A dimensional synthesis method based on the Back Propagation (BP) neural network is proposed in this paper to realize the path generation of a spherical four-bar mechanism without prescribed timing. By analyzing the coupler curve of the spherical four-bar mechanism, a method is proposed to determine the input angles and the coupler angles. Based on the relationship between the coupler angles and both input angles and central angles of links, a BP neural network is established to recognize the central angles of links of the desired mechanism. The main advantage of this method is that the objective function has fewer optimization variables. For path generation without prescribed timing, the dimension of the optimization variables is 4 and does not change with the increase of the number of prescribed points, so that more accurate optimization results can be obtained. Four examples are presented to demonstrate the feasibility and efficacy of the proposed method. It is worth noting that, in the third example, compared with the reference, the design result shows that the number of function evaluations is reduced by 99.93% and the error is reduced by 94.17%.
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