Position Error Research Articles

Evaluation of inner product-based demultiplexing of vortex-based underwater acoustic communications signals in realistic environments.

Acoustic vortex beams have garnered recent interest as an avenue to improve underwater acoustic communication bandwidth and speed. Design and deployment of these systems in ocean environments and at operational ranges has yet to be demonstrated due to the challenging and dynamic nature of the underwater acoustic environment. This manuscript presents methods to model the time series of vortex-based communication signals in ocean environments using ray tracing algorithms. The methods are used to assess the effects of Doppler, ocean turbulence, positional error, and range-dependent environmental parameters on the inner product demultiplexing of the communication signals encoded in the acoustic orbital angular momentum.

A high precision 3-D tropospheric delay model over China using ERA5 data

The zenith tropospheric delay (ZTD) is an important error in Global Navigation Satellite System (GNSS) navigation and positioning. The current most empirical tropospheric delay models are two-dimensional with low spatial and temporal resolution and cannot capture high-frequent accurate ZTD variations in small areas and short periods, particularly in Mainland China with diverse climate changes and large terrain differences. In this paper, a high precision three-dimensional (3-D) tropospheric delay grid model (ZTD_3D) over China with a horizontal resolution of 0.25° × 0.25° and a time resolution of 1 hour was established with the piecewise function describing the height change of ZTD from 2016-2019 fifth-generation European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis data (ERA5). The performance of the proposed model is verified by using radiosonde data and ZTD products from the Crustal Movement Observation Network of China (CMONOC), as well as the global pressure and temperature models (GPT2, GPT3-1 and GPT3-5). Results show that the RMS of ZTD_3D model is 2.04 cm when compared to radiosonde observations, and the accuracy is 55.1 %, 54.7 % and 63.1 % higher than that of GPT3-1 model, GPT3-5 model and GPT2 model, respectively, while the RMS of ZTD_3D model is 3.66 cm when compared to GPS ZTD from CMONOC, and the accuracy is 1.6 % and 29.7 % higher than that of GPT3-5 mode and GPT2 model, respectively. The application of the ZTD_3D model in GNSS precise point positioning (PPP) has showed accuracy improvement in the vertical direction. The model proposed in this study can provide accurate ZTD information and a reliable tropospheric delay correction model for precise GNSS positioning.

A universal calibration framework for mixed-reality assisted surgery

Background:Mixed-reality-assisted surgery has become increasingly prominent, offering real-time 3D visualization of target anatomy such as tumors. These systems facilitate translating preoperative 3D surgical plans to the patient’s body intraoperatively and allow for interactive modifications based on the patient’s real-time conditions. However, achieving sub-millimetre accuracy in mixed-reality (MR) visualization and interaction is crucial to mitigate device-related risks and enhance surgical precision. Objective:Given the critical role of camera calibration in hologram-to-patient anatomy registration, this study aims to develop a new device-agnostic and robust calibration method capable of achieving sub-millimetre accuracy, addressing the prevalent uncertainties associated with MR camera-to-world calibration. Methods:We utilized the precision of surgical navigation systems (NAV) to address the hand-eye calibration problem, thereby localizing the MR camera within a navigated surgical scene. The proposed calibration method was integrated into a representative surgery system and subjected to rigorous testing across various 2D and 3D camera trajectories that simulate surgeon head movements. Results:The calibration method demonstrated positional errors as low as 0.2 mm in spatial trajectories, with a standard error also at 0.2 mm, underscoring its robustness against camera motion. This accuracy complies with the accuracy and stability requirements essential for surgical applications. Conclusion:The proposed fiducial-based hand-eye calibration method effectively incorporates the accuracy and reliability of surgical navigation systems into MR camera systems used in intraoperative applications. This integration facilitates high precision in surgical navigation, proving critical for enhancing surgical outcomes in mixed-reality-assisted procedures.

Ultrasound-assisted aberration correction of transcranial photoacoustic imaging based on angular spectrum theory

To correct the refraction aberration induced by the skull in photoacoustic imaging, a method for phase distortion compensation is proposed based on the angular spectrum theory with the aid of ultrasonic signals. This method first updates the speed of sound distribution by iteratively performing aberration correction in the ultrasonic reconstruction. Then the speed of sound distribution obtained with ultrasound-assisted serves as prior knowledge to address phase distortion compensation by adjusting the phase shift factor of the wavefront in different media. Finally, the aberration-corrected ultrasonic-photoacoustic dual-modality image can be obtained. Numerical simulations and phantom experiments confirm the effectiveness of this method. Specifically, in simulations, the position error of the proposed method is reduced from −13.61% to 1.27% in depth compared to the method based on the reconstruction with constant speed. Moreover, a real ex-vivo rabbit skull experiment illustrates the potential biological application of the proposed method in transcranial photoacoustic imaging.

