To design a clamping-pot-type wide-narrow-row pot seedling transplanting (WPST) mechanism with desired spatial beak-shaped trajectory and working posture, a new design method of planetary gear train transplanting mechanism (PGTM) with non-circular gears based on several key spatial poses (position and posture) was proposed. The PGTM was simplified to a spatial open-loop chain with two-revolute (2R) joints. The geometric constraint equations containing only the structural parameters of the chain were then established on the basis of the three key spatial poses, and the homotopy algorithm was used to obtain all the required parameters of the mechanism. In accordance with the parameters obtained, the relative angular displacement relation between the planet carrier and the transplanting arm was optimized, the trajectory of the mechanism was replayed, and the total transmission ratio was determined. The degree of freedom of the spatial 2R mechanism was reduced by attaching to the unequal gear pair, and the transmission ratio was distributed in accordance with the gear type to realize the design of a non-circular gear pitch curve. Lastly, a clamping-pot-type PGTM for rice WPST driven by the combination of planar non-circular and non-conical gears was designed, and virtual simulation and prototype test were conducted. Results showed that the simulation and prototype test trajectories were consistent with the desired trajectory. Under the operating speeds of 50 r/min and 90 r/min, the success rates of seedling picking were 95.32% and 90.15%, respectively, which verified the feasibility of the theoretical method. This method could provide a reference for the design of a spatial PGTM with nonuniform transmission.