Abstract
Geometric tolerancing analysis consists of simulating the behavior of a mechanical system according to geometric defects in the constituent parts. The aim is to verify system compliance in terms of the functional requirements for its expected operation. When carrying out the simulation the geometric specifications of the constituent parts and specifications of parts potentially in contact must be taken into account. One approach using polytopes consists of characterizing the specifications of the parts, the specifications of the contacts and the functional requirements of the mechanical system using sets of geometric constraints. This article describes modeling different sets of constraints manipulated by polytopes. We introduce the operations that are applied (Minkowski sum and intersection) to determine the relative position of any two surfaces of a mechanical system. Finally, tolerancing analysis of a simple mechanical system is described.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Fleming, A.D.: Geometric relationships between toleranced features. Artificial Intelligence 37, 403–412 (1988)
Rossignac, R., Requicha, A.A.G.: Offsetting operations in solid modelling. Computer Aided Geometric Design 3, 129–148 (1986)
ISO1101, Geometrical Product Specifications (GPS), Geometrical tolerancing, Tolerances of form, orientation, location and run-out (2004)
Teissandier, D., Delos, V., Couétard, Y.: Operations on polytopes: application to tolerance analysis. In: Proc. of 6th CIRP Seminar on Computer Aided Tolerancing, Enschede (Netherlands), pp. 425–433 (1999) ISBN 0-7923-5654-3
Teissandier, D., Delos, V.: Algorithm to calculate the Minkowski sums of 3-polytopes based on normal fans. Computer-Aided Design 43, 1567–1576 (2011)
Giordano, M., Duret, D.: Clearance Space and Deviation Space. In: Proc. of 3rd CIRP Seminar on Computer Aided Tolerancing, Cachan (France), pp. 179–196 (1993) ISBN 2-212-08779-9
Ballu, A., Mathieu, L., Legoff, O.: Representation of Mechanical Assemblies and Specifications by Graphs. In: Geometric Tolerancing of Products, pp. 87–110. ISTE-WILEY (2010) ISBN 978-1-84821-118-6
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Homri, L., Teissandier, D., Ballu, A. (2013). Tolerancing Analysis by Operations on Polytopes. In: Haddar, M., Romdhane, L., Louati, J., Ben Amara, A. (eds) Design and Modeling of Mechanical Systems. Lecture Notes in Mechanical Engineering. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37143-1_71
Download citation
DOI: https://doi.org/10.1007/978-3-642-37143-1_71
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-37142-4
Online ISBN: 978-3-642-37143-1
eBook Packages: EngineeringEngineering (R0)