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Why not just use 3 digital pins from the Arduino?
example: Arduino Pro Mini.
I think someone (Adafruit?) makes a servo shield that can control several servos.
I suspect the problem with your simple diagram is that there needs to be a regular signal for every servo all the time. You can't ignore ServoA while you attend to ServoB.
...R
You can use an Arduino Pro Mini which is quite small. It can be programmed with the Arduino IDE and can use digitalRead() to sense the value of a digital output pin on the main Arduino. Each Pro Mini should be able to control twelve servos (just like the Arduino UNO). You will need a USB-to-Serial adapter to program the Pro Mini.
The Arduino Nano is somewhat bigger but has the USB-to-Serial adapter built in.
is there a way to use 3 servo's with 1 digital pin like in the picture?
There are servo controllers that take take commands via serial input.