Planetary Gear Sets: The Fixed Member Changes the Speed Relation

Choose the reference member

Carnegie Mellon’s mechanism tutorial explains planetary motion by considering gear speeds relative to the carrier. The carrier’s motion makes the relation different from a fixed-axis train. Primary reference: planetary gear train analysis.

An epicyclic arrangement must identify what is fixed and which members provide input and output. Tooth counts alone cannot fill those roles. A diagram that names only the sun and ring therefore leaves the speed calculation incomplete.

A fictional sun-ring example

Assume a simple ideal sun/planet/internal-ring set with sun 30 teeth and ring 90 teeth. Its relative-speed relation is (ωₛ−ω꜀)/(ωᵣ−ω꜀) = −90/30. With the ring fixed and sun at 400 RPM, solving gives carrier speed 100 RPM in the same sense.

With the carrier fixed instead and sun still at 400 RPM, the ring is approximately −133.33 RPM. The identical tooth counts now produce a different output speed and direction because the fixed member changed. These invented rows are not specifications for a supplied gearbox.

Keep the member ledger

Record sun, ring and carrier identities, their constrained or driven states and the output requested. Preserve a consistent sign convention beside the equation. If more members can move independently, an additional constraint may be needed rather than one guessed fixed member.

Ask the supplier which arrangement its ratio label describes. Capacity, efficiency and compatible planet geometry remain separate from this kinematic relation. This guide provides no instructions to lock a gearbox member or alter a machine transmission; it clarifies the assumptions needed to interpret an offered planetary ratio.

Customer Questions

Primary References

These references support the technical principles discussed in this guide. The worked examples and review questions are educational.

• Primary reference: planetary gear train analysis