Making a Violin using distance controllers and rollers

Ok so I am rather new to this. I have an Uno which i had to get for a physics class 3 years ago, but it has just been sitting idle ever since. I now have a daughter and I think it would be fun to build her a Violin using Balsa, Pine and an Arduino. I am not sure of all of the technical stuff yet, but I was thinking about that if I could have the bow ride on 4 rollers like in a mouse for scrolling, and then have 4 different distance sensors to show where finger placement is that it could be a crude, maybe not beautiful sounding, violin. I would like to get some input on this idea. thanks in advance.