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.
is radius of sphere at -X/Y plane of sphere
is sphere radius
is % from sphere center to top of sphere
is X postion on sphere at
is Y position on sphere at
is Z position on sphere at
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.