Rotation Angle Measurement Research Articles

Reliability and validity of a method to measure trunk rotation angle from images using a camera and posture mirror

This study aimed to measure trunk rotation angle representations from images using a single camera combined with a posture mirror and to examine its reliability and validity. We applied a trunk rotation angle model using a tripod and markers simulating trunk rotation. We compared two methods of trunk rotation angle measurement: the conventional method from the superior aspect using a manual goniometer and a novel measurement method using images from a digital camera and a posture mirror. Measurement error was calculated as the average absolute error between the angle measured by the goniometer and that calculated from the camera and mirror image. The intraclass correlation coefficient (ICC 1, 1) and ICC (2, 1) were calculated as the intra-rater reliability and agreement between the measurement angles of the two methods, respectively. Systematic errors of the angles measured by the two methods were examined by a Bland‒Altman analysis. The mean (SD) of the mean absolute error was 1.17° (0.71°). ICC (1, 1) was 0.978, and ICC (2, 1) was 0.991. The Bland‒Altman analysis showed no systematic errors. The results suggest the validity and accuracy of our novel method to measure the angle of trunk rotation, which does not require high-cost equipment or a special environment.

Evaluation of the prevalence of adolescent scoliosis and its associated factors in Gansu Province, China: a cross-sectional study.

Gansu Province is situated in the northwest region of China, characterized by diverse and complex topography and a rich diversity of ethnic groups. This study aims to explore the prevalence and risk factors of adolescent suspected scoliosis in Gansu Province through a cross-sectional population study. From April 2022 to July 2022, a prospective cross-sectional study was conducted in Baiyin City, Jinchang City, Lanzhou City, Linxia Hui Autonomous Prefecture, and Gannan Tibetan Autonomous Prefecture in Gansu Province. The screening covered 3,118 middle and high school students across 24 institutions, including middle and high schools. Diagnosis of suspected scoliosis was established through visual inspection, the Adams forward bend test, and measurement of trunk rotation angle. Employing a custom-designed questionnaire, demographic data were collected, and the prevalence of suspected scoliosis was calculated. Univariate and multivariate logistic regression analyses were employed to assess factors associated with suspected scoliosis. A total of 3,044 participants were ultimately included in the analysis. The overall prevalence of suspected scoliosis was 5.68% in Gansu Province. The peak prevalence for boy is at 14 years (6.70%), while for girl, it is at 15 years (8.75%). Lanzhou City exhibits the highest prevalence rates (boy, 9.82%; girl, 10.16). The results of univariate logistic regression analysis presented that BMI (OR = 0.92, 95% CI: 0.88-0.96), altitude of habitation (1,600 m-2000 m) (OR = 0.50, 95% CI: 0.34-0.73), altitude of habitation (2000 m-3321 m) (OR = 0.58, 95% CI: 0.40-0.83), family medical history (OR = 1.56, 95% CI: 1.02-2.31), and shoulders of unequal height (OR = 1.49, 95% CI: 1.09-2.03) were significantly correlated with suspected scoliosis. The multivariate logistic regression analysis indicated that BMI (OR = 0.91, 95% CI: 0.86-0.95), altitude of habitation (1,600 m-2000 m) (OR = 0.35, 95% CI: 0.23-0.54), altitude of habitation (2000 m-3321 m) (OR = 0.39, 95% CI: 0.24-0.60), family medical history (OR = 1.66, 95% CI:1.08-2.49), and shoulders of unequal height (OR = 1.45, 95% CI:1.06-1.99) were independently associated with suspected scoliosis. Low BMI, residence at an altitude of 1,600 m-3321 m, family medical history, and shoulders of unequal height were independently associated with an increased prevalence of suspected scoliosis. It is recommended to promptly screen high-risk adolescents for suspected scoliosis, provide effective preventive and intervention measures.

Preliminary field estimation of vertical displacements of prestressed concrete bridges under construction based on measured strains and inclinations

The development of continuous and automatic quantitative monitoring methods will improve bridge construction. This paper proposes a method for estimating vertical bridge displacement during construction based on the Bayesian inverse problem. The proposed method is applied to a bridge under construction in Japan. Case studies suggest that the observed rotation angle is more important than the observed strain for the estimation of vertical displacement. Based on strain and rotation angle measurements, vertical bridge displacement was estimated with an accuracy of less than 2 mm, as determined from a comparison with displacements obtained in a leveling survey. The 95 % confidence interval of the estimation error is consistent with the scatter of measured data of displacement, rotation angle, and strain.

