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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.

$\displaystyle rzt$ is radius of sphere at http://latex.codecogs.com/png.latex?t-X/Y plane of sphere

$\displaystyle sr$ is sphere radius

$\displaystyle t$ is % from sphere center to top of sphere

$\displaystyle xt$ is X postion on sphere at $\displaystyle t$

$\displaystyle yt$ is Y position on sphere at $\displaystyle t$

$\displaystyle zt$ is Z position on sphere at $\displaystyle t$

$\displaystyle rzt = \sqrt{sr^2-zt^2$

$\displaystyle zt = sr * sin(90*t)$

$\displaystyle xt = rzt * cos(t*360*2*\pi*sr*90/360/.3)$

$\displaystyle yt = rzt * sin(t*360*2*\pi*sr*90/360/.3)$

Thanks

CM

Re: Cartesian Coordinates on Spherical Helix

Quote:

Originally Posted by

**cm3798** $\displaystyle zt = sr * sin(90*t)$

$\displaystyle xt = rzt * cos(t*360*2*\pi*sr*90/360/.3)$

$\displaystyle yt = rzt * sin(t*360*2*\pi*sr*90/360/.3)$

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?

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.

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.

Re: Cartesian Coordinates on Spherical Helix

Both the .375 and .300 are in space (cord).

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