Objectives The ship shafting alignment system, as a core piece of equipment in shipbuilding, relies heavily on parallel mechanisms to achieve high-precision pose adjustment of shaft segments. However, in practical engineering applications, multiple error sources—such as coordinate system deviations caused by uneven foundation surfaces, manufacturing and assembly errors of the mechanism, drive-quantity errors of linear guides, angular errors of actuator axes, contact position errors between actuator ends and shaft segments, and distance deviations between parallel branches—couple with one another. This coupling leads to discrepancies between the theoretical kinematic model and the actual operating behavior, resulting in reduced positioning accuracy of the shaft segments and affecting the overall quality and efficiency of ship assembly. Therefore, the aim of this study is to identify the various error parameters of the ship shafting alignment system, quantitatively correct the kinematic model to minimize residual errors in shaft-segment pose adjustment, and develop a dedicated kinematic calibration algorithm for the ship shafting alignment system, thereby providing technical support for improving the docking accuracy and operational reliability of the system under real-world conditions.

Methods First, considering the structural characteristics of the ship shafting alignment system composed of two parallel actuators with five degrees of freedom, a spatial closed-loop vector equation of the system was established using the vector method. By differentiating and linearizing this equation, the mapping relationship between various error sources (such as drive-quantity errors, angular errors, contact position errors, and inter-actuator distance errors) and pose deviations was clarified, resulting in a linearized error model. Second, considering that the linearized error model is based on the small error assumption and may become invalid when errors exceed certain limits, a Bayesian inferential framework was adopted to estimate the identifiable parameter intervals of the model. Through Monte Carlo simulation generating extensive pose data, effective samples were screened, and the posterior distributions of error parameters was calculated to define the reliable applicability range of the model, ensuring that subsequent parameter identification and pose compensation occur within a valid domain. Finally, the Levenberg-Marquardt (LM) algorithm was selected for parameter identification. To further enhance iteration efficiency and convergence performance, a dynamic damping factor adjustment strategy was introduced. The iteration step size was optimized based on the convergence behavior of the pose residual error: if the pose residual error decreases after iteration, the current damping factor is retained; otherwise, the damping factor is adjusted by a specific growth rate before re-iteration, thereby realizing accurate identification of error parameters and effective correction of the kinematic model.

Results Numerical simulation results show that the proposed kinematic calibration method achieves excellent performance in error parameter identification and model correction. The average identification accuracy of error parameters reaches 91.83%, with 15 error parameters exceeding 99% accuracy and 23 error parameters surpassing 80%, indicating high reliability of the identification results. After applying the identified error parameters to correct the kinematic model, the pose accuracy of the shaft segment is significantly improved: position errors in the Y and Z directions are reduced by an average of 80.2% and 59.7% respectively, while the rotational attitude error around the Z-axis decreases by an average of 72.9%. Although the rotational error around the Y-axis remains largely unchanged, this is mainly attributed to the random selection of pose configurations, which affects the identification accuracy of key geometric parameters. In addition, when measurement noise is introduced (0.001 mm for position and 0.000 1° for attitude), 19 parameters maintain identification accuracy above 90% and 21 parameters above 80%, demonstrating strong noise immunity and robustness of the algorithm.

Conclusions The research verifies the accuracy of the established linearized error model and the effectiveness of the improved LM algorithm. The proposed kinematic calibration method can accurately identify various error parameters of the ship shafting alignment system, significantly reduce the pose residual errors of the shaft segments after model correction, and maintain high identification accuracy even under low-level measurement noise. This study addresses a gap in dedicated kinematic calibration method for the ship shafting alignment system, providing a reliable technical reference for positioning compensation in practical engineering applications. It holds important practical significance for improving the assembly precision and efficiency of ship shafting and promotes the intelligent development of ship manufacturing equipment.