Follow one contact
These gears mesh on the outside, and you view both from the same side. Gear A has 18 teeth and turns clockwise at 60 RPM, or revolutions per minute. Gear B has 36 teeth.
B turns in the opposite direction. It has twice as many teeth, so it turns half as fast: 60 × 18 ÷ 36 = 30 RPM, counterclockwise.
In a simple train with no shared shafts, an intermediate gear changes the direction again. Its tooth count cancels from the overall speed ratio. This shortcut does not apply to compound trains with different gears on a shared shaft.
Twice as many teeth, half the speed.
Keep speed across a shared shaft
A has 12 teeth and turns clockwise at 60 RPM. It meshes with B, which has 36 teeth. B turns at 60 × 12 ÷ 36 = 20 RPM, counterclockwise.
B and C are fixed to the same shaft. C has 18 teeth, but it still turns at 20 RPM in the same direction as B. A shared shaft changes neither speed nor direction.
C meshes with D, which has 12 teeth. D turns at 20 × 18 ÷ 12 = 30 RPM, clockwise. There are two meshing contacts, so the direction reverses twice.
Keep a ratio for each mesh: 60 × (12 ÷ 36) × (18 ÷ 12) = 30 RPM. Comparing only A and D would wrongly give 60 RPM. Different tooth counts on B and C make the extra ratio matter.
B and C share a shaft. Only meshing contacts reverse direction.
Follow two shared shafts
A has 24 teeth and turns clockwise at 60 RPM. Follow the train to F. B and C share a shaft; D and E share another shaft. The tooth counts are shown below the diagram.
At a mesh, reverse direction and multiply by driving teeth ÷ driven teeth. At a shared shaft, copy both speed and direction. Work through each connection before choosing F’s motion.
B and C share a shaft. D and E share another.
Try it
How fast, and in which direction, does F turn?
- 120 RPM · Clockwise
- 120 RPM · Counterclockwise
Show the answer
120 RPM · Counterclockwise
Correct. 60 × (24 ÷ 12) × (18 ÷ 36) × (24 ÷ 12) = 120 RPM. The three meshes make F turn counterclockwise. Each shared shaft preserves speed and direction.
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