A brief progress report: yesterday and today I worked on the base and the support system for the tube. I'm required to use some 20% of the supplied bicycle parts; I think we're up to nine, nearly half way. The functional parts are still to come, and I can begin on these tomorrow.
At least the device has a name; there's only one Google reference to a Cycloidoscope, where a William West Esq. demonstrated some experiments with the same to a meeting of the Leeds Philosophical and Literary Society in 1848. (Whatever was the purpose of William's apparatus, it was unlikely to have had the least connection with the 2012 model.)

The decorative black gear wheel on the base is not yet attached, but will eventually be fastened with turned ebony or wenge pegs. It would be nice to inlay it, but..........really.........

Detail of securing/friction screw securing support forks to base.

End details, pivot securing nut.