# Determination of Kinematic and Dynamic Characteristics of Oscillating Conveyor Mechanism
## 6 Conclusions  
The kinematic analysis of the vibration conveyor mechanism provided insights into the motion of its components, including their positions, velocities, and accelerations. By modeling the geometric and trigonometric relationships between the links, the study established how the angular displacements, velocities, and accelerations evolve over time. The analysis highlighted the importance of understanding the interplay between link lengths, joint angles, and motion constraints for optimizing the mechanism's design and ensuring smooth operation. The results can be used to predict motion trajectories and to ensure that the conveyor operates within its intended range of motion, minimizing the risk of mechanical interference or instability. Dynamic analysis revealed the forces and torques acting on the vibration conveyor system, accounting for inertia, damping, and external forces. The study demonstrated how the system responds to dynamic loads and how these forces influence the stability and efficiency of the mechanism. The derived equations of motion captured the nonlinear interactions between the system's components, including the effects of centrifugal and inertial forces. By quantifying these forces, the analysis enabled the identification of optimal operating conditions and highlighted the need for proper force balancing and damping to minimize vibrations and wear. The numerical approximation provided a practical method for solving the nonlinear differential equations governing the vibration conveyor mechanism. Methods such as [PERSON]'s method and the Runge-Kutta approach allowed for accurate simulations of the system's behavior over time. These techniques enabled the visualization of time-dependent variables, such as angular velocity and system forces, under varying conditions. The numerical results closely matched the expected theoretical outcomes, validating the mathematical model and the approximations used. This approach is particularly valuable when exact analytical solutions are intractable, offering a reliable way to simulate and analyze complex dynamic systems. The combination of kinematic analysis, dynamic analysis, and numerical approximation provides a comprehensive understanding of the vibration conveyor mechanism. This multi-faceted approach facilitates: Insights into motion and force interactions, enabling improved designs for efficiency and reliability. By simulating system responses under various conditions, potential failure modes can be identified early. Accurate modeling supports fine-tuning of operational parameters to achieve desired performance. The methodologies and results from this study can be extended to similar mechanisms, laying the foundation for robust mechanical system analysis and design in industrial applications. Conceptualization, A.Z. ; methodology, A.Z. ; software, A.Z. ; validation, A.Z. ; formal analysis, A.Z. and K.A. ; investigation, A.Z. ; resources, A.A. and G.B. ; data curation, A.O. ; writing--original draft preparation, A.Z., G.B. and K.A. ; writing--review and editing, A.Z., A.A. and A.O. ; visualization, A.Z. and A.O. ; supervision, A.Z. ; project administration, A.Z. and A.A.; funding acquisition, A.Z., G.B. and K.A. All authors have read and agreed to the published version of the manuscript. This research was funded by Almaty University of Power Engineering and Telecommunications named after [PERSON], grant number AP19677356. Not applicable. The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.