Flexure hinge and compliant motion calculator

Small-deflection rectangular cantilever flexure; end transverse force.

linkages-flexure.napkin / editable

SCENARIO COMPARISON

Compare the numbers.

This source describes an analytical model. Its quantities and checks are the view.

Scenario	inertiamm^4	deflectionmm	stressMPa
	0.104167	1.024	96
	0.104167	0.524288	76.8

All calculated quantities are listed with the inputs. Switch to Source to inspect the equations.

SCENARIOS / CALCULATED VALUESSAME SOURCE

Change an input to see the consequences.

elastic stress budget96.00 MPa✓ passes

BASELINE INPUTS

length40 mmwidth10 mmthickness0.5 mmforce1 Nmodulus200 GPa

CALCULATED

inertia0.10417 mm^4

deflection1.024 mm

stress96 MPa

Edits change the baseline source.

THE SOURCE

Edits below update the same model.

# Flexure hinge and compliant motion
# Scope: Small-deflection rectangular cantilever flexure; end transverse force.
# Status: illustrative worked example; engineering review pending.
# Inputs are example values. Checks are editable example requirements, not standards.

length = 40 mm
width = 10 mm
thickness = 0.5 mm
force = 1 N
modulus = 200 GPa

inertia := width*thickness^3/12 [mm^4]
deflection := force*length^3/(3*modulus*inertia) [mm]
stress := 6*force*length/(width*thickness^2) [MPa]

check elastic stress budget: stress <= 250 MPa

scenario alternative: length = 32 mm

Calculated from your source · not saved

Baseline · Baseline

elastic stress budget96.00 MPa ✓ passes

alternative · alternative

elastic stress budget76.80 MPa ✓ passes

Illustrative first-order example. Checks are editable requirements, not design standards. The broader topic may require additional equations, data, and validation.

Formula and units

This example uses the following equations. Input names and units match the editable source above.

inertia: inertia = width*thickness^3/12 [mm^4]
deflection: deflection = force*length^3/(3*modulus*inertia) [mm]
stress: stress = 6*force*length/(width*thickness^2) [MPa]

Original worked example

These are the baseline values in the downloadable source. Edits above let you test your own values.

Given

length: 40 mm
width: 10 mm
thickness: 0.5 mm
force: 1 N
modulus: 200 GPa

Calculated

inertia: 0.104167 mm^4
deflection: 1.024 mm
stress: 96 MPa

Assumptions and limits

Small-deflection rectangular cantilever flexure; end transverse force.

The requirement checks use the limits written in this example. Passing a check does not establish that the model covers every load, material behavior, or operating condition in a real design.

Download this .napkin example ↓

Take it further with your agent

Napkin keeps the inputs, equations, checks and assumptions together in one study. Your agent sets it up; you change the numbers.

Try with Claude ↗

codex 'Use Napkin (https://napkin.engineering/mcp, or the local Napkin plugin) to build a study: Flexure hinge and compliant motion. Inputs: beam geometry; modulus; desired rotation or displacement. Outputs: stiffness; force; strain screening. Model scope: Planar rigid-link geometry with explicit joints and branches. Read napkin_capabilities and the current snapshot. Ask me for the values that matter, label assumptions with units, author .napkin source, validate it and apply it with napkin_source using the current revision, then open the study. Add checks for the limits I supply. Keep unsupported analyses explicit.'

Claude needs the Napkin connector; Codex needs the Napkin plugin. Set up your agent ↗

The broader study

The topic brief below describes the broader scope. The worked example above states the particular calculation it implements.

Inputs: beam geometry, modulus, desired rotation or displacement
Outputs: stiffness, force, strain screening
Modes: calculate, compare, sweep
Drawing: Interactive linkage

EXECUTABLE WORKED EXAMPLE · FIRST-ORDER MODEL · CHECK THE SCOPE & ASSUMPTIONS