Ellipse Rolling around a Circle

ellipse eccentricity

0.85

generator offset

0

semimajor axis

1.279

roll the ellipse

3.5

This Demonstration draws a roulette of a generator point on an ellipse that rolls without slipping around a circle.

Varying the ellipse semimajor axis or eccentricity will change the circumference ratio

p

q

between the central circle and the ellipse. A closed curve can be obtained after

q

complete revolutions around the circle. By then the ellipse will have made

p+q

revolutions around its axis.

Changing the pole offset will further create a variety of curves. The bookmarks and snapshots give some examples.