Planetary gear assembly conditions

A planetary set can have the right ratio on paper and still be impossible to build. Three rules decide whether the planets fit between the sun and ring, sit evenly around the carrier, and clear each other. All three are checks on tooth counts.

1. Coaxial condition

Each planet meshes with the sun on one side and the ring on the other, so the sun–planet centre distance must equal the planet–ring centre distance. For gears of the same module with no profile shift, that reduces to:

So you choose any two counts and the third follows. With a 19-tooth sun and a 71-tooth ring the planets need (71 − 19) / 2 = 26 teeth. If Zr − Zs is odd there is no whole planet count, and the set only works with profile shift or a non-standard centre distance.

2. Equal spacing condition

The planets are identical, so each must meet the sun and ring at the same point in the tooth pattern. That is only possible at carrier angles that are whole multiples of 360° / (Zs + Zr). To place N planets evenly at 360° / N:

For 19 + 71 = 90 teeth, 2, 3, 5 and 6 planets divide evenly and 4 does not. When the sum does not divide, planets can still go in at the nearest allowed angles, but the spacing comes out slightly uneven. That leaves the carrier out of balance and the planets sharing load unequally. GearStudio places planets this way and flags the uneven case.

3. Neighbour (adjacency) condition

Adjacent planets must not touch. Their centres sit on a circle of radius a = m · (Zs + Zp) / 2, so the distance between neighbours is the chord 2a · sin(180° / N). It must be larger than the planet's outside diameter:

That form assumes standard full-depth teeth (addendum of one module) and no profile shift. Leave real clearance above zero: the planet carrier, bearings and any planet pins need room too.

How many planets fit around the sun?

For a 19-tooth sun, 26-tooth planets and a 71-tooth ring, the centre distance is 22.5 modules and the planet outside diameter is 28 modules.

Three planets is the practical answer for this set. Four would fit physically, but two pairs would sit 88° apart and two 92°.

What are hunting teeth, and do they matter?

One more check is not required for assembly but affects wear. If the sun and planet counts share a common factor, the same pairs of teeth meet over and over, so any defect on one tooth repeatedly hits the same few mating teeth. Counts with no common factor (19 and 26, or 26 and 71) spread contact across every tooth. GearStudio reports this for both meshes.

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