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CALCULATORS / GEARS AND GEAR TRAINS

Planetary gear system calculator

Ideal fixed-ring sun-input planetary; integer tooth compatibility.

⌑ One ratio, three ways to hold it.PLANETARY SET / SPEEDS / FEASIBILITYG01
Hold one member, drive another, and the third follows.
SUN IN · 1200 rpmCARRIER OUT · 300.0 rpmPITCH CIRCLES · HEAVY LINE = HELD MEMBER
AXIAL VIEWIDEAL KINEMATICS
ASSUMPTIONS

Simple planetary set, one module, ideal rigid kinematics. A negative speed turns the other way. No efficiency, torque, bearing loads, backlash, tooth strength or profile shift.

gears-planetary.napkin / editable
✓ checks pass

SCENARIO COMPARISON

Compare the numbers.

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

ScenarioplanetratiooutputSpeedrpmoutputTorqueN*m
2042504
224.75210.5264.75

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.

planet tooth integer0.00 ✓ passes

BASELINE INPUTS

CALCULATED

planet20
ratio4
outputSpeed250 rpm
outputTorque4 N*m

Edits change the baseline source.

Calculated from your source · not saved
Baseline · Baseline
planet tooth integer0.00 ✓ passes
alternative · alternative
planet tooth integer0.00 ✓ 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.

planet
planet = (ring-sun)/2
ratio
ratio = 1+ring/sun
output speed
outputSpeed = inputSpeed/ratio [rpm]
output torque
outputTorque = inputTorque*ratio [N*m]

Original worked example

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

Given

sun
20
ring
60
input speed
1000 rpm
input torque
1 N*m

Calculated

planet
20
ratio
4
output speed
250 rpm
output torque
4 N*m

Assumptions and limits

Ideal fixed-ring sun-input planetary; integer tooth compatibility.

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: Planetary gear system. Inputs: sun, ring and planet teeth; held member; input member. Outputs: ratio; member speeds; geometry feasibility. 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: sun, ring and planet teeth, held member, input member
  • Outputs: ratio, member speeds, geometry feasibility
  • Modes: calculate, compare, sweep
  • Drawing: Animated gear assembly

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

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