Steam Locomotive Valve Gear Rigging

Hello. I am a Blender steam locomotive modeller and a railroad buff. Using Neal Hirsig’s Rocket Steam Locomotive tutorial, I have been able to rig locomotive valve gear WITHOUT any armatures, bones or weight painting–using only constraints. I want to start on something more complex–a locomotive using Walschaerts valve gear.

I want to know what sort of constraints I need to set up to get the rear end of the radius rod (8) to follow the curve of the expansion (reverse) link (7) when lifted by the reach rod (3) AND move forward and backward as the link oscillates.

The second animated GIF in the above link under the heading “Technical details” demonstrates what I want to happen. Thank you!