Research on four-bar linkage trajectory synthesis using extreme gradient boosting and genetic algorithm

The current study on the synthesis problems of four-bar mechanism trajectories primarily relies on establishing a numerical atlas based on trajectory characteristics and employing neural networks to synthesize mechanism parameters. However, this approach has several shortcomings, including a vast database, inefficient retrieval, and challenges in maintaining accuracy. This paper presents a method for synthesizing a trajectory-generation mechanism that combines the extreme gradient boosting (XGBoost) algorithm with a genetic algorithm (GA). The purpose is to synthesize, based on a particular trajectory, the dimensions and installation position parameters of a four-bar mechanism. The paper classifies the trajectories according to their shape features and geometric center placements, thereby improving the accuracy of the XGBoost model for synthesizing mechanisms. The XGBoost algorithm is employed to synthesize the basic dimensional parameters for the mechanism, with the relative slopes of trajectories as input features. The synthesized basic dimensional parameters are turned into parameters for the actual mechanism by researching the scaling, translation, and rotation relationships between mechanisms and the trajectories they generate. The accuracy of the generated trajectories from the synthesized mechanism can be improved by applying GA to optimize the mechanism parameters. Five comparative examples are provided in this research for the different scenarios of given trajectory curves and trajectory points. The effectiveness and accuracy of the proposed approach in this study are validated in comparison to existing research methods by comparing errors between the generated trajectories and the given trajectories. Graphical Abstract