eliptical jigs

[scottreaves]

If I draw an eliptical arch @ the inside radius. How do I extrpalate outward for a casing that is 4" wide @ all points. Can this be accomplished by extending the radius by a given amount? how do I determine this amount?

 

[Adrian2]

Dear Scott;

I am not too clear on exactly what you you are after but if its the equation of an ellipse you want to fool around with, try this this link:

http://mathworld.wolfram.com/Ellipse.html

If thats not helpful please repost and give a little extra background info.

Regards Adrian D.

 

[metman]

Scott

If you can get your hands on a drafting manual that explains the four-center method for constructing an ellipse, it might help to answer your question. With this construction method you end up with two arcs that blend so nicely that visually you cannot tell that it is actually a discontinous curve. If you compare the equation of a circle to that for an ellipse, within the region of the larger arc, the difference between a true radius and the actual x,y position on the ellipse is minute. In other words, this construction method gives you a definite line of demarcation (or theoretically very close)where the larger radius diverges from the elliptical form and should help you to easily determine how far to extrapolate.

I discovered this phenomenon during the derivation of an equation for relating end mill diameter/spindle axis angle vs approximate radius of cut and maximum depth allowable on manual vertical milling machine. This was prior to CNC when toolmakers used this method of approximating an oddball concave radius.

Hope this helps,

Leonard Jesus is The TRUTH