Incorrect application of the epicycloid equation to the planetary mechanism of the cotton harvester

Abstract

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.

Refinement of the contamination formation mechanism in the pneumatic transporting system of a cotton harvester using a new U-shaped receiving chamber

“…At that, light fractions of free fine trash and dust are removed through the separator, and fine trash combined with the cotton falls into the hopper. The process of contamination formation in the pneumatic transport system of a vertical-spindle cotton harvester [23] showed that the soaring velocities of trash particles and cotton lobules differ. The following calculation method is presented to explain the reduction in cotton contamination when using the new U-shaped receiving chamber.…”

“…The results of experimental studies conducted by the authors [23] to determine the mechanism of contamination formation during machine harvesting by vertical-spindle machines (17XVtype) are shown in Table 2. The analysis of Table 2 shows that fine trash in the zone of the transporting corridor of the harvester makes up 2.98%, and in the hopper, it amounts to 4.46%.…”

Modeling spindle drive device of the cotton harvester

“…(1) where 12 Ugear ratio of a simple drum gear; It is known from theoretical mechanics that if the axes of rotational motions of rigid bodies are parallel, then their angular velocities in absolute motion are equal to the algebraic sum of angular velocities in relative and translational motions [16]. Based on this theorem, for each link of the planetary mechanism, except for the carrier, we can write the following equality:…”