This is the badge from a Columbian Press, a printing machine designed in the USA and made in Edinburgh and now in the National Museum of Scotland.
The counterweight that is partly visible at the top of the photo is in the shape of an American Eagle.
The explanatory panel states that the printing press was designed by a George C Clymer in 1813. The press wasn’t a success in the USA so he brought his design to Scotland.
The panel also explained that the name of the press came from the name Columbia, which is the female personification of the USA. Who knew?
According to Wikipedia, the name Columbia was dreamed up by Samuel Johnson to describe the British Colonies in America at a time when reports of debates in the UK Parliament had to be disguised because it was illegal to report them directly.
The name was adopted by the founding fathers to add gravitas to their country to combat the UK’s Britannia when the US was working towards independence.