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TECHNICAL PAPERS

Statistical Modelling of Nominal and Measured Mechanical Surfaces

[+] Author and Article Information
Paolo Chiabert, Mario Costa

Polytechnic of Turin, Corso Duca degli Abruzzi 24, Turin, Italy 10129

J. Comput. Inf. Sci. Eng 3(1), 87-94 (May 15, 2003) (8 pages) doi:10.1115/1.1569941 History: Received October 01, 2002; Revised March 01, 2003; Online May 15, 2003
Copyright © 2003 by ASME
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References

Srinivasan,  V., 1999, “A GPS Language Based on a Classification of Symmetry Groups,” Comput.-Aided Des., 31(11), pp. 659–668.
Requicha,  A., 1983, “Toward a Theory of Geometric Tolerancing,” Int. J. Robot. Res., 2(2), pp. 45–60, Winter.
Van Houten F, Kals, H., Editors, 1999, Global Consistency of Tolerancing, Dordrecht, Kluwer Academic.
Srinivasan, V., 2001, “An Integrated View of Geometrical Product Specification and Verification,” Proc. of the 7th CIRP Int. Seminar on CAT, Cachan, pp. 7–16.
Parzen,  E., 1962, “On Estimation of a Probability Density Function and Mode,” Expert Sys. Applic., 33, pp. 1065–1076.
O’Connor, M., Srinivasan, V., 1996, “Connected Lie and Symmetry Subgroups of the Rigid Motions: Foundations and Classification,” IBM Research Report, RC 20512.
Humienny, Z., et al., 2001, Geometrical Product Specification, Warsaw University of Technology Printing House.
Hervé, J., 1976, “La géometrie du groupe des déplacements appliquée à l’analyze cinématique des mécanismes,” Thèse de Doctorat d’Etat en Sciences Physiques.
Clément, A., Rivière, A., and Temmerman, M., 1994, “Cotation tridimensionnelle des systèmes mécaniques,” PYC Edition.
Karger, A., and Novak, J., 1985, Space Kinematics and Lie Groups, Gordon and Breach Science Publishers, New York.
Fukunaga, K., 1972, Introduction to Statistical Pattern Recognition. New York, Academic Press.
El Maragy, H. A., Editor, 1998, Geometric Design Tolerancing: Theories, Standards and Applications, London, Chapman & Hall.

Figures

Grahic Jump Location
Analysis of the PDF under the hypothesis of cylindrical (left, center) and axial (right) symmetry
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Analysis of the PDF under the hypothesis of cylindrical (a, b) and axial (c) symmetry
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Sampling of a spherical surface
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PDF M1, reconstructed from D
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Sampling of a composed axial surface
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2D/3D plot of the reconstructed PDF M5
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Decomposition of the axial model M5
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Parameters of the cylindrical model M2
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Cylinder (a) and near-cylindrical models (b, c)
Grahic Jump Location
Analysis of the PDF under the hypothesis of cylindrical (left, center) and axial (right) symmetry

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