32.  I'm having problems with a school assignment.  Can someone help please?

I have include a very simple 2D schematic below (bad drawing) to simplify what I'm trying to explain and do here. So I have two parts with faces parallel to each other (in red), There are two plates (top/bottom) that the parts are connected to with the bottom in a fixed geometry. In the middle there is a flexible rod acting as a spine. The parts are connected to the two top and bottom plates via ball joints that can rotate freely.

What I want to accomplish is to compress the right side and make the two parallel parts (in red) come together. I want them to do so without any deviation to the sides. Note that when you compress it, via advanced fixture movement or force on the top one in downward direction, the structure will pivot to the left. I want something like a rigid connection between the two faces, but I want the distance between them to be able to change.

What would be a simple way of constraining the two faces in order for them to come together in parallel? Could spring connectors connected to the notes at the end of the plate work? Compression? Elongation? With minimal normal stiffness and high tangential stiffness?

Note: The links are flexible too. Main problem is getting the two faces to come together in parallel. Also I'm running the simulation in nonlinear static.

Please help.