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Math Help - Involute Spline Function

  1. #1
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    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
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  2. #2
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    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
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  3. #3
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    Thank You.

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

    Thanks again.

    FlabbyRoach
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  4. #4
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    Grandad's Avatar
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    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
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