Abstract
This work is to contribute to three goals: a mathematical model of part geometric deviations, computation principles for three dimensional tolerance chains and a tolerance scheme in a mathematical form. We use an example to show present conclusions of this work according to the second goal. Then, we focus on a new problem faced in achieving the whole process of tolerancing. If the small displacement torsor is a useful tool to describe the relative situation of two simple surfaces, it’s more difficult to describe the relative situation of two parts involving several different couples of surfaces, what is wanted in mechanism study. We first explain the combinatory nature of this problem and ways to reduce it.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ballot E. “Lois de comportement géométrique des mécanismes pour le tolérancement” Thèse de Doctorat de l’Ecole Normale Supérieure de Cachan.
Ballot E. and Bourdet P. “A computational method for the consequences of geometrical errors in mechanisms” Geometric Design Tolerancing: theories, standards and application, edited by El Maraghy. Chapman & Hall, ISBN 0–412–83000–0, 488pp.
Ballot E. and Bourdet P. “A mathematical model of geometric errors in the case of specification and 3D control of mechanical part” Advanced mathematical tool in metrology IV in Series on advances in mathematics for applied sciences, World Scientific, Vol. 53.
Bourdet P. and Clément A. A study of optimal-criteria identification based-on the small-displacement screw model. Annals of the CIRP, Vol. 37, pp. 503–506.
Bourdet P., Mathieu L., Lartigue C. and Ballu A. “The concept of small displacement torsor in metrology” Advanced mathematical tool in metrology II in Series on advances in mathematics for applied sciences, World Scientific, Vol. 40.
Clement A., Desrochers A. and Riviere A. Theory and practice of 3-D tolerancing for assembly. CIRP International Working Seminar on Tolerancing, Penn State, pp. 25–55.
Gupta S., Turner J. U., «Variational solid modeling for tolerance analysis», IEEE Computer Graphics & Applications, Vol. 17, No. 5, pp. 64–74.
Requicha A.A.G. Toward a Theory of Geometrical Tolerancing. The International Journal of Robotics Research, Vol. 2, No. 4, pp. 45–60.
Rivest L., Fortin C., Morel C., «Tolerancing a solid model with a kinematic formulation», Computer-aided design, Vol. 26, No. 6, pp. 465–485.
Sodhi R. and Turner J. U. Relative positioning of variational part models for design analysis. Computer-aided design, Vol. 26, No. 5, pp. 366–378.
Wolfram S; “Mathematica: A system for doing mathematics by computer” Addison-Wesley.
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
Ballot, E., Bourdet, P., Thiébaut, F. (2003). Determination of relative situations of parts for tolerance computation. 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_7
Download citation
DOI: https://doi.org/10.1007/978-94-017-1691-8_7
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-6342-7
Online ISBN: 978-94-017-1691-8
eBook Packages: Springer Book Archive