Spatial Curves Research Articles

Parameter Selection for Milling Machining of Thin-Walled Parts Based on Spatial Distribution of Side Blades

In the machining of thin-walled components, the tool’s side edges play a pivotal role in the cutting process. This paper presents the establishment of the AdvantEdge 3D simulation model for the analysis of the contact conditions and the variation in cutting forces between the side edge and the machined surface across varying cutting depths. Subsequently, milling experiments were conducted to assess the impact of the side edge’s contact conditions on the surface quality of the machined parts, considering different cutting depths. The findings reveal that during side milling of thin-walled components, a lower number of teeth result in reduced cutting edges, decreased cutting forces, and improved surface quality. The selection of cutting depth should be made with due consideration to the contact conditions between the tool’s side edge and the workpiece. Ideally, the cutting depth should be less than the pitch of the side edge’s spatial curve to ensure that only a single cutting edge is engaged in the cutting process.

First intensity interferometry measurements with the H.E.S.S. telescopes

ABSTRACT Intensity interferometry for astrophysical observations has gained increasing interest in the last decade. The method of correlating photon fluxes at different telescopes for high resolution astronomy without access to the phase of the incoming light is insensitive to atmospheric turbulence and does not require high-precision optical path control. The necessary large collection areas can be provided by Imaging Atmospheric Cherenkov Telescopes. Implementation of intensity interferometers to existing telescope systems such as VERITAS and MAGIC has proven to be successful for high-resolution imaging of stars. In 2022 April we equipped two telescopes of the H.E.S.S. array in Namibia with an intensity interferometry setup to measure southern sky stars and star systems during the bright moon period. We mounted an external optical system to the lid of the telescope cameras, which splits the incoming light and feeds it into two photomultipliers in order to measure the zero-baseline correlation within one telescope in addition to the cross-correlation between the telescopes. The optical elements are motorized, which enables live correction of tracking inaccuracies of the telescopes. During the campaign we measured the spatial correlation curves and thereby the angular diameters of λ Sco (Shaula) and σ Sgr (Nunki), while we also performed systematic studies of our interferometer using the multiple star system of α Cru (Acrux).

Simulation of the hexagonal 3D braiding process for stent preforms

Due to the complex braiding process and long development cycle of the hexagonal three-dimensional braided stent, a MatLab based computer-aided braiding method for a stent is proposed to speed up the development process. First, an oblique coordinate system for the chassis and a polar coordinate system for the chassis unit are constructed, respectively, precisely to coordinate the carrier’s movements on the chassis. Subsequently, an iterative formula delineating the trajectory of the carrier is introduced. The formula effectively translates the entire braiding process into the positional coordinates of the carrier on the chassis and the yarn heights on the mandrel during different stages. Based on the specific characteristics of the braiding process and the stent’s structure, the stent is divided into pressing and twisting sections. The interwoven pattern for both the pressing and twisting sections is determined by establishing the basic tiling form, solving the yarn interwoven sequence, judging the interwoven type and computing the number of kinks. Finally, while considering the stent's dimensional parameters and the interwoven pattern of the yarn, the spatial curve equations for the yarns in both the pressing and the twisting sections are formulated. By concatenating these equations for each section, the three-dimensional trajectory equations and a comprehensive solid model of the stent are successfully derived. Through a rigorous comparative analysis of dimensions and the braiding pattern between the three-dimensional solid model and the physical stent preform, the accuracy and fidelity of the model generated through the implementation of computer-aided braiding technology are verified.

Unified seam tracking algorithm via three-point weld representation for autonomous robotic welding

Autonomous robotic welding based on real-time seam tracking has shown excellent prospects in the field of intelligent manufacturing. In previous research, real-time seam tracking requires teaching trajectories, which has significant limitations. Moreover, as different types of welds have different shapes, their geometric distribution also exists in various forms such as straight lines, planar curves, and spatial curves, which brings significant challenges to the visual recognition of welds. The use of existing methods for tracking specific types of welds has limited applications. Currently, the existing methods are carried out for tracking specific types of welds, resulting in limited application scope. To handle various types of weld joints, a unified tracking paradigm named the three-point seam tracking algorithm (TSTA) is proposed in this study. First, a feature description method using three feature points is established to define different weld joints. The feature points are employed to reconstruct the position and attitude of welds, which allows the method to track welds of arbitrary geometries. Subsequently, a recognition method for the feature points combining morphology extraction and kernel correlation filter (KCF) tracker is designed. Combined with their respective advantages, the algorithm can identify the three feature points accurately and robustly in strong-noise environments. Extensive experiments including actual welding were conducted to verify the superiority of the proposed TSTA. Eleven representative types of weld seams were tested and all of them could be tracked in real time without any prior information. Compared with similar studies, the proposed recognition algorithm currently achieves the highest accuracy and best robustness. The TSTA provides a complete solution in autonomous robotic welding for unknown welds and shows excellent application prospects.

