This thread might help.

Helix torus problem

posts #3 and #6 in particular

At a quick glance

R1 is the big radius, the radius of the toroid.

R2 is cross radius, the width of the ribbon.

$\beta$ controls how many turns of the ribbon in a full circle.

For a full circle $t:[0,2\pi]$

You will have $\beta$ turns per circle.

R1 is equivalent to R in my mathematica sheet

R2 I have set in code to be 1

$\beta$ corresponds with my $\omega$