# Involute Spline Function

• March 11th 2010, 06:46 AM
FlabbyRoach
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
• March 12th 2010, 01:03 AM
Hello FlabbyRoach
Quote:

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 $30.693^o$.

• March 12th 2010, 03:01 AM
FlabbyRoach
Thank You.

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

Thanks again.

FlabbyRoach
• March 12th 2010, 12:49 PM
Hello FlabbyRoach
Quote:

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:
$\tan\theta-\theta = k$,
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.