I should mention that it was my first go with Google SketchUp (quite a lousy proggy for serious work I think) and since it was only ment to spark off some idea for those in need of such a gizmo, I didn't waste too much time getting the proportions right.
The "hole" is supposed to be some 5 to 8 mm (or more) larger in diameter than the cap, so it will fit a small range of cap diameters.
The "blue things" (the grippers) is shown with just a small part outside the ring shape, but this can be adjusted to the exact measures you want and it should probably have been shown a little concave as the other side (only I didn't want to spend more time on SketchUp). they might need a small "centering" spring between the two halves to keep the Blue Things from blocking the "loading".
I think it will be a challenge to do it with only two "blue things", since it wouldn't center the cap properly for a good grip.
Ment as a starting point for those wanting to experiment, as I have no time for making it right away (although I know it will work when I make it, since it is so simple).
As mentioned, it will need 3 little pieces of piano wire to keep the cap and perhaps an eject mechanism (a rod through a center hole should do), if you want to lose the cap instead of replacing it on the bottle.