Gear center distance calculator

External spur pair with matching module.

gears-center-distance.napkin / editable

Dashed circles mark pitch geometry. Tooth outlines are schematic, not manufacturing profiles. Labels come from the evaluated .napkin model.

GEARS / TOOTH SCHEMATICSAME SOURCE

Change an input to see the consequences.

center distance budget60.00 mm✓ passes

whole teethA0.00 ✓ passes

positive teethA20.00 ✓ passes

whole teethB0.00 ✓ passes

positive teethB40.00 ✓ passes

BASELINE INPUTS

module2 mmteethA20 teethB40

CALCULATED

distance60 mm

Edits change the baseline source.

THE SOURCE

Edits below update the same model.

# Gear center distance
# Scope: External spur pair with matching module.
# Status: illustrative worked example; engineering review pending.
# Inputs are example values. Checks are editable example requirements, not standards.

module = 2 mm
teethA = 20
teethB = 40

distance := module*(teethA+teethB)/2 [mm]

check center distance budget: distance <= 70 mm

scenario alternative: module = 1.6 mm


# Diagram dimensions are illustrative; teeth are schematic, not manufacturing profiles.
check whole teethA: abs(teethA-round(teethA)) <= 0
check positive teethA: teethA >= 3
check whole teethB: abs(teethB-round(teethB)) <= 0
check positive teethB: teethB >= 3

Calculated from your source · not saved

Baseline · Baseline

center distance budget60.00 mm ✓ passes

whole teethA0.00 ✓ passes

positive teethA20.00 ✓ passes

whole teethB0.00 ✓ passes

positive teethB40.00 ✓ passes

alternative · alternative

center distance budget48.00 mm ✓ passes

whole teethA0.00 ✓ passes

positive teethA20.00 ✓ passes

whole teethB0.00 ✓ passes

positive teethB40.00 ✓ 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.

distance: distance = module*(teethA+teethB)/2 [mm]

Original worked example

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

Given

module: 2 mm
teeth a: 20
teeth b: 40

Calculated

distance: 60 mm

Assumptions and limits

External spur pair with matching module.

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: Gear center distance. Inputs: modules; tooth counts; internal or external mesh. Outputs: nominal shaft spacing. 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: modules, tooth counts, internal or external mesh
Outputs: nominal shaft spacing
Modes: calculate, compare, sweep
Drawing: Animated gear assembly

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

Gear center distance calculator

Formula and units

Original worked example

Given

Calculated

Assumptions and limits

Take it further with your agent

The broader study

More in gears and gear trains