In this study, we aim to identify shortcomings in the operation of multisatellite planetary gearboxes and to justify improved designs of planetary self-aligning mechanisms, which allow torque to be transmitted through all installed satellites. To that end, we studied a domestic planetary three-satellite MPZ gearbox installed on a magnetic separator, designed for wet separation of strongly magnetic ores and materials into magnetic and non-magnetic products, and a planetary gearbox of a special structure. 3D models of the classical three-satellite and single-sliding self-aligning gearboxes were constructed in the 3D module of the T-Flex CAD software. The performance of the mechanisms was evaluated by structural analysis and Chebyshev’s mobility formula. The constructed 3D models were used to study the engagement process of the classical three-satellite and single-sliding self-aligning gearbox. The latter is distinguished by the presence of two levers, which are introduced additionally to three satellites. During the research, the lateral clearance between the pairs of satellite teeth and center wheels was accepted according to GOST 1643–81. The conducted analysis of contacts at rotation of the central driving wheel by 30°, 110°, 200°, and 310° established further designing of the applied planetary gears to be inexpedient due to impossibility of realization of power transfer simultaneously through all satellites. The main disadvantage of the operation of multisatellite gearboxes was found to be the requirement for the side clearance selection, which should ensure the operability of the transmission at the moment of motion transfer. When designing multi-satellite single-slide selfaligning planetary mechanisms, additional levers should be introduced into the structure, the number of which should be equal to the number of satellites. Hence, the use of self-aligning planetary gears makes it possible to reduce the dimensions due to the uniform distribution of the transmitted torque, since the calculated value of the torque can be reduced by the number of satellites. This allows the gears to be adapted to the working loading conditions, which significantly improves the performance of the entire machine or unit.