Gears and gear ratios explained for aptitude tests

Gear questions turn up in almost every mechanical aptitude test, including the mechanical comprehension section of the EIAT. They look fiddly, but nearly all of them come down to three rules. Learn those and you can answer most gear questions in seconds, without any arithmetic.

Rule 1: meshed gears turn in opposite directions

When the teeth of two gears are locked together, one gear pushes the other round the opposite way. If the first turns clockwise, the second turns counterclockwise.

In a row of gears, the direction flips at every mesh. So:

• The first, third, fifth gear (and so on) all turn the same way.
• The second, fourth, sixth gear all turn the opposite way.

That is the quickest way to answer a long gear train: count along the row. An odd-numbered gear matches the first; an even-numbered gear is reversed.

Rule 2: an idler gear changes direction, not speed

A gear placed between two others just to connect them is called an idler. It reverses the direction one more time, but it does not change the overall speed ratio between the first and last gears. That ratio depends only on the tooth counts of the first and last gear.

Test questions like idlers because they look as if they should matter. Their size does not affect the final speed; their only effect is on direction.

Rule 3: fewer teeth means faster

Every tooth that passes the meshing point on one gear pushes exactly one tooth on the other. So a small gear has to make more turns to keep up with a large one.

The speed ratio is the tooth ratio turned upside down:

• A 20-tooth gear driving a 40-tooth gear: the 40-tooth gear turns half as fast — one turn for every two of the small gear.
• A 36-tooth gear driving a 12-tooth gear: the 12-tooth gear turns three times as fast.

If a question gives diameters instead of teeth, the same rule applies: the smaller gear turns faster.

Speed and turning force trade off

You cannot get something for nothing. When a small gear drives a larger one, the larger gear turns more slowly but with more turning force (torque). When a large gear drives a small one, you gain speed and lose turning force. That is why low gears in a vehicle make it easier to climb hills: the engine turns fast, the wheels turn slowly, and the wheels get more force.

Gears on the same shaft

Two gears fixed to the same shaft always turn in the same direction at the same speed, whatever their sizes — they are effectively one part. This appears in compound gear trains, where a small and a large gear share a shaft to multiply the ratio. Treat each shared shaft as a single turning unit and apply the three rules either side of it.

Belts, chains and racks

• A belt or chain running around two wheels makes both turn the same way — unlike meshed gears. Bicycles are the everyday example.
• A crossed belt, twisted into a figure eight, makes them turn in opposite directions.
• A rack and pinion turns rotation into straight-line movement: a gear (the pinion) runs along a toothed bar (the rack). Which way the rack moves depends on which side of the gear it sits: picture the teeth at the point where they meet, and the rack moves the same way those teeth are moving.

A worked example

Four gears sit in a row. Gear 1 has 12 teeth and turns clockwise. Gears 2 and 3 are idlers. Gear 4 has 24 teeth. Which way does gear 4 turn, and how fast compared with gear 1?

Direction: gear 4 is an even-numbered gear, so it turns the opposite way to gear 1 — counterclockwise.

Speed: ignore the idlers. Gear 1 has 12 teeth and gear 4 has 24, so gear 4 turns half as fast.

Practice

The mechanical section of our EIAT practice includes gear trains, gear pairs and racks, each drawn as a diagram with the reasoning written out.