NC Verification of Up to 5 Axis Machining Processes Using Manifold Stratification

[+] Author and Article Information
Karim Abdel-Malek

Department of Mechanical Engineering and Center for Computer Aided Design, The University of Iowa, Iowa City, IA 52242e-mail: karim-abdel-malek@uiowa.edu

Walter Seaman

Department of Mathematics, The University of Iowa, Iowa City, IA 52242e-mail: walter-seaman@uiowa.edu

Harn-Jou Yeh

Microtek International, Taiwan e-mail: hjyeh@microtek.com.tw

J. Manuf. Sci. Eng 123(1), 99-109 (Nov 01, 1999) (11 pages) doi:10.1115/1.1286168 History: Received February 01, 1999; Revised November 01, 1999
Copyright © 2001 by ASME
Your Session has timed out. Please sign back in to continue.


Wang,  W. P., and Wang,  K. K., 1986, “Geometric Modeling for Swept Volume of Moving Solids,” IEEE Comput. Graphics Appl., 6, No. 12, pp. 8–17.
Boussac, S., and Crosnier, A., 1996, “Swept volumes generated from deformable objects application to NC verification,” Proceedings of the 13th IEEE International Conference on Robotics and Automation, Part 2 (of 4) Apr 22–28, Vol. 2, Minneapolis, MN, pp. 1813–1818.
Liu,  C., and Esterling,  D., 1997, “Solid Modeling of 4-Axis Wire EDM Cut Geometry,” Comput.-Aided Des., 29, No. 12, pp. 803–810.
Blackmore,  D., Leu,  M. C., and Wang,  L. P., 1997, “Sweep-envelope differential equation algorithm and its application to NC machining verification,” Comput.-Aided Des., 29, No. 9, pp. 629–637.
Leu,  M. C., Wang,  L., and Blackmore,  D., 1997, “Verification program for 5-axis NC machining with general APT tools” CIRP Ann. Manuf. Technol., 46, No. 1, pp. 419–424.
Voelker, H. B., and Hunt, W. A., 1985, “The Role of Solid Modeling in Machining Process Modeling and NC Verification,” SAE Tech. Paper #810195.
Menon, J. P., and Voelcker, H. B., 1992, “Toward a comprehensive formulation of NC verification as a mathematical and computational problem,” Proceedings of the 1992 Winter Annual Meeting of ASME, Nov 8–13, 59 , Anaheim, CA, pp. 147–164.
Oliver,  J., and Goodman,  E., 1990, “Direct Dimensional NC Verification” Comput.-Aided Des., 22, pp. 3–9.
Narvekar, A. P., Huang, Y., and Oliver, J., 1992, “Intersection of rays with parametric envelope surfaces representing five-axis NC milling tool swept volumes,” Proceedings of the 1992 18th Annual ASME Design Automation Conference, Vol. 44, Scottsdale, AZ, pp. 223–230.
Takata,  S., Tsai,  M. D., and Inui,  M., 1992, “A cutting simulation system for machinability evaluation using a workpiece model,” Ann. CIRP, 38, pp. 539–542.
Jerard,  R., and Drysdale,  R., 1988, “Geometric Simulation of Numerical Control Machinery,” ASME Comput. Eng., 2, pp. 129–136.
Jerard, R., and Drysdale, R., 1991, “Methods for geometric modeling, simulation, and spatial verification of NC machining programs,” Product Modeling for Computer Aided Design, North Holland, Amsterdam, pp. 1–14.
Koren,  Y., and Lin,  R. S., 1995, “Five-axis surface interpolators,” Ann. CIRP, 44, No 1, pp. 379–382.
Menon,  J. P., and Robinson,  D. M., 1993, “Advanced NC verification via massively parallel raycasting,” ASME Manuf. Rev., 6, pp. 141–154.
