Rotational Errors Research Articles

On the magnitude of error in the determination of rotation axes

Rotation axes (together with rotation angles) are often used to describe crystal orientations and misorientations, and they are also needed to characterize some properties of crystalline materials. Since experimental orientation data are subject to errors, the directions of the axes obtained from such data are also inaccurate. A natural question arises: given the resolution of input rotations, what is the average error of the rotation axes? Assuming that rotation data characterized by a rotation angle ω deviate from the actual data by error rotations with fixed angle δ but which are otherwise random, the average error of the rotation axes of the data is expressed analytically as a function of ω and δ. A scheme for using this formula in practical cases when rotation errors δ follow the von Mises–Fisher distribution is also described. Finally, the impact of crystal symmetry on the determination of the average errors of the axis directions is discussed. The presented results are important for assessing the reliability of rotation axes in studies where the directions of crystal rotations play a role, e.g. in identifying deformation slip mechanisms.

Impact of Glycemic Control on Shoulder Proprioception in Type 2 Diabetes Mellitus: Mediating the Connection - Insights from a Cross-Sectional Analysis.

Shoulder proprioception is vital and this cross-sectional study investigated the association between glycemic control and shoulder joint proprioception in Type 2 Diabetes Mellitus (T2DM). A total of 120 participants, including 60 with T2DM and 60 healthy individuals, were assessed for shoulder joint position sense (JPS) using a digital inclinometer. The T2DM group exhibited significantly greater mean shoulder joint position errors in flexion (4.32° vs 2.15°), abduction, medial rotation, and lateral rotation compared to the healthy group (p < 0.001). The study found significantly greater shoulder joint position errors in the T2DM group compared to the healthy group, highlighting notable proprioceptive deficits in individuals with T2DM. Additionally, a significant positive correlation was found between HbA1c levels and shoulder joint position errors in the T2DM group, suggesting a link between long-term glycemic control and proprioceptive accuracy. The significant positive correlation between HbA1c levels and shoulder joint position errors suggests that poor glycemic control is associated with impaired proprioception in T2DM patients. This underscores the need for comprehensive management strategies to mitigate proprioceptive deficits and improve the quality of life in individuals with T2DM.

Haptic Guidance and Haptic Error Amplification in a Virtual Surgical Robotic Training Environment.

Teleoperated robotic systems have introduced more intuitive control for minimally invasive surgery, but the optimal method for training remains unknown. Recent motor learning studies have demonstrated that exaggeration of errors helps trainees learn to perform tasks with greater speed and accuracy. We hypothesized that training in a force field that pushes the user away from a desired path would improve their performance on a virtual reality ring-on-wire task. Thirty-eight surgical novices trained under a no-force, guidance, or error-amplifying force field over five days. Completion time, translational and rotational path error, and combined error-time were evaluated under no force field on the final day. The groups significantly differed in combined error-time, with the guidance group performing the worst. Error-amplifying field participants did not plateau in their performance during training, suggesting that learning was still ongoing. Guidance field participants had the worst performance on the final day, confirming the guidance hypothesis. Observed trends also suggested that participants who had high initial path error benefited more from guidance. Error-amplifying and error-reducing haptic training for robot-assisted telesurgery benefits trainees of different abilities differently, with our results indicating that participants with high initial combined error-time benefited more from guidance and error-amplifying force field training.

Design of a logistics warehouse robot positioning and recognition model based on improved EKF and calibration algorithm

Automatic guided vehicles for logistics warehousing are a key link in the construction of intelligent logistics. To improve the positioning accuracy of warehouse robots, we designed an advanced extended Kalman filter method integrating multiple synchronous positioning techniques and map construction methods, and completed the calibration and detection of pallets based on color image information. The results revealed that the proposed multi-innovation enhanced model achieved minimum relative rotation and absolute trajectory errors of 0.13 and 0.09, outperforming existing models. It showcased excellent mapping fidelity and integrity (above 0.9) across various datasets, with a high loop detection success rate (0.91) enhancing map precision. The tray fusion detection algorithm's AUC (area under the curve) reached 0.92, reflecting a balanced accuracy-recall tradeoff. This research offers robust positioning and mapping capabilities in logistics warehousing environments, effectively identifying errors and ensuring pallet accuracy. The detection error and accuracy of this method are better than the other three models, with the lowest average absolute error of 0.32 and the lowest root-mean-square error of 0.27, and the overall error in the detection of pallets is small. The findings provide strong theoretical backing and technical support for advancing intelligent logistics warehousing technology. Precise positioning and identification capabilities enable logistics and warehousing robots to accurately and quickly complete tasks such as access, handling and sorting of goods, greatly improving the efficiency of warehousing operations, promoting the digital transformation and intelligent development of the logistics and warehousing industry, and improving the competitiveness of the industry and the level of service.

