Originally posted by ZoeB Thanks, I'll try taking the bayonet flange off
The reason it broke is because it's 35 years old and has been on every continent but antarctica. I'd like to send it in to the shop, but I'm 16 and completely broke...
It's probably not necessary to take the mount off at this point. Here are some photos of my lens and what I think happened. The first photo shows the trim ring removed, which will expose six screws. The trim ring unscrews counter-clockwise. Find something round and rubber that you can press against it for a friction grip, without touching the front lens element. Then you need a small screwdriver for the three screws that aren't in cutouts. That allows you to remove the filter ring. The photo shows two of these screws removed. The filter ring should come right off but because this lens is a pancake, it's thin. If you can't get a grip on it, screw a filter into it and that will stick out enough to grab.
More screws are now visible. The inner three screws hold the entire optics (front and rear lens groups plus aperture) to the focusing helix. You only need to remove them if it makes you nervous to work around them. (A simple alignment is necessary if you remove this assembly.) The outer three screws attach the focus ring to the helix.
The focus ring is removed here. Now you can see the steep coarse threads like the ones you've been trying to screw back together. Also, there's a small slotted screw just inside of the orange diamond. That's the stop screw for the focus ring. Your stop screw might be missing, or a couple of the focus ring screws were really loose. That allowed the focus ring to turn past its stops and unscrew the helix.
I counted six possible start points for the coarse helical threads. The aluminum ring on the lens body also has fine-pitched threads. When that aluminum ring is screwed all the way in, that's just a little past infinity focus - there is maybe 5 degrees extra for adjustment room. The helix needs to be reinstalled starting at the other end of the focus travel, so turn the ring about 95 degrees clockwise, then maybe another 5 degrees more to give the threads room to engage. I don't know of any way to do this besides trial and error. Screw in the optical part, and see if all the parts line up in the right place. If they don't, rotate 60 degrees and try again.
With some lenses, it's not that simple. There are guides to move the optics straight in and out. It may be necessary to remove the mount to access those parts. The main ideas are to set the aluminum ring in the right starting spot and trial and error for the helix.