Rich,
The first approach would be to machine two concentric arcs that can be located to your centerpoint. The most precise way to accomplish this would be to use one pair of "fixed" cam followers that follow the most heaving loaded side of the (outer) arc's travel and use a pair of "eccentric" cam followers that will ride on the least heavily loaded side of the (outer) arc. If the loading is light enough, you might get away with a single "eccentric" cam follower riding on the outside edge of the inner arc's travel. If the loading to too great for that, you will need a pair of cam followers to provide proper linkage. If there is a lifting aspect to the loading, either a shoulder or (matched) tapers on the slot and cam followers can deal with that.
Similarly, you can machine concentric arcs as above and make a mating plate with concentric arc "keys" to control alignment.
Similarly, the operation can be done using two (fixed) cam followers on the outsid arc and a single (eccentric) cam follower on the inside arc -- just be aware that the tipping to lock load on this tends to be fairly small & sensitive.
4-bar mechanisms and their derivatives can only approach circular travel. Their default is to construct elliptical or involute paths. It has been several years since I did this, but (as I recall) I did get a 0.02% accurate arc using thee 4-bar mechanisms in concert. This was something I did in 1976, so my recollection of the details is a bit fuzzy...