Rotation Error Prediction of CNC Spindle Based on Short-Time Fourier Transform of Vibration Sensor Signals and Improved Weighted Residual Network.

The spindle rotation error of computer numerical control (CNC) equipment directly reflects the machining quality of the workpiece and is a key indicator reflecting the performance and reliability of CNC equipment. Existing rotation error prediction methods do not consider the importance of different sensor data. This study developed an adaptive weighted deep residual network (ResNet) for predicting spindle rotation errors, thereby establishing accurate mapping between easily obtainable vibration information and difficult-to-obtain rotation errors. Firstly, multi-sensor data are collected by a vibration sensor, and Short-time Fourier Transform (STFT) is adopted to extract the feature information in the original data. Then, an adaptive feature recalibration unit with residual connection is constructed based on the attention weighting operation. By stacking multiple residual blocks and attention weighting units, the data of different channels are adaptively weighted to highlight important information and suppress redundancy information. The weight visualization results indicate that the adaptive weighted ResNet (AWResNet) can learn a set of weights for channel recalibration. The comparison results indicate that AWResNet has higher prediction accuracy than other deep learning models and can be used for spindle rotation error prediction.

Nonlinear dynamics modeling and analysis of aviation drilling actuator feed system considering assembly error

The superior dynamic performance and machining accuracy of the aviation drilling actuator are crucial for high-quality drilling of aviation structural components. It is essential to construct a dynamic model that accurately predicts the dynamic characteristics of the actuator. However, the modeling rarely considers the influence of assembly errors, which makes it difficult to ensure the model precision. In this work, the nonlinear force of the joint surface between the ball screw (BS), rolling bearings and ball linear guide (LG) was derived, taking into account the moving and rotation errors of the guide rail (GR) and the misalignment errors of the bearings. A dynamic model with six degree-of-freedom (DOF) was established for the aviation drilling actuator. The Runge-Kutta method was selected to solve the model, and the model accuracy was verified by experiments. The influence of various assembly errors and worktable feed position on the vibration response of the aviation drilling actuator in three directions was analyzed by the time history, frequency spectrum, phase diagram, and amplitude-frequency curve. The research results indicate that variations in assembly errors and feed position affect the dynamic properties of the system. The moving errors along the horizontal and vertical directions and the rotation errors around the horizontal and vertical directions of the GR notably affect the amplitude-frequency characteristics and vibration displacement of the two directions. The bearing misalignment error in the horizontal plane significantly affects the axial vibration of the drilling actuator. The maximum vibration response in the three directions is achieved when the feed position is in the middle of the BS. Therefore, dynamic model analysis can provide theoretical guidance for adjusting assembly errors and selecting reasonable machining positions to improve the stability and machining accuracy of aviation drilling actuator.

Semiglobal Exponential Stability for Dual-Quaternion-Based Rigid-Body Tracking Control

Semi-Global Exponential Stability (SGES) is proven for the combined attitude and position rigid-body motion tracking problem, presenting a significant upgrade compared to previously proposed controllers which can only guarantee asymptotic stability. Dual quaternions are used to jointly represent the rotational and translational tracking error dynamics of the rigid body. A novel nonlinear feedback tracking controller is proposed, and a Lyapunov-based analysis is provided to prove SGES of the closed-loop dynamics. The analysis does not place any restrictions on the reference trajectory or the feedback gains. This stronger SGES result aids in further analyzing the robustness of the rigid-body system by establishing input-to-state stability (ISS) in the presence of time-varying additive and bounded external disturbances. Motivated by the fact that, in many aerospace applications, stringent adherence to safety constraints such as approach path and input constraints is critical for overall mission success, a framework for safe control of spacecraft is presented that combines the proposed feedback controller with control barrier functions. Numerical simulations are provided to verify the SGES and ISS results and also showcase the efficacy of the proposed nonlinear feedback controller in several nontrivial scenarios, including trajectory tracking, transposition and docking, flip maneuvers, collision avoidance, and rendezvous.

