Al et al,

I have had no opportunity to play with node editor for the last couple of months,
but this weekend I teased apart your Spir-Curve nod to comprehend your method.

After researching roulette curves, I started from scratch to produce this very simple scheme (no trig) based on your method for Trochoid curves.

It can also create Epicycloids by flipping the vectors
(i.e. multiplying by -1 bottom most node)

Now I am going to try and get my head around your geodesic nod.
It looks amazing!

Have a great weekend

James