<p>A dimensional synthesis method using a Back Propagation (BP) neural network is proposed in this paper of path generation of a planar four-bar mechanism. Previous research revealed that coupler angles correlate exclusively with link length ratios, which allows them to be used to determine the linkage lengths. Based on this relationship, the path generation problem is addressed by solving two key points: (1) coupler angle extraction from design requirements, and (2) geometric parameter derivation from extracted coupler angle. For the geometric parameter derivation task (2), a BP neural network model is developed to establish a mapping between coupler angles and the link lengths of the mechanisms. This model enables direct determination of the mechanism’s dimensions from coupler angles, thereby circumventing issues associated with traditional methods such as solving complex nonlinear solutions or dealing with unstable convergence. Regarding the coupler angle extraction task (1), an input angle determination method is proposed to convert unprescribed timing problems into prescribed timing cases. This conversion enables the extraction of coupler angles, which are then fed into the trained BP neural network to obtain the geometric parameters. The proposed method handles arbitrary design requirements, including both prescribed and unprescribed timing scenarios. Five examples involving different types of coupler curves are presented to demonstrate the feasibility and effectiveness of the proposed method.</p>