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We report an inverse-designed, high numerical aperture (∼0.44), extended depth of focus (EDOF) meta-optic, which exhibits a lens-like point spread function (PSF). The EDOF meta-optic maintains a focusing efficiency comparable to that of a hyperboloid metalens throughout its depth of focus. Exploiting the extended depth of focus and computational post processing, we demonstrate broadband imaging across the full visible spectrum using a 1 mm, f/1 meta-optic. Unlike other canonical EDOF meta-optics, characterized by phase masks such as a log-asphere or cubic function, our design exhibits a highly invariant PSF across ∼290 nm optical bandwidth, which leads to significantly improved image quality, as quantified by structural similarity metrics.

In the presented work, a controlled change by dimensions of a spacecraft descending in the atmosphere of Mars is considered. The aim of the work is to obtain a method for calculating the mass and mass-geometric characteristics of a spacecraft when changing its dimensions, which provides angular velocity passive control during the descent of this spacecraft in a low-density atmosphere. In the process of solving this problem, the geometric and mass-geometric characteristics of the descent spacecraft (volume, cross-sectional area, moments of inertia) were calculated. It is assumed that the outer shape of the spacecraft posterior to the incoming flow is a one-sheet rotational hyperboloid, which changes its dimensions during the spacecraft descent in the low-density atmosphere of Mars. As a result of solving the nonlinear programming problem, the minimum and maximum values of the main axial moments of inertia are obtained, which able to spin the spacecraft relative to the longitudinal axis of symmetry. The initial data for solving the nonlinear programming problem are the minimum volume and the maximum cross-sectional area of the hyperboloid, calculated according to the specified intervals of the variable controlling the dimensions of this surface. The method for calculating the mass and mass-geometric characteristics of a spacecraft when changing its dimensions ispresented, which makes it possible to control the magnitude of the angular velocity of a symmetric spacecraft in the low-density atmosphere of Mars without the use of onboard jet engines. In particular, it is shown in the work that as the height of the hyperboloid increases, the moment of inertia about the spacecraft longitudinal axis of symmetry decreases, accompanied by an increase in the moments of inertia about the transverse axes of symmetry. It can be shown that in this case there is an increase in the angular velocity of the spacecraft about the longitudinal axis, which makes it possible to achieve a stable orientation of the spacecraft upon entering the atmosphere. However, a more detailed study of the dynamics ofthe spacecraft relative motionwith a changeable shape in the atmosphere is beyond the scope of this work, but it can be presented in further publications.

This article presents the deflection and stress responses of the concentric cutout impregnated composite curved/flat panel structure, including the variable cutout profiles (square, circular, and elliptical). The model can compute the structural configuration due to the curvature parameter change, i.e., plate, spherical, cylindrical, elliptical, and hyperboloid. The damaged composite structural model is derived using a cubic-order of displacement field kinematics to maintain the stress–strain continuity. The isoparametric type C0 continuous finite element (FE) modeling steps are adopted to solve the structural equilibrium equation of the cutout abided layered composite panels subjected to uniform mechanical loading via an in-house derived MATLAB code. The model accuracy has been established by comparing the deflections and the stresses with the previously published results. Finally, the layered composite shell panel's critical behavior under the static loading has been examined. Different types of numerical problems are solved by varying the associated design constraint parameter, including the cutout relevant factors (shape and size), to show the proposed model applicability.

Solar concentrating technologies are still relevant due to innovative designs, materials and manufacturing methods. With an increased demand for fresh water, such technologies can be effectively utilized for sea water desalination. Desalination methods utilizing solar energy can significantly contribute towards sustainable and renewable energy solutions. In this work, an attempt is made to design, develop and experimentally analyse the performance of a desalination unit with a hyperboloid concentrator and a helical copper coil receiver. The elliptic hyperboloid concentrator is a special design for concentrating and capturing radiation over a wide incident angle and thus eliminates tracking. Further a CFD analysis was carried out to design and optimize the helical coil receiver dimensions. The optimized receiver was then fabricated. Results showed that, using the hyperboloid concentrator, acceptable quality of potable water, with a salinity of 190 PPM was obtained. The system performance was also impressive with an efficiency improvement of 30% compared to the traditional parabolic dish concentrator. The output temperature obtained was 109 0C using the combined system comprising ETC, parabolic dish and hyperboloid concentrator.

