Muvlo, that actually did make sense … I have been trying it out
Tool>Mods>Deformation>Offset is the key … after that I rotated (revolved?) the blue rings roughly into position with the gyros, and then adjusted the XYZ numbers in the Transform Info sliders … in one case I had to enter 0.01 instead of 0 otherwise the ring would jump into the hole in the center.
[edit follows]
And along the way I learned that there can only be one marker per XYZ location … I had been marking and snapshotting the blue rings before revolving the next one, but since all nine rings share the same pivot point, only the last blue ring was available using the MultiMarker tool.
Workarounds are explained in this QuickLink about markers for concentric objects
Anyways, thanks again, that was just what I was looking for … I’m all set for next time I want to build a cyclotron or something 