Oliver,  J. H., 1990, “Efficient Intersection of Surface Normals with Milling Tool Swept Volumes for Discrete Three-axis NC Verification” ASME DE, 23, No. 1, pp. 159–164.
Liang, X., Xiao, T., Han, X., and Ruan, J. X., 1997, Simulation Software GNCV of NC Verification, Author Affiliation: ICIPS Proceedings of the 1997 IEEE International Conference on Intelligent Processing Systems, Part 2 Oct 28–31, Vol. 2, Beijing, China, pp. 1852–1856.
Liu,  C., Esterling,  D. M., Fontdecaba,  J., and Mosel,  E., 1996, “Dimensional verification of NC machining profiles using extended quadtrees,” Comput.-Aided Des., 28, No. 11, pp. 845–852.
Abdel-Malek,  K., and Yeh,  H., 1997, “Geometric Representation of the Swept Volume Using Jacobian Rank-Deficiency Conditions,” Comput.-Aided Des., 29, No. 6, pp. 457–468.
Abdel-Malek,  K., and Yeh,  H. J., 1997, “Analytical Boundary of the Workspace for General 3-DOF Mechanisms,” Int. J. Robot. Res., 16, No. 2, pp. 1–12.
Abdel-Malek,  K., Adkins,  F., Yeh,  H. J., and Haug,  E. J., 1997, “On the Determination of Boundaries to Manipulator Workspaces,” Rob. Comput.-Integr. Manufact., 13, No. 1, pp. 63–72.
Abdel-Malek,  K., Yeh,  H. J., and Othman,  S., 1998, “Swept Volumes, Void and Boundary Identification,” Comput.-Aided Des., 30, No. 13, pp. 1009–1018.
Blackmore,  D., Leu,  M. C., Wang,  L. P., and Jiang,  H., 1997, “Swept Volumes: a retrospective and prospective view,” Neural Parallel Sci. Comput., 5, pp. 81–102.
Ahn,  J. C., Kim,  M. S., and Lim,  S. B., 1997, “Approximate general sweep boundary of 2D curved object,” CVGIP: Comput. Vis. Graph. Image Process., 55, pp. 98–128.
Elber,  G., 1997, “Global error bounds and amelioration of sweep surfaces,” Comput.-Aided Des., 29, pp. 441–447.
Ling,  Z. K., and Chase,  T., 1996, “Generating the swept area of a body undergoing planar motion,” ASME J. Mech. Des., 118, pp. 221–233.
Sourin,  A., and Pasko,  A., 1996, “A function representation for sweeping by a moving solid,” IEEE Trans. Vis. Comput. Graph., 2, pp. 11–18.
Spivak, M., 1968, Calculus on Manifolds, Benjamin/Cummings.
Guillemin, V., and Pollack, A., 1974, Differential Topology, Prentice-Hall, Englewood Cliffs, NJ.
Lu, Y. C., 1976, Singularity Theory and an Introduction to Catastrophe Theory, Springer-Verlag, New York.
Farin, G., 1993, Curves and Surfaces for Computer Aided Geometric Design, Academic Press, San Diego, CA.


Grahic Jump Location
Identifying the boundary using admissible directions
Grahic Jump Location
Varieties due to (a) p1,p2,p7; (b) p3,p4; and (c) p5,p6
Grahic Jump Location
Varieties due to (a) p63,p65 and (b) p71,p72. Varieties due to (c) p79−p86 and (d) p31−p38. Varieties due to (e) p39−p46 and (f) p33⋯p27.
Grahic Jump Location
(a) Subvarieties of ξ27 shown as curves. (b) The reducible variety ξ27.
Grahic Jump Location
(a) Four reducible varieties. (b) The boundary to the manifold (material removed).
Grahic Jump Location
A four parameter verification
Grahic Jump Location
Varieties due to p6 and p7
Grahic Jump Location
(a) Cross section at zi=0. (b) Cross-section at zi=1.
Grahic Jump Location
Area of each cross section through the swept volume versus the z-elevation




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In