As stated, I'm looking for a clock motor that I could control with an Arduino.
Small additional difficulty, I want to decorrelate the movements of the hands (minutes and hours). Normally, when I move the minute hand, the hour hand moves in the same direction but for longer. I want to be able to move them at the same time, in the direction I want and at the speed I want (as if there were two motors).
Do you think there is a device like this?
If not, how can I do it myself?
The hands of a regular clock are mounted on concentric shafts and linked together by gearing of specific ratios. 12 to 1 for the minute to hour hand for example. You will either need two motors to do what you want or devise a method to engage each hand independently with one motor. Two motors seems like the easiest method.
Are you making your clock yourself or modifying an existing clock?
Some clocks don't use a conventional rotating motor; instead, they use a kind of solenoid to advance the mechanism a step at a time - maybe you could look into that...?
EDIT
It might be worth you browsing through the rest of that site:
@heyheychicken
I’d start by taking a clock apart and noting how the concentric shafts/gears are arranged. You’ll probably find that the concentric shafts can be driven by a stepper motor like @J-M-L has illustrated.
An Arduino can drive the one motor found in most clocks, for some interesting effects. Check out the lunch time clock.
One of the vanishingly few Instructables I would actually recommend, except there is one terrible error -- add 10K base resistors between the port pins and the transistors.
“Locate the contacts on the circuit board where the motor is located. Notice these two contacts have traces that go off to the chip (hidden under the black blob). The idea is to use a razor blade or knife to scratch away at these traces until the connection with the chip is visibly broken.
For good measure, I also cut away the timing crystal, rendering the circuit more or less useless.”