Secure a sheet of white paper, then place a sheet of tracing paper on top that you can slide freely: this gives you a physical model of what is known as planar motion.
Now mark a fixed point M = M(t) on the tracing paper (the generating point) and watch the path it traces on the sheet of paper over time t. This path is called a roulette. But why?
Centers of rotation -----------------------
Between two times t and t’, the tracing paper (the moving plane) undergoes either a rotation or a translation. In the first case, there is a fixed point, the center of rotation I (*t*,* t*’); in the second, we may consider there to be one as well, at infinity in the direction perpendicular to the translation.
As t’ tends to t, the center of rotation I (*t*,* t*’) tends to the point I(t), called the instantaneous center of rotation of the planar motion.