Research on Three-Dimensional Shape Curve Reconstruction Technology for a Scraper Conveyor on an Intelligent Working Face.

"Three straight and two flat" is the inevitable demand when realizing the intelligent mining of a fully mechanized mining face. To address the crucial technical issue of lacking accurate perception of the shape of the scraper conveyor during intelligent coal mining, a three-dimensional curvature sensor involving fiber Bragg grating (FBG) is used as a perceptive tool to conduct curve reconstruction research based on different local motion frames and to reconstruct the shape of the scraper conveyor. Firstly, the formation process of the 'S'-shaped bending section of the scraper conveyor during the pushing process is determined. Based on the FBG sensing principle, a mathematical model between the variation in the central wavelength and the strain and curvature is established, and the cubic B-spline interpolation method is employed to continuously process the obtained discrete curvature. Secondly, based on differential geometry, a spatial curve reconstruction algorithm based on the Frenet moving frame is derived, and the shape curve prediction interpolation model is built based on a gated recurrent unit (GRU) model, which reduces the impact of the decrease in curve reconstruction accuracy caused by damage to some grating measuring points. Finally, an experimental platform was designed and built, and sensors with curvature radii of 6 m, 7 m, and 8 m were tested. The experimental results showed that the reconstructed curve was essentially consistent with the actual shape, and the absolute error at the end was about 2 mm. The feasibility of this reconstruction algorithm in engineering has been proven, and this is of great significance in achieving shape curve perception and straightness control for scraper conveyors.

Versatile robotic welding system integrating laser positioning, trajectory fitting and real-time tracking

The three welding modes of laser positioning, trajectory fitting and real-time tracking are key links for flexible robotic welding, because they directly affect the adaptability of welding robots for complex structural parts. Nevertheless, there are few studies on the integration of laser positioning, trajectory fitting and real-time tracking welding. Aiming at the drawback of that the robot cannot efficiently match the corresponding welding process between different working conditions such as short seam, spatial curve seam and long seam welding, a control scheme that can integrate the above three welding modes is proposed in this paper. First, the welding requirements of laser positioning, trajectory fitting and real-time tracking are transformed into a unified 3D coordinate recognition task for integrated welding, so the identification of welding points under three different processes can be obtained through an identical inference. The next, given the fast inference speed of YOLOv5, a joint ROI extraction algorithm with YOLOv5 as the core is applied. To compensate for YOLOv5′s inability to directly locate seam centers, iterative centerline unbiased detector (ICUD) and adaptive feature extraction algorithm (AFEA) are proposed without the need for complex image pre-processing and with very strong immunity to strong exposure and strong arc spatter. Finally, teaching trajectory correction model, B-spline curve fitting model, and 3D coordinate real-time tracking model are presented to enhance the adaptability of the welding robot and to flexibly match the appropriate welding mode in various working conditions. Experimental results indicate that the welding trajectory is basically consistent with the seam centerline when laser positioning and trajectory fitting welding. In real-time tracking welding, the real-time deviation is mainly controlled within the range of ± 0.2 mm, and the average error is 0.1160 mm.

Schumpeterian endogenous growth model under green innovation and its enculturation effect

This paper studies the economic system in which the preference of enterprises and residents to practice green behavior becomes a common form. This economic system shall be referred to as the economic system under the green development pattern, this paper divides its development stage into two parts: the green development transformation stage and the green innovation stage. As the system transitions from the former stage to the latter, the innovation system composed of quality innovation and variety innovation will transition to an innovation system with three innovation modes: quality innovation, variety innovation and green innovation. In the green innovation stage, green innovation is transformed into endogenous elements of the economic system, which requires a study of the endogenous growth model and growth law, in light of new endogenous elements. This paper establishes the Schumpeterian endogenous growth model under the green development pattern (hereafter the Green Schumpeterian Model). This new model takes green innovation into account and combines the growth rate of residents' green behavior awareness level, the green discount rate, and the penetration rate of green innovation. The research findings indicate that green innovation leads to the economic enculturation effect and the environmental enculturation effect in the economic system under the green development pattern, achieving explosive in economic growth and environmental protection. Under the green development pattern, there is a new spatial Kuznets curve relationship between pollution emissions, the green innovation level, and the output level. The point at which pollution emissions reach their peak represents the turning point of the spatial Kuznets curve. Furthermore, by reducing the green discount rate and increasing the growth rate of residents' green behavioral awareness level, a nonlinear positive impact can be observed on the explosive mechanism of green innovation.

