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CALCULATORS / GEARS AND GEAR TRAINS

Gearbox arrangement and envelope calculator

Two external spur outside circles plus supplied housing clearance.

gears-gearbox-envelope.napkin / editable
✓ checks pass
GEARBOX ENVELOPEA20 teethB40 teethHousing 134 × 94 mmClearance 5 mm · centers 60 mm

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.

housing length budget134.00 mm✓ passes
whole teethA0.00 ✓ passes
positive teethA20.00 ✓ passes
whole teethB0.00 ✓ passes
positive teethB40.00 ✓ passes

BASELINE INPUTS

CALCULATED

center60 mm
length134 mm
height94 mm

Edits change the baseline source.

Calculated from your source · not saved
Baseline · Baseline
housing length budget134.00 mm ✓ passes
whole teethA0.00 ✓ passes
positive teethA20.00 ✓ passes
whole teethB0.00 ✓ passes
positive teethB40.00 ✓ passes
alternative · alternative
housing length budget109.20 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.

center
center = module*(teethA+teethB)/2 [mm]
length
length = center+module*(teethA+teethB+4)/2+2*clearance [mm]
height
height = module*(max(teethA,teethB)+2)+2*clearance [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
clearance
5 mm

Calculated

center
60 mm
length
134 mm
height
94 mm

Assumptions and limits

Two external spur outside circles plus supplied housing clearance.

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: Gearbox arrangement and envelope. Inputs: ratios; gear sizes; shaft layout; wall margins. Outputs: packaging envelope; shaft positions. 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: ratios, gear sizes, shaft layout, wall margins
  • Outputs: packaging envelope, shaft positions
  • Modes: calculate, compare, sweep
  • Drawing: Animated gear assembly

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

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