Hi Anthony,

I appreciate you're not UK based, however perhaps this might be of passing interest to someone.

The London Science Museum's permanent Mathematics exhibition http://www.sciencemuseum.org.uk/visitmuseum/galleries/mathematics.aspx has a collection of truly beautiful mechanical drawing instruments dating back 190+ years. I highly recommend a visit to anyone with even a passing interest in the history of technical drawing. My recent visit really put into perspective for me just how far we've come in 200 years. Actually, what really did it, and still makes the hairs on the back of my neck stand on end just thinking about it, was being able to touch Stephenson's 'Rocket', built in 1829 in the same room as look inside the actual Apollo 10 capsule!

Back to Earth now, here's a couple of London Science Museum links showing instruments for drawing ellipses. One is an ellipsograph from 1817, the other a trammel from 1876.
http://www.sciencemuseum.org.uk/objects/mathematics/1909-191.aspx
http://www.sciencemuseum.org.uk/images/I032/10302774.aspx

There's also quite a nice animation of a trammel here:
http://en.wikipedia.org/wiki/Trammel_of_Archimedes


Cheers,
Hamish

hi hamish,

i didn't know trammel's really existed, really neat:

http://www.sciencemuseum.org.uk/objects/mathematics/1876-662.aspx

this tool is awesome too:

http://www.sciencemuseum.org.uk/objects/mathematics/1909-191.aspx

i remember playing with these as a kid:

http://www.sciencemuseum.org.uk/objects/mathematics/1976-61.aspx

thanks for the links, awesome.

hi,

here is an example of the draftmen's method. the results are pretty typical of what I have gotten trying some of the other methods. they just don't seem to work. i could be doing something wrong. but it seems the error is quite large. if i have done everything right, that would leave some of the mechanical drawing tools in the previous link as the only way to draw an ellipse accurately in real life. i imagine you could still define the ellipse by its height and width and that definition could be used by the mechanical tools and cad programs such as moi.

Hi Anthony, from what I can see that you have drawn there, it looks like you are not using "The Draftsman's Method" as described in that previous link (http://www.uwgb.edu/dutchs/MATHALGO/Ellipses.HTM) but rather the "Five-Center Method", is that correct?

The page there mentions the following:


So yes as far as I can tell that method produces a pretty rough approximation which gets worse as the width to height ratio increases.

An ellipse is a continuously changing curve and you simply cannot make a very good approximation of a rather elongated one using only a couple of arc pieces...

- Michael

Just to follow up on this and out of pure curiosity I made an ellipse in NX and simplified it, NX has a tool which can simplify splines into true lines and arcs to the closest approximation.
Anyway, NX simplified a 100mm x 50mm ellipse into 28 arcs.

-

thanks guys, i would have to agree. the pictures are of the draftmen's method. however i tried a bunch of methods and nothing seemed to come close. in their examples they show good agreement. but with the ellipse i have, i don't get good agreement.

the example ellipse i'm working with has the following characteristics:

the height from center is 9.5313263 mm, the width from center is 3.5668193 mm, the foci from center is 8.8387771 mm, and the rho value of the conic section the ellipse started from is 0.4632322 mm.

at this point i'm assuming that if it was the 1950's and i wanted an ellipse with a certain height and width, it would be generated with a special mechanical drawing tool, as shown in previous links.