Results 1 to 4 of 4

Math Help - Involute Spline Function

  1. #1
    Newbie
    Joined
    Mar 2010
    From
    Mentor Ohio
    Posts
    2

    Involute Spline Function

    If VAPA1 = (Tan PA1) - (Arc PA1) = INVPA1
    The AGMA "Manual of Gear Design" book descibes this as a "vectorial angle".

    The book gives an example:

    VAPA1 = (Tan 14.5) - ((PI/180) * 14.5) = .00554
    INVPA1 = .00554

    If I have INVPA2 = .057897
    I need to find PA2

    Suggestions?

    FlabbyRoach
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
    2,570
    Thanks
    1
    Hello FlabbyRoach
    Quote Originally Posted by FlabbyRoach View Post
    If VAPA1 = (Tan PA1) - (Arc PA1) = INVPA1
    The AGMA "Manual of Gear Design" book descibes this as a "vectorial angle".

    The book gives an example:

    VAPA1 = (Tan 14.5) - ((PI/180) * 14.5) = .00554
    INVPA1 = .00554

    If I have INVPA2 = .057897
    I need to find PA2

    Suggestions?

    FlabbyRoach
    Using a spreadsheet, I got 30.693^o.

    Grandad
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Mar 2010
    From
    Mentor Ohio
    Posts
    2
    Thank You.

    Could you explain how to reverse the equation to find that answer?

    Thanks again.

    FlabbyRoach
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
    2,570
    Thanks
    1
    Hello FlabbyRoach
    Quote Originally Posted by FlabbyRoach View Post
    Thank You.

    Could you explain how to reverse the equation to find that answer?

    Thanks again.

    FlabbyRoach
    No, I'm afraid I can't. It's not possible to get an analytical solution to an equation like:
    \tan\theta-\theta = k,
    which is what your equation is - where \theta is an angle measured in radians, and k is a constant.

    The best you can do is to use a numerical method to get an approximation to the answer. As I said, I used Excel, which has a Goal Seek facility. This usually enables you to get an accurate answer to a problem like this very quickly - although in this case, the answer wasn't very accurate, so I refined it manually, using basically a 'trial and error' process to home in on the answer.

    It sounds a bit unsatisfactory, but it's actually very quick and easy to do.

    Grandad
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Need help with B-spline determination
    Posted in the Advanced Math Topics Forum
    Replies: 0
    Last Post: May 25th 2011, 12:42 PM
  2. Spline Function
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: October 26th 2009, 05:40 AM
  3. Cubic Spline Function
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: October 22nd 2009, 05:31 AM
  4. Replies: 1
    Last Post: January 3rd 2009, 01:56 AM
  5. Construct involute
    Posted in the Calculus Forum
    Replies: 2
    Last Post: February 15th 2008, 03:23 AM

Search Tags


/mathhelpforum @mathhelpforum