Rolling with and without Slipping during Orthocycloids Generation
The orthocycloid represents a plane curve generated by a point belonging to a circle which is rolling without slipping along a line. Our original idea (not approached in the specialty literature) is to consider the rolling with slipping of a wheel on a rail, instead of the rolling of the gear “gearwheel –rack” as in the case of the orthocycloid generation. In this case the length of the arc considered on the circle is no longer equal to the segment from the line supporting the rolling. The tracer point belonging to the wheel will generate other curves but orthocycloids. Various curves were obtained. Analyses were made considering the braking due to the friction between the rolling surfaces and respectively the case when the lubricant layer generates a “skating like” rolling. The yielded curves start from the classical form of the orthocycloid and afterward are distorted exhibiting an increased number of loops. Some curves are similar to elongated orthocycloids, obtained in different conditions. The curves resulted from rolling by slipping can be used in various domains.