The development of a new bearing with cylindrical rollers and raceways corresponding to the surface of a one-sheet hyperboloid is considered. The bearing is designed to withstand significant radial and axial loads and is intended to support the rollers in strip-rolling mills.

Hyperbolic towers are towers in the shape of a single-sheet hyperboloid, and they are interesting in architecture. In this paper, we deal with the infinitesimal bending of a curve on a hyperboloid of one sheet; that is, we study the flexibility of the net-like structures used to make a hyperbolic tower. Visualization of infinitesimal bending has been carried out using Mathematica, and some examples are presented and discussed.

The use of aspheric mirrors is a common practice to design astronomical telescopes with a few optical elements. In the most preferred optical design Ritchey Chretien (RC), both primary and secondary mirrors are hyperboloid. Nowadays large telescopes are being built using small mirror segments, however, making aspheric off-axis mirror segments is still a challenge. We have conducted a study in which, we explored the possibility to mimic an aspheric hyperbolic primary mirror by making use of smaller spherical mirror segments. Three different methods have been used to form a large segmented aspheric primary of nearly 12m aperture. In the first method, fixed ROC(radius of curvature) spherical mirror segments are reconfigured by a piston, tip, and tilt (PTT). In the other two methods, in addition to PTT, ROC of the segments are also varied. We further attempted to reduce the telescope wave-front error by varying the segment size and the F ratio of the primary. We found out that none of these three methods provided acceptable image quality unless we incorporate the warping harness in the segment support. The use of the warping harness emulated by Zernike coefficient correction, remarkably reduced the wave-front error and delivered a decent image quality over a large field of view. In this paper, we present the results of our study on designing an RC type optics for a 12m class optical-NIR(Near Infrared) telescope using spherical mirror segments.

The technique of obtaining a hyperboloidal gear engagement with linear contact between a cylindrical involute wheel and a hyperboloid producing worm is considered. The resulting cutting tool greatly simplifies the manufacturing technology of hyperboloid worms and hyperboloid gears along with improved accuracy and roughness of the machined teeth and lower manufacturing costs.

The cutter systems of hypoid gear cutting machines contain groups of inside and outside blades. In these cutter systems, the side cutting edges of the blades machine the convex and concave gear teeth while rotating about the cutter rotation axis. The side cutting edges lay on the rake face formed through the blade, rake, and relief angles; hence, the normal cross-section of the cutter swept surface forms hyperboloid gear teeth. Using the accurate geometry of the cutter system, a relationship between the pressure and spiral angles of the gear tooth and the parameters of the cutter system is developed for the FORMAT machining of a hypoid gear. A new parameterization of the gear tooth surfaces is introduced to determine these angles for the accurate gear tooth by the accurate cutter system. A numerical example with different cutter systems and blade parameters is presented, demonstrating the effects of rake and relief angles over the pressure and spiral angles on mean point projections and gear tooth surface. Finally, the change in pressure and spiral angles with respect to the rake and relief angles are plotted, and the results are analyzed. Finally, it is concluded that the pressure and spiral angles are changed up to a few seconds of a degree in the operating area of the tooth with the change in the back and side rake angles. The side relief angle exhibited little or no effect over the geometry of the gear tooth.

