# Analysis of a Mechanism Used to Operate an Oscillating Separator
## 1 Introduction  
The solid products generated by agriculture, and also those resulting from various industrial processes, are heterogeneous mixtures, i.e., mixtures of components with different characteristics or structures. To be marketed and subsequently used as raw materials in various processes, these products must undergo various operations, including mechanical separation [1, 2, 3, 4, 5]. The process of the mechanical separation of a heterogeneous mixture of solid particles can be carried out on surfaces provided with orifices, which, to make this process as efficient as possible, are subject to different types of movements, including the following [6, 7, 8, 9, 10]:  
* Linear motion--with various types of mechanical devices, horizontal movement is imparted to a work surface to increase the efficiency of the sieving process and prevent smearing. * Circular motion--this motion is generally found in vibrating screens with circular motion and is used for sorting particles into several fractions according to thickness or grain size or for sieving ground products with separation according to particle size. * Elliptical movement--this is a combination of the two types of movement presented above, which is why its efficiency is much higher. * Centrifugal motion--by imposing centrifugal motion on the mass of solid particles inside a perforated drum, the separation of a heterogeneous mixture into at least two fractions can be achieved. * Gyroscopic motion--this requires highly efficient machines used in the long filtration processes of light particles, which use the gyroscopic motion generated by a series of vibrating motors. The simplest and most commonly used method of driving a classic mechanical separator is the crank-rod or four-bar mechanism [11; 12; 13; 14]. Depending on its position on the oscillating surface, and, more precisely, on the free end of the tie rod, different working conditions for this separator can be generated. This mechanism, with its four bars, is widely used because of its simplicity of construction, and according to the literature, it has been subjected to analyses using various methods [15; 16; 17; 18]. The study of the influence of design parameters on mechanism kinematics is essential for several reasons. First, it allows engineers to better understand how different mechanisms work and how they can be improved to work more efficiently. Design parameters such as the size, shape, material, and position of the components of a mechanism can have significant impacts on how the functional parameters, such as the speed and acceleration of the mechanism, vary. For example, changing the dimensions of a mechanism element may improve or deteriorate its performance [19; 20; 21]. Second, understanding the influence of these parameters on mechanism kinematics can help design new mechanisms that are more efficient, durable, and reliable. This can lead to the development of new and better types of equipment that may be more attractive to users. In general, a mechanism analysis is carried out using different methods, such as kinematic models [22; 23; 24], methods based on different calculation algorithms [25; 26; 27], mathematical synthesis [28], different mathematical models [29; 30; 31], etc. Depending on the reference system in which the study is to be carried out, an analysis can be carried out both planarly [32; 33; 34; 35; 36] and spatially [37; 38; 39]. Studies found in the specialized literature have also approached this field from the finite element point of view, and many simulations of the movements of different types of mechanisms have been identified [40; 41; 42; 43]. Within the scientific literature, many comparative studies focused on several types of mechanisms, and the main purpose of these studies was to identify the movements they generated [44; 45; 46; 47; 48]. Also, according to the literature, many studies have determined the movement of the components of specific mechanisms using a very complex calculation that involves the analysis of each component of a mechanism [49; 50; 51].