Calculation of virtual and resultant parts for variational assembly analysis

Abstract

Usually, the design of mechanisms and assemblies uses the perfect model of the part. This type of model can be used within a software application to simulate and to verify the kinematics and dynamic behavior of such mechanisms. However, the analysis of the manufacturing uncertainties is also necessary to control the sensitivity and robustness of the mechanism assembly. To take into account these uncertainties, the designer deals with a class of interchangeable and functionally equivalent parts. When specifying tolerances, he essentially defines the authorized variations of the envelope of the parts and a number of classes can represent the various domains of acceptance of the parts. Since we need to take into account the infinite number of parts allowed by the variational class, the analysis of variational assembly is a hard task. In this paper, an extension of our previous work to calculate the virtual and resultant parts is proposed. The proposed method takes into account the datum chaining in the toleranced part. A kinematics model and robotic parameterisation is used to simulate the possible “motion” of the tolerance zone, allowed by MMC and LMC modifiers. Thus, the analysis of the infinite number of parts is reduced to analyse only two parts for each variational class. The analysis of the Jacobian matrix of the mechanism effectively generates the intersection and the union of all the boundaries of the features of the part. The paper presents also a significant application of this approach.