Trouble changing pivot point mid animation

[exit65]

Using 6.3
I'm trying to animate some chain turning around a set of sprockets and I'm running into some trouble.
Initially the links rotate around the first sprocket using it as a pivot point until it gets to the other side.
At that point I set a second rotate animation using the second sprocket as a pivot point and the link spins around an imaginary axis that doesn't seem to be associated with anything (as seen in  the second image)
I've tried this in every imaginable configuration (global/original local, origin/center, pivot point object axis, dynamic pivot point) and this is not the first time I've had an issue with something like this in keyshot.
It strikes me as weird that such a rudimentary function would cause so many problems. Any advice out there?