This paper presents a framework for worst case analysis of the relative position variation of toleranced parts in assemblies. The framework is based on our general parametric tolerancing model for planar parts. We present six types of relative position constraints designed to model all types of contact and clearance specifications between features of two parts. To model the relative part position variation in the entire assembly, we introduce the assembly graph, a generalization of Latombe's relation graph that includes cycles, toleranced parts, and three degrees of freedom. We show how to compute the sensitivity matrices of each vertex from the pairwise relative position constraints and the assembly graph. These matrices serve to compute the tolerance envelopes bounding the areas occupied by the parts under all possible assembly instances.
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Ostrovsky-Berman, Y., Joskowicz, L. (2007). Relative Positioning of Planar Parts in Toleranced Assemblies. 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_8
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DOI: https://doi.org/10.1007/1-4020-5438-6_8
Publisher Name: Springer, Dordrecht
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