In this work a mathematical model of the motion of a cylinder moving on a plane is deduced using screw theory. The linear Coulomb friction equations are applicable for the maximum static and kinetic friction forces. In the case of the rolling motion of a cylinder, the friction forces are not necessarily maxima. This paper describes the dynamic states of motion of a cylindrical part moving in three separate scenarios by the Euler dual equation. The first scenario is when the cylinder is moving on a horizontal static plane due to an external harmonic force proportional to the mass of the part. For this case, the sliding conditions are expressed as a function of the vibration parameters and generalized based on a harmonic dimensionless variable. The second and third scenarios are when the cylinder is moving by translational displacements on a horizontal and inclined plane.

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