I have a 1980's vintage SR Semi-pro with a Shimano 600 EX rear derailleur. That derailleur comes in two versions: short cage and long cage. The one now on my bike has a long cage. My largest cog in the rear is 27 teeth.

The pins/rivets that hold the parallelogram of my current rear derailleur are somehow loose, due to a crash, or just wear and tear, so that the parallelogram is no longer a true parallelogram, but rather is deformed. This causes the derailleur cage to be bent relative to the chain-line.

I scored a similar derailleur off eBay with the short cage; the pins/rivets on it are tight. Can I swap the cages? If so, how hard is that to do?

Thanks in advance.

Why not just try the short cage RD first. 27T cassettes are usually not beyond the range of short cage RD, though if you have a triple or 50-34
CW then it will not have enough cage wrap. Bent cages may be bent hangers, rule that out as well. Swapping parallelograms involving rivets
and pins will probably require a press or rivet forming tools which can be improvised if you are so minded. There are springs involved hidden
in the works and without an exam it is unclear what the likelihood of parts launched 30' on release a pin might be. Disassembly of the bad
RD should help figure out how easy it will be to do the swap. Might be worthwhile to cruise your LBS for a junked RD for destructive exam
first.

If the derailers and cages are similar enough, you might be able to swap. I tried once years ago and even though I was trying to swap between two RDs of the same model, I couldn't get it to work since they were from different years.

It's simple and sraightforward with some derailers. Others, not so much.

Thanks very much to all of you for the advice. I'll try the short cage first.

One more question: the freewheel on my bike has 7 cogs. The derailleur I scored was advertised as "six speed." Does the seller know something I don't? What could make a derailleur unable to handle 7 cogs?