Posted tagged ‘drawing ellipses’

My elliptical obsession (or why everyone needs a set of trammel points)

November 15, 2014

I’ll admit it.  I have an obsession.  I’m fascinated by ellipses.  I’m amazed at how many different ways you can create an ellipse.  And most of the regular followers of this blog know that I’ve carried on about the subject, ad nauseum.

I’m just going to throw one more method out there for your consideration.  Then, I promise that I won’t visit this subject matter again…

Most serious woodworkers are familiar with the “string and nails” method of making an ellipse.  It’s not a bad method, but it can be imprecise, as nail placement can be a little off and string can stretch.  In fact this method is many times referred to as the Gardener’s Ellipse.  It seems that elliptical garden beds were quite the rage and this became the preferred method of layout.  However, in less agrarian applications, there is another method that is both simple and very precise.  It does require a set of points and some type of marking device.  Usually these points would be manufactured trammel points, although they can be as simple as two nails.  So, here’s the method:

First, strike perpendicular lines;

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Our goal is to create an ellipse with a major axis of 18″ and a minor axis of 12″.  Set the points at half of each axis from the marking device.  In this case half of the minor axis is 6″ and half of the major axis is 9″;

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Secure any type of squared guide in one of the quadrants that you’ve drawn;

Carefully begin to rotate the device while keeping the points in contact with the square guide.  (BTW, most folks will refer to two trammel points on a stick as a “beam compass”.  A beam compass, of course, is used for drawing arcs and circles.  But with the addition of a third point, the beam compass becomes a trammel beam (also referred to as a “trammel rod” or simply “trammel”) and can be used to create elliptical lines, something that can’t be done with dividers or wing compasses, hence the layout of “two arc” ovals.  Many old texts show the trammel being used with a cross shaped guide.  This would have been a common device in engineering or layout departments.)

The following series of pictures demonstrates the actual travel of the trammel beam.

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After one fourth of the ellipse has been drawn simply position the squared guide in the other quadrants and repeat the process.  The result will be a precise, repeatable ellipse.

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A little more about creating an elliptical plan

October 16, 2014

Several folks wrote and said that they were having some difficulty getting their heads around this method.  Well don’t despair.  When I first read about this method, it took me a couple of days for it to sink in.  And, if you don’t have much experience with projective drawing, it’ll take a bit of cogitation.  Of course, at my age, everything takes a long time to sink in.  But it doesn’t necessarily stay “sunk in” for long.

But here’s a little more graphic information that might help.  First off, I elongated the major axis to make the model a little more easily understood.  So remember, A-B is the Minor axis, A-C is the Major axis.  I’ve divided the A-B line into equal segments (with a couple of little “cheater” segments at the ends).

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Again, I extend the segments at right angles to the diagonal line and transfer the line measurements from the semi-circle.

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I join the dots to create the elliptical line.  If I add this elliptical line to the diagonal line running from A to C, I’ve got a 1/2 plan.  I could use a flexible drawing spline to “fair” the line.  Or if I was working with a wooden plan, I’d simply fair the edge with a fine rasp.

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If I want to see a full plan of the ellipse, I simply extend the angled lines and transfer the measurement to the other side.  Again I connect the dots and I see the ellipse in full view.  This is very helpful if I working in scale on a table, as I can quickly determine the appropriate rectangular measurements for the base.

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Hope this helps.

Another way to create an elliptical 1/2 (or 1/4) plan

October 15, 2014

A true ellipse is, in my opinion, is one of the most beautiful shapes in the universe.  Unlike an oval that is drawn with two mirrored radii (or three in the case of a true “egg” shape), the radii of the ellipse continually change.  It’s incredibly strong shape in structural terms and it’s one of the best shapes for table tops.  There are many ways to draw an ellipse.  But here’s an old method that you don’t often see referred to these days.  It’s simple and can be extraordinarily precise.  This method can also be very helpful if you’re creating domed framing for any type of construction.

First, establish a horizontal base line then raise a vertical line.

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Swing a semi-circle with a diameter based on the minor axis of the ellipse.

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Next, open the compass to the length of the major axis and strike a point to the base line.

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Draw a diagonal line from the base line to the top of the diameter, as shown.  Then divide the vertical line into any number of equal segments.  (Note, the more segments, the more precise the plan will be.)  Now, draw lines, parallel to the base line, from the semi-circle and extend them to the diagonal line.

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Extend the lines at right angles to the diagonal line.  (These lines should be longer than the radius of the semi-circle.)

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Set your compass to one of the line segment lengths in the semi-circle.

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Transfer this measurement to the corresponding line that has been raised from the diagonal line.

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It’s difficult to see in the below illustration, but after you have transferred all of the line measurements, you will have, effectively, created a coordinate map.

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Connect the dots and, voila, you have a half or quarter plan based on exact measurements.  (Note that I have “thrown in” a couple of extra lines at the top and bottom of the semi-circle, just to create additional coordinate points.)

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Again, there are many ways to draw true ellipses.  But I find this method produces the best results for large work and it is considerably more precise that the string and nail method.


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