The flexspline and flexible bearing constitute a critical contact pair in a harmonic drive system, and their torsional stiffness has a significant impact on the performance characteristics manifested by the harmonic drive. In this study, a micro scale three-dimensional fractal model was combined with a macro scale finite element simulation method to establish an equivalent torsional stiffness model for the flexspline-flexible bearing contact pair (FS-FB contact pair), which enables the theoretical prediction of the torsional stiffness of this contact pair. A torsional stiffness testing platform was constructed for a harmonic drive, and the consistency between the experimental results of the torsional stiffness curve and the theoretical predictions validates the effectiveness of the proposed model. The influences of torque, installation eccentricity, and deformation coefficient on the torsional stiffness of the FS-FB contact pair were also discussed. The results indicate that the torsional stiffness of the FS-FB contact pair increases nonlinearly with an increase in torque. On the other hand, the torsional stiffness of the FS-FB contact pair decreases with an increase in installation eccentricity, and increases before subsequently decreasing with an increase in deformation coefficient. Moreover, as torque increases, the impact of installation eccentricity and deformation coefficient on the torsional stiffness diminishes. This article provides a theoretical reference for the optimization design and performance enhancement of harmonic drives.

The flexspline, as a core component of the harmonic drive, is highly susceptible to fatigue failure due to elastic deformation and alternating stress during operation. Its performance directly affects the working life of the harmonic drive. In this paper, finite element modeling and analysis were carried out on the polyoxymethylene flexspline (POM FS), resulting in stress, displacement, and strain cloud maps. Then, using the control variable method, the influence of structural parameters such as cylinder length L, wall thickness d, and chamfer radius r on the maximum stress of POM FS was studied, and the structural parameters were optimized. Finally, the fatigue life of POM FS was analyzed based on the S-N curve of POM. The results show that the optimized POM FS has a fatigue life of 18,300 hours, which is 24% higher than the original POM FS with the initial parameters. This paper provides a technical reference for the optimization and improvement of the lifespan of POM FS.

Harmonic drives are critical components in robotic joints, and the hobbing accuracy of flexspline tooth profiles is essential for the transmission accuracy and operational stability of harmonic drives. The objective of this study is to propose an analysis method for the hobbing accuracy of flexspline tooth profiles. Firstly, a synthetic volumetric error model considering both geometric errors and thermal deformations was established based on the multi-body system theory. This model demonstrates the correlation between individual errors of the hobbing machine tool components and the spatial machining accuracy. Furthermore, the kinematic relationship of flexspline hobbing was established. Through kinematic analysis, it is concluded that the radial position deviation of the hob along the Y direction in the hobbing coordinate system directly affects the machining accuracy of the flexspline tooth profile. This deviation leads to variations in the tooth thickness of the flexspline tooth profile. Finally, theoretical tooth thickness deviations of the flexspline tooth profiles were predicted. Actual measurements of the flexspline tooth profiles were conducted, obtaining measured tooth thickness deviations. The measured values were smaller than the theoretical values, indicating the correctness of the established synthetic volumetric error model and the effectiveness of the proposed analysis method for evaluating the hobbing accuracy of flexspline tooth profiles. This research provides valuable technical references for error tracing and compensation in the gear hobbing process.

As a thin-walled, highly deformable precision component, the flexspline is subjected to complex stresses during operation. The fixture is crucial for the manufacturing of the flexspline, requiring a rational structure to ensure manufacturing precision. In this study, a finite element model of a flexspline fixture was established to analyze the contact pressure and strain between the flexspline, expansion sleeve, and core shaft. By utilizing orthogonal experiments and simulations, the maximum contact pressure between the flexspline and the expansion sleeve Pfmax, the maximum contact pressure between the expansion sleeve and the core shaft Pemax, and the maximum strain εfmax of the flexspline were obtained under varying pulling force F, taper angle α, and the number of clamps S. Range analysis was conducted to investigate the impact of F, α, and S on Pfmax, Pemax, and εfmax. These findings provide valuable references for designing and optimizing harmonic drive flexspline fixtures.

To address the challenges of constrained grid-like compartments, a motion framework integrating adaptive obstacle avoidance planning and active disturbance rejection control is proposed. First, an Adaptive Rapidly exploring Random Tree Star (Adaptive RRT*) algorithm based on multi-source state feedback is developed. Scaled-down model simulations show that, compared to conventional algorithms, its path length (374.28 mm), planning time (0.30 s), and node count (50.83) are reduced by at least 29.5%, 64.7%, and 28.6%, respectively, achieving a 100% planning success rate. Next, a control scheme based on Extended State Observer–Model Predictive Control (ESO-MPC) is designed. Simulations indicate that under nominal conditions, tracking errors are reduced by 5.78–84.35% compared to traditional MPC. Under a 20% link mass perturbation, the scheme effectively eliminates phase lag. Under complex scenarios involving parameter perturbation and a 0.6 N·m step torque disturbance, the tracking error reduction ranges from 25.27% to 87.59%, exhibiting excellent disturbance rejection robustness. Physical experiments conducted on a scaled-down experimental platform further verify that the maximum tracking errors of the manipulator end-effector along the x, y, and z axes under ESO-MPC are 0.88 mm, 0.85 mm, and 0.89 mm, respectively, significantly outperforming the 2.41 mm, 2.39 mm, and 2.47 mm observed with MPC. Finally, obstacle avoidance and trajectory-tracking simulations of an industrial manipulator in a full-scale ship compartment environment validate the engineering feasibility of the proposed framework.

To address the influence of multi-source probabilistic uncertain parameters on the dynamic transmission error (DTE) of harmonic drives, this paper proposes a robust DTE modeling and multi-objective optimization method. First, a Chebyshev surrogate model is constructed by integrating the measured static transmission error (STE) probability model, system dynamic equations, and identified nominal parameters. Prototype validations show a prediction mean absolute percentage error (MAPE) of 8.14% and a mean absolute error (MAE) of 7.761″. Meanwhile, compared to the original dynamic equations, the surrogate model reduces the single-evaluation time from 0.147 s to 0.000003 s (a 49,000-fold acceleration), effectively overcoming the efficiency bottleneck of numerical integration in dynamic response evaluation. Secondly, to achieve the collaborative optimization of system transmission accuracy and anti-disturbance robustness, a Chebyshev–AMP–MOPSO algorithm integrating a diversity entropy state-driven weight and a pyramid-hierarchical dual-track search strategy is proposed, which improves upon the issues of local convergence and uneven solution set distribution in the classical MOPSO and NSGA-II algorithms. On this basis, parameter optimization under three decision preferences was completed. The accuracy-first scheme reduces the DTE mean by 3.67%, the robustness-first scheme reduces the standard deviation by 9.36%, and the balanced scheme improves both. Finally, comparative tests on five prototypes show the actual dynamic parameters’ deviation (D_i) relative to the theoretical optimal configuration exhibits a consistent corresponding trend with measured DTE means. Prototypes with the minimum (D_i = 0.365) and maximum (D_i = 0.474) deviations yield the lowest and highest measured means, respectively, matching theoretical optimization expectations.