Academic literature on the topic 'Catenary curve'

Study casts of the lower arches of 35 children in whom arch alignment was considered acceptable, were examined using a reflex microscope. Arch perimeter was calculated mathematically from a method which required measurement of the mesio-distal widths of the teeth only. This was described as the ‘overlap’ method. Arch perimeter was also calculated using individualized catenary curves for each subject. Two calculations were made, recording arch width either at the distal contact points of the first permanent molars or between their mesio-buccal cusps. Arch perimeter measured from the length of the catenary curves was consistently shorter than that calculted by the overlap method. The variation ranged from 0·02 to 4·58 mm. The catenary constructed using the distal molar contacts gave a better representation of the actual arch form: the mean discrepancy was 2·36 mm, compared with 2·86 mm with the second method where arch width was measured between mesio-buccal cusps. Both techniques for calculation of arch perimeter were heghly reproducible. The catenary curve only approximated arch form well when the arch was relatively narrow across the inter canine region. For square arches this method was unsatisfactory. It is suggested that alternative techniques would be more reliable and the overlap method desribed here is considered satisfactory.

Catenary works as a key part in the electric railway traction power supply system, which is exposed outdoors for a long time and the failure rate is very high. Once a failure occurs, it will directly affect the driving safety. Based on the above, a model of identifying the health status for the catenary based on firefly algorithm optimized extreme learning machine combined with variational mode decomposition is proposed in this paper. Variational mode decomposition is used to decompose the original detection curve of catenary into a series of intrinsic mode function components, and the intrinsic mode function components filtered by the correlation coefficient method after decomposing each detection curve are input into the firefly algorithm optimized extreme learning machine model to realize health status identification. Compared with some other models, the results show that the proposed model has better health status identification effect.

In order to study temperature effect on initial curve of main cable, three different temperature models were built about temperature changes of main cable along span direction, and iteration calculation methods to find initial curve of main cable in variable temperature field was proposed based on the theory that the length of non-stress wire strand is persistence in unloaded cable station and construction completion station. The catenary equation in variable temperature field was deduced and the suspender length variation as well as horizontal component of cable forces were calculated based on the catenary equation. Taking some suspension bridge for an example, suspender length variation, horizontal component of the cable forces and node coordinate under three different temperature models were calculated by iteration calculation methods.

In recent years, the speed and the current transmission density of high-speed railways are increased. As a result, the rate of the occurrence of pantograph–catenary arc also increases, which directly influences the service performance of the pantograph–catenary system. The detection and identification of the pantograph–catenary arc is of great significance for evaluating the off-line level to ensure the safe operation of the pantograph–catenary system. The currently used conventional optical arc detection method would be distorted by strong sunlight or other environmental lights in the actual operation, which would affect the accuracy of detection. On the contrary, the arc sound signal is not affected by the diurnal variation and can be easily obtained; it can also be distinguished well from other interfering sounds. In this paper, a new method that uses the arc sound is proposed to realize the effective detection of the pantograph–catenary arc. The frequency spectrum and the intensity characteristics of the pantograph–catenary arc sound are analyzed. The results show that the frequency band of the arc sound signal is wide and mainly gets distributed at 5–17 kHz. The curve of the sound waveform is drawn by calculating the short-time average energy, which is used to obtain the arc’s starting time, duration, and intensity, for calculating the off-line rate.

Based on FANUC nc lathe catenary macro program, explores the rule curve macro program compiling method, using a simple example is given to illustrate the macro program programming method, the workpiece coordinate origin is not Z zero programming method, the continuous processing same shape graphics macro programming method, provides the programming method of the other special rule curve and reference .

The catenary is the curve that a free-hanging chain assumes under its own weight, and thought to be a “true mathematical and mechanical form” in architecture by Robert Hooke in the 1670s, with nevertheless no significant phenomena observed in optics. We show that the optical catenary can serve as a unique building block of metasurfaces to produce continuous and linear phase shift covering [0, 2π], a mission that is extremely difficult if not impossible for state-of-the-art technology. Via catenary arrays, planar optical devices are designed and experimentally characterized to generate various kinds of beams carrying orbital angular momentum (OAM). These devices can operate in an ultra-broadband spectrum because the anisotropic modes associated with the spin-orbit interaction are almost independent of the incident light frequency. By combining the optical and topological characteristics, our approach would allow the complete control of photons within a single nanometric layer.

Advances in the field of material engineering, computerization, automation, and equipment miniaturization enable modernization of the existing technologies and development of new solutions for construction, inspection, and renovation of underground pipelines. Underground pipe installations are used in the energy sector, gas industry, telecommunications, water and sewage transport, heating, chemical industry, and environmental engineering. In order to build new pipeline networks, dig and no-dig techniques are used. Horizontal Directional Drilling (HDD) is one of the most popular trenchless technologies. The effectiveness of HDD technology application is mostly determined by its properly designed trajectory. Drilling failures and complications, which often accompany the application of the HDD technology, result from poor design of the well path in relation to the existing geological and drilling conditions. The article presented two concepts of Horizontal Directional Drilling well path trajectory design: Classic sectional, which is a combination of straight and curvilinear sections, and a single-section chain curve trajectory (catenary). Taking into account the advantages and disadvantages of the catenary trajectory relative to the sectional trajectory, the author’s solution was presented, which was the implementation of the sectional trajectory with a maximum shape similarity to the catenary trajectory. The new approach allowed us to take advantage of a chain curve trajectory and was easier to implement using the available technology. The least squares method, based on deviations from a catenary trajectory, was set as the matching criterion. The process of searching for a trajectory, being a combination of straight and curvilinear sections as similar as possible to a catenary-type trajectory, was carried out using two methodologies: State space search and a genetic algorithm. The article shows the pros and cons of both optimization methodologies. Taking into account the technical and technological limitations of HDD drilling devices, a new approach was proposed, combining the methodology of state space search with the genetic algorithm. A calculation example showed the application of the proposed methodology in an engineering design process.

Catenary theory is recognized as the most effective suspension theory which can reflect the real situation of suspension. Catenary equation belongs to transcendental function, so there are some difficulties in calculation and application. Parabola theory, suspension curve theory and perturbation method are gradually formed as the theoretical basis for the study of suspension cables. This paper takes the 500m spherical radio telescope project as the background. The modeling method of suspension cable under multiple concentrated loads is analyzed, and the mathematical model of supporting cable after load is derived. The research in this paper provides a reference for the establishment of mathematical model of suspension cable in practice.