# Gears

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## What are Gears?

Gears consist of toothed wheels fixed to shafts. The teeth interlock with each other, and as the first shaft (the driver shaft) rotates, the motion is transmitted to the second or driven shaft. The motion output at the driven shaft will be different from the motion input at the driver shaft - in place, speed, direction and other ways.

A number of gears connected together are called a gear train. The input (eg a motor) is connected to the driver gear. The output, (eg the wheel of a buggy) is connected to the driven gear.

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## Spur Gears

The photograph below shows a simple gear train made up of a couple of spur gears. These are the common gears (or cogs) that look like wheels with teeth around the rim. Next to it is a diagram showing how you would draw this gear train in an exam.

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## Gear Ratio

Where there are two gears of different sizes, the smaller gear will rotate faster than the larger gear. The difference between these two speeds is called the velocity ratio, or the gear ratio, and can be calculated using the number of teeth. The formula is

Gear ratio = the number of teeth on the driven gear divided by the number of teeth on the driver gear.

Example:

Gear ratio = 60 ÷ 15 = 4.

In other words, the driver gear revolves four times to make the driven gear revolve once.

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## Output speed

If you know the gear ratio, and the speed input at the driver gear, you can calculate the speed output at the driven gear using the formula:

Output speed = input speed divided by gear ratio

So if the gear ratio is 4 and the driver gear is revolving at 200 rpm then the output speed = 200 ÷ 4 = 50 rpm.

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## Compound Gear Trains

Where very large speed reductions are required, several pairs of gears can be used in a compound gear train. A small gear drives a large gear. The large gear has a smaller gear on the same shaft. This smaller gear drives a large gear. With each transfer, the speed is significantly reduced.

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## Rack and Pinion Gears

A pinion is a round cog and the rack is a flat bar with teeth. The driver cog either moves along the rack, as in a rack and pinion (funicular) railway - or else the driver cog moves the rack, as in the steering system in cars. Rack and pinion change rotary motion into linear motion.

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