Match position with offset pivot

Hi all,

I’m having difficulty understanding a math problem.
In the real world, I have a chair attached to a rail that can move in one axis (x) and can rotate in one axis (yaw) . The chair has a motion controller attached to the back of it and I’m attempting to match the rotation and position of motion controller on a virtual copy of the chair.
The problem I am having is this: when the real world chair rotates, because the motion controller isn’t mounted at the chairs pivot, the virtual chair slides forward as the physical chair rotates and the motion controller is offset.
I’m having difficulty working out the maths to account for the offset.
I hope this makes sense. I’ll try to upload some images to better explain the problem once I get to my pc.

I’d appreciate any help on this. I don’t think I’m capable of understanding the maths involved!