Abstract—High-precision mechanical assemblies require accurate error propagation models to predict error accumulation in the final assembly and ensure optimal performance and reliability. Conventional linear models exhibit limited accuracy in predicting geometric errors. To address these limitations, this study proposes a modified connective assembly model based on second-order nonlinear error propagation using homogeneous transformation matrices. The model is implemented in Python and validated against existing linear and fully nonlinear assembly models to evaluate predictive accuracy and computational efficiency. At an angular orientation error of 1.0°, the linear model exhibits Z-direction errors of 0.40 mm, 0.60 mm, and 0.80 mm for 4, 6, and 8 component assemblies, respectively, whereas the fully nonlinear model predicts 0.10 mm, −0.57 mm, and −2.18 mm. The developed model reduces these discrepancies to 0.23 mm, −0.25 mm, and −1.59 mm, achieving improved predictive accuracy of 56.67%, 72.65%, and 80.20%, respectively, over the linear model. Similarly, under a geometric run-out tolerance of 1.0 mm, the linear model predicts an error of −1.60 mm, −2.40 mm, and −3.20 mm, compared to −1.70 mm, −2.79 mm, and −4.18 mm for the fully nonlinear model in the Z-direction. The proposed model narrows these gaps to −1.66 mm, −2.68 mm, and −3.99 mm, delivering predictive accuracy of 60.00%, 71.79%, and 80.61%, respectively. Moreover, Monte Carlo simulation results on 4-component assembly confirm that the proposed model replicates the statistical characteristics of the fully nonlinear model while reducing execution time from 9.34 s to 4.82 s, achieving a 48.39% reduction in execution time.

Keywords—high precision components, mechanical assemblies, variation propagations, modified connective assembly model

Cite: Muhammad Arif, Tanweer Hussain, Nayyar Hussain Mirjat, and Asif Ali Shaikh, "Modified Connective Assembly Model for Error Propagation Analysis of High-Precision Assembly of Mechanical Components," International Journal of Mechanical Engineering and Robotics Research, Vol. 15, No. 1, pp. 12-27, 2026. doi: 10.18178/ijmerr.15.1.12-27

Copyright © 2026 by the authors. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).