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Bojan Gjoshevski
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Thanks,From my point of view and from the evidence (photos and videos), the shoulder of your tire on the rim is good.
There's just an optical effect linked to the marks/dirt on the tire. But your rear tire runs smoothly and as well as you'd expect!
Have you explored the possibility of a foreign body in the tire (e.g. mounting residue) that could be causing a random imbalance? If I were you, I'd use a static hand balancer to check your two wheels on this and other points.
Wheel axle misalignment (usually caused by impact: potholes, kerbs, front or rear impacts) can also lead to shimmy.
On the front wheel, this can be seen immediately when the wheel is turned with a workshop stand to keep the fork upright.
On the rear wheel, if the axle was misaligned, this would be immediately apparent when turning the wheel with the scooter on the center stand. Not so in your case. On the other hand, if the swingarm axle was bent, it wouldn't be noticeable under these control conditions.
For the front end, I also encourage you to check the lateral AND axial play of the steering. Also check fork tubes for tightness and evenness of tube insertion heights at the fork tees.
For the rear, I encourage you to check the swingarm axle bearings and the straightness of the axle itself.
Finally, if there's nothing else obvious, I'd check the condition of the transmission and, last but not least, the tightening torques of the frame/motor rigidity assemblies.