I was sent the following YouTube link http://showyou.com/v/y-pNe6fsaCVtI/crazy-circle-illusion?u=multimotion which shows a series of 'balls' moving around a circle. The caption with this link was: "Eight Balls Moving in Straight Lines Interesting......it's all in the timing. Eight Balls Moving in Straight Lines Who would think of this?"
A Cycloid created by tracing a point on a circle as it travels along a line, but they become more interesting when the point is traced as the wheel of circle is inside or outside of a circle.
Many moons ago I created a number of these off shoots and had them prepared on Overhead Projector Slides.
The ones I created consisted of drawing circles from equidistant points on a circle to a point inside or outside the circle and similarly with a point on a line with the points on the circle.
A great practice for measuring and using the compass and the students end up with interesting designs.