In the context of sustainable manufacturing, efficient collaboration between humans and machines is crucial for improving assembly quality and efficiency. However, traditional methods for action recognition and human–robot collaborative assembly often face challenges such as low efficiency, low accuracy, and poor robustness. To solve such problems, this paper proposes an assembly action-recognition method based on a hybrid convolutional neural network. Firstly, an assembly action-recognition model is proposed using skeletal sequences and a hybrid convolutional neural network model combining Spatial Temporal Graph Convolutional Networks (ST-GCNs) and One-Dimensional Convolutional Neural Networks (1DCNNs) to sense and recognize human behavior actions during the assembly process. This model combines the joint spatial relationship and temporal information extraction ability of the ST-GCN model with the temporal feature extraction ability of the 1DCNN model. By incorporating Batch Normalization (BN) layers and Dropout layers, the generalization performance of the model is enhanced. Secondly, the model is validated on a self-constructed dataset of assembly actions, and the results show that the recognition accuracy of the model can reach 91.7%, demonstrating its superiority. Finally, a digital workshop application system based on digital twins is developed. To test the effectiveness of the proposed method, three sets of control experiments were designed to evaluate both objective and subjective aspects and verify the feasibility of the method presented in this paper. Compared with traditional assembly systems, the proposed method optimizes the recognition of human–robot collaborative assembly actions and applies them to intelligent control systems using digital-twin technology. This intelligent assembly method improves assembly efficiency and saves assembly time. It enables efficient and sustainable collaboration between humans and robots in assembly, leading to a positive and sustainable impact on the manufacturing industry.