This paper presents the mathematical model for rolling behaviors of a small regular polygonal part on an inclined plane. Throughout the numerical analysis performed with the simulation program which has been experimentally validated, it is shown that the number of edges of the rolling polygonal part can be a measure for the energy dissipation rather than the coefficient of friction. The appropriate slope angle has been found to be around 20 degree for roughness-separation as well as shape-separation of polygonal parts which have small number of edges. In additions, the vibratory motion applied to the inclined plane is able to cause mixed parts to be separated more effectively according to the shape or the roughness. Finally, a couple of parts separation methods based on the analysis results are presented, and are validated through the numerical simulation.