Went for a bike ride today and thought the chain had slipped. Stopped and found the upper pulley wheel of the rear derailleur assembly was completely out of contact with the chain (please see photo)! Nothing we do seems to bring it back into contact (have no idea how this can even happen?). Would so appreciate if anyone has any idea what broke and what we need to do to fix it? Thanks so much!
The derailleur is supposed to be mounted to the dropout at the hanger, circled in red here. It is not. It should have been mounted using a bracket that runs between the hanger and the part circled in blue, and that bracket clearly is not present. Also, something is pulling the parallelogram part of the derailleur, which is normally almost horizontal, so that it's vertical, and the jockey pulley is riding behind the chain as a result.
Basically, the rear end of your drivetrain is completely messed up. At minimum, I think you need a new bracket for the derailleur; the derailleur hanger's threading might have gotten stripped in whatever mishap caused this, and the derailleur might be broken in some other way. It's hard to tell from this photo.
Your rear derailleur has failed.
Look closely and if it is floppy there's either a broken spring, or a lug has been torn off. To my eyes, the whole derailleur has become separated from the hanger in the photo ? The cable entry point is to the forward, which is something I've never seen, and implies it has all rotated.
Bodging might work, but the safest solution is to replace the derailleur, with the same specs. You may as well replace the inner and outer cable at the same time because old ones are fiddly.
I think that the derailleur's attachment to the hanger (bridging the hanger and the b-tension joint, outlined red) was pivoted way clockwise of its intended position (either by a collision or bad installation), causing the knuckle assembly (orange, yellow, green) to move rearwards and overextending the cage (also possibly damaging the spring). I've seen some rock-bottom level Shimano derailleurs where the hanger bolt eyelet (blue) only has a measly plastic as a spacer/bushing that can be easily removable during an unwise service, causing the entire attachment to bind to the hanger as you tighten the hanger bolt during installation.
here's the actual rear derailleur you have, with the hanger attachment and an additional built-in cable guide pulley.
In any case, I suggest you grab yourself a new rear derailleur with the same speeds as your shifter and cassette and, if you can shell out more, buy a new chain, cassette, and chainrings/crankset (if the chainrings are nonremovable). Overhauling it is possible, but the hanger attachment (mostly stamped steel) may be bent already, the cage spring might be damaged (or if not, out of tension), and the jockey wheels are in DIRE need of replacing.
Looking at the derailleur, it looks like it got bumped up to something while riding and pushed it back. You could loosen it up the b-knucle bolt (circled in red, by someone else.) and that should help the derailleur go back to its normal position. But looking at other factors, both derailleur pulleys did their job. It is time for new derailleur, your local bike shop would probably recommend new chain, cassette and probably cranks, just an observation by looking at how sharp the pulleys are.
