Dynamic Equilibrium in Mechanical Systems with a Kinematic Lock: Classical, Exotic and Mixed Mode

This paper presents a theoretical model of a mechanical system (planetary chain mechanism and differential) closed in a kinematic feedback loop. Three dynamic regimes are analysed. Classical Mode (CM) – excitation by external torques; the results are fully consistent with conservation laws. Exotic Mode (EM) – excitation solely by built‑in tension (F0); because of the kinematic lock the tension cannot relax, which results in continuous acceleration of all moving elements. In EM the carrier (C) exhibits a negative dynamic contribution – although its physical moment of inertia (IC) is positive and constant throughout all regimes, in the dynamic equations it acts as an energy source. Mixed Mode (MM) – simultaneous action of external torques and built‑in tension. It is proved that superposition holds for angular accelerations, while powers are not additive due to the quadratic dependence, revealing an interaction term as a measurable proof of the existence of the EM component. The paper concludes that the model is mathematically consistent and calls for experimental verification, with emphasis on the mixed mode as the most realistic framework for testing.