Edit (14-02-19): today published Bed_Hoist_for_a_3DPrinter (D-Bot, CoreXY)-_Version_2, www.thingiverse.com/thing:3427719.
That version 2 supersedes this one, because it is simpler: 1 belt, simpler parts.
No solution for the 2 mm-wave-error yet, though.
For a time I worked with one hoist and belt in this first version and that went ok, even somewhat better than with 2 belts.
So if you already have made version 1, perhaps you can leave version 2 for what it is and try it with 1 bed hoist: just move one hoist to the middle, uncouple the other one and look how that goes. ;-)
But if you are new to this concept or want to try other worm gears, forget version 1 and go for version 2.
A system for Z-axis movement with hoist action.
I looked for a way to replace the lead screws with something else and found that I needed only 1 motor with a 20:1 worm gear to hoist and lower my bed, which weighs some 4.5kg together with its support frame.
The motor action is brought via a ø5mm rod to 2 sets of timing pulleys to 2 of the usual GT2 belts.Pulleys without teeth are used to force the belt over as much of the teeth as possible.
All supported by ball bearings, 2 of them flanged to prevent sideways movement.
The Gt2 belts are captured with a remix of a nice thing I saw, among others, called "Separate GT2 belt tensioner" by MrArrow1961, https://www.thingiverse.com/thing:910725.
A bit more difficult to print than the usual solution, but easier to finetune belt tension and to place/remove the belt with it.
I made this thing so I can use it with my D-Bot_Linear_Z-guide, https://www.thingiverse.com/thing:2779260, but it is independent of it.
However, trying it in a system with wheels for the Z-axis gave me insurmountable problems, because without the support of the lead screws the bed angled so much downwards that this could not be compensated for with the usual bed supports.Just too much play in those wheel systems, whatever I tried with 3 of 4 wheels. So be warned. ;-)
No such problem with the linear Z-guides.
All in all I found this thing much simpler and quieter than the lead screw configurations I tried.
As accurate also, I think. Compared to the loads they are made for, I feel this load won't stretch the belts so as to give wrong printing heights.Somewhere (can't find it any more) I even saw a pre-load advised by the manufacturer of some 2kg, so that should be ok.
Though, of course, it doesn't harm to check once in a while when height is of an essence with your print..
For materials, assembling specifics, more images and more rationales, see the"Notes.pdf¨ in the "Thing Files".
The nimble motor support and motor are very present in the pictures, alas (because it has nothing to do with this thing), but to dismantle the whole thing etc. only to make a picture without it was a bit too much trouble for my liking. ;-)
Edit (03-04-18) Added Stringsupport.stl and holes for strings to hoist -> Hoist-v!.stl. I have not yet printed them, but that should not be a problem.
Changed Notes again accordingly -> Notes-v1c.pdf
Edit (04-04-18) Sorry, there was a problem, Stringsupport-v1.stl should work...
Edit (05-04-18) Added Stringsupport_XL.stl, for those who need a bit more room for their weight and a small change to normal stringsupport -> Stringsupport-v1a
Edit (15-04-18) Updated a picture
Edit (31-07-18) I am going for an improvement, proposed by ZaKote, (thanks, ZaKote :-) ), see comments, and will replace the threaded rod (+nuts, etc) with a ø5mm rod with shaft collars. Changed the text above and the notes: Notes-v2.pdf accordingly. The pictures have to wait until it becomes reality. ;-)
Edit (16-09-18) Had at first a bit of a problem finding a good rod, so I added a url of a seller who delivered ito the Notes -> Notes-v2a.pdf. Finally made the first prints with the ø5mm rod and indeed the result was much better. I thought at first that the problem (see comments) was completely gone, but then I saw there still was a bit of same same, though much less (wonder what the cause of that is...).
Edit (09-10-18) replaced pictures.
Edit (07-11-18) Replaced counterweight system with belts with adjustable belt tensioners. Version1 of the hoist is still perfectly usable, but those holes for strings are superfluous so I went back to the old hoist.
Adapted Notes -> v3a. Photo's will follow.
Edit (08-11-18) added photos. This improvement does nothing for the 2mm wave (see comments), but I'm waiting for another GT2 pulley, hopefully of a better quality...
Edit (29-11-18) correction in Notes : 8x GT2 idler pulleys 20 without teeth, ø3mm bore, belt width 6mm -> v3c. Thanks ZaKote