In the article, with the aim of finding alternative mechanical energy sources, as a result of kinematic analysis of two mathematical models of the designs of simple toothed planetary mechanisms with rotating eccentric masses of satellites, analytical dependencies of the circulation of the kinetic energy of these masses depending on the rotation speed of the carrier, the eccentric mass, the geometric dimensions of the mechanism and the angle of rotation of the carrier are obtained, and an analysis of the change in the kinetic energy of the mechanisms in accordance with the law of conservation of angular momentum depending on the change in the moment of inertia of the rotating elements of the mechanism in extreme positions is also carried out. The obtained analytical dependences reflect the cyclic change of the kinetic energy of the eccentric masses during the period of rotation of the mechanism. The results of the work are applicable for designing simple planetary mechanisms both in terms of assessing the influence of the eccentric masses of the satellites on the vibration of the mechanisms and in terms of designing alternative planetary transmission mechanisms for power plants.