Making closed loop joint articulation

I am making end_effector from mesh

Desired action is opening front constructed with four beams if the above pin moves back and forth.

The rings will move horizontally while the beams are moving, but I go to struggles to make them move appropriately.

First, I am getting hard with closed loop joint problem. I changed all joints without an prismatic joint for pin to guide joint, and I checked Exclude From Articulation a joint for breaking loop. However, the checked joint always be uncoupled when simulation.

Second, The rings are not moves in any way. I do not know the reason why it always be come to the original position. (24.9 KB)

This is my usd file I am working. Can someone guide me?