You must have a very different definition of "cheap" if you are looking for that resolution and speed. Good luck.I believe the RepRap project gets those kinds of distance and resolution, but nowhere near that kind of speed.If you want that kind of speed AND resolution, you are probably looking at something more capable (and more ($$$) than Arduino.
QuoteI'm not sure the Arduino would be the limiting factor; I was basing my evaluation on the stated desired resolution multiplied by the stated desired speed. But maybe with one Arduino per axis, it is doable. But that makes coordinating diagonal and arc moves more difficult.
I'm not sure the Arduino would be the limiting factor;