# Print-in-place: planetary gearbox, herringbone, 4 : 1

> How do you 3D print a planetary gearbox already assembled?

- Category: 3D printing › Print-in-place mechanisms
- Kind: Hardware
- Basis: Xem Studio design; involute gearing per ISO 53 (20° basic rack), double helical 30°, normal module 1.5; one designed running gap of 0.40 mm
- Page: https://xemstudio.com/objects/print-in-place-planetary-gearbox/ · JSON: https://xemstudio.com/api/geometry?object=print-in-place-planetary-gearbox · Plain text: https://xemstudio.com/objects/print-in-place-planetary-gearbox/sheet.txt
- License: dimension sheet CC BY 4.0 (Xem Studio); files Xem Studio Design License (free to use and sell from, not to redistribute as files: https://xemstudio.com/license/)
- Use in every chat: add https://xemstudio.com/mcp as a connector (https://xemstudio.com/use-with-ai/)

## Overall (mm)

| length | width | height |
|---|---|---|
| 112.0 | 112.0 | 48.0 |

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

## Notes

- 3D print in place — prints already assembled, moving, in one job. Drawn at true size with no printer tolerance added; the 0.40 mm running gaps are part of the design.
- Running gap 0.40 mm per side, 0.80 mm on diameter — part of the design, drawn as is. On the 45° faces the same 0.40 mm is measured square to the face (0.57 mm along the axis).
- Bed: sun, three planets, ring and carrier all stand on the bed: the gears on their bottom faces, the carrier on its three pins (each a 45° cone in a planet's counterbore). The carrier grows up from the pins as three 45° cones that merge into one three-lobed dome above the gears.
- Support while printing: herringbone flanks lean 28° (base helix) and the carrier's underside is all 45° cone, 0.40 mm clear of the planet tops and bores; the sun's knob flares out at 45° above the carrier. Nothing is flat over air.
- Captured: the herringbone (two opposed 30° helices) locks each planet axially between sun and ring; each planet's 45° counterbore holds the carrier's pin base below it; the carrier's cones close over the planets above. Nothing can come out.
- Freeing it: hold the ring and turn the sun knob slowly in both directions until it runs smoothly (a screwdriver fits the slot); the carrier follows at a quarter of the speed.
- Motion: continuous; ratio 4 : 1 (sun : carrier, ring fixed); planets spin 1× the sun-relative-to-carrier speed. Checked in the transverse section through a quarter turn of the sun: min gap 0.454 mm in the section (≥ 0.40 square to the flanks).
- Involute teeth: 20° normal pressure angle, addendum 1.0 m, dedendum 1.25 m (ring: tips at 0.88 m inside the pitch circle, the catalog ring's rule); every tooth thinned so the running gap is 0.40 mm square to the flanks at the exact centre distance.

## Sizes

| key | value | what |
|---|---|---|
| gap_mm | 0.4 | running gap per side on every moving interface (radial, axial, under captured parts) — part of the design, not a tolerance |
| module_n_mm | 1.5 | normal module |
| helix_deg | 30.0 | herringbone (double helical), 20° normal pressure angle, ISO 53 basic rack |
| teeth_sun | 18 |  |
| teeth_planet | 18 | three planets |
| teeth_ring | 54 |  |
| face_w_mm | 12.0 | all gears |
| ratio | 4 : 1 | sun in, carrier out, ring fixed |
| center_distance_mm | 31.18 | sun to planet |
| flank_gap_mm | 0.4 | square to the tooth flanks: sun and planet teeth thinned 0.20 mm per flank (0.226 in the transverse section), ring spaces opened 0.238 (measured in the model: 0.401 sun–planet, 0.402 ring–planet) |
| pin_d_mm | 11.0 | carrier pins, 45° base cone Ø14 on the bed |
| bore_d_mm | 11.8 | planet bores, 45° counterbore below |
| ring_od_mm | 112 | 4 × Ø4.5 on Ø105 |
| height_mm | 48.0 | to the top of the sun knob |
| planet_axial_play_mm | 0.86 | herringbone end play (computed) |
| carrier_holes | 3 × Ø3.4 on Ø40 | output |
| sun_shaft_d_mm | 7.6 | runs in the carrier's Ø8.4 centre bore |

## Where the files are

- Xem Studio: [Print-in-place mechanism design (geometry computed in the generator)](https://xemstudio.com/) — web — Xem Studio design

## Free STEP/STL (7 parts, Xem Studio Design License, Xem Studio)

Index: https://xemstudio.com/files/hardware/print-in-place-planetary-gearbox/index.json · license: https://xemstudio.com/files/hardware/print-in-place-planetary-gearbox/LICENSE.md

