Motion analysis and structural parameter optimization for nested multi-link transplanting mechanism of variable plant spacing transplanting machine

The nested multi-link transplanting mechanism features a compact structure suitable for transplanting machines and enables zero-speed transplanting, which is crucial for high-quality seedling establishment. To address the challenge of existing transplanting mechanisms being unable to ensure the transplanting effect when the plant spacing changes, this study investigated the influence of key structural parameters of nested multi-link mechanisms on the motion characteristics and planting performance of transplanting devices. First, we derived the kinematic model of the nested multi-link transplanting mechanism and developed a MATLAB/GUI interface to simulate end-effector trajectories. We then quantified how individual parameters affect both the trajectory and the tip velocity of the planting end-effector. Third, we formulated a multi-objective optimization problem to maintain consistent planting depth, seedling uprightness, and adequate trajectory height across three spacing settings (350, 400 and 450 mm) and solved it with a multi-objective genetic algorithm (MOGA) to obtain Pareto-optimal structural parameters. Finally, to validate the proposed model, we compared the simulated end-effector trajectories with high-speed video data collected from a physical prototype. Simulations reveal that adjusting only the vertical position of the power-transmission pivot (point B) is sufficient to maintain transplant quality across all target spacings. Field tests at 400 mm spacing yielded a 98% qualified-planting rate with an improvement of 3.56 percentage points higher than the pre-optimization baseline. Additionally, the lodging planting rate was 1.11%, the missing planting rate was 0.22%, the coefficient of variation for plant spacing was 3.01%, and the planting depth qualification rate was 95.11%, all meeting transplanting standard requirements. These findings demonstrate that the proposed MOGA-based parameter calibration consistently achieves high transplant quality under variable spacing conditions, thereby providing a practical design framework for precision vegetable transplanters., and thus provides valuable insights for improving nested multi-link transplanting mechanisms and advancing mechanized vegetable cultivation.