Recessed bookcase hinge

Warning: this hinge is provided as-is. It works for me and a 130cm×47cm×2mm PC sheet, but it is wobbly and does not work evenly. This has lots to do with the PC sheet wobbliness, the hinge size and the hinge material (ABS). Do customize its thickness and try it out yourself.

Now, warnings aside:

I have a recess in a wall (formerly a door) that now houses bookshelves. I wanted to add some door to keep dust away. I wanted the door and the hinges to stay behind the wall plane and I wanted the door to open at least 90° and not obscure the recess when open. And I wanted the hinge not to take space for the books.
Obviously, with so many restrictions I could find no match on the market, so I made my own.

The idea of this hinge is as follows:

• there's a part fixed to a shelf (screwed from the bottom) and so fixed to the wall, cyan and blue on the picture
• there's a part fixed to the door, red and maroon on the picture
• there's a part - a bar - connecting those two, dark green on the picture
• there's a part - a gear - rotating freely on a shaft in the middle of the bar, light green on the picture
• the parts fixed to the door and the wall have fixed gears
• the three gear interlock so that when you open the door, the door rotate slower around the bar than the bar around the wall.
• as a result, when the bar rotates 180°, the door rotate some 80° in the opposite direction, so overall the door open about 100° (slightly beyond straight angle)
• after opening the door, the door moves twice the bar length forward, and by the length of the part fixed to them sideways.

This was designed for 2mm thick door because I planned to use acrylic glass / polycarbonate sheet. I was not aware how wobbly such a sheet is. If I were to get me another, I'd probably go for a 4mm acrylic glass.
Also, I fitted 2cm tall hinge out of ABS, which is not sturdy enough and is sagging (the bar slightly bends under the load). Making a aluminium cast would probably do the job (I don't think a sturdier plastic would do better), but so far I'm too lazy for this.

This design need a couple of M4x20 flat countersunk bolts to act as shafts and fasten parts together, a tap to cut the thread in plastic, 2.9mm diameter wood screws for fastening to a shelf, and suitable screws for fastening to the door.
The height of the hinge is customizable in .scad file.