Scalable Nanoimprint Manufacturing of Functional Multilayer Metasurface Devices

AbstractOptical metasurfaces, consisting of subwavelength‐scale meta‐atom arrays, hold great promise of overcoming the fundamental limitations of conventional optics. Due to their structural complexity, metasurfaces usually require high‐resolution yet slow and expensive fabrication processes. Here, using a metasurface polarimetric imaging device as an example, the photonic structures and the Nanoimprint lithography (NIL) processes are designed, creating two separate NIL molds over a patterning area of &gt; 20 mm2 with designed Moiré alignment markers by electron‐beam writing, and further subsequently integrate silicon and aluminum metasurface structures on a chip. Uniquely, the silicon and aluminum metasurfaces are fabricated by using the nanolithography and 3D pattern‐transfer capabilities of NIL, respectively, achieving nanometer‐scale linewidth uniformity, sub‐200 nm translational overlay accuracy, and &lt;0.017 rotational alignment error while significantly reducing fabrication complexity and surface roughness. The micro‐sized multilayer metasurfaces have high circular polarization extinction ratios as large as ≈20 and ≈80 in blue and red wavelengths. Further, the metasurface chip‐integrated CMOS imager demonstrates high accuracy in broad‐band, full Stokes parameter analysis in the visible wavelength ranges and single‐shot polarimetric imaging. This novel, NIL‐based, multilayered nanomanufacturing approach is applicable to the scalable production of large‐area functional structures for ultra‐compact optic, electronic, and quantum devices.

The Application Characteristics and Creation of Digital Sculpture Based on Parameter Model

Recently, digital sculpture based on parametric models has emerged both domestically and internationally. To improve the accuracy and efficiency of constructing digital sculpture parameter models, this study proposes a method for constructing digital sculpture parameter models based on improved point cloud registration algorithms by iterating the nearest point algorithm and multi-scale matrix descriptors to increase the iteration efficiency and accuracy of point cloud registration algorithms. The results show that under the Bunny model, the number of three scale feature points is 2146, and the coarse registration error is 0.925 * 10-6 m; As the noise increases, the efficiency of the algorithm proposed in the study increases by an average of 10.1%. The average relative rotation error is reduced by 1-2 orders of magnitude, and the registration time is shortened by 62.7% on average. For a 30dB noise point cloud, it is reduced by one order of magnitude, and as the noise increases, the efficiency of the algorithm proposed in the study increases by an average of 10.1%. In the Dragon model, the number of three scale feature points is 2235, the coarse registration time is only 26 seconds, and the registration error is 0.285 * 10-5m; The average relative rotation error is reduced by 1-2 orders of magnitude, and the registration time is shortened by 62.7% on average. The digital sculpture creation method on the ground of parameter models proposed in this study has improved the registration accuracy and efficiency of parameter models.

Modeling, detection, and validation for geometric errors in machine tools

Abstract This study aims to enhance the spatial precision of five-axis machining centers through a comprehensive exploration of geometric errors, encompassing modeling, efficient detection, and compensation validation. Our approach begins with the establishment of a kinematic error model covering XYZ translational axes and AC rotational axes, providing an in-depth understanding of error origins and interrelationships. Utilizing a laser tracker, we conduct direct measurements of the geometric errors associated with translational axes, and a rotational axis error detection model is developed by using a ball bar, allowing for indirect analysis of rotational axis geometric errors. The validity of both the kinematic error model and error detection is further confirmed through practical on-machine measurements.

Time crystal embodies chimeralike state in periodically driven quantum spin system

Chimera states are a captivating occurrence in which a system composed of multiple interconnected elements exhibits a distinctive combination of synchronized and desynchronized behavior. The emergence of these states can be attributed to the complex interdependence between quantum entanglement and the delicate balance of interactions among system constituents. The emergence of discrete-time crystal (DTC) in typical many-body periodically driven systems occurs when there is a breaking of time translation symmetry. Coexisting coupled DTC and a ferromagnetic dynamically many-body localized (DMBL) phase at distinct regions have been investigated under the controlled spin rotational error of a disorder-free spin-1/2 chain for different types of spin-spin interactions. We contribute a novel approach for the emergence of the DTC-DMBL-chimeralike state, which is robust against external static fields in a periodically driven quantum many-body system.

