KEVOS® MAKEOS · Gears
Planetary Gear Train
What ratio, output speed and torque does this planetary (epicyclic) gear set give?
Ratio, output speed and torque of a simple planetary gear set with the ring, sun or carrier held, the planet tooth count and the equal-spacing assembly check.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Sun teeth | teeth | Teeth on the sun gear. |
| Ring teeth | teeth | Teeth on the internal ring gear. |
| Number of planets | planets | Number of equally spaced planets. |
| Arrangement | choice | Which member is held, which is the input and which is the output. |
| Input speed | rpm | Input speed. |
| Input torque | N·m | Input torque. |
| Efficiency | % | Overall efficiency of the stage. |
Method and formulas
- Planet teeth = (Zr − Zs) ÷ 2 (standard gears, same module).
- Ring fixed: i = 1 + Zr/Zs. Sun fixed: i = 1 + Zs/Zr. Carrier fixed: i = −Zr/Zs (output reverses).
- Equal spacing requires (Zs + Zr) ÷ number of planets to be a whole number.
- Example: sun 24, ring 72 with the ring fixed gives 4:1 and 375 rpm.
Limitations
- Standard, unshifted gears of one module; profile-shifted sets can break the planet-count rule.
- Load sharing between planets is assumed equal.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Design or check a planetary reduction
- Choose tooth counts that assemble
- Find speed and torque at the output
Who it is for
- Gear designers
- Machinists
- Maintenance engineers
What you get
- Planet teeth
- Ratio and direction
- Output speed and torque
- Assembly check
Interpreting the result
- Check each mesh (sun–planet and planet–ring) for strength with its own tangential force.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2211, 2122–2160. Topic reference; no source tables or recommended settings are reproduced.
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