Among the least developed capabilities in well-developed mathematical models for geometric tolerances are the representation of tolerances on form, orientation, and of Rule {\#}1 in the Standards, i.e. the coupling between form and allowable variations for either size or position of a feature. This paper uses Tolerance-Maps¹ (T-Maps¹) to describe these aspects of geometric tolerances for the straightness and orientation of an axis within its tolerance-zone on position. A Tolerance-Map is a hypothetical point-space, the size and shape of which reflect all variational possibilities for a target feature; for an axis, it is constructed in four-dimensional space. The Tolerance-Map for straightness is modeled with a geometrically similar, but smaller-sized, four-dimensional shape to the 4D shape for position; it is a subset within the T-Map for position. Another internal subset describes the displacement possibilities for the subset T-Maps that limits form. The T-Map for orientation and position together is formed most reliably by truncating the T-Map for position alone.
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.; “oning and Tolerancing”; The American Society of Mechanical Engineers, NY.
Bhide, S. (2002). A New Mathematical Model for Geometric Tolerances Applied to Cylindrical Features, MS Thesis, Arizona State University.
Bhide, S., Davidson, J.K., and Shah, J.J.; “A New Mathematical Model for Geometric Tolerances as Applied to Axes", In: CD Proc., ASME Des. Technical Conf’s., #DETC2003/DAC-48736; Chicago, IL.
Davidson, J.K., MujezinoviéA., and Shah, J. J. “A New Mathematical Model for Geometric Tolerances as Applied to Round Faces”, ASME Transactions, J. of Mechanical Design, 124, pp. 609-622.
Davidson, J.K. and Shah, J.J. (2002). “Geometric tolerances: A new application for line geometry and screws.” IMechE J. of Mechanical Eng. Science, Part C, 216 (C1), pp. 95-104.
Davidson, J.K. and Hunt, K.H. (2004). Robots and Screw Theory. Oxford.
Giordano, M., Pairel, E., and Samper, S. (1999). “Mathematical representation of tolerance zones.” In Global Consistency of Tolerances, Proc., 6th CIRP Int’l Seminar on Computer-Aided Tolerancing, Univ. of Twente, Enschede, Netherlands, March 22-24 (ed. F. vanHouten and H. Kals), pp. 177-86.
Giordano, M., Kataya, B., and Samper, S. “Tolerance analysis and synthesis by means of clearance and deviation spaces.” In Geometric Product Specification and Verification, Proc., 7th CIRP Int’l Seminar on CAT, Ecole Norm. Superieure, Cachan, France, April 24-25, (eds. P. Bourdet and L. Mathieu), pp. 345-354.
"Geometric tolerancing—Tolerancing of form, orientation, location, and run-out—Generalities, definitions, symbols, and indications on drawings”; International Organization for Standardization.
MujezinoviéA., Davidson, J.K., and Shah, J. J. “A New Mathematical Model for Geometric Tolerances as Applied to Polygonal Faces”, ASME Trans., J. of Mechanical Design, \bibitem126, pp. 504-518.
Pasupathy, T.M.K., Morse, E.P., and Wilhelm, R.G. “A Survey of Mathematical Methods for the Construction of Geometric Tolerance Zones”, ASME Transactions, J. of Computing & Information Science in Engr., 3, pp. 64-75.
Roy, U. and Li, B. (1999). “Representation and interpretation of geometric tolerances for polyhedral objects– I: Form tolerance.” Computer-Aided Design 30, pp. 151-161.
Whitney, D. E., Gilbert, O. L., and Jastrzebski, M. (1994). “Representation of geometric variations using matrix transforms for statistical tolerance analysis in assemblies”, Research in Engineering Design, 6, pp. 191-210.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Springer
About this paper
Cite this paper
Bhide, S., Ameta, G., Davidson, J., Shah, J. (2007). Tolerance-Maps Applied to the Straightness and Orientation of an Axis. In: Davidson, J.K. (eds) Models for Computer Aided Tolerancing in Design and Manufacturing. Springer, Dordrecht. https://doi.org/10.1007/1-4020-5438-6_6
Download citation
DOI: https://doi.org/10.1007/1-4020-5438-6_6
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-5437-2
Online ISBN: 978-1-4020-5438-9
eBook Packages: EngineeringEngineering (R0)