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This study develops an integrated electromechanical model of a seed-removing device used in a saw-type cotton gin. The modeled machine unit comprises a squirrel-cage induction motor, an elastic-dissipative belt transmission, a perforated seed-removing tube rigidly connected to a ring gear, planet gears mounted on a fixed carrier, and an auger rigidly connected to the sun gear. The equations of motion were derived using Lagrange’s equations of the second kind, while the induction motor was represented by the dynamic characteristic proposed by A.E. Levin. The moments of inertia of the rotating components were identified experimentally by the acceleration method, and the resulting nonlinear ordinary differential equations were solved by a fourth-order Runge-Kutta scheme. The model reproduces the start-up, transient, and steady-state stages and makes it possible to evaluate angular velocities, torques, angular accelerations, power demand, and rotational irregularity. For the 3 kW, 735 rpm induction motor, the rated torque was 38.98 N·m, whereas the calculated peak starting torque reached 101.63 N·m, corresponding to a starting-torque ratio of 2.61. The transient process lasted approximately 3.5 s, and the maximum motor angular acceleration reached 2988.6 rad/s² at t = 2.25 s. Parametric calculations showed that the resistance moment of the perforated tube and the inertia of the auger exert the strongest influence on rotational irregularity, whereas the inertia and resistance of the planet gears have a comparatively weak effect. A reduction in the effective elastic-dissipative parameter of the belt drive from 17.7 to approximately 10.3 N·m/rad reduced the auger irregularity from 0.435 to 0.420 and decreased motor power consumption from about 2.55 to 2.50 kW. The proposed model provides a system-level framework for selecting drive parameters and limiting torsional oscillations in planetary-driven cotton-processing machinery.