HOIMotion: Forecasting Human Motion During Human-Object Interactions Using Egocentric 3D Object Bounding Boxes.

We present HOIMotion - a novel approach for human motion forecasting during human-object interactions that integrates information about past body poses and egocentric 3D object bounding boxes. Human motion forecasting is important in many augmented reality applications but most existing methods have only used past body poses to predict future motion. HOIMotion first uses an encoder-residual graph convolutional network (GCN) and multi-layer perceptrons to extract features from body poses and egocentric 3D object bounding boxes, respectively. Our method then fuses pose and object features into a novel pose-object graph and uses a residual-decoder GCN to forecast future body motion. We extensively evaluate our method on the Aria digital twin (ADT) and MoGaze datasets and show that HOIMotion consistently outperforms state-of-the-art methods by a large margin of up to 8.7% on ADT and 7.2% on MoGaze in terms of mean per joint position error. Complementing these evaluations, we report a human study (N=20) that shows that the improvements achieved by our method result in forecasted poses being perceived as both more precise and more realistic than those of existing methods. Taken together, these results reveal the significant information content available in egocentric 3D object bounding boxes for human motion forecasting and the effectiveness of our method in exploiting this information.

Optimization of Stator Structure for Improved Accuracy in Variable Reluctance Resolvers Using Advanced Machine Learning Techniques

This study presents an optimized design for a Segmented Sinusoidal Parameter Winding with Magnetic Wedge Variable Reluctance Resolver (SSPWMW-VRR), addressing challenges like winding asymmetry and harmonic distortion in conventional designs. By integrating particle swarm optimization (PSO) for winding design, magnetic equivalent circuit (MEC) analysis for leakage flux, and machine learning techniques (XGBoost and Multi-Layer Perceptron), the stator slot shape was fine-tuned for improved accuracy. XGBoost outperformed MLP in prediction accuracy with a mean absolute error (MAE) of 0.1172. Finite element analysis (FEA) simulations and experimental validation demonstrated a reduction in position errors from ±30′ in conventional VRRs to ±5′ in the optimized design, along with significant harmonic reduction.

Feasibility of augmented reality using dental arch-based registration applied to navigation in mandibular distraction osteogenesis: a phantom experiment

ObjectiveDistraction osteogenesis is a primary treatment for severe mandibular hypoplasia. Achieving the ideal mandible movement direction through precise distraction vector control is still a challenge in this surgery. Therefore, the aim of this study was to apply Optical See-Through (OST) Augmented Reality (AR) technology for intraoperative navigation during mandibular distractor installation and analyze the feasibility to evaluate the effectiveness of AR in a phantom experiment.MethodsPhantom was made of 3D-printed mandibular models based on preoperative CT scans and dental arch scans of real patients. Ten sets of 3D-printed mandible models were included in this study, with each set consisting of two identical mandible models assigned to the AR group and free-hand group. 10 sets of mandibular distraction osteogenesis surgical plans were designed using software, and the same set of plans was shared between the AR and free-hand groups. Surgeons performed bilateral mandibular distraction osteogenesis tasks under the guidance of AR navigation, or the reference of the preoperative surgical plan displayed on the computer screen. The differences in angular errors of distraction vectors and the distance errors of distractor positions under the guidance of the two methods were analyzed and compared.Results40 distractors were implanted in both groups, with 20 cases in each. In intra-group comparisons between the left and right sides, the AR group exhibited a three-dimensional spatial angle error of 1.88 (0.59, 2.48) on the left and 2.71 (1.33, 3.55) on the right, with P = 0.085, indicating no significant bias in guiding surgery on both sides of the mandible. In comparisons between the AR group and the traditional free-hand (FH) group, the average angle error was 1.94 (1.30, 2.93) in the AR group and 5.06 (3.61, 9.22) in the free-hand group, with P < 0.0001, resulting in a 61.6% improvement in accuracy. The average displacement error was 1.53 ± 0.54 mm in the AR group and 3.56 ± 1.89 mm in the free-hand group, with P < 0.0001, indicating a 57% improvement in accuracy.ConclusionAugmented Reality technology for intraoperative navigation in mandibular distraction osteogenesis is accurate and feasible. A large randomized controlled trial with long-term follow-up is needed to confirm these findings.Trial RegistrationThe project has been registered with the Chinese Clinical Trial Registry, with registration number ChiCTR2300068417. Date of Registration: 17 February 2023.