Solar chimney power plant (SCPP) is an interesting project to produce clean and sustainable energy. An efficient SCPP system requires a very high chimney, and thus the optimization of the chimney shape presents an important way to enhance the SCPP performance. The aim of this paper is to analyze the effect of the divergent chimney shape on the airflow behavior inside SCPP. A comparison between four chimney shapes is carried out using CFD method: two cylindrical chimneys with different diameters and two divergent chimneys with different shapes. Indeed, both parameters were studied: the ratio of the inlet and outlet diameter of the chimney and the shape of the chimney which both hyperboloid and conical. The SCPP prototype was tested numerically and experimentally to validate the present computational outcomes. The obtained results confirm that the divergence shape affects directly the efficiency of the SCPP system. Moreover, the hyperboloid chimney presents the efficient solution which produces an important power output with keeping the chimney height constant.

For most re-entry capsules, the shape of the forebody of the capsule is designed based on the blunted nose cone. A similar shape can be created using a hyperboloid of revolution that can control the nose bluntness and the half angle of the cone easily. In this study, the hypersonic aerodynamic characteristics of re-entry capsules designed with hyperbolic contours were investigated using the CFD code, FaSTAR, developed by Japan Aerospace Exploration Agency (JAXA). The CFD results showed that, using the hyperbolic contours, the drag and lift coefficients can be increased compared to those for the Hayabusa re-entry capsule without changing the shape of the capsule drastically. This suggests that shape design based on the hyperbolic contours can improve the aerodynamic characteristics of re-entry capsules.

In this paper, in order to study the changes of reflection coefficient and radiation performance before and after different curved surfaces are conformal, a central embedded rectangular microstrip patch antenna is designed, which achieves good impedance matching in Ku band and cascaded one-minute four-T power divider to form a $2 \times 2$ small planar array. Then, conformal with single and hyperboloid carriers, the variation rules of central frequency, bandwidth and maximum gain of $2 \times 2$ array antennas with cylindrical radius 50mm, 60mm and 70mm, and convex paraboloid and concave paraboloid radius of 500mm 600mm and 700mm are discussed, and the variation rules of reflection coefficient and far-field two-dimensional pattern before and after different surface conformal are summarized.

Purpose of research. Improving the finishing performance of coarse-grained gear wheels on software-controlled machines. Methods. The method of discrete copying, the theory of designing cutting tools, methods of mathematical and computer programming. Results. It is an urgent task to improve the performance of fine milling of coarse-grained gear wheels by using the capabilities of modern software-controlled equipment. Here we consider the issues of improving the finishing performance of coarse-grained gear wheels on software-controlled machines of hyperboloid mills equipped with interchangeable polyhedral plates (IPP) with a straight cutting edge located at an angle λ to the instrument axis of rotation. It is proposed a method for controlling the accuracy of shaping surfaces, generatrix of which forms a section (set of sections) of convex curves by installing a cutting tool relative to the evolvent profile (fourth axis of the machine) and relative to the feed direction (fifth axis of the machine). The authors have developed a discrete copying method with a set of hyperboloid cutters of tooth surface of coarse-grained gear wheels. It allows us to ensure the 6th degree of accuracy in the parameter of the tooth profile error. Conclusion. The results of the study improve the finishing performance treatment of the teeth of coarse-grained gear wheels on software-controlled machines by reducing the number of passes required for machining one side of the tooth in comparison with the methods of continuous rolling and high-speed end milling. The proposed designs of cutting tools have sufficient versatility to handle a wide range of coarse-grained gear wheels, which is important in the repair and small-scale production.

In this paper the issue of approximation of the hyperboloid offset surface off(S(t, v); d) at distance d by the hyperboloid surface S 1(ϕ, v) is considered. The problem of determining various surfaces approximating the hyperboloid offset surface off (S(t, v); d) is important due to the applications of the hyperboloid as a mathematical model for miscellaneous objects in the architecture and construction industry. The paper presents the method of determining the angles and coordinates of points of various surfaces approximating the hyperboloid of revolution. A two-sheet hyperboloid offset surface can be used for modelling double-layer domes. A one-sheet hyperboloid offset surface was used to model the reinforced structure of the cooling tower.

