The purpose of a gearbox is to provide variable transmission of a constant RPM for variable needs. Think of a petrol car. The engine is designed to run best at a certain number of RPM, that is, revolutions per minute. It can go a bit above and a bit below this number, but so long as the engine is running, it “wants” to turn the drive shaft this particular number of times per minute. But, we can’t connect this to the wheels directly – when the car is moving very slowly, the wheels won’t be turning nearly that fast, and when the car is speeding down the highway they will be turning quite quickly. So the solution is a gearbox, a set of different gear ratios. If we match a larger gear to a smaller, the smaller will turn more times for each one rotation of the larger gear, and vice versa. Because the gearbox can shift between several different gear ratios, and the engine can tolerate some variance in RPM, we can provide every precise RPM that the wheels will move at.
This has another added benefit: gear ratios provide a lever action. It takes a lot of power to get a car moving from fully stopped, because it is heavy. More power than a single rotation of the engine could possibly provide. Luckily, when you use a lower gear ratio, the power or torque of the rotation is multiplied.
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