MULTI-SENSOR CAMERA MODEL FOR CONTROLLING COORDINATES OF POINTS ON THE SURFACE OF TELESCOPES

A new optoelectronic system for measuring the reflective mirror surface distortion of large telescopes is discussed in this study. This system comprises a multi-matrix structure of CMOS sensors, each sensor responsible for capturing an image of a control point on the mirror surface through a common objective. Simulation and calculation studies show that during operation, the position of the multi-sensor camera on the supporting ring is determined by control points on the telescope surface. The more control points, the higher the accuracy of the calculations. Simulation results indicate that the camera position error falls within acceptable limits when using 5 or more control points. Experimental results show that when calculating simultaneously with 3 control points, the error in determining the angular position of the camera reaches a value of  = 0.302 arc minutes, which is 2 - 2.5 times smaller than when calculating with only one control point.

Enhanced Depth Control and Stability in Submersible Pylon Inspection Robots Using IMU-Based Extended Kalman Filter and PID Control

The research developed a Submersible Pylon Inspection Robot (SPIR) to clean and inspect underwater structures automatically, facing challenges in stability and depth of operation. Integrating the Inertial Measurement Unit (IMU) with the Extended Kalman Filter (EKF), as well as implementing customized PID controls, aims to improve the accuracy and stability of SPIR in dynamic underwater environments. The results show that the SPIR control system can follow the reference depth at shallow depths well, but has difficulty maintaining stability at deeper depths. The position error graph on the Z-axis shows the initial fluctuation that decreases over time, reflecting the increased calibration. The use of drive motors also shows different working patterns, with some motors active in depth settings and others for stabilization. This study shows that the integration approach of IMU, EKF, and PID control can improve SPIR performance, although further adjustments are required to meet the extreme challenges in underwater environments.

Parameter Identification and Energy Dissipation Analysis of Premium Connections Based on the Iwan Model

The premium connection is an important section of the tubing column. Under intricate downhole conditions, axial vibration generates alternating loads that cause energy dissipation between the sealing surfaces of the premium connection, reducing sealing performance. To investigate this issue, the mutual conversion process of sticking, slipping, and macroscopic slipping stages between the sealing surfaces of the premium connection under axial loads must be assessed. In this study, a finite element analysis model of a taper–taper Φ88.9 mm × 6.45 mm P110 premium connection is developed based on the discrete Iwan model’s ontological relationship, and the sealing surface’s force–displacement hysteresis curve is obtained. The equivalent Iwan model for this particular premium connection is constructed by discretizing the hysteresis curve and identifying the model’s four sets of parameters. The correctness of the parameter identification method of the equivalent Iwan model is verified by comparing and analyzing the similarity of the two models. The energy dissipation in the sealing surfaces of the premium connection for different working conditions under dynamic loading is analyzed. This study reveals that the area similarity of the hysteresis curves of the two models is more than 92%, while the positional error is less than 2%. The sealing surface displacement amplitude of the premium connection is between 0.04 mm and 0.07 mm, while the sealing surface energy dissipation increases linearly, which may lead to a decline in sealing performance.

Comparison of Machine Learning Models and Feature Importance Investigation of Intelligent Fault Diagnosis Methods for Robots Based on Datasets Across Various Distributions

Intelligent fault detection is an important component of the industrial and automation fields. However, conventional research on intelligent fault detection mainly focuses on industrial production equipment, while there is little research on intelligent fault detection scenarios for robots. Based on a hexapod robot joints dataset, this paper investigates intelligent fault diagnosis tasks in the field of robotics. Firstly, the dataset is clustered into two new datasets with different distributions through k-means method, which is used to simulate the practicality of imbalanced distribution between healthy and fault data. Afterwards, several multioutput machine learning classification models were established to predict robot joints with faults. In two datasets with different distributions, the larger one is used as the training set and the smaller one is used as the testing set. The article compares the performance of these models with prediction accuracy as the main indicator. And based on the results, the paper selects the model with the highest accuracy for further exploration of feature importance. Finally, the article explains the significance of the results and analyzes possible reasons. The experimental results show that the random forest model better overcomes the problem of data distribution differences and has the highest accuracy. In the random forest model, the importance of position data representing position error is higher than that of slope with respect to the axis data representing angle error. This result may be related to the distribution of feature values and the fact that position data contains more crucial information.

