Once the assembly has been described, an algebraic model is created, in which each dimension is
represented by a vector, with a nominal length +/- a tolerance. The vectors are linked into chains or loops,
describing each critical clearance or assembly feature in terms of the contributing dimensions. The chains
form vector loops describing the interaction and accumulation of the three sources of variation in the
assembly.
Small variations are applied to each source and analyzed statistically to predict the resulting variation in the
critical assembly features. Solutions for the mean and standard deviations are obtained by matrix algebra.
Only two assemblies are analyzed: one for the mean and another for the variance of the assembly features.
The same modeling elements may be used to model complex assemblies. It just takes more vector loops.
The solution may be obtained by computationally efficient tools available on a desktop computer. It is also well
suited for integration with a commercial CAD system.
Benefits of tolerance analysis include reduced reject rates, fewer problems on the assembly floor, reduced
costs, and shorter time to market. Critical requirements of shaft alignment, gear meshing and controls in
transmissions and gear trains are ideally suited for this efficient, comprehensive system.

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