## 3 Description of Mechanism Parameters and the Work Cycle  
Parameter optimization of the rice seedling-transplanting mechanism is a multimodal optimization problem with strong coupling. In this study, based on the kinematic model of the transplanting mechanism of rice pot seedlings, a visual parameter-optimization software (V1.0) for the transplanting mechanism was developed. The software controls the shape of the mechanism through parameters, changes the shape of the mechanism in real time by changing the parameters, and observes the end-motion trajectory of the mechanism and the transmission-ratio curve of non-circular gears in real time. The software includes a custom menu bar, a graphic-display area, a parameter-control area and a result-display area. The custom menu bar can save and open the mechanism parameters and can save the mechanism diagram; the graphic-display area can display the relative motion and absolute motion of the mechanism relative to the ground in real time and can also observe the initial installation position of the mechanism; and the result-display area can numerically calculate the agronomic objectives of rice transplanting, including the seedling-picking angle, seedling-pushing angle, trajectory height, planting-arm interference, hole width, and minimum gear modulus. The transplanting mechanism for picking-type rice pot seedlings was optimized and designed, taking into account the digital requirements for transplanting trajectory and attitude. A set of the mechanism parameters that meet the requirements of transplanting trajectory and attitude were obtained: r\({}_{1}\) = 21 mm, \(\theta_{1}\) = 20\({}^{\circ}\), r\({}_{2}\) = 28 mm, \(\theta_{2}\) = 45\({}^{\circ}\), r\({}_{3}\) = 50 mm, \(\theta_{3}\) = 76\({}^{\circ}\), r\({}_{4}\) = 49 mm, \(\theta_{4}\) = 105\({}^{\circ}\), r\({}_{5}\) = 58 mm, \(\theta_{5}\) = 132\({}^{\circ}\), r\({}_{6}\) = 47 mm, \(\theta_{6}\) = 165\({}^{\circ}\), r\({}_{7}\) = 18 mm, \(\theta_{7}\) = 195\({}^{\circ}\), r\({}_{8}\) = 12 mm, \(\theta_{8}\) = 225\({}^{\circ}\), r\({}_{9}\) = 28 mm, \(\theta_{9}\) = 255\({}^{\circ}\), r\({}_{10}\) = 60 mm, \(\theta_{10}\) = 285\({}^{\circ}\), r\({}_{11}\) = 48 mm, \(\theta_{11}\) = 316\({}^{\circ}\), r\({}_{12}\) = 24 mm, \(\theta_{12}\) = 345\({}^{\circ}\), \(\varphi_{0}\) = 86\({}^{\circ}\), \(\omega_{0}\) = -53\({}^{\circ}\), \(\beta_{0}\) = -29\({}^{\circ}\), \(S\) = 150 mm, H\({}_{0}\) = 65 mm. r\({}_{1}\) represents the radius of the non-circular-geat pitch curve that controls the vertex of the polygon; \(\phi_{1}\) represents the pole angle at which the non-circular-geat pitch curve controls the vertex of the polygon; \(\varphi_{0}\) indicates the initial assembly angle of the planetary carrier (gearbox); \(\omega_{0}\) indicates the corner angle of the planetary carrier (gearbox); \(\beta_{0}\) indicates the initial assembly angle of the transplanting arm relative to the planetary gear; S represents the distance from the center of rotation of the planetary gear to the end of the clamp slice; and H\({}_{0}\) represents the vertical distance from the center of rotation of the planetary gear to the clamp slice. Based on this set of mechanism parameters, the digital feature parameters of the transplanting trajectory and attitude were determined and are shown in Table 1.  
Based on the parameters of the non-circular-gear transplanting mechanism optimized in this paper, a three-dimensional model was established, and kinematic simulation was carried out to obtain the trajectory of the end of the planting arm, as shown in Figure 7. The simulated transplanting trajectory is retracted by pushing the stem back and pulling the seedling stalk out of the rice pot (Figure 7a). Then, the planting arm clamps the rice seedlings and rotates at a certain angle to reach the seedling-pushing position, the seedling-pushing rod ejects upward, and the rice seedlings are planted upright to the ground (Figure 7b), such that the simulated transplanting trajectory meets the requirements of anthropomorphic manual rice transplanting.