Worm-drive ratio and efficiency calculator

Ideal worm speed ratio with supplied efficiency; no self-locking prediction.

gears-worm.napkin / editable

SCENARIO COMPARISON

Compare the numbers.

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

Scenario	ratio	speedrpm	torqueN*m
	20	75	12
	40	37.5	24

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 torque target12.00 N*m✓ passes

BASELINE INPUTS

starts2 wheelTeeth40 inputSpeed1500 rpminputTorque1 N*mefficiency0.6

CALCULATED

ratio20

speed75 rpm

torque12 N*m

Edits change the baseline source.

THE SOURCE

Edits below update the same model.

# Worm-drive ratio and efficiency
# Scope: Ideal worm speed ratio with supplied efficiency; no self-locking prediction.
# Status: illustrative worked example; engineering review pending.
# Inputs are example values. Checks are editable example requirements, not standards.

starts = 2
wheelTeeth = 40
inputSpeed = 1500 rpm
inputTorque = 1 N*m
efficiency = 0.6

ratio := wheelTeeth/starts
speed := inputSpeed/ratio [rpm]
torque := inputTorque*ratio*efficiency [N*m]

check output torque target: torque >= 10 N*m

scenario alternative: starts = 1

Calculated from your source · not saved

Baseline · Baseline

output torque target12.00 N*m ✓ passes

alternative · alternative

output torque target24.00 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.

ratio: ratio = wheelTeeth/starts
speed: speed = inputSpeed/ratio [rpm]
torque: torque = inputTorque*ratio*efficiency [N*m]

Original worked example

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

Given

starts: 2
wheel teeth: 40
input speed: 1500 rpm
input torque: 1 N*m
efficiency: 0.6

Calculated

ratio: 20
speed: 75 rpm
torque: 12 N*m

Assumptions and limits

Ideal worm speed ratio with supplied efficiency; no self-locking prediction.

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: Worm-drive ratio and efficiency. Inputs: starts; wheel teeth; lead angle; friction. Outputs: ratio; conditional efficiency; self-lock screening. 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: starts, wheel teeth, lead angle, friction
Outputs: ratio, conditional efficiency, self-lock screening
Modes: calculate, compare, sweep
Drawing: Animated gear assembly

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