Dave, I thought you'd know me better by now. Of course I want to comment!
In the second example, I'm assuming at rest the spokes are hanging. In helospeak they now have flapping hinges.
With that disk, when you move the axle, you impart no torque to the disk. The result of the original angular momentum plus the zero torque you added, equals the original angular momentum. So the disk doesn't tilt like the first one.
So why does the disk roll? Because the tension in the spoke pulls the masses into a plane that is perpendicular to the axis of rotation.
Also, because the second wheel is not rigid, it's not right to call it a gyroscope.
[ 02 December 2001: Message edited by: heedm ]