Ultra-sensitive measurement of small optical rotation angles using quantum entanglement based on a quasi-Wollaston prism beam splitter

The measurement of optical rotation is fundamental to optical atomic magnetometry. Ultra-high sensitivity has been achieved by employing a quasi-Wollaston prism as the beam splitter within a quantum entanglement state, complemented by synchronous detection. Initially, we designed a quasi-Wollaston prism and intentionally rotated the crystal axis of the exit prism element by a specific bias angle. A linearly polarized light beam, incident upon this prism, is divided into three beams, with the intensity of each beam correlated through quantum entanglement. Subsequently, we formulated the equations for optical rotation angles by synchronously detecting the intensities of these beams, distinguishing between differential and reference signals. Theoretical analysis indicates that the measurement uncertainty for optical rotation angles, when using quantum entanglement, exceeds the conventional photon shot noise limit. Moreover, we have experimentally validated the effectiveness of our method. In DC mode, the experimental results reveal that the measurement uncertainty for optical rotation angles is 4.7 × 10−9 rad, implying a sensitivity of 4.7 × 10−10 rad/Hz1/2 for each 0.01 s measurement duration. In light intensity modulation mode, the uncertainty is 48.9 × 10−9 rad, indicating a sensitivity of 4.89 × 10−9 rad/Hz1/2 per 0.01 s measurement duration. This study presents a novel approach for measuring small optical rotation angles with unprecedentedly low uncertainty and high sensitivity, potentially playing a pivotal role in advancing all-optical atomic magnetometers and magneto-optical effect research.

Multi-thread two-dimensional digital image correlation for full-field displacement and rotation angle measurement

Multi-thread two-dimensional digital image correlation for full-field displacement and rotation angle measurement

Polarimeter–interferometer diagnostic using terahertz solid-state sources for fluctuation measurements on Keda Torus eXperiment (KTX)

A multi-channel polarimeter–interferometer has been developed on the Keda Torus eXperiment (KTX) for the study of equilibrium dynamics and internal magnetic fluctuations. A three-wave technique based on terahertz solid-state sources (~650 GHz) is applied for simultaneous measurements of electron density and Faraday rotation angle. The output power of the microwave source is 2 mW. Faraday rotation effect using a rotating wave plate is tested with phase noise less than 0.8°, and the density phase noise is less than 0.9°. Measurement of Faraday rotation angle and density for discharges on KTX have demonstrated high sensitivity to internal MHD activities.

High-precision measurement of the complex magneto-optical Kerr effect using weak measurement

The present paper introduces a quantum weak measurement (WM) scheme for the measurement of the complex magneto-optical Kerr effect (MOKE). We achieve the simultaneous measurement of the Kerr rotation angle and the ellipticity in a single WM process by utilizing two auxiliary pointers derived from the same meter state. The experimental measurement precision for both the Kerr rotation angle and the ellipticity is capable of reaching 10−4 deg. This technique is also employed for the determination of the complex magneto-optical constant Q. The proposed method overcomes the limitation of acquiring the complex magneto-optical Kerr parameters through a multi-step measurement process, which was previously encountered. This breakthrough holds immense significance for efficiently measuring and applying the complex MOKE with high precision and cost-effectiveness.

Accurate rotation identification of flexural structures using long-gauge fiber optical sensors

