Judgment criterion of reproducible trajectory in reverse engineering of noncircular gears

For the noncircular gear planetary gear train mechanism shown in Figure 1, the noncircular closed track of the end point of the output component of the mechanism is determined by the unequal speed transmission ratio of the gear and the mechanism parameters. Because the mechanism is a single degree of freedom transmission structure, the track form that the mechanism can realize is limited. Whether the expected track can be realized by this transmission mechanism is a clear problem in reverse engineering design.

1.Planet frame 2.Sun gear 3.First intermediate gear 4.Second intermediate gear 5.Planet gear 6.Picking-up seedling arm 7.Expected trajectory 8.Bowl

According to the establishment of the reverse engineering design model of the mechanism, the expected trajectory (Fig. 2a) is given based on the curve fitting technology, and the motion law of member 1 (planet carrier) and member 6 (seedling taking arm) can be obtained from the trajectory. Since the noncircular gear can only drive in one direction, and the member 6 can only move in one direction relative to the member 1, the monotonicity of the rotation angle of the member 2 relative to the member 1 can be used as the judgment basis for whether the expected trajectory can be realized. If it cannot be realized, it can also judge which part of the trajectory cannot be realized, so as to provide guidance for the correction of the trajectory.

For the two trajectories shown in Fig. 2a, the two trajectories are defined in the same coordinate system, and the farthest point from the track to the coordinate origin is recorded as 1. The whole cycle track adopts 1200 data points. Fig. 2B shows the rotation angle of the member 6 corresponding to the track relative to the member 1. Since the curve II in the relative rotation angle diagram (Fig. 2b) increases monotonously, it can be realized theoretically by noncircular gear planetary gear train mechanism, As curve 1 increases non monotonically, trajectory 1 can be modified accordingly according to the non monotonic increase interval of rotation angle curve 1.

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