Trigonometric Measurements Research Articles

Initial point positioning of weld seam and robot pose estimation based on binocular vision

Abstract In order to rapidly identify and locate the weld seam initial point in robotic automated welding, we established a binocular vision system and proposed a weld seam initial point localization algorithm named WIPL-Net. Built upon the Fully Convolutional One-Stage object detection network, WIPL-Net introduces a lightweight ResNext as its backbone network and incorporates channel attention and enhanced feature fusion mechanisms to enhance feature detection and extraction capabilities. Subsequently, WIPL-Net is utilized to obtain the weld seam’s initial point, and its three-dimensional coordinates are determined through trigonometric measurements. To further estimate the robot’s posture at the initial point, we performed sparse three-dimensional reconstruction of the local region centered on the weld seam initial point based on You Only Look At Coefficients of Tensors instance segmentation and feature point matching. Finally, we conducted comparative experiments on WIPL-Net and conducted weld seam initial point localization experiments in real welding scenarios. The results demonstrate that our proposed method achieves a positioning error of less than 1.2 mm for the weld seam’s initial point and a pose error of less than 10 degrees for the robot, meeting the requirement for real-time positioning of the weld seam’s initial point.

The high energy Universe at ultra-high resolution: the power and promise of X-ray interferometry

We propose the development of X-ray interferometry (XRI), to reveal the Universe at high energies with ultra-high spatial resolution. With baselines which can be accommodated on a single spacecraft, XRI can reach 100 μ as resolution at 10 Å (1.2 keV) and 20 μ as at 2 Å (6 keV), enabling imaging and imaging-spectroscopy of (for example) X-ray coronae of nearby accreting supermassive black holes (SMBH) and the SMBH ‘shadow’; SMBH accretion flows and outflows; X-ray binary winds and orbits; stellar coronae within sim 100 pc and many exoplanets which transit across them. For sufficiently luminous sources XRI will resolve sub-pc scales across the entire observable Universe, revealing accreting binary SMBHs and enabling trigonometric measurements of the Hubble constant with X-ray light echoes from quasars or explosive transients. A multi-spacecraft ‘constellation’ interferometer would resolve well below 1 μ as, enabling SMBH event horizons to be resolved in many active galaxies and the detailed study of the effects of strong field gravity on the dynamics and emission from accreting gas close to the black hole.

WITHIN-SESSION RELIABILITY FOR INTER-LIMB ASYMMETRIES IN ANKLE DORSIFLEXION RANGE OF MOTION MEASURED DURING THE WEIGHT-BEARING LUNGE TEST

The identification of asymmetrical inter-limb ankle dorsiflexion range of motion (DF ROM) has the potential to influence the course of treatment during the rehabilitation process, with limitations in ankle DF ROM potentially increasing injury risk. However, reliability for methods to identify ankle DF ROM asymmetries remain under described in the literature. To determine the reliability of the trigonometric calculation method for measuring ankle DF ROM during the weight-bearing lunge test (WBLT) for both a single limb and the symmetry values. The secondary purpose was to establish values of ankle DF ROM asymmetry and identify the influence of leg dominance on ankle DF ROM. Cross-sectional study. Ankle DF ROM was measured bilaterally in 50 healthy and recreationally active participants (28 men, 22 women, age = 22 ± 4 years, height = 172.8 ± 10.8 cm, body mass 71.5 ± 15.1 kg), using the trigonometric measurement method during the WBLT. Each ankle was measured twice in a single testing session to establish within-session reliability. Values are presented for asymmetries in DF ROM. No differences were identified between the dominant and non-dominant limb (p = 0.862). Within-session reliability for measuring a single limb was classified as 'good' (ICC = 0.98) with a minimal detectable change value of 1.7 °. For measuring ankle DF ROM asymmetry, reliability was established as 'good' (ICC = 0.85) and a minimal detectable change value of 2.1 ° was determined. Although symmetry in ankle DF ROM may not be assumed, the magnitude of asymmetry may be less than previously reported in a population of recreationally active individuals. Discrepancies between previous research and the findings of the present study may have been impacted by differences in measurement methods. Furthermore, clinicians should be aware that the error associated with measures of asymmetry for ankle DF ROM during the WBLT is greater than that of a single limb. 2b.

