Method of reduction in machine dynamics problems and its implementation on the example of determining the reduced moment of inertia of a simple mechanism using Python

This article presents the theoretical foundations of the reduction method as an effective tool for simplifying the dynamic analysis of complex mechanical systems with a single degree of freedom. The physical principles of reduction—the equality of kinetic energies and the equivalence of the powers of external and reduced forces—are considered, allowing a real multilink mechanism to be replaced with its dynamic model in the form of a single imaginary link (the reduction link). Analytical dependencies for calculating the reduced moment of inertia of a slidercrank mechanism with zero eccentricity are derived in detail, including exact and approximate relationships for small angles. Using a twostroke internal combustion engine of an autonomous electrical installation as an example, numerical calculations of the reduced moment of inertia for 12 characteristic positions of the mechanism during a single operating cycle are performed. To automate the calculations, Python code has been developed and presented, implementing the calculations using the obtained formulas and visualizing the results. It is demonstrated how modern IT tools improve the clarity and efficiency of engineering problem solving. Particular attention is paid to the pedagogical aspect: the use of programming in combination with fundamental sections of mechanics contributes to the development of interdisciplinary competencies in students, integrating knowledge from the theory of mechanisms and machines, theoretical mechanics, and digital technologies, which meets the requirements of modern engineering education.