Allow me to weigh in here. The arm for that extractor is near impossible to find. Usually when these fail that tiny piece of spring steel pressed into the inner part of the extractor gear is gone / missing, the gear would have stress cracks and that little swing arm is usually *****-ed (messed up beyond all recognition). That seems not to be the problem here. Yours appears good.
Use a correct size, hollow ground screwdriver or screwdriver-bit to remove the top screw on the barrel just above the cylinder. That screw holds the piece of spring steel (bent to a right angle where it touches the rear of the cylinder) that retains the cylinder from popping out when you open the revolver as to extract the shells.
After that top screw is out, slide the retaining bit of spring steel out rearward (it some right out easily). Then, raise and hold the latch as high as it will go and unscrew the cylinder counter clockwise as you pull it toward you.
If anything goes wrong here, e.g. if the cylinder comes straight out without having to pull or unscrew it out, contact me via email.
Either post or send me (via email) pictures of the barrel and cylinder with the cylinder removed. Close up on the threads of the cylinder axis tube.
Let's see what you have, exactly at this point of dissembly. Remember a few rules ... 1. don't ever FORCE anything back in place and 2. NEVER try to pry the sideplate off (even though this process does not require it removed) 3. Another is that you always point the long part of the barrel away from you but if you made it to this forum, we usually presume you know this already).
Often the spring (a coil spring) installed on the center extractor rod ... when old and worn ... stretches or starts to "unwind" / broaden to the point that it chafes the inside of the cylinder axis hole causing it to hang up ... exactly what you describe. (other issues could cause the same issue, too, but that spring is prime suspect). Another is that it had been apart and whomever reassembled it did not match the gear and internal teeth , tooth for tooth, likely had been one or more teeth off.
Check the cylinder axis tube (it stays on the frame when you take the cylinder out) for tightness and alignment. If the axis tube is loose or worn could be either "the" or part of the problem.
If everything seems OK clean well, some oil, then reset / match the gear teeth that they match, tooth for tooth.
Make sure the joint screw is installed properly. Match the alignment strike on the pin to the correct side with the matching strike line. That alignment strike is only on one side of the frame, the right side, IIRC.
Don't over tighten the screw, although if it is in the correct position, it should not matter. Either way just snug it and try again.
