A flexure bearing guides limited motion through elastic deformation rather than sliding or rolling contact. A thin blade or other compliant element bends as the moving body changes position. This calculator estimates blade stress under a constant-curvature assumption and compares it with an entered reference stress; it does not predict fatigue life or positioning accuracy.
Flexure Bearing Interactive Calculator
Compare blade length and ideal bending stress using thickness, length/thickness ratio and one-sided travel angle. The entered reference stress is not automatically a fatigue allowable.
Equation Used
The model assumes a thin blade with constant curvature θ/L, giving outer-fiber stress σ = E·t·θ/(2L). With the entered ratio q = L/t, this becomes Eθ/(2q). It is an ideal elastic result; root concentrations, other forces and boundary-condition changes are not included.
- The calculation uses a fixed illustrative elastic modulus E = 193000 MPa; it does not select material or temper.
- Blade bends with approximately constant curvature.
- Travel angle is the one-sided peak rotation from neutral.
- Stress concentration at the root fillet is not included.
Motion through elastic bending
A flexure stores elastic strain energy as it bends. Its geometry provides compliance in the desired direction and stiffness against other motions. There is no sliding or rolling bearing surface at the flexible element.
That avoids clearance backlash and contact friction at that element, but does not guarantee zero hysteresis or unlimited life. Material behavior, stress, assembly joints and the rest of the stage still affect performance.
A simple blade can translate as well as rotate. Cross-spring and compound arrangements can reduce unwanted motion, but the actual pivot path depends on the geometry. The drawing is a blade illustration, not a solved precision stage.
Limited-travel precision guidance
Flexures can guide small motions in positioning and optical mechanisms where contact friction or lubrication would be undesirable. The required travel, load and environment determine the design.
The calculator has no payload, blade width, damping or sensor model. It therefore cannot predict resolution, resonance frequency, actuator torque or the motion accuracy of a finished instrument.
Constant-curvature blade stress
Let q = L/t be the length/thickness ratio and θ the entered one-sided rotation converted from degrees to radians. The calculator sets L = tq and uses σ = Eθ/(2q), with E fixed at 193000 MPa.
This follows the small-strain elastic relation σ = Eκt/2 with curvature κ = θ/L. It assumes constant curvature along the active blade. A blade loaded by an end force, a notch flexure or an assembled cross-spring pivot may have a different stress distribution.
The final comparisons are 100σ/S percent and S/σ, where S is the entered reference stress. They do not validate S as a yield or fatigue limit. Stress concentration, residual stress and cyclic material data are absent.
Example: angle and length ratio
Enter thickness t = 0.25 mm, L/t = 100, one-sided travel θ = 3° and reference stress S = 280 MPa. Blade length is 25 mm, θ is 0.05236 rad, and ideal stress is 50.53 MPa.
The stress/reference percentage is 18.05% and reference/stress is 5.54. These are arithmetic comparisons, not a verified fatigue-life margin.
At the same ratio, increasing thickness also increases blade length, so ideal stress stays unchanged. Increasing angle to 6° doubles stress to 101.05 MPa. The tool does not calculate the blade stiffness or actuator torque.
Travel and geometry set the limits
Flexures offer motion without a rubbing bearing interface, but their deflection is limited by geometry and material behavior. A simple flexure cannot provide indefinite one-way rotation without accumulating deformation.
A real design also needs load, stability, stress concentration, fatigue and unwanted-motion checks. The constant-curvature comparison does not specify a universal blade thickness, fillet size, surface finish or operating life.
Frequently asked questions
Why does thickness not change ideal stress at fixed L/t?
Changing thickness at fixed ratio also changes length proportionally. In this model, t/L cancels and stress depends on angle and the ratio.
What does Reference stress mean?
It is a comparison value entered by the user. The tool does not derive a permissible yield or fatigue stress from material data.
Is this a cantilever end-force formula?
No. It assumes constant curvature. Other loading and boundary conditions can produce different peak stresses.
Does the tool calculate fatigue cycles?
No. It has no fatigue curve, mean-stress correction or stress-concentration input.
Can the result predict resonance?
No. Blade width, supported mass and damping are not inputs.
Are all flexure pivots fixed-axis mechanisms?
No. Some geometries have parasitic translation or center shift. Their motion must be evaluated from the actual configuration.
Further reading
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