I just wanted to follow up on this post so that anyone having the same problem can have a complete reference. For future reference this was a Deadpool figure based on the Bucky-Cap model, the left arm elbow at the second joint (the one furthest from the shoulder in the elbow). This should work for all the double joints in the elbows and knees. I GOT THE JOINT TO WORK!!
First a list of what I did not do:
1. Use a lot of force, I didnt want to break the joint..i prefer a stuck joint to a jacked up figure
2.Hairdryer, this may work for some people but I was a bit too shy to try it
3. HOT water, same reason
4. Tools, unless you count fingernails I didn;t use any because I didn't want to gouge or mar the figure. Also its sometimes hard to gauge force through a tool so I didnt want to chance destroying the arm
Here is what I did:
Soaked arm in lukewarm water with hand soap for 20 minutes. I chose handsoap because it is a little more gentle than other soaps usually so I wanted to minimize potential damage to paint. 20 minutes because the water was still a bit warm and I wanted the joint to be above room temp
I wiggled the joint gently for about 10 minutes taking care to not strain the joint. I didn't want to destroy any inner workings of the joint and end up with one that swings freely. This attempt didn't yield any movement.
hand soap with no liquid at room temp.
put a very very small drop of soap on the end of a toothpick and carefully applied it to the joint. I then wiggled the joint gently for about ten minutes. I did notice that the joint moved very slightly after this attempt and decided to followup later with more wiggling.
I did not add any more soap but simply wiggled the joint along whatever range of motion I could get for that time. To extend the range of motion I held the connector piece between the fore arm and the upper arm gently with my fingernails while I gently applied a very small but steady amount of pressure to the fore arm in the direction I wanted to extend the range of motion. After a few nights of doing this 4 or 5 times I finally got the fore arm to pop past the first position (fully extended) and into the second position (in between fully flexed and fully extended). Once this was achieved the arm would move normally (or with a small bit more that normal) amount of resistance.
Again, the key here is that I placed priority on not destroying the limb and took great care in moving the limb. I believe the soap applications prior to the followup was very important because it acted as a lubricant, to that end I didn;t want to try WD-40 or any other oil/grease based lubricant because I was worried the paint was oil based and would be smeared. The drawbacks to using soap are that a very basic soap may also affect paint (thats why i chose handsoap) and the soap may later dry into a crust inside the joint rendering it stuck again. While nothing can be done about the risk to the paint except minimizing the amount of soap applied (especially undiluted) any crust may be washed out by soaking or rinsing the joint.
I hope this helps, I tried to be as detailed as possible because to my knowledge there is no other clear guide to doing this with minimal risk to the figure.