Compound gear-train sizing calculator

Two ideal external gear pairs; losses supplied as one efficiency.

gears-compound-train.napkin / editable

SCENARIO COMPARISON

Compare the numbers.

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

Scenario	ratio	outputrpm	torqueMultiplier
	9	333.333	8.1
	11.25	266.667	10.125

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.

output speed target333.33 rpm✓ passes

BASELINE INPUTS

driverA20 drivenA60 driverB15 drivenB45 speed3000 rpmefficiency0.9

CALCULATED

ratio9

output333.33 rpm

torqueMultiplier8.1

Edits change the baseline source.

THE SOURCE

Edits below update the same model.

# Compound gear-train sizing
# Scope: Two ideal external gear pairs; losses supplied as one efficiency.
# Status: illustrative worked example; engineering review pending.
# Inputs are example values. Checks are editable example requirements, not standards.

driverA = 20
drivenA = 60
driverB = 15
drivenB = 45
speed = 3000 rpm
efficiency = 0.9

ratio := drivenA*drivenB/(driverA*driverB)
output := speed/ratio [rpm]
torqueMultiplier := ratio*efficiency

check output speed target: output >= 300 rpm

scenario alternative: driverA = 16

Calculated from your source · not saved

Baseline · Baseline

output speed target333.33 rpm ✓ passes

alternative · alternative

output speed target266.67 rpm × fails

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.

ratio: ratio = drivenA*drivenB/(driverA*driverB)
output: output = speed/ratio [rpm]
torque multiplier: torqueMultiplier = ratio*efficiency

Original worked example

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

Given

driver a: 20
driven a: 60
driver b: 15
driven b: 45
speed: 3000 rpm
efficiency: 0.9

Calculated

ratio: 9
output: 333.333 rpm
torque multiplier: 8.1

Assumptions and limits

Two ideal external gear pairs; losses supplied as one efficiency.

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: Compound gear-train sizing. Inputs: target ratio; allowed stages and tooth counts. Outputs: feasible tooth combinations; stage ratios. Model scope: Rigid involute-gear kinematics; qualified stress approximations. 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: target ratio, allowed stages and tooth counts
Outputs: feasible tooth combinations, stage ratios
Modes: calculate, compare, sweep
Drawing: Animated gear assembly

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