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Using a basic, two-groove Archimedes trammel, is there a geometry or configuration that can draw a circle instead of an ellipse?

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  • $\begingroup$ doesn't the midpoint between the two joints follow the path of a circle? $\endgroup$ – Dan Rust Dec 18 '16 at 0:24
  • $\begingroup$ Yes. Do they even make elipses? $\endgroup$ – wesssg Dec 18 '16 at 0:25
  • $\begingroup$ I thought it mad circle with varying radius $\endgroup$ – wesssg Dec 18 '16 at 0:25
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    $\begingroup$ No, any point which is exterior to the arm connected by the two joints will clearly follow the path of an ellipse, and indeed by symmetry arguments, I believe the only point where a circle will be drawn is if the point being followed is the midpoint on the arm. $\endgroup$ – Dan Rust Dec 18 '16 at 0:28
  • $\begingroup$ @wesssg it is designed to make ellipses. ref: Trammel of Archimedes $\endgroup$ – achille hui Dec 18 '16 at 0:32
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No.

Examine the GIF of a trammel from Wikipedia and note the following:

The distance from the "pen" to the nearer block (pivot) is the same as the shortest distance from the center of the resulting ellipse to the ellipse. (The "short radius"; I forget the technical term.)

The distance from the pen to the further block is the "long radius" of the ellipse.

So to make a circle, both pivots would have to be coincident (at the same point), which would have to be fixed in the center rather than moving on the two tracks.

At that point you don't have a trammel anymore, you have a compass.


If you arrange the pen between the two pivots, equidistant from each, it will in fact trace a circle. That would follow the "two grooves" aspect of a trammel, but I don't think it could technically be called a trammel anymore. If you're willing to call that a trammel, then the answer would be "yes."

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  • $\begingroup$ That makes sense. At least now I know it's technically possible to create a circle with only straight tools, in oscillation, without having to affix anything to a centre point on the surface/object being inscribed. $\endgroup$ – Walf Dec 18 '16 at 5:42
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    $\begingroup$ Re: "short radius", "long radius": These are known as the "semiminor axis" and "semimajor axis", respectively. $\endgroup$ – ruakh Dec 18 '16 at 5:43

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