Rotary Memory and Positioning

Connect a shaft encoder to the shaft, and a counter to the encoder. Note the number position of the readout at the desired location. Reposition to that number when required. Scale your encoder to the desired accuracy by ratio coupling the shafts. Reference all movements to the index of the encoder. Implement automatic shaft positioning by adding a stepper motor and counting encoder pulses. Scale accuracy of the stepper by ratio coupling as well. Arduino project.

To do this manually, all you need is a disk with 4 holes in the correct positions and a locking push button with a pin on it to engage the holes.

If electrically, micro-switches and a motor. If electronically, an encoder, control circuit and a stepper motor.

<Edit> OOPS thought I was replying to OP. LITT you must have edited your response, too.

Yes you are correct. As implied by the wording of the OP he wants to position manually, record or memorize the location, and then go back to the locations automatically by pushing buttons. Rudimentary CNC. Sorry, I thought you read it.

Better to have an absolute encoder and programm the position after it is set by hand.

The µP will go to the programmed position. It saves the counter problem and correlated errors.