Photometric, kinematic, and variability study in the young open cluster NGC 1960

ABSTRACT We present a comprehensive photometric analysis of a young open cluster NGC 1960 (= M36) along with the long-term variability study of this cluster. Based on the kinematic data of Gaia DR2, the membership probabilities of 3871 stars are ascertained in the cluster field among which 262 stars are found to be cluster members. Considering the kinematic and trigonometric measurements of the cluster members, we estimate a mean cluster parallax of 0.86 ± 0.05 mas and mean proper motions of μRA = −0.143 ± 0.008 mas yr−1 and μDec. = −3.395 ± 0.008 mas yr−1. We obtain basic parameters of the cluster such as E(B − V) = 0.24 ± 0.02 mag, log(Age/yr) = 7.44 ± 0.02, and d = 1.17 ± 0.06 kpc. The mass function slope in the cluster for the stars in the mass range of 0.72–7.32 M⊙ is found to be γ = −1.26 ± 0.19. We find that mass segregation is still taking place in the cluster which is yet to be dynamically relaxed. This work also presents first high-precision variability survey in the central 13 arcmin × 13 arcmin region of the cluster. The V-band photometric data accumulated on 43 nights over a period of more than 3 yr reveals 76 variable stars among which 72 are periodic variables. Among them, 59 are short period (P < 1 d) and 13 are long period (P > 1 d). The variable stars have V magnitudes ranging between 9.1 to 19.4 mag and periods between 41 min and 10.74 d. On the basis of their locations in the H–R diagram, periods, and characteristic light curves, 20 periodic variables belong to the cluster are classified as 2 δ-Scuti, 3 γ-Dor, 2 slowly pulsating B stars, 5 rotational variables, 2 non-pulsating B stars, and 6 as miscellaneous variables.

Feasibility study of high-precision trigonometric elevation replacing second-order level in tunnel penetration control survey

Based on the principle of trigonometric elevation measurement and the law of error propagation, the trigonometric elevation formula is derived in this paper. The factors that cause the trigonometric measurement error are analyzed accurately. It is considered that the use of a high-precision total station for the trigonometric elevation measurement under opposite conditions can reach the second-order level measurement accuracy.

Noise reduction in modulation measurement profilometry based on the wavelet transform method

Modulation measurement profilometry can achieve the reconstruction of a tested object with complex or step-like surface. The technology applying coaxial and coimage plane optical systems in which the projection axis coincides with the observation axis can effectively avoid the defects of shadow, shade, and phase discontinuity. All of these weaknesses are largely present in optical three-dimensional sensing based on trigonometric measurement principle. However, in the practical application, the captured fringe patterns are always inevitably influenced by noise, which will directly affect the measurement accuracy. As a well-known and remarkable time-frequency analysis tool, the wavelet transform (WT) method has a strong noise immunity and is suitable to analyze nonstationary signals. Comparisons between the WT method and the Fourier transform method are made not only by computer simulations appearing robust within various types of noise but also the practical experiment. It shows that the WT method is helpful in the enhancement of measurement accuracy. Additionally, experiment further verifies its strong antinoise ability.

METHODS FOR THE UPDATE AND VERIFICATION OF FOREST SURFACE MODEL

The digital terrain model (DTM) represents the bare ground earth's surface without any objects like vegetation and buildings. In contrast to a DTM, Digital surface model (DSM) represents the earth's surface including all objects on it. The DTM mostly does not change as frequently as the DSM. The most important changes of the DSM are in the forest areas due to the vegetation growth. Using the LIDAR technology the canopy height model (CHM) is obtained by subtracting the DTM and the corresponding DSM. The DSM is calculated from the first pulse echo and DTM from the last pulse echo data. The main problem of the DSM and CHM data using is the actuality of the airborne laser scanning. <br><br> This paper describes the method of calculating the CHM and DSM data changes using the relations between the canopy height and age of trees. To get a present basic reference data model of the canopy height, the photogrammetric and trigonometric measurements of single trees were used. Comparing the heights of corresponding trees on the aerial photographs of various ages, the statistical sets of the tree growth rate were obtained. These statistical data and LIDAR data were compared with the growth curve of the spruce forest, which corresponds to a similar natural environment (soil quality, climate characteristics, geographic location, etc.) to get the updating characteristics.

METHODS FOR THE UPDATE AND VERIFICATION OF FOREST SURFACE MODEL

Abstract. The digital terrain model (DTM) represents the bare ground earth's surface without any objects like vegetation and buildings. In contrast to a DTM, Digital surface model (DSM) represents the earth's surface including all objects on it. The DTM mostly does not change as frequently as the DSM. The most important changes of the DSM are in the forest areas due to the vegetation growth. Using the LIDAR technology the canopy height model (CHM) is obtained by subtracting the DTM and the corresponding DSM. The DSM is calculated from the first pulse echo and DTM from the last pulse echo data. The main problem of the DSM and CHM data using is the actuality of the airborne laser scanning. This paper describes the method of calculating the CHM and DSM data changes using the relations between the canopy height and age of trees. To get a present basic reference data model of the canopy height, the photogrammetric and trigonometric measurements of single trees were used. Comparing the heights of corresponding trees on the aerial photographs of various ages, the statistical sets of the tree growth rate were obtained. These statistical data and LIDAR data were compared with the growth curve of the spruce forest, which corresponds to a similar natural environment (soil quality, climate characteristics, geographic location, etc.) to get the updating characteristics.