In the application of the 13.5-nm extreme ultraviolet (EUV) collector optics of the discharge produced plasma (DPP) source, the Wolter-I structure based on the X-ray grazing incidence optical design is usually adopted. The requirement of the surface roughness of this collector optics is demanding, which should reach to several nanometers. Currently, the mandrel replication is the main fabrication technology of this collector optics. Obviously, the requirement of the surface roughness of the mandrel used for the replication process should reach to the same level of the collector optics. However, the fabrication of the Wolter-I mandrel with high surface quality requirement still faces great challenge. In this paper, we propose a method that applies an elastic spherical tool to polish the surface of the Wolter-I mandrel, in which the shape of the elastic sphere can be changed relatively easily to accommodate the aspherical surface of the Wolter-I mandrel. A mathematical model regarding the movement trace of the polishing tool was established. Based on this model, the contact force between the polishing sphere and the aspherical surface can be controlled to point from the center of the polishing sphere in the normal direction to the polishing point. The influence of the polishing parameters on the material removal thicknesses is simulated and analyzed. The polishing experiments of ellipsoid and hyperboloid are carried out considering the difference of the diameter of each radial section on the Wolter-I mandrel surface. The proposed method is proved to reduce the surface roughness of the mandrel coated with chemically deposited nickel-phosphorous (NiP) alloy after diamond turning effectively. The root mean square (RMS) roughness of the mandrel surface after polishing can be reduced to 1.56 nm. It indicates that this method is suitable for further polishing of nickel-plated Wolter-I mandrel after ultra-precision turning. As a result, the manufacturing precision and efficiency of the Wolter-I mandrels can be improved by using the proposed polishing approach in this study, and the manufacturing cost can be reduced accordingly.

This paper describes the design of a modulated FSS subreflector for a S/Ka-band Cassegrain dual-reflector system. The FSS subreflector separates the radiation from the S-band (2.0-2.3 GHz) and Ka-band (25.5-2.7.5 GHz). To simplify the manufacturing of the subreflector, a conical FSS subreflector is considered. Instead of using a periodic FSS where all array elements are identical, a modulated FSS subreflector with varying sized array elements is considered. The FSS elements are optimized to emulate an axial displaced hyperboloid surface, thereby compensating for the non-optimal conical subreflector surface. In Ka-band, the optimized modulated FSS subreflector improves the peak gain of the antenna system with more 6 dBs compared to the use of a periodic FSS.

This paper introduces the testing of annular hyperboloid mirror with 460mm diameter in the Cassegrain system. To improve the testing efficiency and meet the requirements of utilization, the study is carried out from three stages: precision grinding, precision polishing, and optical coating. In the precision grinding stage, the annular Zernike polynomial is used to fit the measured surface combining with the data measured from the coordinate measuring machine, so that it can facilitate the testing of the distribution of the surface shape deviation over the entire surface. During the precision polishing stage, a feasible Offner compensator is designed to achieve the goal of high-precision testing of the hyperboloid surface, with a measurement accuracy of RMS≤0.02λ. Also, 0.5-0.7μm and 3-5μm dual-band high reflectivity and high uniformity reflective coating is designed for the Cassegrain system requirements, the actual test reflectivity is 96.2%, which can meet the design requirements.

Since a replication-type of the Wolter mirror is obtained as the negative shape of its mandrel via shape replication represented by electroforming, a high precision mandrel fabrication process is essential for nano-focusing with the mirror at synchrotron radiation facilities. In particular, three-dimensional shape measurement technique for the mandrel is required. In this study, we developed the high precision three-dimensional shape measurement system dedicated for the Wolter mandrels. First, the shape error distributions of the ellipsoidal surface and the hyperboloid surface were measured independently. The geometrical relation between the surfaces was constrained by the longitudinal profiles which include the intersection measured by a profilometer. The diameter was also measured and finally the three-dimensional shape distribution was obtained. Applying this system, we fabricated a high precision Wolter mandrel.

