Incorrect application of the epicycloid equation to the planetary mechanism of the cotton harvester
The content of the paper is based on the mathematical construction of the parametric equation of the epi- and hypocycloid curve described by a circle point. The purpose of the paper is to present the equations of epi- and hypocycloids in a parametric form in relation to the epi- and hypocyclic mechanism in a form convenient for calculation; to present the results of computational experiments on constructing phase trajectories of motion of a moving point of an epi- and hypocycloid. A detailed analysis of the analytical model of epi- and hypocycloids circumscribed by a point of a circle (on a moving circle) has been made. The equations of epi- and hypocycloids are presented in parametric form as applied to the epi- and hypocyclic mechanism in a form convenient for calculation. The results of studies on the construction of phase trajectories of a moving point of an epi- and hypocycloid with an analysis of the obtained curves are presented. The analytical model of epi- and hypocycloids is of practical importance, since it allows designing geared linkage mechanisms formed by attaching two-wire Assur group of various modifications to the planetary mechanism, as the primary mechanism.