Assembly Error Modeling Method Based on Jacobian-Torsor Embedded Neural Network

In high-precision manufacturing domains such as military equipment and aerospace, assembly accuracy of complex products fundamentally determines their core performance and operational reliability. Traditional assembly error modeling approaches encounter significant limitations when characterizing the nonlinear behaviors of 'geometry-mechanics' coupling, particularly in addressing contact deformation and dynamic coupling effects. To overcome these challenges, this paper introduces an innovative Jacobian-Torsor embedded neural network approach. The proposed method incorporates the Jacobian-Torsor theory by imposing physical constraints within the neural network architecture, enabling precise modeling of nonlinear mechanisms through a joint optimization framework that combines the 'Jacobian-Torsor loss function' with network prediction errors. The approach leverages the multi-layer nonlinear mapping capabilities of neural networks to capture implicit correlations while employing kinematic constraints from Jacobian-Torsor theory to regularize network training, thereby significantly enhancing small-sample generalization and physical interpretability. Experimental validation on a dual-axis turntable demonstrates substantial improvements, with prediction errors reduced by 46.51%, 37.44%, and 50.86% in the x, y, and z directions respectively, compared to conventional networks without Jacobian embedding. This cross-domain fusion framework, integrating physical mechanism constraints and datadriven fitting, establishes a novel pathway for addressing the nonlinear transfer challenges in high-precision assembly applications.