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Open AccessArticle

On Modeling the Bending Stiffness of Thin Semi-Circular Flexure Hinges for Precision Applications

1
Precision Engineering Group, Institute for Design and Precision Engineering, Department of Mechanical Engineering, Technische Universität Ilmenau, 98693 Ilmenau, Germany
2
Compliant Systems Group, Department of Mechanical Engineering, Technische Universität Ilmenau, 98693 Ilmenau, Germany
3
Process Measurement Technology Group, Institute of Process Measurement and Sensor Technology, Department of Mechanical Engineering, Technische Universität Ilmenau, 98693 Ilmenau, Germany
*
Author to whom correspondence should be addressed.
Actuators 2018, 7(4), 86; https://doi.org/10.3390/act7040086
Received: 30 October 2018 / Revised: 3 December 2018 / Accepted: 4 December 2018 / Published: 6 December 2018
(This article belongs to the Special Issue Design and Control of Compliant Manipulators)
Compliant mechanisms based on flexure hinges are widely used in precision engineering applications. Among those are devices such as precision balances and mass comparators with achievable resolutions and uncertainties in the nano-newton range. The exact knowledge of the mechanical properties of notch hinges and their modeling is essential for the design and the goal-oriented adjustment of these devices. It is shown in this article that many analytical equations available in the literature for calculating the bending stiffness of thin semi-circular flexure hinges cause deviations of up to 12% compared to simulation results based on the three-dimensional finite element model for the considered parameter range. A close examination of the stress state within the loaded hinge reveals possible reasons for this deviation. The article explains this phenomenon in detail and shows the limitations of existing analytical models depending on specific geometric ratios. An accurate determination of the bending stiffness of semi-circular flexure hinges in a wide range of geometric parameters without the need for an elaborate finite element analysis is proposed in form of FEM-based correction factors for analytical equations referring to Euler-Bernoulli’s beam theory. View Full-Text
Keywords: compliant mechanism; flexure hinge; bending stiffness; finite element method compliant mechanism; flexure hinge; bending stiffness; finite element method
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Torres Melgarejo, M.A.; Darnieder, M.; Linß, S.; Zentner, L.; Fröhlich, T.; Theska, R. On Modeling the Bending Stiffness of Thin Semi-Circular Flexure Hinges for Precision Applications. Actuators 2018, 7, 86.

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