Question to Art about elliptical gear

[Rlarsson]

Hi, I think only Art are able to answer this question, but all input are welcome.

I would like to do some calculations on 1:st order elliptical gears.
For this I need to know;
1) Actual gear ratio as a function of driving axle angle (input).
2) The driven axle angle (output) as a function of actual gear ratio.

Can You provide equations that describe these properties for 1:st order elliptical gears?
I fully understand if You are not willing to share that, just say no in that case.

As an alternative, would it be possible to add an output function for NonCircular gears that produces a text file with three columns: Driving axle angle, Actual gear ratio, Driven axle angle?
Function options would be: Angle to rotate Driving axle angle and total number of data points/compute steps.


I made an attempt to create an equation that describes 1:st order elliptical gears, but they don't look elliptical and clearly differs from your definition:) That's why I'm asking You for help.

Just for Your information, this was my thinking:
Came up with an equation for the gear ratio and ploted the shape according to attached images.
The radius is ploted as R = CD/(1+n) , CD = Center distance and n = actual gear ratio.

Maximum gear ratio i called m, the minimum is 1/m.
In the image, center distance is 32 and m=3, largest radius is 24 and minimum radius is 8.

/Roger

[Rlarsson]

I will answer myself: Why not use the definition of the ellips, dumbass!  ???

Anyway, I was a little to fast to ask, but the output data file would be nice to have.

/Roger

[ArtF]

Hi Roger:

  One problem you'd have is there are many formulas for ellipses. Not all ellipses make good
gears in terms of scaling, so my formula is more easily scaleable so various orders of ellipses will
mate properly.

Here the formula I use..

a = major axis radius.
e = eccentricity
p  = a * ( 1-e^2);
r =  order^2 * p;
radiusAtAngle = r / sqrt(  (order^2 * ( 1-e^2)) + e^2 + e*cos(order*angle));

  This will give you the radius at any angle, your instantaneous ratio will of course be
ratio = radius / (center-radius);

Hope this helps,
Art

[Rlarsson]

Outstanding Art!

The best answer I possibly could think of, You are my hero!

Many thanks/
Roger

[Rlarsson]

Hi Art,

a humble question, do you have an idea why I get different shape compared to Gearotic?

With the same values for Major axis radius, Eccentricity and Order I get Center Distance = 37.4 in Gearotic but 31.3 in my calculation. Is there anything missing in the formula?

If possible, please have a look at attached screen dump from Gearotic and PDF with may calculation.

/Roger

[ArtF]

Hi:

Sorry, I think I screwed you on the parens..

Here is what I use..

r = r / (sqrt( (order * order * ( 1 - e * e)) + e * e) + e * cos( order * ( ang) ));

so you have a paren out of order .. the answer at 0 should be 9.33612

Art

[Rlarsson]

Right, now it works as expected!

Thanks again/
Roger

[ArtF]

No trouble. :)