There’s an infinite family of solutions if you allow both the radius of the big circle and the number of rollers to be variable. Basically, for every amount of rollers there is a single radius which works. I think you’ll have to lock down the number of rollers N, the spacing s (which I’m assuming is measured in distance units as the minimal distance between adjacent rollers, rather than angles) and the radius r of each roller. You can then express the radius R of the big circle using those three variables. Would that be ok?