Transmission: It is the place where the different "gears" of the cars are located.
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There is a shaft that comes from the engine and then there is another one that comes out of it and goes to the wheels. Through a set of gears, it moves at different speeds even when the engine moves at just one constant speed, so it takes advantage of the engine's power. They may be manual or automatic.
I removed the car battery to diagnose it to be sure what the problem was when the gear shifter isn't turning to drive. Since then the smart key wasn't communicating with the car any longer