I can describe the elements of the rigging and what is necessary to achieve the correct animations.
One of the main things to solve is the bone constraints so they can move around the curve. In Blender, this is the Follow Path constraint. While this works perfect for one bone, you can’t string together several bones and expect them all to just follow the leader. Instead, each bone is independent and they all have to be located at the origin to begin with. Every bone gets a follow path constraint except that the offset value is incremented so they can be distributed around the curve so each one starts its path behind the last.
At this point, you could create a mesh with a curve modifier that also wraps the curve. But then you have to assign the vertex groups and weights to the mesh by hand. Instead, I start with a single segment and duplicate it enough times to fill the curve length. This makes it easy to create a vertex group and set 100% weight to its matching bone before joining the segments into a single mesh and smoothing the weights after.
Assuming the bones and mesh are now in the correct locations with the vertex weights, it still won’t operate correctly because the rest pose of the armature is not really in the shape of the curve. The bone constraints have only temporarily translated them.
You need to duplicate the armature to preserve the follow track constraints and animation. This will be the control rig. The second armature will be used to deform the mesh. To set the rest pose, you would apply the constraint influence. Then, add a different bone constraint to the deform rig, copy transforms, with the target being the matching bone of the control rig. This way, the deform rig animates along with the control rig and carries the mesh with it.
To finish it off, you would bake the animation of the deform rig and export it with keyframe 0 as the rest pose. The control rig is not needed after baking. Always before baking, make a save point because this step removes the bone constraints.
Here is the Blender file and script I used to discover this. Maybe this is overkill for a conveyer belt but I sure learned a lot about making armatures from this.