My first thought is a curve to use as a path. Then use hooks to bones of an Armature for the wobble. You can use empties, but then you have to manage all those actions if you later decide to expand your animation. Then use follow path constraint on belt mesh point it to the curve and check follow and offset. With offset you have a 0.00 to 1.00 range 0 being start of curve and 1 being the end of the curve. I personally would setup a driver using a bone, because I like to keep as much of the animation data attached to a rig.
