Thank you all for your replies.
Sometimes a piece of flexible plastic tubing, like aquarium tubing, makes a good ad-hoc shaft coupler. It might help to build up the setting knob with vinyl tape or something similar.
That's an interesting approach which would certainly simplify things, though I'm not sure on how sturdy of a connection I'd be able to make.
Except mechanical side of things (where back side picture would be more useful), I was thinking that arduino would also need to read a current position of hands, at at least at one point for self-calibration. To read, two IR proximity sensors installed on front panel or just behind with two small hole may do a trick.
Is it would be the same clock, or this for multiple - production?
I've considered that, though in an early stage, in order to keep it simple, I'd most likely just have the user input the initial time the clock is showing and have the software work around that.
I'm sorry I'm unable to provide any backside pictures, as I don't actually own one of these yet. I'll probably try to swing by Ikea one of these days. Anyhow, they're probably similar to this.
I'm trying to get a working prototype by now, but I do intend to produce a small number of these.
Radio-controlled clock movements must include some sort of sensor, but I don't know the details. My guess is that they know when they are at 12:00 and rely on counting steps from there.
btw another way of solving the problem would be to buy a cheap radio-controlled clock and use the Arduino to generate a substitute radio signal, using a coil of wire to couple it to the clock's antenna. The radio frequency used is low (e.g. 60kHz in the UK), so it can be generated by one of the timers in the Arduino.
That's a brilliant suggestion. I had no idea of how widespread these RC clocks were or that they took steps in minutes.
I like both of your approaches. I think using the Arduino to generate a radio signal would be an elegant solution, although from the videos I've seen on youtube they don't seem to move as fast as I'd like. Also, how would I guarantee the 'main' radio signal wouldn't override the generated signal?
I think I might get a faster movement if I made the minute hand take quicker steps, as you first suggested, though I have no idea on how fast I could push these.