A description of a simple cylindrical worm drive is given here:
http://www.otvinta.com/tutorials.html

There is a globoid description here:
http://www.otvinta.com/tutorial02.html
http://www.otvinta.com/globoid.html

Piotr Połowniak and Mariusz Sobolak have one paper in English on:
"Mathematical description of tooth flank surface of
globoidal worm gear with straight axial tooth..."
with complicated mathematics,
and several versions in a foreign language.
Maybe next winter I'll have a look... No time now :-(

- Brian