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Unformatted text preview: et al. And various equations and inequations modelize the geometrical behavior of the mechanism. Composition relations of displacements in the various topological loops of graph (Figure 1) express the geometrical behavior of the mechanism. The composition relations define compatibility equations between deviation, gaps, … (for design tolerances : [Ballot et al, 1997], for manufacturing tolerances : [Villeneuve et al, 2001]. A compatibility equation is a KC relation. Example:
− α1a /1 + α1a / 2 a + α 2 a / 2 − α 2b / 2 − α1b / 2b + α1b /1 = 0 − β1a /1 + β1a / 2 a + β 2 a / 2 − β 2b / 2 − β1b / 2b + β1b /1 = 0 or Y = f (X ) Interface constraints limit the geometrical behavior of the mechanism and characterize non-interference between surfaces [Dantan et al, 2005]; they are KC level constraints. Example: (v ia / ja ,O − z M α ia / ja )2 + (u ia / ja ,O − z M β ia / ja )2 ≤ (d ja − d ia )2
4 A geometrical specification is a condition on part deviation (Key Characteristics); it is a KC level constraints. Example:
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