Comparison of a Multiple Regression Model and a two-Regime Model of a Vertical Refraction/ Porovnanie Viacnásobného Regresného Modelu A Dvojrežimového Modelu Vertikálnej Refrakcie

Abstract Accuracy of the trigonometric measurement of elevations is affected by the systematic influence of a vertical refraction, which is caused by changes of meteorological parameters. Submitted paper deals with a modelling of the impact of the vertical refraction using selected meteorological parameters. At first, a concise derivation of a physical principle of the vertical refraction is given. Then, a multiple regression model and its extension into a form of two-regime model are given. Division into two regimes provides a threshold function, which expresses the dependence of the original explanatory variables. Different types of the threshold function are considered and finally a comparison of the quality of the proposed models and application of a chosen model on the results of repeated trigonometric measurements is given.

A geometrically determined distance to a far-off black hole

Trigonometric measurements might ultimately be applied to the most remote objects in the universe.

Map of Maryland and Virginia of 1660-1670 Created by Augustin Herrmann

In the paper a little known large 4-folio map of the territory of the later US states Virginia and Maryland is introduced. The map, which was surveyed and composed between 1660 and 1670, is exceptional from several points of view: the vast impenetrable territory covering a strip of land of about 700 × 400 km was mapped by one man, Augustin Herrman “Bohemian” (as he called himself) and by his crew during 10-year surveying and trigonometric measurements. It seems that this extraordinary map belongs among the first geodetically surveyed maps of the American territory. In 1960 altogether 5 copies of the map, complete in four parts, were known in British, French and American Libraries and map collections.

Textile-based Micro Electro Mechanical System (MEMS) Accelerometer for Pelvic Tilt Mesurement

This project proposes the application of textile-based MEMS accelerometer for measuring pelvic tilt angle. Textile-based accelerometer provides an alternative to the costly and hazardous radiographic measurement of pelvic tilt. The flexibility of textile structure makes it more advantageous to conform to body contour than rigid digital inclinometer and more accurate than indirect trigonometric measurement. Conventional MEMS devices are usually constructed from silicon-based material, which is expensive and requires access to clean room equipments. Textile material is relatively low-cost, flexible, lightweight, readily available, environmental friendly and easy to use. Silver nanoparticles (AgNPs) are used here as the transducer material to induce piezoresistive effect when stress is applied on the textile. The electrode and resistor parts of the accelerometer were made by stamping different volume of AgNPs on a cotton cloth. Starch ironing method was used to stiffen the textile. The force is applied by the 10g mass attached at the tip of the accelerometer. The working principle of this accelerometer is based on piezoresistive effect generated by the conductive nanomaterials patterned on textile substrate. When a force is applied, the accelerometer experiences mechanical stress which causes change in its resistance. The initial resistance for the accelerometers ranges from 17.00 to 30.97 MΩ. When the tilt angle increases, the relative resistance change also increases in nearly linear behavior. The concept of textile-based accelerometer is proven feasible as there is a transducible effect of resistance change when the sample is tilted.

Reducing the impact of a vertical refraction by a two-regime model

Reducing the impact of a vertical refraction by a two-regime model This paper deals with the creation of a mathematical model to eliminate or reduce the impact of a vertical refraction from the results of repeated trigonometric measurements of elevations. A multiple regression model with air temperature and pressure as the explanatory variables is proposed and subsequently modified into the form of a two-regime model. The threshold parameter is given by the threshold function, which represents an approximation of the relationship between the atmospheric pressure and temperature. An investigation of the quality of the proposed models and the application of the selected model on the experimental measurement results is also performed.

A new absolute magnitude calibration with 2MASS for cataclysmic variables

Using reliable trigonometric measurements, we find that the absolute magnitude of cataclysmic variables depends on the orbital period and de-reddened ( J − H) 0 and ( H − K s ) 0 colours of 2MASS (Two Micron All Sky Survey) photometric system. The calibration equation covers the ranges 0.032 d < P orb ⩽ 0.454 d , −0.08 < ( J − H) 0 ⩽ 1.54, −0.03 < ( H − K s ) 0 ⩽ 0.56 and 2.0 < M J < 11.7; It is based on trigonometric parallaxes with relative errors of ( σ π / π) ⩽ 0.4. By using the period-luminosity-colours (PLCs) relation, we estimated the distances of cataclysmic variables with orbital periods and 2MASS observations and compared them with distances found from other methods. We suggest that the PLCs relation can be a useful statistical tool to estimate the distances of cataclysmic variables.

