I've got a partially disassembled 85/1.8 preset Vivitar. T-mount, lots of aperture blades as usual for old preset stuff. I've seen 135/3.5s with similar cosmetics which might be internally similar.
Haven't been able to find how the mount end of the helical attaches to the mount itself. Seems like the mount is glued to the helical end, which doesn't really make sense. This lens is slightly cock-eyed at that glued joint, so it always focused off-center and I want to correct it to eventually test it and then slim down my 85mm choices.
The T-mounts just screwed on. Misalignment sounds like cross threaded, impact or impact caused the mount to hop a thread.
Sacrilegious I know but a strap wrench or two might help. They also may make things worse, much worse.
Update: It turns out the mount side of the helicoid IS glued into the outer cosmetic sleeve, as well as retained by 3 screws. Whoever glued it in was not paying attention, it had to be a good 8-12 degrees off axis. Maybe the glue was an amateur repair attempt but who knows, the lens has been around since the '70s at least.
Got it all back together with no issues now. Pretty solid little lens, I hope it's IQ is good.
I tried nail polish remover first off and it worked well. I've had good luck with very light applications of 100% acetone before (no damage to anodized aluminum which is what this lens is made of), so gave it a couple drops and it popped right apart.
Not sure what glue it was, but it did not "melt" or deform at all but rather just gave up the hold on the aluminum and splintered apart or cracked when direct bending pressure was applied.