Finding the coefficient of rolling friction using a pericycloidal pendulum

The paper presents a method of establishing the coefficient of rolling friction by the study of the damped motion of a pericycloidal pendulum. The pericycloid is the curve described by a point belonging to a mobile circle, which is in pure rolling around a fixed circle, accomplishing an interior contact. For a pendulum with known inertial characteristics, mass and moment of inertia, the equation of motion is found starting from the assumption of a linear dependence between the friction torque and the normal reaction force from contact point. Using an experimental set-up, the law obeyed by damped angular amplitude versus time is found for a pericycloidal pendulum. The experimental data are compared to the theoretical ones, by superposition; thus, the value of coefficient of rolling friction is obtained. The values are in a good agreement with the ones from technical literature.