For each class ci i17 a semi parametric model mi and

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Unformatted text preview: ne Table I; Classes of invariant surfaces in ℜ3 Given any S∈ℜ3, let: Aut(S) be the group of automorphisms of S, i.e. Aut(S)={g∈T(3)×SO(3): gS=S}; Aut0(S) be the connected component of Aut(S) that contains the identity rigid motion I3. Set S is assigned to class Ci if and only if Aut0(S)=Gi. According to Table I, seven semi-parametric models can describe all Statistical Modelling 171 elementary surfaces in the Euclidean space. Moreover, each semi-parametric model has an intrinsic Euclidean reference system which localizes the surface in the space. The MRGE (Minimum Reference Geometric Element), is composed of a set of elements (point, line and plane) derived from the semi-parametric model associated to the surface. The classification proposed in Table I can also be applied to the description of invariant surfaces building up any complex mechanical model. Prof. A. Clement adopted such a classification to develop a new tolerancing approach based on TTRS (Topologically and Technologically Related Surfaces), which reduces to only 28 situations all the possible combinations of elementary surfaces describing mechanical parts. [Clement et al., 1994]. 1.3. Duality between Specification and Ver...
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This note was uploaded on 08/03/2010 for the course DD 1234 taught by Professor Zczxc during the Spring '10 term at Magnolia Bible.

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