I think this is pretty close to what Tom is getting at... Notwithstanding the problems others have already mentioned, I have a few of my own.
First, you'd have to have an unlimited number of gears to cover every latitude, and those gears would interfere with each other. I say that because at all southern latitudes the southern focal point appears due south. With just a finite number of gears, at some points it would appear to be to the left or right of due south. And when you have even more than one gear, theres the problem of how there are that many gears showing basically the same stars. Are they multiple stars, or is that just some optical illusion?
Secondly, unless you're directly underneath one, the polar focal points should appear to be ovoid and remain in the sky, and yet they are circular regardless of location, and dip below the horizon no less.. I'm sure that will be explained as some kind of optical illusion though...
Thirdly, the gears proposal should show the 2 different hemisphere fields pulling away from each other at some point. Here you have some curving, no doubt, but the spacing between the stars is not increasing in any meaningful way.
This panoramic looks pretty much like it's pulling away, but if you look at it in
this VR mov from the
Barden Ridge Observatory, you can see that it is in fact not doing so.
This VR mov is unrelated, but very cool.