Helical-gear geometry and forces calculator

Normal-to-transverse module conversion for a helical gear.

gears-helical.napkin / editable

SCENARIO COMPARISON

Compare the numbers.

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

Scenario	transverseModulemm	pitchmm
	2.12836	63.8507
	1.70268	51.0805

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.

pitch diameter budget63.85 mm✓ passes

BASELINE INPUTS

normalModule2 mmhelix20 degteeth30

CALCULATED

transverseModule2.1284 mm

pitch63.851 mm

Edits change the baseline source.

THE SOURCE

Edits below update the same model.

# Helical-gear geometry and forces
# Scope: Normal-to-transverse module conversion for a helical gear.
# Status: illustrative worked example; engineering review pending.
# Inputs are example values. Checks are editable example requirements, not standards.

normalModule = 2 mm
helix = 20 deg
teeth = 30

transverseModule := normalModule/cos(helix) [mm]
pitch := transverseModule*teeth [mm]

check pitch diameter budget: pitch <= 70 mm

scenario alternative: normalModule = 1.6 mm

Calculated from your source · not saved

Baseline · Baseline

pitch diameter budget63.85 mm ✓ passes

alternative · alternative

pitch diameter budget51.08 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.

transverse module: transverseModule = normalModule/cos(helix) [mm]
pitch: pitch = transverseModule*teeth [mm]

Original worked example

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

Given

normal module: 2 mm
helix: 20 deg
teeth: 30

Calculated

transverse module: 2.12836 mm
pitch: 63.8507 mm

Assumptions and limits

Normal-to-transverse module conversion for a helical gear.

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: Helical-gear geometry and forces. Inputs: normal module; helix angle; teeth; torque. Outputs: pitch geometry; axial and radial forces. 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: normal module, helix angle, teeth, torque
Outputs: pitch geometry, axial and radial forces
Modes: calculate, compare, sweep
Drawing: Animated gear assembly

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