Standard ovals? Question on reversing geometry.

[BackToBattery]

So, I'm trying to design a replacement part in AutoCad to have milled out at a local job shop. I was hoping to take some measurements and reverse the shape into an equation, which I could then plot and import into AutoCad.

 

The problem is, the shape doesn't seem to fit any standard I can find. It's an oval shape, giving the impression of a 'squished circle'. It's not an ellipse, nor a Cassinian oval (though the latter is a *much* closer approximation than an ellipse).

 

I've taken a compass and calipers and tried all the combinations of overlapping circles and ellipses I can think of. I've even gone as far as taking multiple measurements and plotting the points in Origin as both a Cartesian arrangement and in Polar, and then attempting non-linear curve fits. So far, all of my efforts have borne no fruit.

 

Now, the original part was designed in the mid-60's, so my assumption is that it was drafted by hand, and I have a hard time believing such things were done completely arbitrarily.

 

So, I suppose my questions are: A) Is/was there a series of 'standard oval shapes' for use in technical design that I could refer to? and/or B) Does anyone know of a way of reversing this shape mathematically that I haven't covered already?

 

I've traced out the basic shape onto some standard quad ruled graph paper, which I've scanned in and attached here, in hopes that it might be recognizable.

 

 

Any help is appreciated tremendously.

[ReMark]

Might it be considered semi-elliptical?

[BIGAL]

Just Google "Ellipse formula" you will get equations. Then you can do a lisp to draw.

[ReMark]

BIGAL: Not sure if you read it but BackToBattery wrote, "It's not an ellipse, nor a Cassinian oval..."

[Dadgad]

Welcome to CADTutor.

 

This sounds like a job for Lee Mac!

Hopefully he will see this thread and have some insight for you.

[cwake]

Yes, a maths degree should help! My first reaction is that it looks like each quadrant is either an inverse or logarithmic function which is then mirrored to the other three quadrants.

[steven-g]

If it was the sixties it's probably a french curve that was used. They are still about or plenty of images on the internet to test against, but you might need to do some digging to find the mathematics behind them http://jeremykun.com/category/design/ could be a start

[SEANT]

Compare the data to parabolic quadrants. It looks pretty close. In AutoCAD, to replicate a parabolic curve:

 

 

Command: _spline

Current settings: Method=Fit Knots=Chord

Specify first point or [Method/Knots/Object]: m

Enter spline creation method [Fit/CV] : cv

Current settings: Method=CV Degree=3

Specify first point or [Method/Degree/Object]: d

Enter degree of spline : 2

Current settings: Method=CV Degree=2

Specify first point or [Method/Degree/Object]:

 

 

If a bounding box is used, select a midpoint of a side, a corner, and the adjacent midpoint. See attached.

Oval.dwg