Linear encoder with motor feedback/control (like a volume control that can move)

I'm looking to make a kid's toy controlled with Arduino that will have a knob that controls an action. This is easy enough to do with a potentiometer or rotary encoder -- BUT, I want the Arduino to be able to turn the knob too.

My old Sony stereo had a volume knob that you could turn, but the remote control could also turn the volume knob when you used the remote <== that's exactly what I want.

I'm having trouble finding this - a linear encoder with a tiny motor. Surely this must exist as a part? But my searches for "linear encoder with servo motor" or "potentiomeer with motor" aren't yielding anything.

Any suggestions?

You can get motorized volume knobs. So the knob itself turns when actuated remotely.

There's two reasons not to do this...

  1. Audio volume knobs have a "logarithmic" curve to match the human perception of "volume". From the Arduino's point of view, most of the action occurs in the last quarter of the knob turn. You could replace the pot inside, if you really had to.

  2. It's mechanically complex and unreliable. Much better to use an encoder with no markings on the knob. Most audio equipment does this - there's no 'dot' on the volume knob so it doesn't need to turn when the remote adjusts the volume.