Citation: Mos , negut , u, E.; Tomozei, C.; Panainte-Leh˘ adus , , M.; Chit , imus , , D.; Irimia, O. Geometric Calculation of the Inﬂuence of an Oscillating Sieve’s Actuation Mechanism Position on Its Motion. Processes 2022, 10, 1760. https://doi.org/10.3390/pr10091760 Academic Editor: Alexander S. Novikov Received: 29 July 2022 Accepted: 30 August 2022 Published: 2 September 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional afﬁl- iations. Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). processes Article Geometric Calculation of the Inﬂuence of an Oscillating Sieve’s Actuation Mechanism Position on Its Motion Emilian Mos , negut , u , Claudia Tomozei *, Mirela Panainte-Lehădus , * , Dana Chit , imus , and Oana Irimia Department of Environmental Engineering and Mechanical Engineering, Faculty of Engineering, Vasile Alecsandri University of Bacau, 157 Calea Marasesti, 600115 Bacau, Romania * Correspondence: claudia.tomozei@ub.ro (C.T.); mirelap@ub.ro (M.P.-L.) Abstract: This article offers a general approach to studying a four-bar mechanism from a geometric viewpoint. The four-bar mechanism form is used in a large number of existing pieces of machinery and equipment. This type of mechanism, used to drive a screen and generate its oscillating motion, is referred to in this article for its application in separation systems. In the literature, there are numerous approaches for analyzing such a mechanism. In addition to determining this mechanism’s geometry, an examination of the inﬂuence of the drive system’s position on the motion of the tie rods, or the support system of an oscillating site, is also conducted. In the investigation, the connecting rod angle was adjusted between −45 degrees and 60 degrees without respect to the horizontal. The following parameters, which correspond to the operation of the oscillating sieve motion, were obtained from the determined mathematical relations: the movement made by the free end of the tie rod; the tie rod’s angle in relation to the crank movement varies; and variation in the angle the tie rod achieves based on the drive system’s inclination angle. From the analysis, it was discovered that the drive system’s position in relation to the other components of the assembly had a direct inﬂuence. The calculation steps were designed to be performed using Mathcad 15. Keywords: crank mechanism; mathematical coordinates; description of motion 1. Introduction The process of separating the components of a heterogeneous mixture involves differ- ent types of equipment that perform the process using different working principles. One of the most widely used methods of separating a mixture of solid particles is by separating the size of the solid particles using sieves. The working principle of a separation system based on sieves presupposes the exis- tence of a surface with holes of different shapes and sizes through which the solid particles pass and a drive system for the respective surface. The simplest drive system for a sieve is the crank mechanism, a system that generates an oscillating motion [1–3]. From a constructive point of view, the assembly made by the crank mechanism and the support system of the sieve, the tie rod, is nothing more than a system of four bars [4–7]. Four-bar ﬂat connections are widely used in various automatic devices and equipment such as automobiles, biometric prostheses, steam engine mechanisms, bicycle and solar panel rotating mechanisms, automatic garage door openers, machine steering mechanisms, medical equipment, robotics, etc., in which it is necessary to transform rotational movement into translational movement [8–21]. Though there are many research methods for determining the geometric parameters of the links that ensure continuous motion, in contrast, elements of the system, including the construction of the mechanism, meeting workspace restrictions, and the kinematic and dynamic conditions of the transmission motion, are incompletely speciﬁed, and most of them are analyzed graphically [4–7,9–11,16–45]. The system elements described above are commonly analyzed from a theoretical point of view by applying a series of methods: the hybrid cuckoo and ﬁreﬂy algorithm [8]; Processes 2022, 10, 1760. https://doi.org/10.3390/pr10091760 https://www.mdpi.com/journal/processes