Parametric kinematic tolerance analysis of planar mechanisms

Elisha Sacks*, Leo Joskowicz

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

36 Scopus citations


We present an efficient algorithm for worst-case and statistical kinematic tolerance analysis of mechanisms with parametric part tolerances. The algorithm derives the kinematic variation directly from the part geometry, the part degrees of freedom, and the allowable parameter variations. It first derives a geometric representation of the kinematic variation as parametric surfaces in the mechanism configuration space. It then performs sensitivity analysis on the surfaces and combines the results. In addition to traditional quantitative variations, the results reveal qualitative variations, such as play, undercutting, interference, and jamming. Our implementation handles planar mechanisms with one degree of freedom per part, including ones with higher pairs and multiple contacts. It is fast enough to be practical for full parametric models of complex mechanisms and for parametric representations of geometric tolerances, such as offsets, which typically require many parameters. The algorithm extends to linkage mechanisms when coupled with linkage analysis software. We demonstrate the implementation on a 26 parameter model of a Geneva pair and on an 82 parameter model of a camera shutter mechanism.

Original languageAmerican English
Pages (from-to)333-342
Number of pages10
JournalCAD Computer Aided Design
Issue number5
StatePublished - May 1997

Bibliographical note

Funding Information:
*Supported in part by NSF grant CCR-9505745 from the CISE program in numeric, symbolic, and geometric computation and by the Pursue Center for Computational Image Analysis and Scientific Visualization. t Computer Science Department, Purdue University, West Lafayette, IN 47907, USA IInstitute of Computer Science, The Hebrew University, Jerusalem 9 1904. Israel Paper received: 3 May 1996. Revised: 1 August 1996

Funding Information:
Elisha Sacks is supported in part by NSF grant CCR-9505745,b y a Purdue global initiative faculty grant, and by the Purdue Center for Scientific Visualization and Image Analysis. M. Jakiela and R. Gupta of the MIT Mechanical Engineering Department provided preliminary parametric models of the camera parts.


  • Computational kinematics
  • Multiple contact mechanisms
  • Parametric tolerance


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