Rolling with and without Slipping, during Epicycloids Generation

Abstract

The starting point consists in the modality to generate epicycloids when two external circles are considered. The mobile circle is rolling on the fix circle without slipping, such as two arcs belonging to these circles are equal. The specialty literature presents an example with a simple planetary gear in which the “satellite porting” arm provides the rolling of the mobile circle on the fix circle. Our original idea, not approached in the specialty literature, considers the rolling with slipping of the mobile circle on the fix circle. Instead of the gears providing the rolling without slipping, two wheels with smooth surfaces are used now. The case when the two involved arc are no longer equal is analysed. Between them appear either frictions generating braking or “skating like” rolling when the lubricant layer is too thick. An analysis of the theoretical case when the slipping has a sense opposite to that of a normal rolling is also performer. A significant class of curves was obtained. Some are even epicycloids obtained with slipping, with other parameters.