Of course, as the wikipedia on that Greek device notes, the Muslim World also had a technological flowering that might have supported mecha at some point.
And it's an idea for a Silly Story!
So, you start with your average, run-of-the-mill Bored Godling plot device. Said godling decides that it would be really interesting to see what sorts of mecha might appear at each period, given a couple of points of inspiration in the right brains and an appropriate rubberizing of physics. He takes a bunch of parallel worlds, and does the neccessary things to start the mecha revolution in different times and places. Then, just for fun, he grabs one representative mecha out of each appropriate time and sets them in a tournament against each other, with an appropriately improbable prize.
There are, of course, better and less cliched ways to write this particular story, but I don't currently have the spare cycles to come up with them.
And it's an idea for a Silly Story!
So, you start with your average, run-of-the-mill Bored Godling plot device. Said godling decides that it would be really interesting to see what sorts of mecha might appear at each period, given a couple of points of inspiration in the right brains and an appropriate rubberizing of physics. He takes a bunch of parallel worlds, and does the neccessary things to start the mecha revolution in different times and places. Then, just for fun, he grabs one representative mecha out of each appropriate time and sets them in a tournament against each other, with an appropriately improbable prize.
There are, of course, better and less cliched ways to write this particular story, but I don't currently have the spare cycles to come up with them.