How does a clutch and gears work on cars / motorcycles?
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A manual car connects the engine to the wheels through a clutch and a gearbox.
The engine works best if it turns at certain speeds, but the wheels need to cover a much wider range. So, we use the gearbox to handle that.
For each gear setting, the gearbox has one gear connected to the engine, and one connected to the wheels. The speed of the wheels is determined, both by the speed of the engine, and the size of each gear – the bigger the engine gear and the smaller the wheel gear, the faster the wheels. The gearshift lever controls which set of gears is used.
But, if you shift gears while the vehicle is running, the engine will be forced to speed up or slow down very suddenly, which is bad for it. That’s what the clutch is for.
The clutch allows the engine to be disconnected from the gearbox. Then, the gears can be adjusted, and the engine reconnected slowly, to give it time to speed up or slow down before the clutch reconnects fully.
(Automatic cars work roughly the same, though the gear set is selected automatically, and often a non-solid connection between engine and gearbox is used to avoid suddenly speeding or slowing the engine when the gear changes.)
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