Riccati equations of opposite torsions from the Lie-Darboux method for spatial curves and possible applications

A novel formulation of the Lie-Darboux method of obtaining the Riccati equations for the spatial curves in Euclidean three-dimensional space is presented. It leads to two Riccati equations that differ by the sign of torsion. The case of cylindrical helices is used as an illustrative example. Possible applications in Physics are suggested.

Safety Evaluation for Highway Geometric Design Based on Spatial Path Properties

Safety is an important aspect of road design. In highway geometric design, road engineers use a two-stage design method due to its convenience, but the available two-dimensional design tools on the market are believed to impose limitations. Horizontal and vertical alignment parameters are considered and determined at the designer’s discretion, potentially downplaying the three-dimensional characters of spatial curves. This study focuses on the three-dimensional characteristics of highway alignments and investigates a safety evaluation method to establish the relationship between crash rate and spatial curve properties. This will necessitate an analytical investigation into the effects of higher-order properties, such as curvature and torsion, on the geometry of spatial Cartesian curves. First, these combinations of horizontal and vertical alignments were categorized into six classifications, each with its own spatial expression in mathematical form. After manipulating the curvature and torsion of the spatial curve algebraically, the correlation between geometric design variables and crash rate was ultimately established. A few cases involving geometric design data and crash facts were utilized for verification. The results revealed a considerable positive correlation between curvature or torsion variance and crashes per million vehicles kilometers, as a slight difference between curvature and torsion could also be spotted. And curvature distribution is correlated with collision frequency more closely than torsion spatial variation.

О ВЫЧИСЛЕНИИ ПРЕДЕЛЬНЫХ ТОЧЕК НА КРИВЫХ РАВНОВЕСИЙ В ЗАДАЧАХ УСТОЙЧИВОСТИ ПОДКРЕПЛЕННЫХ ПЛАСТИН

This paper presents a methodology for calculating limit points on equilibrium curves for stability problems of stiffened plates with initial imperfections. The values of critical loads are obtained and their corresponding general and local forms of stability loss from linear and nonlinear solutions are shown. To determine the coordinates of limit points on spatial curves, the method of non-specific continuations proposed by G.A. Manujlov is used. The diagrams of equilibrium states of connected solutions with limit points are constructed. The numerical solution of the above problems showed a good enough agreement with the semianalytical solution for the case of wave formation in an edge.

On [formula omitted] and [formula omitted] Hermite interpolation by spatial Algebraic-Trigonometric Pythagorean Hodograph curves with polynomial parametric speed

In this paper we focus on the class of Algebraic-Trigonometric Pythagorean Hodograph curves (ATPH for short) that is characterized by a purely polynomial parametric speed. Within such a class of ATPH curves, we first construct interpolants to spatial G1 Hermite data equipped with curvature values. With respect to the solutions proposed in [24], the G1 Hermite ATPH interpolants we here propose are characterized by C0- and C1-continuous curvature plots. Secondly, we investigate the existence of ATPH interpolants to spatial G2 Hermite data and show that solutions exist under some restrictions on the Hermite input data.

Dynamic monitoring of saturation profiles during two phase immiscible displacements in confined sand packs using time-domain analysis of the frequency domain electromagnetic sweeps

Water saturation 1D spatial profiles were monitored using real-time domain analysis of the measured frequency domain complex reflection coefficients of electromagnetic sweeps during oil and deionized water flood experiments at ambient conditions. Gravity and viscous induced fingering and piston-like displacement scenarios were explored. A patented coaxial transmission line core holder was designed to host saturated sand packs compressed in their axial and radial dimensions. An inverse chirp z-transform algorithm was used to convert the measured responses from frequency to time domain. An optimization routine was developed to convert the resulting time domain step responses to water saturation profiles at every pore volume fraction of fluids injected. Advancing and trailing fronts and their breakthrough times were detected. Darcy's flow analysis was performed to extract 1D pressure distribution spatial profiles and dynamic capillary pressure curves for 3 drainage floods. The oil ganglia flow and gravity fluid separation were detected in water floods.

