Thread: 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

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 .

Grandad

Thank You.

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

Thanks again.

FlabbyRoach

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:

,

which is what your equation is - where is an angle measured in radians, and 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