Follow a gear train

Reverse direction at each contact and use tooth counts to find the next speed.

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.

AB

Twice as many teeth, half the speed.

A: 18 teeth · 60 RPM · Clockwise
B: 36 teeth · 30 RPM · Counterclockwise

Add an intermediate gear

Add gear C with 12 teeth. B turns at 30 RPM, counterclockwise. At the next contact the direction reverses again, and C turns at 30 × 36 ÷ 12 = 90 RPM, clockwise.

A and C turn in the same direction because there are two contacts. The intermediate tooth count cancels in the overall speed calculation: 60 × 18 ÷ 12 = 90 RPM.

ABC

Two contacts reverse the direction twice.

A: 18 teeth · 60 RPM · Clockwise
B: 36 teeth · 30 RPM · Counterclockwise
C: 12 teeth · 90 RPM · Clockwise

Try a new pair

In this new pair, A has 24 teeth and turns clockwise at 30 RPM. B has 12 teeth.

Follow the contact to find B’s direction. Then compare the tooth counts to find its speed. Choose both parts together.

AB

Follow the single contact from A to B.

A: 24 teeth · 30 RPM · Clockwise
B: 12 teeth · To find

Try it

How fast, and in which direction, does B turn in this new pair?

  1. 30 RPM · Clockwise
  2. 60 RPM · Counterclockwise
Show the answer

60 RPM · Counterclockwise

Correct. One contact makes B turn counterclockwise. Its speed is 30 × 24 ÷ 12 = 60 RPM because it has half as many teeth as A.

Enable JavaScript to answer interactively and save your place.

Practice this method