A novel planar motion generation method based on the synthesis of planetary gear train with noncircular gears

Four-bar linkage has been used in motion generation synthesis for a long time, but there are inevitably some shortcomings such as order defects and poor design flexibility. In this work, a planetary gear train with noncircular gears is proposed to realize planar motion generation synthesis. Compared with the four-bar linkage, it has the advantages of a compact structure, full rotatability, and flexible design. The planetary gear train with noncircular gears is composed of two interrelated parts: a two-stage noncircular gear pair and the RR dyad. The synthesis method is divided mainly into three steps: First, the constraint equation of RR dyad for planar motion generation is established, and a solution region of the double revolute joint (RR) dyads is calculated by kinematic mapping theory. Second, after the full rotatability identification of RR dyads and the determination of each transmission ratio, the centrodes of two-stage noncircular gear pairs, which correspond to the specific RR dyad, are obtained. Finally, the planetary gear train with noncir-cular gears is established to pass the given poses. This method has a universal significance and can be applied to many practical cases.