So the individual frames were created in Photoshop, I see. How did you animate the arm, exactly?
Well, there are a few ways you can do it--Photoshop actually has a nifty animation program built into it that lets you layer, animate, and edit frames all at the same time, then you can save it as an animated gif. But I didn't use that here (because I didn't know about it at the time.)

I did it manually, just by flipping between layers in Photoshop. What you need to do is make each frame on a separate layer and make sure they are positioned exactly on top of each other, then you can click back and forth between them and redraw the animated element as needed. It's pretty much a digital version of a standard old fashioned cell animation process, where the animators would do their work on transparent paper and flip back and forth to see how the animation was progressing. Then I used a separate gif creator program to create the animated image.