Results 1 to 6 of 6

Math Help - Cartesian Coordinates on Spherical Helix

  1. #1
    Newbie
    Joined
    Jun 2012
    From
    indiana
    Posts
    5

    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 -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
    Attached Thumbnails Attached Thumbnails Cartesian Coordinates on Spherical Helix-spherical_helix.jpg  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Reckoner's Avatar
    Joined
    May 2008
    From
    Baltimore, MD (USA)
    Posts
    1,024
    Thanks
    75
    Awards
    1

    Re: Cartesian Coordinates on Spherical Helix

    Quote Originally Posted by cm3798 View Post
    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?
    Last edited by Reckoner; June 19th 2012 at 08:18 AM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jun 2012
    From
    indiana
    Posts
    5

    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.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor Reckoner's Avatar
    Joined
    May 2008
    From
    Baltimore, MD (USA)
    Posts
    1,024
    Thanks
    75
    Awards
    1

    Re: Cartesian Coordinates on Spherical Helix

    Quote Originally Posted by cm3798 View Post
    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.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Jun 2012
    From
    indiana
    Posts
    5

    Re: Cartesian Coordinates on Spherical Helix

    Both the .375 and .300 are in space (cord).
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Jun 2012
    From
    indiana
    Posts
    5

    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
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. find X/Y/Z points on spherical helix
    Posted in the Geometry Forum
    Replies: 0
    Last Post: June 14th 2012, 11:47 AM
  2. Replies: 1
    Last Post: March 28th 2011, 10:40 PM
  3. Replies: 10
    Last Post: September 24th 2010, 04:33 AM
  4. [SOLVED] Cartesian equation of a helix.
    Posted in the Advanced Math Topics Forum
    Replies: 3
    Last Post: September 14th 2010, 02:22 AM
  5. Replies: 0
    Last Post: March 13th 2010, 02:08 PM

Search Tags


/mathhelpforum @mathhelpforum