# Cartesian Coordinates on Spherical Helix

Printable View

• June 19th 2012, 07:23 AM
cm3798
Cartesian Coordinates on Spherical Helix
I'm a Manufacturing Engineer that is a little rusty on my math skills needing some help for a problem concerning a helix on a sphere. I first asked my question in the pre-university math geometry section but have not received any responses so here I am asking again and hoping someone can point me in the right direction.

I'm trying to find the X/Y/Z coordinates of points spaced .375" apart on a .300" lead spherical helix. I have the following formulas to find the coordinates at t position on the sphere where t=1 is the top of the sphere and t=0 is the center of the sphere.
$rzt$ is radius of sphere at http://latex.codecogs.com/png.latex?t-X/Y plane of sphere
$sr$ is sphere radius
$t$ is % from sphere center to top of sphere
$xt$ is X postion on sphere at $t$
$yt$ is Y position on sphere at $t$
$zt$ is Z position on sphere at $t$
$rzt = \sqrt{sr^2-zt^2$
$zt = sr * sin(90*t)$
$xt = rzt * cos(t*360*2*\pi*sr*90/360/.3)$
$yt = rzt * sin(t*360*2*\pi*sr*90/360/.3)$

Thanks
CM
• June 19th 2012, 08:13 AM
Reckoner
Re: Cartesian Coordinates on Spherical Helix
Quote:

Originally Posted by cm3798
$zt = sr * sin(90*t)$
$xt = rzt * cos(t*360*2*\pi*sr*90/360/.3)$
$yt = rzt * sin(t*360*2*\pi*sr*90/360/.3)$

From your picture it looks like the spiral makes about five passes around the hemisphere, but when I graph your functions I'm getting way more than five revolutions (the actual number depends on the radius). Is this correct? And I assume that all of the angles are in degrees?
• June 19th 2012, 10:06 AM
cm3798
Re: Cartesian Coordinates on Spherical Helix
starting at t=1 ending at t=0 with sr=.944 I get the attached picture. Yes the number of turns will be dependant on the radius and yes angles are in degrees.
• June 19th 2012, 10:18 AM
Reckoner
Re: Cartesian Coordinates on Spherical Helix
Quote:

Originally Posted by cm3798
starting at t=1 ending at t=0 with sr=.944 I get the attached picture. Yes the number of turns will be dependant on the radius and yes angles are in degrees.

Okay, just checking.

One further clarification before I put too much time into this: do you want the distance in space between the points to be 0.375", or do you want the distance along the curve to be 0.375"? Or did you want the distance along a segment of a great circle of the sphere to be 0.375"? From the picture I assume you meant the first one, but I'd like to make sure.
• June 19th 2012, 10:26 AM
cm3798
Re: Cartesian Coordinates on Spherical Helix
Both the .375 and .300 are in space (cord).
• June 22nd 2012, 05:40 AM
cm3798
Re: Cartesian Coordinates on Spherical Helix
I could really use some assistance here. If my question is unclear please let me know. Any suggestion or comments would be greatly appreciated.

Thank you!
CM