The operation effectiveness of multi-bar transplanting mechanisms is low, and the specific changing law of the transmission ratio (the curve of the transmission ratio has twice unequal amplitude [TUA] fluctuation.), which is needed in vegetable pot seedling transplanting, is difficult to fulfill using a planetary gear train with noncircular gears and a single-planet carrier. To address this problem, we propose a noncircular gear pair that comprises an incomplete noncircular gear, rack, partial noncircular gear, and elliptical gear. The structural characteristics and the working principle of the TUA gear pair were analyzed. The pitch curve equation of the noncircular TUA gears was derived from the relationship of the angular displacement of the corresponding pitch curves. The influence of central angle α and eccentricity k on the shape of the pitch curve, angular displacement, and transmission ratio of the TUA gear pair was analyzed. The TUA gear pair was applied to a proposed vegetable seedling pickup mechanism (SPM) considering the design requirements. Finally, the feasibility of the new noncircular TUA gear transmission mechanism was verified by an SPM test.

The displacement graphs (d-graphs) are the final form of planetary gear trains (PGTs) synthesis. The existing configuration synthesis methods for the d-graphs of PGTs need rotation graphs (r-graphs) as the intermediate step and produce a large amount of isomorphic KCs. This paper proposes a method to obtain d-graphs directly from the geared graph. Meanwhile, a uniform isomorphism identification method suitable for parent graphs, geared graphs, and d-graphs is presented. Finally, a fully automatic method based on parent graphs is tested on synthesizing 1-DOF PGTs with up to nine links. Our synthesis results and those in the literature are comparatively analyzed, and the reasons for contradictory synthesis results are analyzed.

An important step in the structural synthesis of kinematic chains (KCs) or mechanisms is the detection of isomorphic structures. Although many detection methods have been proposed, most of them require complex computations and have poor versatility. In this study, a simple detection method is proposed based on a compound topological invariant (CTI), which comprises the fourth power of adjacency matrix and eigenvalues. Besides two complex 15- and 28-link planar simple-joint KCs (PSKCs), the method is tested on the complete atlas of contracted graphs with up to six independent loops, PSKCs with up to 13 links, 8-link 1-degree-of-freedom (DOF) planar multiple-joint KCs (PMKCs), and 6-link 1-DOF planetary gear trains (PGTs). All the results are in agreement with the reported results in the literature. Our method possesses good versatility and has been verified as being reliable and efficient.

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.

A novel hybrid six-bar mechanism with non-circular gear constraints and its optimal synthesis method for complex multi-pose rigid body guidance tasks are proposed. An innovative optimization module is proposed to optimize the non-circularity and smoothness of non-circular gear pitch curves. The optimization synthesis of this mechanism is divided into two steps. The first step is to conduct multi-objective constraint optimization with pose error and non-circular gear pitch curve as optimization objectives to obtain the required diversified non-inferior solution set. Second, a set of solutions are selected from the solution set to construct the optimization function of non-circular gear pitch curves. The non-circularity and smoothness of the pitch curve are optimized to the maximum extent, and the pose change is ensured to be small. Finally, the multi-pose picking and planting of vegetable pot seedlings were realized using the proposed mechanism and optimization synthesis method. The final optimization design results show that the error between the actual pose and the required pose of the compact hybrid mechanism is small. The optimization effect of non-circularity and smoothness of non-circular gear pitch curves is pronounced. The effectiveness of the mechanism is verified via kinematic simulation.