This is a mechanical device that draws an ellipse. It is based
on the Trammel of Archimedes. The shuttles appear to be, but,
they are not the fixed points (the foci) described in the
definition of an ellipse: the locus of points for which the
sum of the distances from each point to two fixed points is
equal. This a special device for drawing ellipses. The
relationship to the formula, (x2 / a2) +
(y2 / b2) = 1, for an ellipse centered
around (0,0) is not readily apparent. The semi major axis and
the semi minor axis are represented, though. Do you see them?
Do you know how to draw an ellipse using a string and two
pins? Do you want to know? See Ellipse Foci for an animation
of the method.
Do you know that a circle is a special ellipse where the foci
are one point? Think about it. The semi major and semi minor
axes are the same length.