- print-in-place-planetary-gearbox-assembly: [STEP](https://xemstudio.com/files/hardware/print-in-place-planetary-gearbox/print-in-place-planetary-gearbox-assembly.step) · [STL](https://xemstudio.com/files/hardware/print-in-place-planetary-gearbox/print-in-place-planetary-gearbox-assembly.stl) — The whole print as laid on the bed (6 bodies, already assembled); STEP keeps each moving body a separate solid
- print-in-place-planetary-gearbox-ring: [STEP](https://xemstudio.com/files/hardware/print-in-place-planetary-gearbox/print-in-place-planetary-gearbox-ring.step) · [STL](https://xemstudio.com/files/hardware/print-in-place-planetary-gearbox/print-in-place-planetary-gearbox-ring.stl) — Ring gear 54 teeth, herringbone, Ø112 × 12, 4 × Ø4.5
- print-in-place-planetary-gearbox-sun: [STEP](https://xemstudio.com/files/hardware/print-in-place-planetary-gearbox/print-in-place-planetary-gearbox-sun.step) · [STL](https://xemstudio.com/files/hardware/print-in-place-planetary-gearbox/print-in-place-planetary-gearbox-sun.stl) — Sun 18 teeth with shaft Ø7.6 and slotted knob
- print-in-place-planetary-gearbox-planet-1: [STEP](https://xemstudio.com/files/hardware/print-in-place-planetary-gearbox/print-in-place-planetary-gearbox-planet-1.step) · [STL](https://xemstudio.com/files/hardware/print-in-place-planetary-gearbox/print-in-place-planetary-gearbox-planet-1.stl) — Planet 18 teeth, Ø11.8 bore with 45° counterbore
- print-in-place-planetary-gearbox-planet-2: [STEP](https://xemstudio.com/files/hardware/print-in-place-planetary-gearbox/print-in-place-planetary-gearbox-planet-2.step) · [STL](https://xemstudio.com/files/hardware/print-in-place-planetary-gearbox/print-in-place-planetary-gearbox-planet-2.stl) — Planet 18 teeth, Ø11.8 bore with 45° counterbore
- print-in-place-planetary-gearbox-planet-3: [STEP](https://xemstudio.com/files/hardware/print-in-place-planetary-gearbox/print-in-place-planetary-gearbox-planet-3.step) · [STL](https://xemstudio.com/files/hardware/print-in-place-planetary-gearbox/print-in-place-planetary-gearbox-planet-3.stl) — Planet 18 teeth, Ø11.8 bore with 45° counterbore
- print-in-place-planetary-gearbox-carrier: [STEP](https://xemstudio.com/files/hardware/print-in-place-planetary-gearbox/print-in-place-planetary-gearbox-carrier.step) · [STL](https://xemstudio.com/files/hardware/print-in-place-planetary-gearbox/print-in-place-planetary-gearbox-carrier.stl) — Carrier: three Ø11 pins on 45° bases, 45° cone dome, Ø8.4 centre bore, 3 × Ø3.4

## Questions

**How are the gears kept from falling out?**

Herringbone teeth: the two opposed helices of each planet interlock with the sun and the ring, so no gear can slide axially; the carrier hangs on the planets by its 45° pin bases.

**What is the gear ratio?**

4 : 1 — sun 18 teeth, ring 54: carrier turns once for every 4 turns of the sun.

## Fits with

- [Print-in-place: captive wheel on a printed axle (Ø40 × 12)](https://xemstudio.com/objects/print-in-place-captive-wheel-axle/)
- [Print-in-place: barrel hinge, three knuckles, folds 180° (48.8 mm)](https://xemstudio.com/objects/print-in-place-barrel-hinge-180/)
- [Print-in-place: seven-knuckle hinge on a captive through-pin (58.4 mm)](https://xemstudio.com/objects/print-in-place-multi-knuckle-hinge/)
- [Print-in-place: captive turntable with V-ridge retention (Ø80 platter)](https://xemstudio.com/objects/print-in-place-captive-turntable/)
- [Print-in-place: linear slider on a dovetail rail with end stops (100 mm)](https://xemstudio.com/objects/print-in-place-dovetail-slider/)
- [Print-in-place: articulated chain, 6 links, 20 mm pitch](https://xemstudio.com/objects/print-in-place-articulated-chain/)
- [Print-in-place: captive ball joint, Ø24 ball, limited cone](https://xemstudio.com/objects/print-in-place-ball-joint/)
- [Print-in-place: push button with flexure return and click](https://xemstudio.com/objects/print-in-place-push-button-flexure/)