GPS HEIGHT MEASUREMENT OF PEAK BOLIVAR, VENEZUELA

Based on a series of GPS observations made in 2002 on the summit of Peak Bolívar, the highest Venezuelan mountain, and on seven other nearby sites along the Venezuelan Andes, including another three of the highest peaks of the country; and using a recently derived local geoid for Venezuela, we have determined the orthometric height of Peak Bolívar as 4978.4 ± 0.4 m. This height is 23.6 m smaller than the height obtained by combining trigonometric triangulation techniques and barometric measurements in the nearby town of Mérida in 1912, and 28.6 m smaller than the current official altitude that dates from 1928.

Possible Fluctuation of the Position of Sagittarius A* Relative to Extragalactic Radio Sources

When we measure the position of an extragalactic radio source through the Galaxy, apparent position wander will be induced because of the gravitational deflection by intervening stars in the Galaxy. When measuring the annual parallax of a radio source with respect to the nearby extragalactic radio sources, such position wander should be taken into account. This effect is especially serious in the case of the trigonometric measurement of Sgr A*, located in the Galactic center. We estimated the optical depth and the event rate of the position wander of the extragalactic radio sources near Sgr A* and found that such position wander degrades the measurement of trigonometric parallax of Sgr A* significantly. For observations with an accuracy of 10 μas, the probability of degradation is a few tens of percent. Several years of continuous observation are needed for the separation of this gravitational position wander from the annual parallactic motion. Even for observations with an accuracy of 25 μas, a few years of continuous observation are needed to eliminate the effect of position wander.

On the pulsation parallax of the variable star RR Lyr

We show that a straightforward application of the predicted relation connecting the absolute K magnitude of fundamental RR Lyrae variables to their period and metal content, together with current evolutionary predictions on the mass and luminosity of Horizontal Branch stars, supply a distance estimate to the prototype star RR Lyr in close agreement with the recent parallax determination by the Hubble Space Telescope (HST; Benedict et al.), largely unaffected by the interstellar extinction correction. Adopting (A V ) = 0.12 ′ 0.10 mag as a safe estimate of the extinction correction to RR Lyr, we obtain a 'pulsation' parallax π p l u s = 3.858 ′ 0.131 mas which agrees quite well, and with a smaller formal error, with the HST measurement (π a b s = 3.82 ′ 0.20 mas) and with the weighted average of HST, Hipparcos, and ground-based determinations ((π a b s ) = 3.87 ′ 0.19 mas). This result suggests that nearinfrared magnitudes and pulsation models could constrain the distance to well-studied RR Lyrae stars, both in the field and in globular clusters, with an accuracy better than current direct trigonometric measurements.

Necessity of sine-cosine joint measurement.

The quantum measurement of trigonometric variables is revisted. We show that the probability distributions of the sine and cosine operators of Susskind and Glogower [Physics 1, 49 (1964)] suffer unphysical features for nonclassical states. We suggest that any measurement of a trigonometric variable needs necessarily a joint measurement of the two cosine-sine phase quadratures. In this way unphysical quantum statistics are avoided, and no violation of the trigonometric calculus occurs for expected values. We show that this trigonometric measurement can be defined in general terms in the framework of quantum estimation theory.

Trinocular Vision Using Edge Continuity and Local Features

AbstractIn the mechanical recognition of three‐dimensional shape, position and orientation of the object, it is important to obtain information concerning the distance to the object (depth). One of the powerful approaches for this purpose is the binocular vision (stereo method), in which two cameras are used to determine the distance based on the principle of trigonometric measurement. In this method, the three‐dimensional position of a point can easily be determined if the correspondences of feature points are established between the two images. However, the correspondence is not easy if the two images have a large number of feature points. We investigated the correspondence problem, and solved the difficulty by introducing another camera, realizing the trinocular vision and applying a simple geometrical processing. However, when the number of the feature points on the image is increased in this method, the correspondence is sometimes not unique, leading to more than one corresponding point. To solve this problem, the edge continuity and the local property of the image are combined with the geometrical constraints by trinocular vision, arriving at a satisfactory result.

A technique for estimating mechanical work of individual muscles in the cat during treadmill locomotion

Mechanical work, the product of force and length change, was assessed in selected hindlimb extensors of two adult cats during three different speeds of unrestrained treadmill locomotion. Forces were measured using implanted transducers placed on the soleus (SOL) and medial gastrocnemius (MG) tendons. A three dimensional technique of muscle length estimation using high speed cinematography was found preferable to either two dimensional or trigonometric measurements derived from anatomical and kinematic parameters. Length excursions increased in both muscles as treadmill speed increased. However, at all speeds of locomotion, the uniarticular SOL exhibited a greater range of motion than the biarticular MG. Increases in treadmill speed resulted in higher peak forces in the MG and constant or slightly lower peak forces in the SOL. These speed-dependent changes in length and force resulted in higher total positive work, lower total negative work, and higher net work for both muscles with increasing speeds. These data illustrate the importance of three-dimensional kinematics in determining changes in muscle length and describe the relative force and work changes in a slow and fast ankle extensor with changes in speed of locomotion.