It’s easier to visualize a bike’s gears than a car’s transmission, so I’m going to compare the two so that you might have an easier time understanding the concept. (There are actually bikes with continuously variable gear systems, but they’re rare, and work differently than the hypothetical I’m going talk about.)
So the purpose of a transmission or gearing system for either a car or a bike is to take the rotation of the engine or pedaling and convert it to a different speed of rotation for the wheels. Car engines and human feet work best when turning at certain speeds, and that’s rarely the same speed you want your wheels to be turning.
Bike gears do this with toothed gears and a chain, and most cars do it with gears turning other gears. The exact details differ a lot, but generally speaking the effect is the same. When we talk about switching gears on a bike or a car, the system is literally changing which gears are used to transfer power from the engine/pedals to the wheels.
If you look at the stack of gears in a bike’s transmission, you’ll see that it almost forms a cone. What CVT basically does is replace those distinct gears with a cone so that you don’t have to shift from one gear to the next, you can just slide a little bit up or down the cone as you need to. That’s the “continuous” part of CVT. Instead of having distinct gears with interruptions between them, there is a unbroken/continuous shift between different gear ratios. (Of course, if you just replaced gears and a chain with a smooth cone and a belt, the belt would just slip off, and there’s a lot of engineering that went into making a system that actually works, but the general principle is the same.)
You can drive a CVT just like an automatic. The system will change the gearing to suit the needs of the car. The exact feel of acceleration will be a little different, but no change on the part of the driver is needed.
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