DaVinci (and others) designed volley guns, which were multi-barreled, carriage mounted guns that fired all barrels simultaneously. They might be considered machine guns, and they predate the Puckle Gun.
Are you ready for the most expensive machine gun bought at auction. Forgotten Weapons channel has the word on this gun. After his talk I just think of all the grunts who fired this gun and thought nothing how much it cost. And its a very good example of supply and demand. Not enough of something people want the price will go up.
It doesn't meet today's legal definition, but that wouldn't stop the ATF, the media or the left (but I repeat myself) from classifying it as a 'machine gun'. Hell, the ATF went so far as to issue a determination in Sept of 2004 that a shoestring was a 'machine gun'.