compact 3D printer, Ultimaker style

Hello,

UPDATE

The printer is already working:

https://www.youtube.com/watch?v=NrBtfCKOoGY
https://www.youtube.com/watch?v=RauPpPLwE_4
https://www.youtube.com/watch?v=UAfh85p1Af8

A little bit of description and the project files (yet messy, I'm going clean this up) can be found here (Polish):

https://www.elektroda.pl/rtvforum/topic3990756.html

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The goal of this project is to create a compact 3D printer, where printing volume is as close as possible to the overall volume of the printer.

My assumptions:
- Ultimaker-like head movement mechanism,
- standard components, easy to obtain (pulleys, rods, belts, bearings etc.)
- Stationary heatbed - gantry moved also in Z direction
- magnetic heatbed from Prusa MK2/MK3.
- printing area: at least 200x200 mm, 220x200 already, 220 mm in Z direction. Size can be adapted.
- printer size: 335x335x350 mm. Will fit IKEA Kallax bookshelf.
- easy to create a closed chambe