Optimal interpolation with spatial rational Pythagorean hodograph curves

Using a residuum approach, we provide a complete description of the space of the rational spatial curves of given tangent directions. The rational Pythagorean hodograph curves are obtained as a special case when the norm of the direction field is a perfect square. The basis for the curve space is given explicitly. Consequently a number of interpolation problems (G1, C1, C2, C1/G2) in this space become linear, cusp avoidance can be encoded by linear inequalities, and optimization problems like minimal energy or optimal length are quadratic and can be solved efficiently via quadratic programming. We outline the interpolation/optimization strategy and demonstrate it on several examples.

Future mathematics teachers’ implementation of research activities based on dynamic mathematics software GeoGebra

Problem statement. The digital transformation of higher education significantly affects the organization of pedagogical universities students’ research activities. Therefore, two important problems can be identified. Firstly, the matter of discovering information technology tools and directions for their use for the implementation of research work of future mathematics teachers studying in 1-2 courses. And secondly, the problem of choosing a mathematical topic, the solution of which with the help of digital technologies would lead to some interesting results that have elements of novelty. The purpose of this study is to identify the line of research of a mathematical nature, the implementation of which relies heavily on the dynamic mathematics software GeoGebra’s features. Methodology. Some features of the GeoGebra dynamic mathematics software and its application in geometric studies are analyzed. To study geometric figures, methods of visualization of mathematical objects and of experimental mathematics are used. Results. Some possibilities of dynamic mathematics software applicability in research and development of pedagogical universities’ mathematical profile students are considered. In these circumstances, the emphasis is on research related to the study of spatial curves and their planar projections, the construction of which naturally relies on the principles of displaying three-dimensional objects on a screen. The role of dynamic mathematics software in such studies mainly lies in the visualization of considered geometric objects, which makes it possible to identify possible properties of the constructed curves, and then, using available mathematical apparatus, to confirm their validity. Conclusion. The direction of designing and studying geometric objects using the GeoGebra dynamic mathematics software, which formed the basis of several research works of undergraduate students, is presented.

Research on Arc Sag Measurement Methods for Transmission Lines Based on Deep Learning and Photogrammetry Technology

Arc sag is an important parameter in the design and operation and maintenance of transmission lines and is directly related to the safety and reliability of grid operation. The current arc sag measurement method is inefficient and costly, which makes it difficult to meet the engineering demand for fast inspection of transmission lines. In view of this, this paper proposes an automatic spacer bar segmentation algorithm, CM-Mask-RCNN, that combines the CAB attention mechanism and MHSA self-attention mechanism, which automatically extracts the spacer bars and calculates the center coordinates, and combines classical algorithms such as beam method leveling, spatial front rendezvous, and spatial curve fitting, based on UAV inspection video data, to realize arc sag measurement with a low cost and high efficiency. It is experimentally verified that the CM-Mask-RCNN algorithm proposed in this paper achieves an AP index of 73.40% on the self-built dataset, which is better than the Yolact++, U-net, and Mask-RCNN algorithms. In addition, it is also verified that the adopted approach of fusing CAB and MHSA attention mechanisms can effectively improve the segmentation performance of the model, and this combination improves the model performance more significantly compared with other attention mechanisms, with an AP improvement of 2.24%. The algorithm in this paper was used to perform arc sag measurement experiments on 10 different transmission lines, and the measurement errors are all within ±2.5%, with an average error of −0.11, which verifies the effectiveness of the arc sag measurement method proposed in this paper for transmission lines.

Characteristics of anthropogenic heat with different modeling ideas and its driving effect on urban heat islands in seven typical Chinese cities

Anthropogenic heat (AH), an essential urban heat source, is often overlooked or simplified in research on the multiple temporal and spatial driving mechanisms of the urban heat island (UHI), and case studies investigating the impacts of different AH connotations are scarce. This study estimated the AH in seven typical Chinese cities based on a remote sensing surface energy balance model (AHseb) and an energy consumption inventory-machine learning model (AHinv). The intensity of the surface UHI was extracted using land surface temperatures, and then the linear mixed-effects model and geographic detectors were used to analyze the driving effect of AH on the UHI. Despite the similar shapes of the spatial profile curves, the AH derived from the two models differed in both temporal and spatial characteristics, which was more typical in winter and in urban centers, and AHinv had a more notable central spread feature than AHseb. The AH driving effects on UHI were notably influenced by spatial and temporal heterogeneity, particularly in regions with distinct background climates. However, after controlling for the random effects of the background climate, AH still exhibited a considerable enhancing effect on the UHI. AHseb outperformed AHinv in terms of linear positive correlation and interpretation rate for UHI. Meanwhile, interactions with other potential factors enhanced AH driving effects. Consequently, UHI mitigation must be tailored to the local context by integrating multiple drivers, and for the heating effects of AH, it is necessary to develop specific mitigation measures by limiting the conversion of AHinv to AHseb in addition to reducing the heat production. The findings offer guidance for analyzing and optimizing urban thermal climates with a focus on AH or energy consumption control.

