New Results of an Analytical Study of Self-Aligning Articulated Hinge-Lever Pendulum Mechanisms

R. Nauryzbaev, M. S. Nabiollina, Meirambay Toilybayev, K. Sansyzbayev, Y. Zhaparkulova, K. Kaliyeva

2023

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DOI 10.25103/jestr.161.25
Data confidence 70 medium
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Abstract

The equation of motion of the mechanism with (n+n1) moving links, the equation of motion of the drive link is obtained.An exact analytical solution of a nonlinear differential equation is found.Based on the formula of the modern theory of mechanisms, a mathematical model of the structures of the self-aligning mechanism of the physical pendulum is determined.The parameters and the main operating modes of rational design, and the regular design of the pendulum-type mechanism are established.An innovative (unified) method of analytical research of the main object has been created.Based on this research method, structural geometric, kinematic general models of self-aligning flat two-link, three-link, four-link, fivelink articulated lever mechanisms of the physical pendulum have been developed.The oscillations of the leading link of the physical pendulum mechanism are investigated based on their specific mathematical models.A flat, complex, closed kinematic chain of six (n+n1) = six moving links and two closed loops (A and B) is investigated separately.A structural, geometric, kinematic general model of a self-adjusting, flat, six-linked hinged-lever physical pendulum mechanism is developed and a non-linear differential equation of motion is derived.The parameters and basic modes of operation of rational design and regular design are established.A comprehensive, unified and consistent method of research of a selfaligned, six-linked flat articulated lever mechanism of the physical pendulum II second class, third family from structure to dynamic synthesis is established.