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.

中文翻译：

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通过运动映射进行行星齿轮系尺寸合成的新方法

输出连杆（行星齿轮）所经过的运动轨迹与非圆齿轮行星齿轮系姿态的合成可分为两个阶段：开链2R机构（行星齿轮架）的尺寸合成和传动的优化非圆齿轮副的比率。根据运动映射理论，通过五个预设位姿可以获得不止一个闭合耦合器轨迹。在行星齿轮系合成过程中，很难同时考虑轨迹形状、姿态和齿轮比。因此，这项工作提出了一种合成行星齿轮系的新方法，其中选择不同轨迹的不同路径段，并采用一组相同类型的 2R 机构穿过它们以重建新的闭合轨迹。随后，非圆齿轮副的传动比可以利用2R机构的相对角位移来确定。为了提高非圆齿轮节曲线的圆度，使用遗传算法实现了两个优化步骤，而无需交替必要开放轨迹的数据点。例如，利用该方法获得水稻盆栽育苗机制。