Schreyer, B.
, Keck, L.
, Pratt, J.
and Schlamminger, S.
(2026),
Stable numerical technique to calculate the bending of flexures with extreme aspect ratios, Measurement Science & Technology, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=960242
(Accessed March 26, 2026)
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
Secure .gov websites use HTTPS
A lock (
) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.
Stable numerical technique to calculate the bending of flexures with extreme aspect ratios
Published
Author(s)
, Lorenz Keck, ,
Abstract
In designing single-sided clamped flexures as part of torsion balances or pendulums for scientific use, structures become thin and long and semi-analytic calculations of their bending become infeasible with standard double-precision variables. Semi-analytic calculations can be more efficient than finite element methods, allowing faster design optimization. We present straightforward analytical results demonstrating that the failure of the semi-analytic bending simulation, computed using double precision, arises from the exponential growth of the bending angle. To address this issue, we developed a Runge-Kutta 45 integration scheme combined with a semi-analytic bending model which successfully yields accurate results where standard double-precision bending model implementations fail.Citation
Measurement Science & Technology
Pub Type
Journals
Download Paper
Keywords
arbitrary precision, compliant mechanism, double precision, Euler-Bernoulli beam, Runge-Kutta
Citation
Issues
If you have any questions about this publication or are having problems accessing it, please contact [email protected].
Created March 19, 2026, Updated March 25, 2026