RESEARCH CONCERNING THE DYNAMICS OF PLANE MECHANISMS

In the paper is presented a method of studying the dynamics of plane mechanisms based on the determination of the variation of the balancing moment on the cinematic cycle. The components of the balancing moment due to the gravitational forces, forces and moments of inertia, as well as those corresponding to the technological resistances are highlighted. A series of results of the simulations performed in the case of a plane mechanism are finally presented.


INTRODUCTION
The dynamic study of the mechanisms represents an essential stage in the evaluation of the performances during their operation and in terms of their optimal design [1][2][3][4][5]. Therefore, the identification and evaluation of the influence of all factors on the dynamics of the mechanisms is a field of study of great importance [6,7]. In this paper a method of studying the dynamics of plane mechanisms is presented. The method is based on the evaluation of the balancing moment by taking into account the influence of the gravitational forces, of the forces and of the moments of inertia, as well as of those corresponding to the technological resistances. Based on the presented method a computer program has been developed and the results of the simulations performed in the case of a plane mechanism are finally presented.

THEORETICAL CONSIDERATIONS AND SIMULATION RESULTS
The balancing moment is applied to the driving element of a plane mechanism and realizes together with all the categories of forces and moments that act on the components of the mechanism its dynamic movement balance. When the variation during a cinematic cycle of the technological forces and moments is known the values of the balancing moment corresponds to the values of the driving moment. From the expression of the dynamic balance in powers of all the categories of forces and moments that act on the n moving cinematic elements of a plane mechanism it results: where: In the above relations it was considered that the plane of the motion of the mechanism is the plane (Oxy) and the gravitational acceleration g acts in the opposite direction to the axis (Oy). The projections on the (Ox) and (Oy) axes of the velocities and accelerations  The presented method was applied for the dynamic study of the mechanism in Figure 1.  C is located at the center of gravity of the triangle BCD. Elements 1, 2 and 4 are made of steel bars with a round section of radius equal to 0.015 m. The thickness of the element 3 is equal to 0.01 m.

Romanian Journal of Petroleum & Gas Technology VOL. III (LXXIV) • No. 1/2022
The element 5 mass is equal to 1 kg. On element 5 acts the ru F technological force equal to: The mechanism has two independent loops [8]  . By projecting the two vector equations on the (Ox) and (Oy) axes, the following equation systems are obtained:

in its component: O-A-B-C-O and C-D-
By solving the two systems of equations, the angles 2  , 3  and 4  and the displacement 5 s may be calculated with the following relations: x y calculates arctan(y/x) by taking into account the signs of x and y and: where: The coordinates of the centers of gravity of the component elements can then be easily determined by projecting the corresponding position vectors on the (Ox) and (Oy) axes, using the angles 2  , 3  and 4  calculated with the previous relations.
To dynamically analyze the mechanism a computer program has been developed using Maple programming language. With this computer program it has been analyzed the influence of the components

CONCLUSIONS
In this paper it was presented a method that allows studying the dynamics of plane mechanisms. The method based on the evaluation of the balancing moment has been transposed into a computer program and applied in the case of a plane mechanism having in the component two independent loops. The results obtained from the simulations highlighted the weight of the components due to the weight of the mechanism elements, to the forces and moments of inertia and to the technological resistances on the variation of the balancing moment.