Pure rotation of a prism on a ramp

In this work, we study a prism with a cross section in polygon rolling on a ramp inclined at a small angle. The prism under gravity rolls purely around each individual edge, intermittently interrupted by a sequence of face collisions between the side face of the prism and the ramp. By limiting the prism in a planar motion, we propose a mathematical model to deal with the events of the impacts. With a pair of laser-Doppler vibrometers, experiments are also conducted to measure the motions of various prisms made of different materials and with different edge number. Not only are good agreements achieved between our numerical and experimental results, but also an intriguing physical phenomenon is discovered: the purely rolling motion is nearly independent of the prism's materials, yet it is closely related to the prism's geometry. Imagine that an ideal circular section can be approximately equivalent to a polygon with a large enough edge number N, the finding presented in this paper may help discover the physical mechanism of rolling friction.