Abstract
A mathematical model is presented for representing the tolerances of planar surfaces. The model is compatible with the ASME/ISO Standards for geometric tolerances. Central to the new model is a Tolerance-Map® 1, a hypothetical volume of points which corresponds to all possible locations and variations of a segment of a plane which can arise from tolerances on size, form, and orientation. This model is one part of a bi-level model that we are developing for geometric tolerances. The new model makes stackup relations apparent in an assembly, and these can be used both to allocate size and orientational tolerances and to identify sensitivities. All stackup relations can be met for 100% interchangeability or for a specified probability.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
ASME Y14.5M.; “Dimensioning and Tolerancing”The American Society of Mechanical Engineers, NY.
Chase K., Gao J., Magelby S., Sorensen C. (1998). “Including geometric feature variations in tolerance analysis of mechanical assemblies”; In: IIE Transactions, 28, pp 795–807.
Clément, A., Rivière, A., and Serré, P.; “The TTRS: a common declarative model for relative positioning, tolerancing and assembly”; In: MICAD Proc., 11, No. 1–2, pp. 149–264.
Coxeter, H. S. M.; Introduction to Geometry; 2nd ed. Wiley.
Davidson, J.K., Mujezinovid, A., and Shah, J. J.; “A New Mathematical Model for Geometric Tolerances as Applied to Round Faces”, In: CD Proc., ASME Des. Technical Conf’s., #DETC00/DAC-14249; Baltimore, MD.
Davidson, J.K. and Shah, J.J.; “Geometric Tolerances: A New Application for Line Geometry and Screws”; In: CD Proc. for the Symp.Commem. the Legacy, Works, and Life of Sir Robert S. Ball, Cambridge, UK.
Giordano, M., Pairel, E., and Samper, S.; “Mathematical representation of tolerance zones”; In: Proc., 6th CIRP Int’l Seminar on ComputerAided Tolerancing, pp. 177–86.
Gossard, D. C., Zuffante, R. P. and Sakurai, H.; “Representing dimensions, tolerances, and features in MCAE systems”; In: IEEE Comp. Gr. and Appl. 8(2), pp. 51–59.
Geometric tolerancing—Tolerancing of form, orientation, location, and run-out—Generalities, definitions, symbols, and indications on drawings”; International Organization for Standardization.
Kandikjian, T., Shah, J.J., and Davidson, J.K.; “A mechanism for validating dimensioning & tol. schemes in CAD systems”; CAD, (in press).
Laperrière, L. and Lafond, P.; “Tolerance analysis and synthesis using virtual joints”; In: Proc., 6th CIRP Int’l Seminar on ComputerAided Tolerancing, pp. 405–414.
Mujezinovid, A.;, A.; “A new mathematical model for representing geometric tolerances”; MSc thesis, Arizona State Univ., Tempe, AZ, May, 1999.
Requicha, A. A. G.; Toward a theory of geometric tolerances; Int. J.of Robotics Research, 2(4), pp. 45–60.
Shah J. J., Yan Y., Zhang B-C.; “Dimension and tolerance modeling and transformations in feature based design and manufacturing”; In: J. Integrated Manufacturing, 9, N5, pp. 475–488.
Teissandier, D., Delos, V., and Couetard, Y.; “Operations on polytopes: application to tolerance analysis”; In: Proc., 6th CIRP Int’l Seminar on Computer-Aided Tolerancing, pp. 425–434.
Turner, J. U.; “Exploiting solid models for tolerance computations”; In: Geometric Modeling for Product Engineering, pp. 237–258, North-Holland.
Whitney, D. E., Gilbert, O. L., and Jastrzebski, M.; “Representation of geometric variations using matrix transforms for statistical tolerance analysis in assemblies”; In: Research in Engineering Design, 6, pp. 191–210.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Bhide, S., Davidson, J.K., Shah, J.J. (2003). Areal Coordinates: The Basis of a Mathematical Model for Geometric Tolerances. In: Bourdet, P., Mathieu, L. (eds) Geometric Product Specification and Verification: Integration of Functionality. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1691-8_4
Download citation
DOI: https://doi.org/10.1007/978-94-017-1691-8_4
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-6342-7
Online ISBN: 978-94-017-1691-8
eBook Packages: Springer Book Archive