Weighted Centroid Amorphous Algorithm for Position Error Minimization in WSN

ABSTRACTWireless Sensor Networks (WSNs) have numerous applications, one of which is localization. Localization is crucial for determining the position of unknown sensor nodes in the deployment environment. Localization techniques are broadly classified into two categories: range based and range‐free. Range‐free localization techniques are gaining popularity as they are easy to implement and do not require external hardware. In this proposed work, a hybrid localization algorithm named the Weighted Centroid Amorphous algorithm is proposed to reduce the position error in WSN. Instead of the conventional centroid algorithm, a weighted centroid algorithm is used. The weight in this work is considered as a function of the hop value and hop size estimated by the Amorphous algorithm. Ten nearest beacon nodes are considered to determine the coordinates of a single unknown node. The hop value and hop size of that unknown node are calculated from the 10 nearest beacon nodes, and by using the hop value and hop size, the weight is calculated. After the weight estimation, the weighted sum is calculated, and using the weighted sum, the coordinates of an unknown node are determined. Simulation results indicate that the proposed Weighted Centroid Amorphous method achieves superior accuracy, with rates of 90.41%, 89.57%, and 86.10% compared to the traditional Amorphous, improved Amorphous, and Ensemble approach, respectively.

Cardiac motion in patients with ventricular tachycardia: potential implications for the treatment of patients candidates to stereotactic arrhythmia radio-ablation (STAR)

Abstract Background Stereotactic arrhythmia radio-ablation (STAR) has proven to be a valid alternative treatment for refractory ventricular tachycardia (VT) in patients who are unsuitable to undergo standard catheter ablation (CA). It consists in the application of external beam radiotherapy in a single dose of 25 Gy to the target areas. There is increased research activity on better understanding the complex and fast motion of the heart and on reducing radiation toxicity. Purpose In the context of an in silico study to evaluate the feasibility of STAR with protons in patients with VT, the initial findings related to cardiac motion on the first 10 patients are here presented. Methods Prior to CA, each patient underwent ECG gated CT scans in expiratory breath-hold, with and without contrast and reconstructed at 30% (systole) and 80% (diastole) of the cardiac R-R cycle. Contouring of the ablation target as a clinical target volume (CTV) for proton treatment planning was performed based on a standard electrophysiological study with 3D eletroanatomical mapping. Two different treatment plans were created: the first with only the diastolic CTV as target (gated treatment), the second including both diastolic and systolic CTVs to create an Internal Target Volume (ITV) in the hypothesis of non-gated treatment. Robust optimization was used to create the Planning Target Volume (PTV). Results The target volumes used for treatment planning are given in Table 1. The median CTV was 10.90 (2.93-36.94) cm3 for diastole and 14.26 (1.73-36.31) cm3 for systole. These volumes are somewhat smaller than those reported in patients treated previously with STAR: this difference may be due to the fact that no respiratory motion was included in the target contour and that the study population includes many patients referred for ventricular ectopic beats without structural heart disease, where the ablation target is expected to be smaller as compared to patients with VT in structural heart disease. Despite a small median difference between the diastolic and systolic CTV of 0.53 (0.03-9.61) cm3, the ITV approach resulted in a median increase in volume compared to the largest of the two CTVs of 29 % (1%-44%). When considering the proton range uncertainty and potential errors in patient positioning (PTV), the target is this time enlarged by a factor 2.9 (1.9-3.9). This data indicates that both cardiac motion and uncertainties in patient positioning before treatment will have a large impact on the treatment volume thus affecting the amount of surrounding tissue exposed to radiation. Conclusion The ablation target contour at systole and diastole are of similar magnitude but their non-overlap results in a large increase in treated volume when radiation delivery is not gated for cardiac motion. Further analysis shall investigate on a case-by-case basis the potential reduction in risk of healthy tissue toxicity with cardiac-gated proton delivery.Table 1

GNSS interference detection: Methodology utilising ADS-B NACp indicator and GPS almanac data

Abstract The threat of GNSS interference poses a great danger to many critical infrastructure systems including air navigation. With a focus on mitigating this threat, this paper proposes a methodology for detecting GNSS interference. The methodology utilises the quality indicator NACp transmitted in ADS-B messages and GPS almanac data for interference detection. The NACp indicator enables estimation of the position error derived from GPS, which is compared with the HDOP value of the GPS satellite constellation. Based on this comparison, the developed detection algorithm determines whether the aircraft is affected by jamming. The detection methodology is evaluated on datasets obtained during deliberate experiments with GPS jamming. The proposed methodology provides a way to detect GNSS interference, facilitating mitigation of its impact on air traffic operation.

