Fitted bed sheet clip - version 2

Fitted sheets folds over the corners of a mattress, held in place by elastic. But sometimes they slip up, releasing from under the mattress. Additional elastic is required to keep the corners put.

I tried https://www.printables.com/model/513308-bed-sheet-clip  but they don't grip well enough on thin or smooth sheets (works better on thicker edging). A different concept: which tightens the bite when pulling harder.
https://www.thingiverse.com/thing:2452561 
https://cults3d.com/en/3d-model/home/bed-sheet-table-cloth-tarp-retaining-clip 

Features:

• allows the use either a flat 3/4inch/19mm elastic band or a string.
• four different styles (called rings).
• five different keys for different sheet thickness.
• slight narrowing on the minor hole locks the key in place, to prevent it sliding out.

The rings (outer parts) have fixed openings for the keys (can be adjusted in the code), but the standard STLs given here should work for all sheets. 

The five keys are designed to accommodate different sheet thicknesses. Each key is marked with a number formed as int(100*sheet-thick[mm]), i.e., 20 means 200 um gap between the ring and wedge. Keys with larger numbers fit more loosely in the rings to allow thicker sheets.  My regular summer sheets measure 180-230 um per single sheet. A light knee blanket works with the ‘50’ key.  Print all sizes keys and test which one is the best for your sheets.

The code implements two rings:

• a larger major ring to allow key entry of the key into the ring.
• a smaller minor ring to grip the sheet around the key.

The key and ring have a wedge-shaped contact to

• allow support free printing
• ensure better grip on the sheet.
• wedge on the ring is trimmed to allow for sheet folding.

Both the ring and the keys have minute internally embedded holes or slits to force the slicer to create inner paths to strengthen the model. These are not visible outside, except inside the text on the key. After slicing the lines can be studied by analysing the gcode.

If the rings are printed flat-face down, layer separation may happen under stress during use, when printed by some printers or poor filament. If this happens turn the key on a round edge and print with support on the flanges. This was not necessary when printing on my MK3S+, the print was strong.

You may have to fine tune some of the parameters for your printer.

You can change various parameters in the design. Some combinations don't work, mostly because of impossible fillets. If you get BRep_API errors disable filleting, set doFilletChamfer=False and then do debugging to find the cause.

The cadquery environment used when build this model is described in cadquery.yml which has many more modules that you would normally require to create the cadquery environment: I only use cadquery and numpy here.  Printables does not support the yml format, so I had to change the filetype to txt, please download the txt file and rename to yml.   To recreate the environment install conda (https://www.anaconda.com/download) and do this command: conda env create -f cadquery.yml  
The cadquery docs are here: https://cadquery.readthedocs.io/en/latest/intro.html

Based on the concept used by jslheureux (cults3d), but this model is complete/major rework.