# Helix torus problem

• Apr 23rd 2014, 12:41 PM
sirMAXX
Helix torus problem
Hello everyone.
I've been looking for a solution to a problem that only seems to get more difficult the more I search or an answer.
It starts out with finding a solution to write the equation for a helix torus, which is not too difficult, but then it starts to get confusing when I ask for a double helix, but as a 'twisted ribbon'.
It would be similar to a DNA ribbon but solid, like if you were to take a strip of metal and twisted it at both ends.
I can show a figure of that, it would be the figure under "Helix B"...
http://www.nature.com/nature/journal...66ab.eps.2.gif
The ribbon would have a curve that follows the axis of a torus.
Finding an equation thus far would be a great help.

My problem however does go into further detail from here, the 'ribbon' that I have in mind has a more exotic shape if I were to show a cross section of it and would eventually have to be converted into another expression; but I wouldn't expect anyone to want to go into further detail.
Would it possible to have someone get me started and then figure out where I need to go from here?
• Apr 24th 2014, 12:00 PM
sirMAXX
Re: Helix torus problem
I finally found an example I'd be happy with, it's a twisted ribbon with a 90 degree curved section. Ignore the super imposed arrows.
Attachment 30768
• Apr 25th 2014, 01:05 AM
romsek
Re: Helix torus problem
is this what you are after?

Attachment 30769
• Apr 25th 2014, 01:16 PM
sirMAXX
Re: Helix torus problem
Ah-ha! Yes. :)
• Apr 25th 2014, 02:04 PM
sirMAXX
Re: Helix torus problem
So w, is the number of turns in a 180 degree section and the negative 1 over 2, is the inside and outside of the torus?
• Apr 25th 2014, 03:44 PM
romsek
Re: Helix torus problem
Quote:

Originally Posted by sirMAXX
So w, is the number of turns in a 180 degree section and the negative 1 over 2, is the inside and outside of the torus?

what this does is that a line segment from (0,0,-1/2) to (0,0,1/2), parameterized by $s$, translate that out to the perimeter of a circle radius R, and rotate that segment about the line tangent to the circle, as you noted, $2 \omega$ times in the entire circle. $\theta=1$ does a single circle. $\omega$ can be varied as you like. $\theta$ should probably remain 1. You can vary $R$ and you can vary the limits on $s$ to get different sized toroid ribbons.
• Apr 26th 2014, 04:31 PM
sirMAXX
Re: Helix torus problem