See this video on how to build the bed: https://www.youtube.com/watch?v=CWHxK8Uck-s

You'll need to print the following parts:

4x bottom-frame-joint.stl (with support!)
4x top-frame-joint.stl or 4x top-frame-joint-15x15.stl (with support!)
1x tensor-bracket.stl (with support!)
1x all the other parts (without support)

Other parts:

1x stepper motor + toothed pulley as seen in the photos
2x square aluminum tubing 285x20x20, 1.5mm wall thickness
2x square aluminum tubing 205x20x20, 1.5mm wall thickness
1x circular belt GT2, 6mm wide, at least 1360mm long, preferably longer, I'm using 1524mm
3x smooth pulley GT2, 16mm diameter, 5mm hole
4x toothed pulley GT2, 16mm diameter, 8mm hole, 20 teeth
4x threaded rod M8 105mm
8x M8 nut
4x M8 washer
8x skate bearing (ABEC number unimportant)
3x M5x30 screw
3x M5 butterfly nut

And depending on availability in your region you also need either:

2x square aluminum tubing 285x16x16, 1.5mm wall thickness
2x square aluminum tubing 205x16x16, 1.5mm wall thickness
(make sure you print 4x top-frame-joint.stl)

or:

2x square aluminum tubing 287x15x15, 1.5mm wall thickness
2x square aluminum tubing 205715x15, 1.5mm wall thickness
(make sure you print 4x top-frame-joint-15x15.stl)

And some assorted screws I'm not 100% sure about right now:
4x M3x10 screw (for stepper motor)
2x M3x25 or M3x30 (for motor mount against tube)
2x M5x25 or M5x30 (for smooth pulleys on the motor mount)
1x M5x20 (for tensor bracket)

The stepper motor I took from a 3D printer and the belt and pulleys are also the kind that are used in many popular 3D printers so they should be easy enough to find.

Btw, one of the disadvantages of this design, with the stepper motor and other pieces being inside the cutting area, is that you'll need a solid bed plate or the laser might cut the 3d printed pieces or even your stepper motor to shreds! It also limits the full range the bed can travel but in my case I don't mind so much, I don't plan on using very thick materials.

More exact instructions will be added at a later date!