Effects of Cervical Mobilization on Balance and Proprioception in Patients With Nonspecific Neck Pain

ObjectiveThis study investigates the effect of cervical mobilization on balance and cervical proprioception in patients with nonspecific neck pain. MethodsA prospective, double-blind, randomized clinical trial was conducted involving a 3-week treatment protocol for which 66 patients were randomly assigned to 2 groups. Both groups underwent conventional physiotherapy (hot pack and transcutaneous electrical nerve stimulation) twice a week for 3 weeks along with additional cervical mobilization in the mobilization group, and sham mobilization in the sham control group. Static and dynamic balance, cervical proprioception, cervical mobility, and pain intensity were evaluated using a Kinesthetic Skill Training System 3000 device, the “Joint Position Error Test,” Cervical Range-of-Motion Instrument, and the visual analog scale, respectively. ResultsAfter treatment, significant improvements were noted in dynamic balance, mobility, pain intensity (P < .001, P < .001, P < .001, respectively), and proprioception in the left direction of rotation in the mobilization group (P = .003) that were significantly greater than those observed in the sham mobilization group (P < .001, P < .001, P < .001, P = .003, respectively). Although a significant decrease was observed in the deficits of static balance (P = .044) and proprioception in the right direction of rotation (P = .011) after mobilization, the changes were similar in both the mobilization and sham mobilization groups (P = .192, P = .154, respectively). ConclusionCervical mobilization led to significant improvements in dynamic balance, pain intensity, mobility, and partial improvements to proprioception in a comparison with a sham mobilization group, while the effect on static balance was not significant.

Three-dimensional source position verification in image-guided high-dose-rate brachytherapy using an XCT-based gel dosimeter.

Comprehensive quality assurance (QA) for a seamless workflow of high-dose-rate brachytherapy, from imaging to planning and irradiation, is uncommon, and QA of the source dwell position is performed in one- or two-dimensions. Gel dosimetry using magnetic resonance imaging (MRI) is effective in verifying the three-dimensional distribution of doses for image-guided brachytherapy (IGBT). However, MRI scanners are not readily accessible, and MRI scanning is time-consuming. Nevertheless, X-ray computed tomography (XCT) is available for IGBT planning. In this study, we designed and developed an efficient method for QA for a seamless workflow of IGBT with a new commercially available XCT-based polymer gel dosimeter. To enable direct insertion of brachytherapy applicators, the gelatinizing agent of the dosimeter was modified. A cylindrical polyvinyl chloride jar was filled with the modified gel dosimeter, which was subsequently used to determine the reproducibility of source dwell positions, detectability of source positional errors from intentionally introduced catheter length offsets, effect of looped source transfer tubes on the average displacement, extent of inter-observer variation, and gel robustness following multiple needle-insertions. Three ProGuide sharp needles were inserted into the jar. The dwell time at each point was determined to identify the irradiated volume with a diameter of approximately 10mm on XCT images. All the times were the same. The plan was delivered using an afterloader with an Ir-192 radioactive source, and the irradiated gel dosimeter was scanned using an XCT scanner. The subtracted images were generated from pre- and post-irradiated images. Volumes with incremented Hounsfield units were manually identified and contoured. The centroid of the volume was defined as the measured source dwell position. Subsequently, planned source dwell positions were extracted from the DICOM file of the plan. Finally, the source dwell positions in plan and irradiated gel were compared in three axes. The hardness of the dosimeter was 1250% greater than that of the previously reported gel dosimeter. Source dwell positions were visually identified in the XCT image. Testing of CT acquisition, planning, irradiation, and analysis was completed in approximately 1h. In the reproducibility test of source dwell positions, created by inserting three needles (each with three source dwell positions), the average displacements of the source positions from the first source dwell position were within 0.5mm in all three directions. In the detectability test, displacements were less than 1mm in the x-y plane but greater than 1mm in the z-axis, which was the source path direction. When errors of 1-3mm were intentionally introduced, the measured displacement was within 0.7mm of the median (range: 0.21-1.65mm) of intentional errors. When the transfer tube was looped, the source dwell position displaced by approximately 1mm. After 20 needle-insertions, the source dwell position displacement was within 1mm. The maximum inter-observer variation of contouring was 0.57mm. The XCT-based gel dosimeter enabled verification of three-dimensional source dwell positions for a seamless workflow of IGBT with high precision and efficiency.

