Rigid Body Physics: Sliding Pivot Point

Background: I have a cam spinning in a circle which drives a rod forwards and backwards. The center of the rod is fixed to a pivot point in line with the center of the cam, so as the cam spins and drives the rod back and forth, the opposite end of the rod rotates in a circle in the opposite direction. As the rod slides back and forth along the pivot the location on the rod where it is pivoting from changes (the pivot itself is fixed, but the rod is moving)

Issue: I’m having problems trying to figure out a constraint at that pivot point. I tried a generic constraint which allowed rotational movement, and movement along the x direction, but because the ends of the rod are rotating the rod needs to move in the y direction as well. I tried putting a peg (cylinder) at the pivot with a slot in the middle of the rod to help constrain it, and it sort of works, but it’s not being constrained properly. I checked and fixed my normals to make sure they are all facing outwards, reduced margins, etc. all trying to get it to behave as expected but can’t get seem to get this working.

Model file here: