“Circular Work in Carpentry and Joinery”, by George Collings.
I am a 31 year old trim carpenter from northern NJ and i am having a hard time with figuiring out ellipses for trim when using a trammel. i can figure out one quarter ellipses when using a framing sq. (or two perpindicular boards), i can also figure ellipses out with one straight edge and points. i need help with the trammel though.
i understand that an ellipse is a section through a cone not paralell to its base
but what is
the semi-axis
semi-major axis
and semi-minor axis in the trammel
any drawings or pictures would be much appreciated
also, any other books on this subject would be highly appreciated to know of
Replies
goosebdg- I love this topic. I will try to post a picture of my elliptical drawing jig tomorrow. Its somewhere here in the archives from years ago.
Basically, its a jig that you can set the semi-minor,,,and semi-major axis to....and draw your ellipse at the end of the tramel bar...or even guide a router on the end of it.
Think of an oval drawn out on a piece of paper. Bisect the long dimension...and also bisect the short dimension. These two lines will meet perpendicular to each other.
The semi-minor axis length is the measurement from the intersection of these two lines...out to the side of the oval on the shortest line. Likewise...the semi-major axis starts from the intersection out to the oval on the longest line.
More explanation is needed...but I will try to post a picture first. Hope this helps you a little bit!
Stan
thank you for your help
i am building in a very rich town and am still busy. thank god. my boss who is unbelievably talented wiil not teach me anything that is tough. (although, he let me just build an extension to a staircase that had a 3 foot radius horizantily and 4 foot radius vertically). he also did not teach me to find roof rafters using sine, cosine and tangent. i did it on my own.
any and all help with trammels and ellipticals would be much appreciated, also books on this would be great even ones for stairs
thank you very much goosebdg
This will give you a bit of info on an ellipse and making a beam to use with a router: http://www.josephfusco.org/Articles/Ellipse/Ellipse.htm
This is also a helpful animation which can help you see how the parts of an ellipse relate to each other: http://josephfusco.org/Flash/Ellipse_layout.html
View Image
http://www.josephfusco.org
http://www.constructionforumsonline.com
"i understand that an ellipse is a section through a cone not paralell to its base"
Actually, an ellipse is a section through a CYLINDER not parallel to its base.
If you think about it, the shape you'd create cutting a cone would have a different curve at each end.
AitchKay
would have a different curve at each end.
Yep, that sounds familiar. oh, you mean it's supposed to be symmetrical? Ok, we'll call it a design feature."Put your creed in your deed." Emerson
"When asked if you can do something, tell'em "Why certainly I can", then get busy and find a way to do it." T. Roosevelt
A section through a cone not parallel to its base at an angle less than the nappe of the cone is an ellipse. The curve will be symmetrical (the same at each end).
The proof of the ellipse (and other conic sections), known to the geometers of classical Greece, employs external tangents to spheres.
Joe Bartok
Edited 7/6/2009 1:30 pm ET by JoeBartok
I never understood why people go to so much trouble to figure out the math behind a pleasing curve. Just take a batten (thin strip of wood that is flexible) and bend it into a curve that looks right, and trace it. Zero math. Very easy. Add a string to the system to lock it into shape like a bow and you can reproduce the curve.Admittedly, this works best for small projects, like furniture. And if you are laying out a curved wall, you will want the precision that math gives you. But it's a technique that will work in many situations.
