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A Closed Form Solution for Nonlinear Tolerance Analysis

Jeff Adams, Sanmina Corp.
Presented June 15, 2000 at the ADCATS 2000 Conference

Motion Limit Analysis (MLA) is a new tool for examining the degree of constraint in mechanical assemblies. It provides a quantitative procedure for detecting over- or under-constrained assemblies. Locational over-constraint of parts can lead to assemblability problems or require the deformation of parts in order to complete an assembly. Such problems can result in increased cost and poor product performance.

MLA uses mathematical screw theory to model constraints between mating parts to determine which of a partís six degrees of freedom have been removed. Seventeen assembly feature types have been modeled. The ability to calculate the rigid body motions of a part being added to an assembly is important. In-process adjustments during assembly can be used to precisely establish key assembly dimensions.

The purpose of MLA is to provide mathematical models of assembly features from which the ability of a feature to position one part relative to another can be calculated. If rigid body motion is allowed, the quantitative amount of motion is of interest. The user of this theory is able to obtain two major types of information about an assembly:

  1. Knowledge of the directions and quantitative amounts of possible motions of each part as it is added to a given assembly station via connection of a defined set of assembly features.

  2. Knowledge of whether or not the defined feature set over-, under-, or exactly- constrains the location and orientation of the added part.

Numerical examples for simple assembly conditions are presented. 

 

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