Aristotle's Wheel

We have a wheel with a smaller wheel attached to it (left side of the diagram). The larger wheel rolls once on a flat surface, so that the red line is the circumference of the larger wheel. During this movement, the smaller wheel rolls along the blue line all the way. The blue and the red are equal length, and both wheels rolled the same number of times, so the circumference of the smaller wheel is the same as that of the larger wheel. What - or where - is the problem?
More GeoGebra at mathhombre.blogspot.com