Development and validation of a collaborative robotic platform based on monocular vision for oral surgery: an in vitro study.

Surgical robots effectively improve the accuracy and safety of surgical procedures. Current optical-navigated oral surgical robots are typically developed based on binocular vision positioning systems, which are susceptible to factors including obscured visibility, limited workplace, and ambient light interference. Hence, the purpose of this study was to develop a lightweight robotic platform based on monocular vision for oral surgery that enhances the precision and efficiency of surgical procedures. A monocular optical positioning system (MOPS) was applied to oral surgical robots, and a semi-autonomous robotic platform was developed utilizing monocular vision. A series of vitro experiments were designed to simulate dental implant procedures to evaluate the performance of optical positioning systems and assess the robotic system accuracy. The singular configuration detection and avoidance test, the collision detection and processing test, and the drilling test under slight movement were conducted to validate the safety of the robotic system. The position error and rotation error of MOPS were 0.0906 ± 0.0762mm and 0.0158 ± 0.0069degrees, respectively. The attitude angle of robotic arms calculated by the forward and inverse solutions was accurate. Additionally, the robot's surgical calibration point exhibited an average error of 0.42mm, with a maximum error of 0.57mm. Meanwhile, the robot system was capable of effectively avoiding singularities and demonstrating robust safety measures in the presence of minor patient movements and collisions during vitro experiment procedures. The results of this in vitro study demonstrate that the accuracy of MOPS meets clinical requirements, making it a promising alternative in the field of oral surgical robots. Further studies will be planned to make the monocular vision oral robot suitable for clinical application.

Impact of commissural versus coronary alignment on risk of coronary obstruction following transcatheter aortic valve implantation.

Transcatheter aortic valve implantation (TAVI) with commissural alignment aims to limit the risk of coronary occlusion and maintain good coronary access. However, due to coronary origin eccentricity within the coronary cusp, coronary-commissural overlap (CCO) may still occur. TAVI using coronary alignment, rather than commissural alignment, may further improve coronary access. To compare rates of CCO after TAVI using commissural versus coronary alignment methodology. Cardiac CT scans from 102 patients with severe (tricuspid) aortic stenosis referred for TAVI were analysed. Native cusp asymmetry and coronary eccentricity were defined and used to simulate TAVI using commissural versus coronary alignment. Rates of optimal coronary alignment (< 10° from cusp centre) and severe misalignment (< 15° from coronary-commissural overlap) were compared. Additionally, the impact of valve misalignment during implantation was assessed. The native right coronary artery (RCA) origin was 15.8° (9.5 to 24°) closer to the right coronary cusp/non-coronary cusp (RCC-NCC) commissure than the centre of the right coronary cusp. The native left coronary artery (LCA) origin was 4.5° (0 to 11.5°) closer to the left coronary cusp/non-coronary cusp (LCC-NCC) commissure than the centre of the left coronary cusp (p < 0.01). Compared to commissural alignment, coronary alignment doubled the proportion of optimally-aligned RCAs (62/102 [60.8%] vs. 31/102 [30.4%]; p < 0.001), without a significant change in optimal LCA alignment (62/102 [60.8% vs. 74/102 [72.6%]; p = 0.07). There were no cases of severe misalignment with either strategy. Simulating 15° of valve misalignment resulted in severe RCA compromise risk in 7/102 (6.9%) of commissural alignment cases, compared to none using coronary alignment. Fluoroscopic projection was similar with both approaches. Coronary alignment resulted in a 2-fold increase of optimal TAVI positioning relative to the RCA ostium when compared to commissural alignment without impacting the LCA. Use of coronary alignment rather than commissural alignment may improve coronary access after TAVI and is less sensitive to valve rotational error, particularly for the right coronary artery.

Ground segmentation based point cloud feature extraction for 3D LiDAR SLAM enhancement

Point cloud preprocessing lays the foundation for the realization of autonomous vehicles (AVs) as it is the backbone of 3D LiDAR simultaneous localization and mapping (SLAM). Matching feature points selection based on multiple classifiers from preprocessing techniques may significantly increase the chances of the good matching result, and thus reduces drift error accumulation. In this paper, a series of point cloud preprocessing and feature extraction methods were proposed, where LiDAR sensor is used only. Experiments indicate that our ground point segmentation algorithm is efficient, comparable to state-of-the-art methods, and even outperforms the general approaches when measured with certain metrics. Improvement in extracting edge features with vertical clustering can ensure stability and geometrical characteristics of features. With the implementation of the proposed point cloud preprocessing techniques on well-known pose estimation framework such as LeGO-LOAM, higher accuracy with the reduction in both rotation and translation error in most dataset sequences is achieved. Finally, the proposed algorithm is examined and evaluated via KITTI, Semantic-KITTI, and our own VLP-16 campus datasets.

