Part of the process of making the revised
Big Gear
experiment is this long flexible rack. It got me thinking about yet another possible mechanism for the flip face project.

I constructed this box with a curved top and a slot…

…fitted a slightly shorter rack into the slot…

…and added a pinion. (With involute gear teeth of course)

With a second side in place holding the pinion, it is just a case of pulling either hand to rotate the axle.

Next, a redesign of the flip-face artwork. As I may have mentioned, it was beginning to creep me out.