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Approximate the swept volume of revolutions along curved trajectories

Published: 04 June 2007 Publication History

Abstract

Swept volume has been applied to many applications areas such as NC machining simulation and verification, robot workspace analysis, collision detection, and CAD. The numerical computation of swept volume remains to be a very challenging problem in terms of simplicity, efficiency and accuracy. The paper presents a novel swept volume approximation method for revolution generator solids sweeping along curved trajectories. This algorithms consists of the following main steps: (1) Discretization of the trajectory curve and establishments of reference frames; (2) Extraction and approximation of envelop profile at each discretized position based on the velocity vector calculated; and (3) Generation of envelop surfaces from the extracted envelop profile curves, and attachment of the ingress and egress surfaces to the envelop surface to form the SV Solid. Examples show that our algorithm is simple, efficient and accurate.

References

[1]
Abdel-Malek, K. and YEH, H. J. 1997. Geometric representation of the swept volume using Jacobian rank-deficiency conditions. Computer Aided Design 29, 6, 457--468.
[2]
Abdel-Malek, K., Blackmore, D., Joy K, I. 2004. Swept volumes: foundations, perspectives and applications. The Intertional Journal of Shape Modeling 23, 5, 1--25.
[3]
Abrams, S. and Allen, P. 2000. Computing swept volumes. The Journal of Visualization and Computer Animation 11, 69--82.
[4]
Bishop, R. L. 1975. There is more than one way to frame a curve, Amer. Math. Monthly, 82, 246--251.
[5]
Blackmore, D. and Leu, M. 1992. Analysis of swept volume via lie group and differential equations. The International Journal of Robotics Research, 11, 6, 516--537.
[6]
Blackmore, D., Leu, M. and Wang, L. P. 1997. Sweep-envelope differential equation algorithm and its application to NC machining verification. Computer Aided Design, 29, 9, 629--637.
[7]
Du, S. J., Surmann, T., Webber, O., et al. 2005. Formulating swept profiles for five-axis tool motions. The International Journal of Machine Tools and Manufacture 45, 7--8, 849--861.
[8]
Guggenheimer, E. 1989. Computing Frames along a Trajectory, Computer Aided Geometric Design 6, 77--78.
[9]
Kim, Y. J., Varadhan, G., Lin, M. C., et al. 2004. Fast swept volume approximation of complex polyhedral models, Computer Aided Design, 36, 1013--1027.
[10]
Klok, F. 1986. Two moving coordinate frames for sweeping along a trajectory. Computer Aided Geometric Design 3, 4, 217--229.
[11]
Mann, S. and Bedi, S. 2002. Generalization of the imprint method to general surfaces of revolution for NC machining. Computer Aided Design, 34, 5, 373--378.
[12]
Martin, R. and Stephenson, P. 1990. Sweeping of three-dimensional objects. Computer Aided Design, 22, 4, 223--234.
[13]
Peternell, M., Pottmann, H., Steiner, T., et al. 2005. Swept Volumes. Computer Aided Design and Applications 2, 1--4, 95--104.
[14]
Piegel, L. and Tiller, W. 1997. The NURBS Book. Springer Verlag, Berlin.
[15]
Pottmann, H., Peternell, M. 2000. Envelopes-computational theory and applications. In Proceedings Of Spring Conference on Computer Graphics and its Applications, Budmerice, 3--23.
[16]
Wang, G. P, Sun J. G. and Wu, X. L. 1998. The NURBS Approximation of Sweep Surfaces. The Chinese Journal of Computer 21, 9, 45--49.
[17]
Wang, W. P. and Wang, K. K. 1986. Geometric modeling for swept volume of moving solids. IEEE Computer Graphic Applications 6, 12, 8--17.
[18]
Weinert, K., Du, S. J., Damm, P., et al. 2004. Swept volume generation for the simulation of machining processes. The International Journal of Machine Tools and Manufacture 44, 6, 617--628.
[19]
Weld, J. and Leu, M. 1990. Geometric representation of swept volume with application to polyhedral objects. The International Journal of Robotics Research 9, 5, 105--117.
[20]
Yu, H. B. and Wang, Y. X. 2003. Swept Volume and Its Application to Mechanical Design. The Journal of Engineering Graphics 1, 63--70.

Cited By

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  • (2010)Conservative swept volume boundary approximationProceedings of the 14th ACM Symposium on Solid and Physical Modeling10.1145/1839778.1839804(171-176)Online publication date: 1-Sep-2010
  • (2009)Reliable sweeps2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling10.1145/1629255.1629306(373-378)Online publication date: 5-Oct-2009
  • (2008)Trimming self-intersections in swept volume solid modelingJournal of Zhejiang University-SCIENCE A10.1631/jzus.A0713579:4(470-480)Online publication date: 1-Apr-2008
  1. Approximate the swept volume of revolutions along curved trajectories

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      cover image ACM Other conferences
      SPM '07: Proceedings of the 2007 ACM symposium on Solid and physical modeling
      June 2007
      455 pages
      ISBN:9781595936660
      DOI:10.1145/1236246
      Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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      Published: 04 June 2007

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      Author Tags

      1. CAD modeling
      2. NC simulation
      3. envelop surface
      4. swept volume
      5. swept volume solid

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      Cited By

      View all
      • (2010)Conservative swept volume boundary approximationProceedings of the 14th ACM Symposium on Solid and Physical Modeling10.1145/1839778.1839804(171-176)Online publication date: 1-Sep-2010
      • (2009)Reliable sweeps2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling10.1145/1629255.1629306(373-378)Online publication date: 5-Oct-2009
      • (2008)Trimming self-intersections in swept volume solid modelingJournal of Zhejiang University-SCIENCE A10.1631/jzus.A0713579:4(470-480)Online publication date: 1-Apr-2008

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