Abstract
This paper presents a dynamic model for the oscillating conveyor mechanism, governed by a differential equation that describes the system’s motion under the influence of both driving and resisting torques. The resistive torque Mr is modeled as a linear function of angular displacement φ6, while the driving torque Md incorporates a damping term proportional to the angular velocity ω1 . The system’s inertial properties are captured through time-dependent terms such as as A(t), B(t), D(t), E(t), F(t), H(t), N(t), M(t), Q(t), R(t), and W(t), which account for the interaction between the mechanical components, including the angular positions and velocities of the system’s joints. A numerical solution is obtained using an approximate calculation method, specifically an explicit finite difference approach, with initial conditions set to ω0 = 0 and φ0 = 0. This method allows for the computation of angular velocities and displacements over discrete time intervals, providing insight into the system’s dynamic behavior. The results demonstrate the importance of damping and nonlinear dynamics in regulating oscillations, offering a framework for understanding the stability and response of oscillating conveyor mechanisms. The model’s sensitivity to initial conditions and the role of numerical stability are discussed, with suggestions for future work to improve accuracy and applicability in real-world systems.