Tolerance envelopes of planar mechanical parts

Y. Ostrovsky-Berman*, L. Joskowicz

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review

4 Scopus citations


We present a framework for the systematic study of parametric variation in planar mechanical parts and for efficiently computing approximations of their tolerance envelopes. Part features are specified by explicit functions defining their position and shape as a function of parameters whose nominal values vary along tolerance intervals. Their tolerance envelopes model perfect form Least and Most Material Conditions (LMC/MMC). Tolerance envelopes are useful in many design tasks such as quantifying functional errors, identifying unexpected part collisions, and determining device assemblability. We derive geometric properties of the tolerance envelopes and describe four efficient algorithms for computing first-order linear approximations with increasing accuracy. Our experimental results on three realistic examples show that the implemented algorithms produce better results in terms of accuracy and running time than the commonly used Monte Carlo method.

Original languageAmerican English
Pages (from-to)135-143
Number of pages9
JournalACM Symposium on Solid Modeling and Applications, SM
StatePublished - 2004
EventNinth ACM Symposium on Solid Modeling and Applications, SM'04 - Genoa, Italy
Duration: 9 Jun 200511 Jun 2005


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