we ain't buidin' a piany<G>http://www.tvwsolar.com
We'll have a kid
Or maybe we'll rent one
He's got to be straight
We don't want a bent one
He'll drink his baby brew
From a big brass cup
Someday he may be president
If things loosen up
sorry not doing small projects, i wish. doing 40 foot wide elliptical decks ,not kiddin'
rich people are still rich and i got my hours cut, because designers can not figure out what they want to do
If you say so, I'll believe you -- I wouldn't think of trying to go toe-to-toe with you when it comes to math. But it's completely counter-intuitive, since if you look at a cone as a stacked series of circles, you are dealing with a very small radius at one end as compared to the other.As I said, I'll believe you, especially if someone wants me to put up money against you on this!That aside, since ellipses generated from cylinders are so much easier to visualize and experiment with, given that a few scraps of PVC pipe and a miter box will serve as your "One picture is worth a thousand words," model, why would someone choose to generate an ellipse starting from a cone?(BTW, while you may lose me, I'm all ears!)AitchKay
Oops. I was aiming that last at you, Joe.AitchKay
It's true that an ellipse is easier to visualize as a plane cutting through a cylinder. And if you think of a series of circles created by planes cutting a cone parallel to its base, it does seem counterintuitive that the curvature of a shape formed by a tilted cutting plane will be the same at both ends.
But looking at the cylinder model, how would one prove the curve is an ellipse? Sure, it's "common knowledge" that such a cut through a cylinder is an ellipse and we know the formula for the foci is the square root of the semi-major axis squared minus the semi-minor axis squared. (This is likely all the OP wanted and I can't help feeling I'm drifting from the intent of the original question ...) How do we show that the sum of the distances from the foci is constant at any point on the curve, beginning with only the geometry?
This is what geometers such as Pythagoras, Euclid, Apollonius, etc., were after ... not just an assertion or hypothesis but an incontrovertible geometric proof. The attached doc and pdf files are my version of a diagram in a Grade 12 math text: the diagram in the book being based on the proof by Apollonius. By rotating the angle of the section plane the same logic can be applied to the other three conic sections (circle, parabola and hyperbola), showing that all the conic sections are untited by the same underlying geometry.
The drawings in the attachments aren't really different from the Wikipedia article I linked to but maybe there's something in there that will click and help explain why the section through the cone at less than the nappe angle produces an ellipse.
Joe Bartok
Thanks, Joe,I'm off to work now, but I'll take a look at it.I think my definition of "nappe" might be different from yours -- can you fill me in? And are there an infinite number of "nappe angles," ranging from just departing from circular (or is a circular slice a nappe as well?), to a slice going from just off the apex to just off the circular base?Thanks again,AitchKay
EDIT ... AitchKay, I just read your last post. The nappe is the sloped surface of the cone, one half of a double cone. Courtesy of Mathworld: nappe.
More on applied conics (off topic again ... no trammel arms here!).
Examples of the "Compound Joint" referenced in the ellipse proof attachments in my previous post may be seen in the first few images in my Photo Gallery. I actually used vector analysis to solve the compound angles but the math was based on the conic model of a compound joint.This round roof into gable thread in the JLC Forums was interesting. The geometry and math threw me at first because the conic section (an ellipse) produced by the sloped cutting plane was further rotated to plan view ... Sloped Frustum of a Pyramid or Cone Calculator and Diagrams. The discussion in the JLC thread was confined to a case where the nappe angle of the cone was greater than the slope of the roof, producing an ellipse. But the plot thickens ... what if we vary the slope of the roof? Intersection of Cone and Slope of Roof ... the curves are all conic sections, united not only by geometry but by a single formula based on the eccentricity, where the eccentricity is a simple ratio of the roof slope and the nappe slope. Kind of neat, isn't it?
Joe Bartok
Edited 7/7/2009 10:12 am ET by JoeBartok
Edited 7/7/2009 10:16 am ET by JoeBartok
Edited 7/7/2009 10:17 am ET by JoeBartok
Edited 7/7/2009 10:17 am ET by JoeBartok
goosebdg- Here are a few pictures of my elliptical drawing jig. If the trammel arm were beefier...it would guide a router.
Those two swivel blocks are dovetailed and ride in the dovetail grooves in the track. All you have to do is measure down from where the pencil goes through a hole at the end of the trammel...the distance of the semi-major axis...and set the pivot point of the dovetail block on that...and the same for the other one down the length of the sem-minor axis length. It draws a very nice ellipse.
Stan
Stan
I dunno if yu have seen one of these devices....
http://www.supertool.com/forsale/t95.jpg
Eric