Combined rotations in technical systems


DOI: 10.34759/trd-2021-120-01

Аuthors

Popov I. P.

Kurgan State University, 63/4, Sovetskaya str., Kurgan, 640020, Russia

e-mail: ip.popow@yandex.ru

Abstract

The purpose of the research consists in generalizing the principle of a combination of movements to the circular movements. The relevance of the work is stipulated by the fact that in technical systems, including aviation and space technology, particularly, in aircraft transmissions, bearings, orbital systems, helicopter mechanisms and many others, combined rotational movements are widespread, and it is important to represent the nature of the total movement when designing. The author considers an xʹ0ʹyʹ coordinate system, which rotates in an x0y one without angular acceleration with the velocity of ɷ. The radius of rotation is ρ1. Wherein 0x||0ʹxʹ, 0y||0ʹyʹ. The object a rotates in a  xʹ0ʹyʹ coordinate system without angular acceleration at a speed ±ɷ. The radius of rotation is ρ2. All standard characteristics of the ellipse were determined in relation to the case under consideration. The elliptical trajectory inclination is set. The article shows that in the case of the trajectory of the total motion is elliptical and the semiaxes are equal to (ρ1+ρ2) and |ρ1–ρ2|, the object performs circular motion in the coordinate system xʹ0ʹyʹ without angular acceleration with velocity –ɷ. Just as the result of the two nonaccelerated movements superposition is also an nonaccelerated movement, i.e. it is uniform and rectilinear movement, at rotations in the same direction the trajectory of the total movement represents a circumference. At circular motions with multiple speeds, the trajectory of the total motion represents spirals. The practical aspect of the study is being determined by the fact that the formulas obtained can be directly used in CAD when performing design work.

Keywords:

combination of movements, circular movements, elliptical trajectory, circular trajectory, multiples of speed

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