TRPC6 deficiency impairs middle cerebral artery myogenic response and brain spatial memory

Transient receptor potential channel 6 (TRPC6) is a nonselective cation channel belonging to the TRP ion channel family and expressed in vascular smooth muscle cells. TRPC6 regulates calcium influx in response to vascular wall mechanical stretch. A previous study reported that TRPC6 is critical for the myogenic response of the middle cerebral artery (MCA). Impaired MCA myogenic response is implicated in cerebral blood flow dysfunction and may promote cognitive deficits. In this study, we investigated whether TRPC6 contributes to the MCA myogenic response at pressure range (from 40 to 180 mmHg) in 12-week-old male wild-type (WT) and whole-body TRPC6 knock-out (TRPC6 KO) mice (n=5-8). Cognitive function (spatial learning and reference memory) was examined at 22 weeks of age using the Morris water maze test. Myogenic response in MCA was similar in WT and TRPC6 KO mice when perfusion pressure was increased from 40 to 80 mmHg. At higher pressures (>120 mmHg), however, TRPC6 KO mice displayed significantly reduced myogenic response compared to WT mice (3 % less of myogenic tone in TRPC6 KO compared to WT) which was further exacerbated when perfusion pressure was increased to 180 mmHg (9 % less of myogenic tone in TRPC6 KO compared to WT). There were no significant differences in wall thickness, wall-to-lumen ratio, vascular distensibility, incremental distensibility, or elastic modulus curves in MCA between WT and TRPC6 KO mice. Compared to WT mice, TRPC6 KO mice displayed similar spatial learning curves after 4 days of training but showed significantly impaired reference memory (14±1 % vs 29±4 % in the target quadrant) and reduced frequency (1.0±0.3 vs 2.1±0.4 in the target area crossing) compared to WT. These findings suggest that TRPC6 deficiency impairs myogenic response at higher perfusion pressures and spatial memory, even at a young age. (AG050049 (F.F), AG057842 (F.F), AG079336 (F.F), NIDDK R00DK113280, R01DK121411, NIGMS P20GM104357 and NIGMS U54GM115428) This is the full abstract presented at the American Physiology Summit 2023 meeting and is only available in HTML format. There are no additional versions or additional content available for this abstract. Physiology was not involved in the peer review process.

花生荚果收获分离输送装置运动分析与试验研究

A peanut harvest separation and conveying device was designed considering the shortage of peanut harvest machinery and poor harvesting effect in China. The interaction between mechanism and pod-soil mixture was analysed to obtain the motion state of peanut relative separation conveyor. ADAMS simulation was applied to obtain the spatial curve of peanut trajectory in the separation process. The study determined that the optimum operating parameters of the separation conveyor were a drum speed of 280 r/min and an inclination angle of 19°. This study provides a theoretical basis for the further design of efficient peanut harvesting device.

Intersection and Flattening of Surfaces in 3D Models through Computer-Extended Descriptive Geometry (CeDG)

Computer-extended Descriptive Geometry (CeDG) is a new approach to solving and building computer models of three-dimensional (3D) geometrical systems through descriptive geometry procedures (thus inheriting invariant-symmetry properties from projective geometry) that have demonstrated reliability and accuracy. CeDG may calculate a parametric implicit functional form for the spatial curves generated in the intersection of two surfaces, as well as of the flattened pattern of any developable surface involved in those encounters. This study first presents the theoretical foundations and methodology to calculate those curves. Secondly, a compound hopper is defined and modeled through CeDG (implemented in GeoGebra) and CAD (Solid Edge© 2023) approaches to evaluate the advantages of CeDG against CAD. The results demonstrate the robustness and accuracy of the CeDG technique for he intersection and flattening of surfaces and the advantages of CeDG against Solid Edge 2023 in solving the hopper case study.

Wage flexibility and employment resilience in the Spanish labour market over the Great Recession

ABSTRACT The Spanish economy is characterized by significant and persistent regional disparities. The Great Recession caused a severe economic downturn, marked by declining wages and rising unemployment, influenced by the internal wage devaluation policies. We investigate the relationship between wage flexibility and regional labour market resilience. We estimate a spatial panel wage curve using microdata from social security records for the period 2002–19 using geographical and time weighted regression techniques. Our findings reveal that regions with higher wage flexibility exhibit higher resilience recovery indices, highlighting the importance of wage flexibility as a short-term adjustment mechanism in response to labour market shocks.