Closed-form compliance equations for elliptic-revolute notch type multiple-axis flexure hinges

Huaxian Wei, Bijan Shirinzadeh, Hui Tang, Xiaodong Niu

Research output: Contribution to journalArticleResearchpeer-review

20 Citations (Scopus)


This paper presents the closed-form compliance equations of elliptic-revolute notch type multiple-axis flexure hinges undergoing small displacement for three-dimensional applications. Analytical compliance equations in six degrees of freedom are explicitly derived based on the beam theory. Comparisons with existing compliance equations of revolute flexure hinges are carried out. The presented compliance equations for the elliptic-revolute flexure hinges can result in the compliance equations for the cylindrical- and circular-revolute flexure hinges. Finite element analyses are performed to verify the developed equations. Numerical simulation is conducted to test the compliance characteristics of the elliptic-revolute flexure hinges. The simplified coefficients between the compliances of the elliptic- and circular-revolute flexure hinges are established. The presented compliance equations are helpful for designing spatial compliant mechanisms based on the elliptic-revolute flexure hinges.

Original languageEnglish
Article number104154
Number of pages12
JournalMechanism and Machine Theory
Publication statusPublished - Feb 2021


  • Compliance equation
  • Elliptic
  • Flexure hinges
  • Multiple-axis
  • Revolute

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