DTP: learning to estimate full-body pose in real-time from sparse VR sensor measurements

For virtual reality (VR) applications, estimating full-body pose in real-time is becoming increasingly popular. Previous works have reconstructed full-body motion in real time from an HTC VIVE headset and five VIVE Tracker measurements by solving the inverse kinematics (IK) problem. However, an IK solver may yield unnatural poses and shaky motion. This paper introduces Deep Tracker poser (DTP): a method for real-time full-body pose estimation in VR. This task is difficult due to the ambiguous mapping from the sparse measurements to full-body pose. The data obtained from VR sensors is calibrated, normalized and fed into the deep neural networks (DNN). To learn from sufficient data, we propose synthesizing a VR sensor dataset called AMASS-VR from the AMASS, a collection of various motion capture datasets. Furthermore, feet tracking loss is a common problem of VIVE Tracker. To improve the accuracy and robustness of DTP to the occlusion noise, we simulate the occlusion noise by Gaussian random noise. Then we synthesize an occlusion dataset AMASS-OCC and fine-tune DTP on that. We evaluate DTP by comparing with other popular methods in terms of the accuracy and computational cost. The results indicate that DTP outperforms others in terms of the positional error (1.04 cm) and rotational error (4.22 °). The quantitative and qualitative results show that DTP reconstructs accurate and natural full-body pose even under serious feet occlusion, which indicates the superiority of the DTP in modelling the mapping from sparse joint data to the full-body pose.

Simulated augmented reality-based calibration of optical see-through head mound display for surgical navigation.

Calibration of an optical see-through head-mounted display is critical for augmented reality-based surgical navigation. While conventional methods have advanced, calibration errors remain significant. Moreover, prior research has focused primarily on calibration accuracy and procedure, neglecting the impact on the overall surgical navigation system. Consequently, these enhancements do not necessarily translate to accurate augmented reality in the optical see-through head mount due to systemic errors, including those in calibration. This study introduces a simulated augmented reality-based calibration to address these issues. By replicating the augmented reality that appeared in the optical see-through head mount, the method achieves calibration that compensates for augmented reality errors, thereby reducing them. The process involves two distinct calibration approaches, followed by adjusting the transformation matrix to minimize displacement in the simulated augmented reality. The efficacy of this method was assessed through two accuracy evaluations: registration accuracy and augmented reality accuracy. Experimental results showed an average translational error of 2.14mm and rotational error of 1.06° across axes in both approaches. Additionally, augmented reality accuracy, measured by the overlay regions' ratio, increased to approximately 95%. These findings confirm the enhancement in both calibration and augmented reality accuracy with the proposed method. The study presents a calibration method using simulated augmented reality, which minimizes augmented reality errors. This approach, requiring minimal manual intervention, offers a more robust and precise calibration technique for augmented reality applications in surgical navigation.

Highly robust and accurate multi-sensor fusion localization system for complex and challenging scenarios

Highly robust and accurate localization using on-board sensors in the absence of GNSS is a key issue for long-term autonomous navigation of vehicles. However, the limited sensing capabilities of a single sensor cannot resist the effects of feature degradation and high-speed motion in complex and challenging scenarios, which results in the fragile of existing LiDAR-based and visual-based localization algorithms. To solve these problems, we propose a highly robust and accurate localization system by fusing information from multi-sensors. Firstly, we propose a global localization method that leverages deep learning models for processing visual information to provide an accurate initial position for vehicles, which solves the problem of global localization of vehicles in the absence of GNSS. Then, we propose a highly robust and accurate LiDAR-Vision-IMU localization method based on pose graph optimization, which integrates LiDAR-based poses and visual-inertial-based poses. The proposed method detects sensor degradation in real time to dynamically adjust the fusion weights, which solves the problem of low localization performance of a single sensor. Finally, we conduct experiments in complex and challenging scenarios, such as urban, tunnels, and unstructured mountains. Experimental results show that our method can achieve a global localization error of less than 0.5 m in complex scenes. In unstructured mountainous scenarios of length 21.1 km, the root mean square errors (RMSE) of translation and rotation are 0.67 m and 0.048rad, respectively. Compared to most existing algorithms, our method achieves the most robust and accurate localization performance.

