Tell us about yourself!
You could use two pins on the rail side creating a line for them to ride along. With one pin on the other side of the wedge for the other rail that rotates. Total of three pins.
You can't use two pins as it would want to bind or spin. One side of the mechanism must ride on some sort of rail system. While the other side runs on a rail system but must be able to rotate inside the rail as it slides. If you are stuck I can try and build one when i get home from some foam board I got using the measurements you provided. And post pictures and measurements of where everything is.
Yes it would probably work better than the prototype i built above where the pin and rail are not centered on each other.
The distance from where the pin is when closed as to open is the same distance as your radius of the circle you want it to open too. Because when the slide is closed it should be 0 from the center, so if i want to lets say have a 10 inch wide circle the slide would have to travel from 0 to the edge being half the distance of the whole circle (the radius) it would slide 5 inches. I drew up a quick sketch to hopefully better explain what i mean.
If you are asking the point of all my math was to lay out the path, then yes most of the math is for that. Cause it can change depending on the size of the iris or quantity of the slides you have.