The rotation of beam and column components is a key parameter in structural health monitoring (SHM), which providing analysis of bending deformation, evaluation of structural stability, and overall structural performance. Conventional sensors directly measuring rotation are typically designed assuming linear behavior. It becomes challenging to achieve precise and rapid measurements of small deformations while accurately measuring significant large deformations. This study obtained experimental and analytical studies to identify the rotation response of flexural structures using long-gauge fiber optical sensor array. Rotation is determined through two mechanisms: the plane section assumption, utilizing strain distributions on the compression and tension sides, and the sectional fiber model (SFM)-based neutral axis identification. In order to discuss the applicability of these two mechanisms from elastic to plastic state, four identification methods are proposed: Method 1 uses strain distribution on the concrete surface to identify rotation, Method 2 uses strain on steel bars, and Methods 3 and 4 use SFM-based neutral axis identification with strain measured on the compression side concrete surface and tension side steel reinforcements, respectively. Laboratory tests of beams and columns as well as field tests were shown. First, a comparison of the rotation identification accuracy among the four methods was conducted using a reinforced concrete (RC) beam test in the elastic state. Results showed good agreement between the rotations identified by all four methods and those directly measured by the tilt meter. And then, the accuracy of rotation identification in crack state and inelastic state was discussed by using a RC column test. The results indicate that, following the occurrence of cracks in concrete surface, neither Method 1 nor Method 2 can accurately identify the rotation. This is attributed to the fact that cracks disrupt the correspondence between the strain on the tension side and the compression side. Meanwhile, Methods 3 and 4 maintain a good rotational identification accuracy even after cracks happened. Moreover, when the steel reinforcement undergoes yielding and the concrete column enters the inelastic state, the rotation results identified by Methods 3 and 4 still match with the directly measured rotations. This underscores the effectiveness of the SFM-based rotational identification under large deformation conditions. Furthermore, experimental results indicate that with the increase in deformations, slip occurred in the sensing units near the column base in the sensor array on the tension side. This shows that the sensing units installed on the steel reinforcement (Method 4) are more suitable for calculating rotations during the large deformation state compared to the sensing units positioned on the concrete surface (Method 3). At last, two case studies involving the monitoring of an actual bridge grid and a bridge column were investigated to assess the effectiveness of dynamic rotation identifications. The performance evaluation results for various rotation angle measurement sensors demonstrate that long-gauge fiber optical sensors can be used for rotation identification, ensuring the stability of dynamic rotation identification.

Automatic Vertebral Rotation Angle Measurement of 3D Vertebrae Based on an Improved Transformer Network.

The measurement of vertebral rotation angles serves as a crucial parameter in spinal assessments, particularly in understanding conditions such as idiopathic scoliosis. Historically, these angles were calculated from 2D CT images. However, such 2D techniques fail to comprehensively capture the intricate three-dimensional deformities inherent in spinal curvatures. To overcome the limitations of manual measurements and 2D imaging, we introduce an entirely automated approach for quantifying vertebral rotation angles using a three-dimensional vertebral model. Our method involves refining a point cloud segmentation network based on a transformer architecture. This enhanced network segments the three-dimensional vertebral point cloud, allowing for accurate measurement of vertebral rotation angles. In contrast to conventional network methodologies, our approach exhibits notable improvements in segmenting vertebral datasets. To validate our approach, we compare our automated measurements with angles derived from prevalent manual labeling techniques. The analysis, conducted through Bland-Altman plots and the corresponding intraclass correlation coefficient results, indicates significant agreement between our automated measurement method and manual measurements. The observed high intraclass correlation coefficients (ranging from 0.980 to 0.993) further underscore the reliability of our automated measurement process. Consequently, our proposed method demonstrates substantial potential for clinical applications, showcasing its capacity to provide accurate and efficient vertebral rotation angle measurements.

Faraday Rotation Angle Measurement based on Coupled Optoelectronic Oscillator with Temperature Compensation

Faraday Rotation Angle Measurement based on Coupled Optoelectronic Oscillator with Temperature Compensation

A Novel Combined Method for Measuring the Three-Dimensional Rotational Angle of a Spherical Joint.

To improve the measurement accuracy of the three-dimensional rotation angle of a spherical joint, a novel approach is proposed in this study, which combines magnetic detection by a Hall sensor and surface feature identification by an eddy current sensor. Firstly, a permanent magnet is embedded in the ball head of a spherical joint, and Hall sensors are set and distributed in the ball socket to measure the variation in the magnetic flux density when the spherical joint rotates, which are related to the 3D rotation angle. In order to further improve the measurement accuracy and robustness, we also set grooves on the ball head and use eddy current sensors to synchronously identify the rotation angle of the ball head. After the combination of two signals is performed, a measurement model is established using the RBF neural network by training, and the real-time measurement of the 3D rotation angle of the spherical joint is realized. The feasibility and superiority of this method are validated through experiments. The experimental results indicate that the measurement accuracy is substantially promoted compared to the preliminary measurement scheme based on spherical coding; the average measurement error of the single axis is reduced by 9'9″. The root mean square errors for the measurements of the 3D rotation angles in this proposed method are as follows: pitch angle α has an error of 1'8″, yaw angle β has an error of 2'15″, and roll angle γ has an error of 29'6″.

