Just wondering how automatic key duplicators work, i.e. you go to a locksmith and they put your key and a blank, and the machine automatically cuts your key. How does it determine the shape of your key (laser? imaging? computer? or does it ‘feel’ the grooves?)?

All those that I have seen "feel" the groves. This is an analog system and although laser or video imaging system could work, the machine would be much more expensive and no more accurate. Why build something more expensive that does no better?

engine cutaway section ...machining operation???