Transplanting rice pot seedlings without damaging the roots, which promotes early tillering, is an effective measure to enhance rice yield and quality. This study aimed to obtain the mechanized-transplanting trajectory and attitude of rice pot seedlings by utilizing non-circular planetary-gear trains, focusing on the three key actions of rice pot-seedling transplanting: seedling picking, conveying, and planting. A lightweight and simplified rice pot-seedling transplanting machinery was designed, referring to the motion characteristics of artificially transplanting rice pot seedlings by first pulling them out and then planting them. Key technologies such as non-circular gear trains, the rice seedling supply system, the transmission system, and the rice seedling-picking device were studied, and their key components were designed and manufactured, resulting in the creation of two physical model machines: an ordinary ride type and a high-speed type. The seedling-picking test and field-transplanting test showed that the rice pot-seedling transplanting mechanism can accomplish the rice pot-seedling picking, rice conveying, and planting actions. The designed operation efficiency yielded a planting-depth qualification rate of over 92%, a seedling injury rate of less than 1.2%, and a missed-transplanting rate of less than 2%.