces 1965 Raven Press Hewlett (New York) English translation
44. M. Do Carmo Differentialgeometrie von Kurven und Flchen 1983 Vieweg Verlag Braunschweig (Wiesbaden)
45. J.W. Harris, and H. Stocker Handbook of mathematics and computational science 1998 Springer-Verlag
46. I.H. Kral Numerical control programming in APT 1986 Prentice-Hall Englewood Cliffs (NJ)
47. Benouamer MO, Michelucci D. Bridging the gap between CSG and Brep via a triple ray representation. In: ACM Symposium on Solid Modeling and Applications, proceedings of the 4th ACM symposium on Solid modeling and applications, Atlanta, GA; 1997. p. 6879.