Or at least I'm assuming that it is. I didn't take any shots of any signs or labels around this one, but it seems similar in some ways to (though far less grand than) the one by Antonio Santucci seen in the previous shot. Also the rings are far more coplanar, so it may in fact be something else.

The museum has an excellent online catalogue of all of its items, which includes about half a dozen armillary spheres. However none of the match the one that we see here which makes me suspect that it may in fact be a different type of astronomical instrument.