John,
I like what you said. A macroscopic example would be a set of Gimbals as used on ships and aircraft. "In inertial navigation, as applied to ships and submarines, a minimum of three gimbals are needed to allow an inertial navigation system (stable table) to remain fixed in inertial space, compensating for changes in the ship's yaw, pitch, and roll". .........."In turn, angular measurement devices called "resolvers" mounted on the three gimbals provide the nine cosine values for the direction cosine matrix needed to orient the ship.Similar sensing platforms are used on aircraft."Wikipedia, Gimbal. Which makes me think this analogy allows a better description of the roll motion I was trying to describe than a second axis on the flip plane, which I'm not sure is right.If you look at the picture of the early Modern dry compass suspended by gimbals it can be seen that three motions are possible; the inner ball can spin, the gimbal on which it is suspended allows what I called flip and the one suspending that gimbal allows what I have called roll.If orientation of observer can also be altered it can be seen that there is very much more variation in possible spin outcomes than might at first be imagined with simple spinning ball visualization.Another macroscopic example of extra degrees of freedom than one axis of rotation is a globe pivoted on the sides but also able to be spun with the pivots sliding around on the equator, and mounted on a rotating platform.