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I had the same issue when printing a different piece with moving parts, turns out I had the nozzle too close to the print bed, which wouldnt necessarily be an issue until printing items with moving parts that requires clearance gap between the pieces. Basically your nozzle is squishing the filament down against the bed closing the gap needed for the parts to spin free.
All you have to do is leave a larger gap from nozzle to bed when leveling your bed next, I use a piece of paper adjusting to where I can just barely start to feel the drag form the nozzle tip on the paper, I used to level my bed with a much greater degree of drag which I thought was needed for good bed adhesion, you want to create as large as a gap as possible but of course if you go too far you wont get good bed adhesion on your fist layers. Make sure to use a skirt around your part to prime the nozzle before the first layer, I have mine set at two 2 layers for my skirt and sometimes half of of the first skirt layer doesnt stick or print which I used to think meant my nozzle was set too high from the bed and would lower it and unknowingly squishing the print down, but dont worry if the first half skirt layer doesnt work, its just priming its self and totally normal, basically dont let this trick you into lowering the nozzle closer to the bed unnecessarily.
Good luck