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 May 6, 2026)
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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
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Keywords
arbitrary precision, compliant mechanism, double precision, Euler-Bernoulli beam, Runge-Kutta
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Created March 19, 2026, Updated March 25, 2026