GENERALIZED 3-D TOLERANCE ANALYSIS OF MECHANICAL ASSEMBLIES WITH SMALL KINEMATIC ADJUSTMENTS

The direct linearization method (DLM) for tolerance analysis of 3-D me chanical assemblies is presented. Vector assembly models are used, bas ed on 3-D vector loops which represent the dimensional chains that pro duce tolerance stackup in an assembly. Tolerance analysis procedures a re formulated for both open and closed loop assembly models. The metho d generalizes assembly variation models to include small kinematic adj ustments between mating parts. Open vector loops describe critical ass embly features. Closed vector loops describe kinematic constraints for an assembly. They result in a set of algebraic equations which are im plicit functions of the resultant assembly dimensions. A general linea rization procedure is outlined, by which the variation of assembly par ameters may be estimated explicitly by matrix algebra. Solutions to an over-determined system or a system having more equations than unknown s are included. A detailed example is presented to demonstrate the pro cedures of applying the DLM to a 3-D mechanical assembly.