Path synthesis of spatial revolute-spherical-cylindrical-revolute mechanisms using deep learning

Abstract The design of single-degree-of-freedom spatial mechanisms tracing a given path is challenging due to the highly non-linear relationships between coupler curves and mechanism parameters. This work introduces an innovative application of deep learning to the spatial path synthesis of one-degree-of-freedom spatial revolute-spherical-cylindrical-revolute (RSCR) mechanisms, aiming to find the non-linear mapping between coupler curve and mechanism parameters and generate diverse solutions to the path synthesis problem. Several deep learning models are explored, including multi-layer perceptron (MLP), variational autoencoder (VAE) plus MLP, and a novel model using conditional - β − VAE (c − β − VAE). We found that the c - β – VAE model with β = 10 achieves superior performance by predicting multiple mechanisms capable of generating paths that closely approximate the desired input path. This study also builds a publicly available database of over 5 million paths and their corresponding RSCR mechanisms. The database provides a solid foundation for training deep learning models. An application in the design of human upper-limb rehabilitation mechanism is presented. Several RSCR mechanisms closely matching the wrist and elbow path collected from human movements are found using our deep learning models. This application underscores the potential of RSCR mechanisms and the effectiveness of our model in addressing complex, real-world spatial mechanism design problems.