To me, the method of @mihai.s is the simplest solution to the problem I presented in the original question. For completeness, I’m including a video of how I applied it, as well as the .skp file.
The steps are:
- remove oval surface
- draw lines forming circular surface
- define new axis at circle’s center
- right click new axis > reset
- use rotation handles (in move tool) to align with global axis
- remove drawn lines and reform oval surface
The key to this method seems to be the “reset” command in step (4). I don’t understand exactly what that does, but the result is that the move tool rotation handles can then easily align the object to the global axes.
Another point: @kevin58 believed the spindle itself was not symmetrical, I tried to check that by drawing 10 circles over the key edges that define the spindle. They all overlapped perfectly as far as I could see. So I conclude that original spindle is symmetrical (again, it was not made by me, but by “SketchUp” in the Warehouse).
I’m not sure how well this method will apply with other off-axis objects, but at least I’ve learned a thing or two. Thanks to all for the help.
off-axis3.skp (281.8 KB)