Parametric kinematic tolerance analysis of general planar systems

Elisha Sacks*, Leo Joskowicz

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

57 Scopus citations


We present an algorithm for functional kinematic tolerance analysis of general planar mechanical systems with parametric toleranoes. The algorithm performs worst-case analysis of systems of curved parts with contact changes, including open and closed kinematic chains. It computes quantitative variations and helps designers detect qualitative variations, such as blocking and undercutting. The algorithm constructs a variation model for each interacting pair of parts: a mapping from the part tolerances and configurations to the kinematic variation of the pair. These models generalize the configuration space representation of nominal kinematics to toleranced parts. They are composed via sensitivity analysis and linear programming to derive the system variation at a given configuration. The variation relative to the nominal system function is computed by sampling the system variation. We demonstrate the algorithm on detailed parametric models of a movie camera film advance and of a micro-mechanical gear discriminator.

Original languageAmerican English
Pages (from-to)707-714
Number of pages8
JournalCAD Computer Aided Design
Issue number9
StatePublished - 1998

Bibliographical note

Funding Information:
Sacks is supported in part by NSF grants CCR-9617600 and CCR-9505745 and by the Purdue Center for Computational Image Analysis and Scientific Visualization. Joskowicz is supported in part by a grant from the Authority for Research and Development, The Hebrew University and by a Guastalla Faculty Fellowship, Israel. Jorg Peters helped generate the three-dimensional configuration space images.


  • Contact analysis
  • Functional tolerance analysis
  • Kinematic variation


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