The way that quadcopters and helicopters are controlled is completely different. There are 4 basic movements that it has to be able to do. Collective (go up/down), pitch (go forward/back), roll (strafe left/right), yaw (turn left/right)
The quadcopters have simple rotors that are one fixed piece. The get more or less lift by having the motors spin faster or slower. That’s something that electric motors are really good at. With four of them, you can easily do all the basic movements. If you want to go forward, you increase the speed of the rotors in the rear, and decrease the ones in the front.
With helicopters, gas turbine engines are not capable of throttling quickly enough to provide controls and it’s more fuel efficient to just have them operate at essentially max speed all the time. The rotor system is significantly more complicated because it’s what does all the controls (except for yaw which the tail does). The angle of the blade actually changes depending on where it is in the rotation.
[Here is an animation showing how the helicopter’s blades change angle](https://www.youtube.com/watch?v=kKkpC_0-wXg)
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