Simultaneous measurement of polarization rotation angle and ellipticity at the quantum noise limit

An experiment has been proposed for laser polarization signal measurement, with the rotation angle and ellipticity being measured simultaneously. The proposed experiment is immune to signal-to-noise ratio degradation due to the finite extinction ratio of polarizing elements used to construct the composite polarization measurement setup. Noise analysis is carried out to show that the proposed scheme allows one to reach the quantum noise limit in the simultaneous measurement of the polarization angle and ellipticity. This work should be of great interest for experiments such as observation of vacuum magnetic birefringence, spin-orbital interaction, material characterization, polarization microscopy, or biomedical optics.

High-precision rotation angle measurement method based on polarization self-mixing interference.

In this study, a high-precision rotation angle measurement method based on polarization self-mixing interference (SMI) is proposed. The higher signal-to-noise ratio SMI signal can be obtained by the differential processing of two polarized SMI signals with opposite phases. In order to reduce the influence of the speckle effect, the envelope signal is used to normalize the SMI signal. The fringe subdivision method is used to improve the accuracy of the rotation angle measurement. The experimental results show that the error of the rotation angle measurement is within ±0.5%, and the measurement range can reach up to 20°.

Target-less approach of wire rope rotation measurement

In the hoisting system of mine and elevator, the wire rope will generate rotational motion with unfixed axis, the rotation angle of which is a vital parameter for the system. Therefore, it is necessary to measure the rotation angle to evaluate the torsional state of the rope. This paper proposes an unfixed-axis wire rope rotation angle measurement method, which mainly includes two parts, the axis positioning of the rope and the rotation tracking process. Firstly, the axis positioning method of the rope is introduced. Then, the geometrical principle of rope rotation measurement and the framework of Lucas–Kanade tracking algorithm are explained. Finally, a simulation test and a rotation experiment verify the performance of the proposed algorithm, and the influence of axis positioning error and radius recognition error on the measurement are discussed. The proposed method provides an effective way for the measurement of wire rope.

A monocular visual single-axis rotation measurement method of multi-rudders based on cooperative targets

To tackle the problem that the rotation angle of multiple rudders needs to be measured in real time and high precision, a measurement method based on cooperative targets is proposed in this paper. Firstly, to detect and encode multiple similar rudders with sparse feature points in complex backgrounds, we design a novel visual cooperative target with encoding information, and study a cooperative target localization algorithm based on contour extraction as well as a corner point extraction algorithm based on a checkerboard grid. Then, through the PnP algorithms and numerous corner points extracted from the cooperative target, an unconstrained optimization model is developed based on the re-projection error, and the Levenberg-Marquard (LM) algorithm is applied to estimate the rotation angle. Finally, an experiment platform is set up to evaluate the accuracy and speed of the algorithm. Compared with the existing methods, the experimental results show that the proposed cooperative target exhibits favorable localization under various typical experimental environments with a detection success rate better than 98%, meanwhile, the actual measurement accuracy of the angle estimation model is better than 0.05° and the average execution time of each measurement is less than 20 ms. Moreover, the proposed method is easy to install and operate in actual measurement, and can achieve simultaneous measurement of the spatial rotation angle of multiple rudders, which is well suited to actual industrial production needs.

Uncertainty Analysis of Spherical Joint Three-Dimensional Rotation Angle Measurement

A precision spherical joint is a type of spherical motion pair that can realize three degrees of rotation freedom. In this paper, a specific method is used to assess the uncertainty of our measurement system. The measurement system uses the codes and eddy current sensor to measure the angle. Different codes are engraved on the surface of the spherical joint. Eddy current sensors are embedded in the spherical socket to detect and recognize the spherical code. The uncertainty of the measurement system hardware and an artificial neural network are studied. Based on the Monte Carlo method, the uncertainty components are evaluated and combined, and the comprehensive uncertainty of the measurement system is obtained. The evaluation results of system measurement uncertainty are verified from specific angles. In the three-axis measurement uncertainty, the minimum is about 2′, and the maximum uncertainty is about 1°. The proposed method can be used to evaluate the uncertainty of other multiple-input multiple-output measurement systems.