The hyperboloid radio tower on Shabolovka Street built by V.G. Shukhov is one of the world known symbols of Moscow and of the USSR television broadcasting. The tower was laser scanned and 3D modeled in detail in 2011–2013 years. Virtual 3D modeling involved a thorough analysis of the existing historical documentation. This analysis revealed many discrepancies between the actual structure of the tower and existing historical documentation (including the design, working and survey documentation). In this paper we describe differences regarding the outline of the tower, structure of legs and connection joints, the height of the tower, and also discuss some assumptions on the change of mounting method during the building of the first two sections.

Magnetically induced topological transitions of isofrequency surfaces of bulk waves propagating through an unbounded biaxial gyrotropic medium are studied. The medium is constructed from a two-component superlattice composed of magnetized ferrite and semiconductor layers. To derive the constitutive parameters of the gyrotropic medium, a homogenization procedure from the effective medium theory is applied. The study is carried out in the frequency range near the frequency of ferromagnetic resonance, where the magnetic subsystem possesses the properties of natural hyperbolic dispersion. The topological transitions from an open type-I hyperboloid to several intricate hyperbolic-like forms are demonstrated for the extraordinary waves. We reveal how realistic material losses change the form of isofrequency surface characterizing hyperbolic dispersion. The obtained results broaden our knowledge on the possible topologies of isofrequency surfaces that can appear in gyrotropic media influenced by an external static magnetic field., 9 pages, 5 figures

Opti-electronic loads with multi-sensor are widely applied in the fields of atmosphere sounding and optical remote sensing. For the purpose of achieving high performance, miniaturization and light weight of multi-band photoelectric load, this paper proposes a structure with common aperture and partial common optical path, then light enters each subsequent light path after decomposed. This structure can improve system stability and avoids boresight errors caused by multi-apertures. The essay analyzes the aberration formula and initial structural parameter’s calculation method of the three-mirror system with the constraint of afocal condition, then eliminate the center occlusion through shifting the optic aperture and design a compact off-axis three-mirror afocal optical system with a folding mirror. The system magnification is 6×, the max aperture is 140 mm, and the max field of view is 4°×2.1°. The modulation transfer function of optical system reaches more than 90% of the diffraction limit. The mirror surface adopts paraboloid and hyperboloid, which are easy to be processed and tested. The size of system is 167×145×211 mm, and the structure is compact enough to meet the application requirements.

A dual-reflector antenna with a self-supported subreflector is proposed. The supporting structure is made of dielectric material and it is part of the feeding of the antenna, which is based onCassegrain optics and works at X-band. The feeding subsystem includes the primary feed, subreflector supporting structure and subreflector surface in a single dielectric piece, resulting in a compact, lightand low-cost solution. First, the subreflector and its feeding subsystem, based on a Dielectric Rectangular Waveguide (DRW) along with a hyperboloid, are described, and the phase center of the DRW and the antenna optics are defined. Then, two effective techniques to mitigate the refraction caused by the dielectric were proposed. Finally, the design was validated through the fabrication of a Cassegrain antenna using a 3Dprinting technique. Measurements and simulations show a very good agreement and an antenna of 26 dBi of directivity with overall very good performances is obtained, validating both the proposed subreflector and the design technique., This work was supported in part by the Ministerio de Ciencia, Innovación y Universidades (ARTEINE) under Project TEC2017-86619-R, in part by the European Space Agency under Contract ESTEC/AO/1-7064/12/NL/MH, and in part by the Gobierno del Principado de Asturias/FEDER under Project GRUPIN-IDI/2018/000191.

The influence of multi-point earthquake excitation on seismic mitigation and isolation control of high-speed railway extradosed cable-stayed bridge is studied. Taking the main bridge of yingshang super large bridge in Shangqiu-hefei-Hangzhou high speed railway as an example, finite element calculation model is established, and nonlinear dynamic time history analysis method is used. the calculation results of internal forces and displacements of the bridge are obtained when the seismic wave velocity is 250m/s, 500m/s, 750m/s, 1500m/s, 2500m/s and infinite (equivalent to uniform excitation) by using common bearing, viscous damper, lock-up devices and hyperboloid spherical seismic isolation bearings, respectively. The results show that: (1) The seismic response of the bridge is different under the action of different seismic wave velocity, when the wave velocity is 750 m/s, the internal force and displacement of the structure reach the peak value; (2) When the traveling wave effect is considered, the internal forces and displacements of the piers with three types of seismic isolation devices and common bearings have an increasing tendency; (3) the viscous damper and the hyperboloid spherical seismic isolation bearings have better seismic performance, while the lock-up devices increase the overall stiffness of the bridge, and thus amplify the internal force response of the structure.

