The paper presents new mechanisms of reciprocating motion, built on the basis of a two-row planetary gear with non-circular gearwheels with two external gears. The desired type of the output link motion is realized by converting the rotationally reciprocating movement of the planetary mechanism output shaft using the transmission “toothed wheel — toothed rack”. The proposed mechanisms are balanced on the example of three planetary gear schemes, with one, two and three satellites. Structural analysis of gears with multiple satellites has shown that the addition of each extra satellite takes away one degree of freedom from the mechanism, as a result of which it becomes immobile. It is proposed to use a counterweight on each additional satellite instead of one two-moving kinematic pair, which leads to the elimination of redundant links. The conditions of static equilibrium for the developed schemes of planetary mechanisms are obtained, which make it possible to locate the centers of mass of the mechanisms on the axis of rotation and thereby significantly reduce noise and vibration in the gear developed on its basis.