MOVEMENT OF OPERATING MEMBERS OF MECHANISMS ALONG ELLIPTIC AND CIRCULAR TRAJECTORIES

Abstract

The work objective is to generalize the principle of combining movements into circular movements. The problem to which the article is devoted is the analytical description of the trajectories of combined movements. Research methods. Analytical geometry methods are used. The coordinate system x'0'y' is considered, which rotates in the coordinate system x0y without angular acceleration with ω velocity. The rotation radius is equal to ρ1. At the same time 0x || 0'x', 0y || 0'y'. Object a rotates in the coordinate system x'0'y' without angular acceleration at the velocity ± ω. The rotation radius is equal to ρ2. The novelty of the work realises in ellipse formulas expressed in terms of radii of opposite directions. The results of the study: it is established that during rotations in opposite directions, the trajectory of the total motion is an ellipse; all the standard characteristics of the ellipse are determined in relation to the case under consideration; the inclination of the elliptical trajectory is established; it is shown that if the trajectory of the total motion is elliptical and the semi-axes are equal to (ρ1 + ρ2) and |ρ1 – ρ2|, then object a moves along a circular in the coordinate system x'0'y' without angular acceleration with velocity - ω; just as the result of the superposition of two non-accelerated movements is also non-accelerated, i.e. uniform and rectilinear motion, with rotations in one direction, the trajectory of the total motion is a circle; with circular movements with multiple velocities, the trajectory of the total motion is snail. Conclusions: the practical aspect of the study is determined by the fact that the formulas obtained can be directly used in CAD when performing design work.