In this chapter, the geometry of the main types of spiral bevel gears is first defined and considerations about the spiral angle are made. The corresponding cutting processes are then briefly described, and the generation of active flank surfaces of the teeth is defined. The main geometrical quantities of these gears are then determined as well as those concerning the equivalent cylindrical gears obtained using the Tredgold approximation. The load analysis of spiral bevel gears is then performed, also defining the thrust characteristic on shafts and bearings. Subsequently, the concepts concerning these gears are extended to the most general gearing case represented by the hypoid gears. The fundamentals of these gears are then provided, based on the kinematics already described for the hyperboloid gears. Two approaches to theoretical analysis are described, the first of more limited validity, and the second more general, but both capable to provide reliable results in terms of geometric and kinematic characteristics of these types of gears. The load analysis is extended to these types of gears, and some indications on the design choices inherent to them to improve their efficiency are provided. Finally, the unified ISO procedure, which allow us to calculate the geometric quantities of spiral bevel and hypoid gears is summarized.

Taking the long-span high-speed railway continuous girder bridge with the main span of 128m in China as an example, a reasonable finite element analysis bridge model adopting hyperboloid spherical seismic isolation bearings is established. Using nonlinear dynamic time history analysis method, the seismic mitigation performance of the bearings on high-speed railway bridges is studied. The parameters of the seismic isolation bearing, including the friction coefficient of the sliding surface and the radius of curvature, are optimized. Numerical analysis results show that: (1) Hyperboloid spherical seismic isolation bearings provide very good mitigation effect. (2)The bending moment at the bottom of the main pier and the displacement of the pier top both decrease first and then increase with the increase of the friction coefficient. The shear force at the bottom of the pier and the pier-beam relative displacement both decrease with the increase of the friction coefficient; The internal forces of the side pier bottom, the displacement of the pier top and the relative pier-beam displacement both decrease with the increase of the friction coefficient. (3)The internal force and the top displacement of each pier have a tendency to increase slowly with the increase of the radius of curvature. The change value is not obvious, and the pier-beam relative displacement increases with the increase of the radius of curvature. The bearing parameters should be determined both on the numerical analysis results and the requirements of the bearing structure size.

The RGHLS is a type of diagrid structure that has been developed in recent years. It consist of two columns. The major columns are designed as inclined members in major direction from bottom to top of RGHLS. They sustain the major percentage of vertical loads. The secondary columns have to be segmented in a helical direction in order to form the hyperboloid latticed shells. Secondary columns sustain much less vertical load than major columns. They are more commonly used in purpose-driven structures, such as water towers (to support a large mass), cooling towers, and aesthetic features. The objective of this study is to compare the result of the Model analysis by changing the shape of major and secondary column and also the performance of the structure when the position of the central axis of the structure is varied with respect to its height. The software used for this study is ANSYS. Height on the either side of the horizontal axis is varied and optimum height that exhibit best result is determined.

