I'm working on the flip face mechanism again. In this model you press down on one hand and the face turns 180°, press the other hand and it turns back.

It turns out to be surprisingly difficult to make a mechanism that turns a piece through 180°. Here's what I'm working on with the moment, let me know if I've missed an obvious easier solution. 

The face is fixed to the semi-circular shape at the top of the sketch below. This part can turn through 90° left and right from its currently position. It's joined to the arms by a long thin paper strip threaded over a couple of rollers. the rollers direct the paper, ensuring that it is being pulled straight down.

(Apologies for the rather rubbishy sketch! I'll try harder next time 🙂

Semi circles are hard in paper, I've gone for a simpler semi-octagon which is a close corollary and works just as well.

Here's the rotating part fitted into place with the paper tape threaded through the support piece and under the first (not actually rolling) roller. 

I'm worried that the rotary piece won't stay in position when pressure is taken from the hand. We'll find out soon!