Parametric equations of the trajectory of a peripheral point on wheels rolling on plane or cycloid surfaces

In this study, we present the parametric equations for the trajectory of a P-point on the periphery of a wheel which rolls without slipping down an inclined plane and a cycloid-shaped ramp. The movement of the wheel was filmed, the position coordinates of P were determined by videoanalysis and they were plotted with the corresponding parametric equations. The results show that P traces a cycloidal path in case of an inclined plane, but in the cycloid-shaped ramp, the path is not a cycloid.