Current measurement method based on integral reconstruction of magnetic rotation angle

In view of the nonlinear limitation of the sine function on the magnetic rotation angle in the optical current sensor based on the light intensity detection mode, this paper proposes a current measurement method based on the integral reconstruction of the magnetic rotation angle, thus avoiding the large current measurement error caused by the approximate linear measurement of the magnetic rotation angle. In this method, the cosine term in the derivative of the sine signal containing the magnetic rotation angle is eliminated by the constant deformation of the trigonometric function, and then the magnetic rotation angle is reconstructed by integration. The experimental results show that within the current range of 0.20 Arms to 2.40 Arms, the measurement error of the current value of the integral reconstruction method is less than 1.30%, the measurement error is less than the approximate linear measurement method, and there is a good linear relationship between the magnetic rotation angle and the current, with a linearity of 99.987%.

Analysis of the accuracy of the signal processing algorithm of the differential phase polarimeter

The purpose of this work is to analyze the effect of the polarimeter signal processing algorithm on the results of measurements of the optical rotation angle of the polarization plane to improve the accuracy of measurements in differential polarimetry. Methods. The paper considers the methods of polarimetry used for the analysis of optically active substances, based on the methods of phase measurements used to calculate the optical rotation angle. The expediency of using the Fourier transform to calculate the phase difference of differential polarimeter signals is noted. To analyze the error of the algorithm, mathematical modeling of the measurement information processing for various signal parameters is applied. Results. The results of the study of the effect of the bit depth of the analog-to-digital converter, the number of samples over the period of the signal and the accumulation time on the accuracy of restoring the phase difference are presented. The influence of the ratio of signal amplitudes and the level of amplitude and phase noise caused by the imperfection of the measuring system has also been investigated. Conclusion. The obtained results make it possible to optimize the operating mode and improve the accuracy of the optical rotation angle measurements using a differential phase polarimeter based on the Fourier transform.

Effect of forearm positions on scapular movements and trunk rotation angles.

[Purpose] The study investigated the impact of distinct forearm positions on scapular movement and trunk rotation angles. [Participants and Methods] We enrolled 23 healthy young males. Measurements of trunk rotation and relative scapular segment angles were acquired under three conditions employing three-dimensional motion analysis, each executed in a seated posture: (1) both forearms in a neutral position, (2) the forearm on the rotational side adopted supination while the opposite forearm utilized pronation, and (3) the forearm on the rotational side employed pronation while the opposite forearm assumed supination. [Results] The scapular angles in all three scenarios reflected downward rotation, posterior tilt, and external rotation of the rotational-side scapula. Conversely, the contralateral scapula exhibited upward rotation, anterior tilt, and internal rotation. Although the scapular and trunk rotation angles corresponded with the three forearm positions, all three were significantly different and were significantly increased when the rotational-side forearm was in supination (opposite side pronation) and decreased when the rotational-side forearm was in pronation (opposite side supination). [Conclusion] During trunk rotation, regular scapular movements were observed, which varied depending on forearm position and influenced the range of trunk rotation.

Differences in Physical Examination Outcomes between Sacroiliac Joint Motion Restricted and Painful Groups in Patients with Lumbopelvic Pain

Background Among sacroiliac joint (SIJ) special tests, motion palpation tests (MPT) are commonly used to assess possible SIJ motion dysfunction. Pain provocation tests (PPT) attempt to assess whether or not the stressed structure is a source of pain. Pain and dysfunction are dissimilar concepts and should be differentiated from each other in clinical practice. Objectives The purpose of this study was to compare differences in physical examination outcomes (hamstring muscle length, isometric gluteus maximus strength, pelvic rotation angle during active straight leg raise (ASLR) and visual analog scale (VAS) between motion-restricted and painful groups of patients with low back pain (LBP). Methods Thirty-two patients between the ages of 18 and 45 participated. Four MPT (Gillet, standing flexion, sitting flexion, and supine to sit) and five PPTs (compression, distraction, Gaenslen's, thigh-thrust, and sacral-thrust) were used for distinguishing subjects with SIJ dysfunction. Independent t-test analysis was used to compare physical examination outcomes between the two groups. Results Results showed that SIJ PPT groups were significant changes (p = 0.028) in hamstring length compared to the SIJ MPT groups, and the subjective pain level (VAS) also showed a significant result. (p < 0.001) In the measurement of the pelvic rotation angle during the ASLR, the MPT group showed a more significant change in pelvic rotation angle than the PPT group (p = 0.043) However, our data did not show a significant difference in the isometric gluteus maximus strength of the two groups. (p = 0.882) Conclusions Based on these results, therapeutic interventions for SIJ dysfunction should be appropriately and harmonized by identifying the differences and unique features of the two test methods, and new evaluation methods combining these two methods are required.