Examples
Archimedes' Trammel
The Archimedes' Trammel mechanism generates an ellipse. Here we use a
point A as the ellipse's center, and put a point E on the same horizontal
line as A. The points C and E are constrained to run along the
ellipse's axes (the green lines), while the distance between them is set
to ab. When we trace the locus of the point D at
distance b from E along the same line, we get an ellipse
with semimajor axis a and semiminor axis b.
Billiards
In American billiards, you need to bounce your cue ball off two
cushions before hitting another ball. How long is the path taken by the cue
ball, A? We can create the correct path by reflecting the target
ball B in the two cushions (IJ and JG),
drawing a line between the cue ball and the twicereflected
target B", then reflecting this line back. The path length is the
same as the distance between the cue ball and the twicereflected
target.

