CALCULATORS / SPRINGS AND ELASTIC ENERGY

Torsion-spring rate calculator

Supplied angular spring rate; linear range only.

springs-torsion.napkin / editable

SCENARIO COMPARISON

Compare the numbers.

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

Scenario	torqueN*m
	0.020472
	0.0183776

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.

torque budget0.02 N*m✓ passes

BASELINE INPUTS

rate0.02 N*m/radangle30 degpreload0.01 N*m

CALCULATED

torque0.020472 N*m

Edits change the baseline source.

THE SOURCE

Edits below update the same model.

# Torsion-spring rate
# Scope: Supplied angular spring rate; linear range only.
# Status: illustrative worked example; engineering review pending.
# Inputs are example values. Checks are editable example requirements, not standards.

rate = 0.02 N*m/rad
angle = 30 deg
preload = 0.01 N*m

torque := preload+rate*angle [N*m]

check torque budget: torque <= 0.04 N*m

scenario alternative: rate = 0.016 N*m/rad

Calculated from your source · not saved

Baseline · Baseline

torque budget0.02 N*m ✓ passes

alternative · alternative

torque budget0.02 N*m ✓ 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.

torque: torque = preload+rate*angle [N*m]

Original worked example

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

Given

rate: 0.02 N*m/rad
angle: 30 deg
preload: 0.01 N*m

Calculated

torque: 0.020472 N*m

Assumptions and limits

Supplied angular spring rate; linear range only.

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: Torsion-spring rate. Inputs: wire size; coil diameter; turns; elastic modulus. Outputs: angular rate; torque; stress screening. Model scope: Linear elasticity within the declared material range. 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: wire size, coil diameter, turns, elastic modulus
Outputs: angular rate, torque, stress screening
Modes: calculate, compare, sweep
Drawing: Spring deformation

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