Rule of thumb · MechanicalNº 44 / 149

One planetary set, three ratios — pick which member you hold

Hold the ring and a sun-in, carrier-out set reduces by 1 + ring/sun. Hold the sun instead and the same metal gives 1 + sun/ring. Hold the carrier and it reverses, at ring/sun. Same three gears, three different answers.

Why it works

A planetary set has three connections and only two independent speeds, so it is not a ratio until you hold something. Grounding a different member changes which two shafts are left to trade speed for torque. That is why an automatic gearbox can change gear with brakes and clutches alone, never sliding a gear in or out — and a 24-tooth sun in a 72-tooth ring gives 4:1, 1.33:1 or −3:1 depending on nothing but which member is held.

When it fails

It stops being a single ratio the moment you release everything: with two members driven the set becomes a differential and the third shaft takes whatever speed the other two dictate. And the sign convention only works because the ring is an internal mesh — swap in an external gear and the direction result inverts.

Do it exactly

Estimate with the rule, then check it against the calculator that models it properly.

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How do you work out a planetary gear ratio?

Hold the ring and a sun-in, carrier-out set reduces by 1 + ring/sun. Hold the sun instead and the same metal gives 1 + sun/ring. Hold the carrier and it reverses, at ring/sun. Same three gears, three different answers. A planetary set has three connections and only two independent speeds, so it is not a ratio until you hold something.

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