Gears

Gears are levers that go round and round, and they make exactly the same trade: force for distance, which in rotation is torque for speed.

Direction

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Two meshed gears turn in opposite directions. Where the teeth meet, one gear's surface moves up while the other's moves down, so the rotations must oppose.

In a train of gears, the direction alternates. Gear 1 one way, gear 2 the other, gear 3 the first way again.

So an odd number of gears means the last turns the same way as the first; an even number means it turns the opposite way. That is the fastest way to answer a direction question about a long train: count the gears.

An idler gear is any gear between the driver and the driven one whose only job is to reverse direction or bridge a gap. As the figure shows, adding one makes the outer gears turn the same way.

Watch it happen. Each gear carries a spoke so you can follow it, and the counters under each one show the ratio as it runs: the small gear clocks two turns while the large one clocks one, with or without the idler.

The gear ratio

Gear ratio = teeth on the driven gear / teeth on the driver.

The driver is the gear being turned by the power source; the driven gear is the one it turns.

A 10-tooth driver turns a 20-tooth driven gear.

Ratio is 20 over 10, which is 2 to 1.

That means:

• The driven gear turns half as fast. Two turns of the small one for one of the large.
• The driven gear has twice the torque.

Speed and torque move in opposite directions, and by the same factor. That is the mechanical advantage trade, in rotation.

Small driving large: slow and strong. That is low gear on a vehicle, and it is why a starter motor's small gear turns a large ring gear on the flywheel.

Large driving small: fast and weak. That is high gear.

Turns

The tooth counts give the turn ratio directly.

How many turns does a 12-tooth gear make for one turn of a 36-tooth gear it meshes with?

The small gear turns more, by the ratio of the tooth counts: 36 over 12 is 3 turns.

Check the direction of the answer. The smaller gear always turns more times, so an answer below 1 for the small gear is wrong.

The idler

An idler changes direction and nothing else.

Its teeth appear in both the numerator and the denominator of a gear train's ratio, so they cancel. In the figure, the 10 to 14 to 20 train has the same overall ratio as 10 straight to 20: 2 to 1.

That is the question: adding an idler does not change the speed or the torque, only the direction. A choice saying the idler alters the ratio is the distractor.

Gear trains

Multiply the ratios of each stage.

A 2-to-1 stage feeding a 3-to-1 stage gives an overall 6 to 1, which is the same compounding rule as combined simple machines.

Torque multiplies by 6 and speed divides by 6.

A compound train is how big reductions stay small. When two gears share a shaft, the second stage starts from the first stage's output, so the ratios multiply: a 10-tooth gear driving a 50-tooth (5 to 1) on a shaft carrying a 15-tooth gear driving a 45-tooth (3 to 1) gives 15 to 1 overall. A speed increase in one stage divides instead: a 4 to 1 reduction followed by a 2 to 1 increase nets 2 to 1.

Real gears lose a little to friction. Multiply the ideal torque by the efficiency: an 8-times torque multiplication at 85 percent efficiency turns 25 foot-pounds into 25 x 8 x 0.85 = 170 foot-pounds.

Belt and chain drives

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A belt or chain drive works on the same ratio, using diameters rather than tooth counts.

The important difference is direction.

• An open belt turns both pulleys the same way.
• A crossed belt turns them opposite ways.
• A chain, like a bicycle's, turns both sprockets the same way.

So gears reverse and belts do not, unless the belt is crossed. That contrast is asked directly, and it is the most useful thing to take from this section.

Belts can slip, which protects machinery from overload but loses exact timing. Chains and gears do not slip, which is why a timing drive uses a chain or a toothed belt rather than a plain one.

Gear types

A worm drive is usually self-locking: the wheel cannot turn the worm back, because the shallow thread angle creates too much friction. That is why hoists and winches use them - the load cannot run backward. A single-thread worm advances the wheel one tooth per turn, so a 40-tooth wheel gives 40 to 1.

A rack and pinion moves the rack one tooth per pinion tooth. A 16-tooth pinion moves the rack 16 tooth spaces per turn.

A planetary gear set has a central sun gear, planet gears around it and an outer ring gear. Holding different members still gives different ratios in one compact package, which is how an automatic transmission shifts.

Drive parts the questions name

Backlash is the free play between meshing teeth. Some is needed, to leave room for lubricant and for expansion as the gears warm up.

Chain against belt: a chain does not slip under high torque but needs lubrication, and it wears at the pins and bushings - which is what "chain stretch" really is. A belt is quieter; a V-belt wedges into its groove to grip harder, and a toothed timing belt cannot slip at all, which is why it keeps an engine's camshaft synchronized with its crankshaft. The camshaft turns at half the crankshaft's speed in a four-stroke engine.

The differential on ice: an ordinary (open) differential sends the drive to the wheel that turns most easily, so the wheel on ice spins and little torque reaches the other. A limited-slip differential sends torque to the wheel with grip.

What you can skip

Across the 166 questions on this topic in our bank:

• Tooth geometry. Involute profiles, diametral pitch and gear modules never appear. The tooth questions count teeth.
• Named variants. Herringbone and hypoid gears never appear.
• Planetary ratio calculations. The planetary questions ask what the parts are and what holding one of them does, not for a computed ratio.

Where people lose points

Saying meshed gears turn the same way. They oppose.

Thinking an idler changes the ratio. It changes direction only.

Inverting the ratio. Driven over driver.

Saying a gear pair increases both speed and torque. Impossible; it is a trade.

Forgetting that a chain or open belt does not reverse direction.

Counting gears rather than meshes for direction. An odd count means the ends match.

Work one in under a minute

A 15-tooth driver gear meshes with a 45-tooth gear. The driver turns at 900 rpm. What is the driven gear's speed and direction, and what happens to the torque?

Ratio: 45 over 15 is 3 to 1.

Speed: 900 divided by 3 is 300 rpm.

Direction: two meshed gears, so opposite to the driver.

Torque: three times the driver's, because speed and torque trade by the same factor.

Three answers, one ratio, and the direction from the mesh count.

Where this leads

The torque idea here gets its own lesson, and the ratio arithmetic is the same one levers and pulleys use.