# Thread: Involute Spline Function

1. ## 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

2. Hello FlabbyRoach
Originally Posted by FlabbyRoach
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 $\displaystyle 30.693^o$.

3. Thank You.

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

Thanks again.

FlabbyRoach

4. Hello FlabbyRoach
Originally Posted by FlabbyRoach
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:
$\displaystyle \tan\theta-\theta = k$,
which is what your equation is - where $\displaystyle \theta$ is an angle measured in radians, and $\displaystyle k$ 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.