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Epicyclic (planetary) gear train: sun 24, planets 18, ring 60

How does a planetary gear train get its ratio? · Hardware · basis: Xem Studio design following Brown No. 502 (1868)

Also called: planetary gear, epicyclic gear, planetary gearbox, sun planet ring gear, tren de engranajes epicicloidal, Planetengetriebe

Exact dimensions. True size, with no printing tolerance added.

sizes
5 in table

Notes

  • A sun gear, three planets on a carrier and a ring gear: hold the ring and drive the sun, and the carrier turns at 1/(1 + N_ring/N_sun) = 24/84 of sun speed (3.5 : 1) in the same direction.
  • Tooth counts satisfy N_ring = N_sun + 2·N_planet (60 = 24 + 36) and (N_sun + N_ring)/planets = 84/3 = 28 (whole), so three equally spaced planets mesh with both at once — checked here at the drawn pose.
  • Hold the carrier instead and the ring turns backwards at 24/60; hold the sun and ring-to-carrier is 60/84. Brown's Nos. 502–507 are the epicyclic trains.
  • Parts (each has its own page): internal-ring-gear-m1-60t, spur-gears-module-1, planet-carrier-3x-r21, dowel-pins-metric.
  • Brown's movement No. 502 (1868) shows it; this model is a Xem Studio design following his figure, every part at true size.

Epicyclic (planetary) gear train: sun 24, planets 18, ring 60 size chart

parametervalue
sun24 T (Ø8 bore)
planets3 × 18 T on Ø5 dowels
ring60 T internal
carrier radius21 mm
ratio, ring fixed3.5 : 1 sun to carrier

Where the files are

Other publishers' files are linked, not hosted. "verify" = check the license at the link before commercial use.

Henry T. Brown (1868, public domain)Five Hundred and Seven Mechanical Movements — scan on archive.orgwebPublisher's page; dimensions are facts
507movements.comBrown's movement No. 502: figure, his text and an animationwebPublisher's page; dimensions are facts

Free files

★ Free files 1 parts. Generated by Xem Studio from the standard; threads are plain cylinders at major diameter. CC BY 4.0. index.json

epicyclic-gear-train-mechanism-assemblyAssembled mechanism, all parts placed at one pose (STEP keeps each part separate)STEP · STL
Let your AI pull this. Add https://xemstudio.com/mcp to Claude, ChatGPT, Cursor or any MCP client (free, no account, one minute) and it can look up exact sizes, mating fits and free STEP/STL from every chat.
Set it up →

Plain text: sheet.txt · JSON: /api/geometry?object=epicyclic-gear-train-mechanism

Epicyclic (planetary) gear train: sun 24, planets 18, ring 60, isometric render of a generated part
Render of epicyclic-gear-train-mechanism-assembly from the free STEP; not to scale.

Fits with

Internal (ring) gear, module 1, 60 teeth, Ø80, isometric render of a generated part
Internal (ring) gear, module 1, 60 teeth, Ø8080.0×80.0×8.0 mm★ 1 file
Spur gears, module 1: 10 to 80 teeth (20° involute), isometric render of a generated part
Spur gears, module 1: 10 to 80 teeth (20° involute)26 sizes★ 26 files
Planet carrier for three planets on a 21 mm radius (Ø52 × 5), isometric render of a generated part
Planet carrier for three planets on a 21 mm radius (Ø52 × 5)52.0×52.0×5.0 mm★ 1 file
Dowel pins, 2–6 mm (ISO 2338 / DIN 6325), isometric render of a generated part
Dowel pins, 2–6 mm (ISO 2338 / DIN 6325)5 sizes★ 23 files

Questions

How does a planetary gear train get its ratio?

A sun gear, three planets on a carrier and a ring gear: hold the ring and drive the sun, and the carrier turns at 1/(1 + N_ring/N_sun) = 24/84 of sun speed (3.5 : 1) in the same direction.

What is the ratio of a planetary gear with the ring fixed?

1 + N_ring/N_sun from sun to carrier: 1 + 60/24 = 3.5 here.