A Normal Displacement Model and Compensation Method of Polishing Tool for Precision CNC Polishing of Aspheric Surface

The position accuracy of the polishing tool affects the surface quality of the polished aspheric surface. The contact deformation among the polishing tool, abrasives, and aspheric part can cause a displacement, which, in turn, will cause a position error of the polishing tool, which will lead to a significant change in the polishing force. In order to resolve this error, this paper proposed a method of normal displacement compensation for a computer numerical controlled (CNC) polishing system by controlling the polishing force. Firstly, the coupling principle between the polishing force and the position of the polishing tool is expounded, and the relationship between normal displacement and deformation is analyzed. Based on Hertz’s theory, a model of normal displacement is established. Then, on the basis of the decoupled polishing system developed, a normal displacement compensation method was proposed. Finally, a group of comparative experiments was carried out to verify the effectiveness of the proposed method. Compared with no displacement compensation, when the part was polished with the normal displacement compensation method, the value of roughness decreased from 0.4 µm to 0.21 µm, and the unevenness coefficient of surface roughness decreased from 112.5% to 19%. The experimental results show that the polishing quality is improved greatly, and the aspheric surfaces can be polished more uniformly with the method proposed in this paper.

A GPU Algorithm for Solving the Positions of New Pulsars

Timing newly discovered pulsars requires gradually building up a timing model that connects observations taken days to months apart. This sometimes can be challenging when our initial knowledge of the pulsar’s position is arcminutes off from its true position. Such a position error leads to significant arrival time shifts as a result of the Earth’s orbital motion. Traditional down-hill fitting timing algorithms become ineffective when our model predicts the wrong pulse rotations for our next observation. For some pulsars whose model prediction is not too far off, the correct rotation number could be found by trial-and-error methods. For the remaining challenging pulsars, a more generalized method is called for. This paper proposes a GPU-based algorithm that could exhaustively search a large area of trail positions for probable timing solutions. This could help find phase-connected timing solutions for new pulsars using brute force.

Adaptive Fault-Tolerant Tracking Control for Multi-Joint Robot Manipulators via Neural Network-Based Synchronization.

In this paper, adaptive fault-tolerant control for multi-joint robot manipulators is proposed through the combination of synchronous techniques and neural networks. By using a synchronization technique, the position error at each joint simultaneously approaches zero during convergence due to the constraints imposed by the synchronization controller. This aspect is particularly important in fault-tolerant control, as it enables the robot to rapidly and effectively reduce the impact of faults, ensuring the performance of the robot when faults occur. Additionally, the neural network technique is used to compensate for uncertainty, disturbances, and faults in the system via online updating. Firstly, novel robust synchronous control for a robot manipulator based on terminal sliding mode control is presented. Subsequently, a combination of the novel synchronous control and neural network is proposed to enhance the fault tolerance of the robot manipulator. Finally, simulation results for a 3-DOF robot manipulator are presented to demonstrate the effectiveness of the proposed controller in comparison to traditional control techniques.

Positioning errors and accuracy of CNC machine tools

Abstract Computerized numerically controlled (CNC) machine tools are a solid foundation for modern industrial manufacturing. These machines provide linear and angular displacements in three or five axes. The accuracy of moving and positioning the tooltip relative to the work part's surface determines the final product's accuracy. Errors due to machine positioning can be linear or angular or both. This work studies the positioning errors of a vertical turning center CNC machine type. This machine has three axes, two linear X (horizontal) and Z (vertical), and one rotation axis “C”. The travel of the spindle carrying the cutting tool along the X-axis is 1400mm, and the travel of the carriage holding the spindle along the Z-axis is 1300mm divided into six latches. The machine rotary table which carries the work part can rotate 360°. A highly precise laser interferometer system determines the linear positioning errors in both the X and Z axes. The angular positioning errors for the “C” rotation axis are determined accurately by an autocollimator system. The positioning error measurements are carried out based on ISO 230-2 as a measurement standard of positioning deviation, accuracy, and repeatability. The collected error measurements in linear displacements and angular rotation are analyzed, interpreted, and compared with manufacturer specifications and ISO 13041-4 allowable tolerances.&amp;#xD;