by RetireeJay » 2017-Jul-Sat-06-Jul
Are you sure you want "CoreXY"? It uses a system of two long belts to position the head, with both motors stationary, mounted on a frame. I think that microscope platforms typically have rack-and-pinion drive instead of belt drive.
Plain vanilla Marlin, which comes pre-installed on the board, will allow you to control motors for X and Y - and Z if you want. Microscopes don't need complex, high speed motion, so Marlin is up to the task. Or, as has been mentioned, there are other less expensive choices such as Arduino or RAMBO or Smoothieboard (the latter may be overkill, but I guess it's easier to program). Part of the cost of the Printrboard is in the controllers for a Hot End and Heated Bed, which you don't need.
Your other challenge will be to create software on your computer (or Raspberry Pi or Arduino, etc) that will take button or joystick inputs and translate that into G-code for your microscope. I've used microscopes, and I know that you don't want to take your eyes away from the 'scope to look at a screen, position a mouse cursor, and click for the desired motion.
Printrbot Plus operational January 2013
Brass threaded rods (5/16" X 18) & nuts for Z axis
GT2 belts & pulleys
Cable chain to reduce probability of fatigue failure in wires
E3D V5 Hot End, 0.4mm nozzle, also 0.8 and 0.25 in use occasionally
PB fan mount + 40mm fan -- using printed mount adapter, not the E3D supplied fan
Injection molded extruder gears
Optical Z "endstop" (custom designed and built)
Have used many pounds of T-Glase filament. Now also doing some work with Ninjaflex SemiFlex
Print on glass with Scotch Craft Stick or other glue stick