Combined rotations in technical systems
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 <sub /> coordinate system, which rotates in an <sub /> one without angular acceleration with the velocity of <sub /> . The radius of rotation is <sub /> . Wherein 0 x ||0ʹ x ʹ, 0 y ||0ʹ y ʹ. The object <sub /> rotates in a <sub /> coordinate system without angular acceleration at a speed <sub /> . The radius of rotation is <sub /> . It has been established that when rotating in opposite directions, the trajectory of the total motion represents an ellipse. 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 <sub /> and <sub /> , the object <sub /> performs circular motion in the coordinate system <sub /> without angular acceleration with velocity <sub /> . 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.