GraM: Geometric Structure Embedding into Attention Mechanisms for 3D Point Cloud Registration

3D point cloud registration is a crucial technology for 3D scene reconstruction and has been successfully applied in various domains, such as smart healthcare and intelligent transportation. With theoretical analysis, we find that geometric structural relationships are essential for 3D point cloud registration. The 3D point cloud registration method achieves excellent performance only when fusing local and global features with geometric structure information. Based on these discoveries, we propose a 3D point cloud registration method based on geometric structure embedding into the attention mechanism (GraM), which can extract the local features of the non-critical point and global features of the corresponding point containing geometric structure information. According to the local and global features, the simple regression operation can obtain the transformation matrix of point cloud pairs, thereby eliminating the semantics that ignores the geometric structure relationship. GraM surpasses the state-of-the-art results by 0.548° and 0.915° regarding the relative rotation error on ModelNet40 and LowModelNet40, respectively.

Iris Recognition based on Statistically Bound Spatial Domain Zero Crossing and Neural Networks

Purpose The iris pattern is an important biological feature of the human body. The recognition of an individual based on an iris pattern is gaining more popularity due to the uniqueness of the pattern among the people. Iris recognition systems have received attention very much due to their rich iris texture which gives robust standards for identifying individuals. Notwithstanding this, there are several challenges in unrestricted recognition environments. Methods This article discusses a highly error-resistant technique to implement a biometric recognition system based on the iris portion of the human eye. All iris recognition algorithms of the current day face a major problem of localization errors and the enormous time involved in this localization process. Spatial domain zero crossing may be the simplest and least complex method for localization. Yet, it has not been used due to its high sensitivity to erroneous edges, as a consequence of which more complex and time-consuming algorithms have taken its place. Appropriate statistical bounds imposed on this process help this method to be the least erroneous and time-consuming. Errors were reduced to 0.022% using this approach on the CASIA v1 &amp; v2 datasets. Time consumption in this stage was the least compared to other algorithms. At the comparison stage, most algorithms use multiple comparisons to account for translation and rotation errors. This is time-consuming and very resource-hungry. Results The current approach discusses a robust method based on a single comparison, which works with a correct recognition of over 99.78% which is clearly demonstrated by tests. Conclusions The technique is to use a neural network trained to recognize special statistical and regional parameters unique to every person’s iris. The algorithm also gives sufficient attention to consider illumination errors, elliptical pupils, excess eyelash errors and bad contrast.

Study on the contact performance of the variable hyperbolic circular arc tooth trace cylindrical gear with installation errors

Abstract. Installation errors are important factor for the contact performance of the variable hyperbolic circular arc tooth trace (VH-CATT) cylindrical gear; the study of the relationship between installation errors and contact performances is beneficial for gear vibration and noise reduction. Firstly, based on the meshing theory, the tooth surface equation and contact ellipse of the VH-CATT cylindrical gear were deduced, and the tooth surface imprinting experiment was realized. Next, the tooth contact analysis model of the VH-CATT cylindrical gear was developed to investigate the influence of the installation errors on the elliptical contact area. Then, the calculation formulas of the tooth surface gap and contact point flexibility matrix were carried out to develop the load tooth contact analysis model of the VH-CATT cylindrical gear. Finally, the influence of the installation errors on the load distribution was investigated. Research shows that the elliptical contact area of the VH-CATT cylindrical gear is a line contact within a certain range and is located in the middle section of the tooth width. The elliptical contact area of the VH-CATT cylindrical gear increases or decreases rapidly when meshing in and out, and all the installation errors have a certain influence on the elliptical contact area, except for the center distance error. The single-tooth meshing area with the installation errors is greater than that of the ideal gear pair. The load distribution area with the installation errors deviates from the middle section, except for the center distance error. The installation rotation errors around the x and y axis have a certain influence on the maximum load of the single-tooth meshing area. The research results provide a basis for improving the bearing capacity of the VH-CATT cylindrical gear and optimizing the design.