Okay, this will probably seem crazy at first but bear with me. What if, instead of using rollers/bearings and a ring/rail to keep the ends of the chain on a point on an arc (which is based on the center of the bit) we instead used linkages? No rollers or anything. My initial concept is a little clunky visually and the physics might not work out in real life once there’s weight on it but imagine two pantograph linkages where the master point is forced to trace a small arc on a circle that makes the other point follow the path we want…
Here’s a quick sketch of the idea:
The points with the black Xs are fixed points that are allowed to pivot, all other points are free pivots. The drawing shows two positions (the black lines and the grey dashed lines). I only drew the right half to keep things simple but you’d need one for each side (they could share the same two fixed points though). The scale here is probably weird and I did not do any math or testing on lengths of linkages but I think you get the idea…
It’s the only way I could think of to mechanically trace a point on an arc without physical access to the actual center of the radius (because that’s a router bit!).
This alleviates costs of bearings, rails, rings, etc. and might prove more accurate since it should eliminate the jerky roller problem. Linkages could be a simple, cheap material and pivot points need not be more complicated than bolts or screws.
Of course this also could be a terrible idea. I might make one to see what it does.