Gearbox arrangement and envelope calculator

Two external spur outside circles plus supplied housing clearance.

gears-gearbox-envelope.napkin / editable

SCENARIO COMPARISON

Compare the numbers.

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

Scenario	centermm	lengthmm	heightmm
	60	134	94
	48	109.2	77.2

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.

housing length budget134.00 mm✓ passes

BASELINE INPUTS

module2 mmteethA20 teethB40 clearance5 mm

CALCULATED

center60 mm

length134 mm

height94 mm

Edits change the baseline source.

THE SOURCE

Edits below update the same model.

# Gearbox arrangement and envelope
# Scope: Two external spur outside circles plus supplied housing clearance.
# 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
clearance = 5 mm

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

check housing length budget: length <= 150 mm

scenario alternative: module = 1.6 mm

Calculated from your source · not saved

Baseline · Baseline

housing length budget134.00 mm ✓ passes

alternative · alternative

housing length budget109.20 mm ✓ 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