This GIF seems to imply that the front leg/hip initiates this. (I apologize if I'm missing something here, since I'm coming in at the tail end of this thread).
The GIF is missing the impact of the stride (for most players, not always for Donaldson and Bonds #750) - the rear leg straightening, which rotates the back knee, which 'pushes' the back hip downward/around, which helps propel the rear elbow, thus the bat head.