For a 2UPR-RPU over-constrained parallel manipulator, some geometric errors result in internal forces and deformations, which limit the improvement of the pose accuracy of the moving platform and shorten the service life of the manipulator. Analysis of these geometric errors is important for restricting them. In this study, an evaluation model is established to analyse the influence of geometric errors on the limbs’ comprehensive deformations for this manipulator. Firstly, the nominal inverse and actual forward kinematics are analysed according to the vector theory and the local product of the exponential formula. Secondly, the evaluation model of the limbs’ comprehensive deformations is established based on kinematics. Thirdly, 41 geometric errors causing internal forces and deformations are identified and the results are verified through simulations based on the evaluation model. Next, two global sensitivity indices are proposed and a sensitivity analysis is conducted using the Monte Carlo method throughout the reachable workspace of the manipulator. The results of the sensitivity analysis indicate that 10 geometric errors have no effects on the average angular comprehensive deformation and that the identified geometric errors have greater effects on the average linear comprehensive deformation. Therefore, the distribution of the global sensitivity index of the average linear comprehensive deformation is more meaningful for accuracy synthesis. Finally, simulations are performed to verify the results of sensitivity analysis.

Based on a composited Newton–Cotes formula, this paper proposes a numerical method to predict milling stability considering regenerative chatter and focusing on rate and prediction accuracy. First, the dynamic model of milling motion is expressed as state-space equations considering regenerative chatter, with the tooth passing period divided into a set of time intervals. Second, a composited Newton–Cotes formula is introduced to calculate the transition function map for each time interval. Third, the state transition matrix is constructed based on the above-mentioned transition function, and the prediction stability boundary is determined by the Floquet theory. Finally, simulation analysis and experimental verification are conducted to verify the effectiveness of the proposed method. The simulation results demonstrate that, for the milling model with a single degree of freedom (DOF), the convergence rate and prediction accuracy of the proposed method are higher than those of the comparison method. The experimental results demonstrate that, for the milling model with two DOFs, the machining parameters below the prediction stability boundary can avoid the chatter as much as possible, ensuring the machined surface quality.

Avoiding chatter in milling processes is critical for obtaining machined parts with high surface quality. In this paper, we propose two methods for predicting the milling stability based on the composite Cotes and Simpson’s 3/8 formulas. First, a time-delay differential equation is established, wherein the regenerative effects are considered. Subsequently, it is discretized into a series of integral equations. Based on these integral equations, a transition matrix is determined using the composite Cotes formula. Finally, the system stability is analyzed according to the Floquet theory to obtain the milling stability lobe diagrams. The simulation results demonstrate that for the single degree of freedom (single-DOF) model, the convergence speed of the composite Cotes-based method is higher than that of the semi-discrete method and the Simpson’s equation method. In addition, the composite Cotes-based method demonstrates high computational efficiency. Moreover, to further improve the convergence speed, a second method based on the Simpson’s 3/8 formula is proposed. The simulation results show that the Simpson’s 3/8-based method has the fastest convergence speed when the radial immersion ratio is large; for the two degrees of freedom (two-DOF) model, it performs better in terms of calculation accuracy and efficiency.

Master–slave bilateral teleoperation systems face several practical challenges, including model uncertainties, time-varying communication delays, and environment-induced force disturbances. To address these issues, this paper proposes an adaptive super-twisting sliding-mode control scheme to achieve high-precision position tracking and real-time force-feedback synchronization. First, joint-space dynamic models are established for both the master and the slave manipulators, and a passive impedance model is adopted to characterize the interaction dynamics at the operator–master and environment–slave interfaces. Second, to attenuate measurement noise in the environment interaction force, a first-order low-pass filter is used to preprocess the raw force measurements, and a radial basis function neural network (RBFNN) is employed to approximate the environment torque online. Furthermore, a super-twisting sliding-mode controller is developed and combined with an adaptive law to compensate online for system uncertainties, including dynamic parameter variations and environment-induced force disturbances. The stability of the resulting closed-loop system is rigorously analyzed using Lyapunov stability theory. Finally, the effectiveness of the proposed method is validated through numerical simulations, virtual experiments conducted in the MuJoCo physics engine, and real-world hardware experiments. The results show that the proposed strategy achieves accurate position synchronization and force tracking while maintaining stable haptic interaction in the presence of bounded time-varying delays, parameter uncertainties, and external disturbances.