Novel approach for planetary gear train dimensional synthesis through kinematic mapping

The synthesis of a kinematic trajectory traversed by an output link (planet gear) and posture of a planetary gear train with noncircular gears can be divided into two phases: dimensional synthesis of the open-chain 2R mechanism (planetary carrier) and optimization of the transmission ratio of noncircular gear pairs. According to kinematic mapping theory, more than one closed coupler trajectory can be obtained by five preset poses. Simultaneous consideration of the trajectory shape, posture, and gear ratio is difficult during planetary gear train synthesis. This work therefore proposes a new method for the synthesis of planetary gear train in which different path segments in different trajectories are selected and a group of same-type 2R mechanisms is employed to pass through them in order to rebuild a new, closed trajectory. Subsequently, the transmission ratio of noncircular gear pairs can be determined using the relative angular displacement of the 2R mechanism. To improve the roundness of the pitch curves of noncircular gears, two optimization steps are implemented using a genetic algorithm without alternating the data points of the requisite open trajectories. For example, a mechanism for rice pot seedling transplanting is obtained by using the method.