This paper presents the instability mechanism of an innovative Rhombic Grid Hyperboloid-Latticed Shell (RGHLS) under vertical load through experimental and numerical investigations. The RGHLS is only composed of bidirectional inclined primary and secondary columns without any circumferential members or lateral braces in its radial direction along its height. Therefore it would likely fail by out-of-plane multi-column interaction instability and the corresponding load-carrying capacity should be predicted. The experimental investigation of a reduced-scale test model of RGHLS was firstly performed to study its vertical load-carrying capacity and the multi-column interaction instability. A special spatial beam-string device for vertical multi-point loading of the test model has been initially designed and fabricated to precisely distribute the concentrated load to the top of the columns according to proportional distribution of loads required by designers. The experimental results revealed that the inclined columns indeed exhibited strong mutual restraining actions, and the ratio of the actual ultimate load-carrying capacity of the test model to its design load was 3.37, indicating a reasonable safety margin. In addition, FE numerical results of the test model corresponded well with the experimental results. Ultimately, additional FE numerical analyses have been conducted on the test model. Accordingly the effects of the ratio of stiffness between the secondary and primary columns, overall initial geometric imperfection, in-plane stiffness of top ring beam, and dimensions of portal columns on the load-carrying capacity and failure mode of RGHLS have been investigated extensively. As a result, the ratio of stiffness between the secondary and primary columns has been particularly recommended within a range of 0.46–0.70, so as to eliminate premature failure of X-joints prior to the instability of columns in the prototype of RGHLS.

A single-layered triband transmissive/reflective frequency selective surface (FSS) with incident angle up to 80° and polarization stability is designed, simulated, and measured. The periodic element includes a compact hexagonal arrangement of Y-slot and Y-patch, which can effectively reduce unit spacing to 0.16 $\lambda $ . Compared with the conventional hexagonal arrangement, compact arranged Y-unit has a larger band range from 1 to 40 GHz using grating lobes suppression. Controllable passband in X -band and reflectband in Ku -band and Ka -band are proposed. Transmission loss is less than 1 dB in 9.41 GHz in bandwidth of 5% when the incident angle is from 0° to 80°, while the return loss in bandwidth of 5% when 14.5 and 35 GHz is less than about 1 dB when incident angle range is from 0° to 80°/60° for dual polarization, respectively. Hyperboloid FSS is simulated, and performance of transmission and reflection is good. To the best of our knowledge, this is the first report of single-layered FSS that simultaneously operates for angle of incidence more than 60° in X/Ku/Ka -bands for dual polarization.

Traditional nasal surgery requires the doctor's left hand to carry the endoscope and right hand to complete the surgical operation using unstable images, potentially leading to danger due to mental fatigue, which may greatly prolong the operation time. Previously, robots in robot assisted endoscope sinus surgery (RAESS) only used simple linear motion control, lacked a dynamic tracking mechanism, and had no effective safety protection constraints, such as virtual fixtures or real-time force sensors. This paper describes an innovative and secure robotic control strategy for a dynamic automatic tracking endoscope with doctor input based on the mixed constraint of a dual-layer hyperboloid virtual fixture generated by a series of key points around the nasal cavity and a model of the threshold contact force. A tracking control strategy is set up after calibrating the navigation system and motion filtering via a human-machine interaction. Several experiments show that the hyperboloid virtual fixtures can generate an efficient constraint of different robotic motions and that the robot can automatically execute a track mission with high precision. The proposed safety protection method can be easily applied to patients with different nose shapes and greatly improve the quality of surgery.

The rhombic grid hyperboloid-latticed shells (RGHLSs) in the China Comic and Animation Museum (CCAM) are located on the ground floor, and they sustain enormous vertical and horizontal loads induced from upper building structures on top of them. Each RGHLS consists of numerous bidirectional inclined major and secondary columns that intertwine with one another to form a rhombic grid with X-shaped joints. Without both horizontal circumferential members and horizontal lateral braces in the radial direction of the RGHLS, as well as the existence of significant difference of compressive stiffness between major and secondary columns, the RGHLS would ultimately fail in a complicated form of in-plane and out-of-plane multi-column interaction instability in addition to its overall twist deformation under relatively low vertical loads. Currently, no design method for estimating its design strength and safety is available. Therefore, the load-carrying capacity of the RGHLS must be examined experimentally. This paper selects the RGHLS denoted by Y4 in the structure of the CCAM as the prototype, and presents an experimental investigation of its reduced scale (1:1/4) test model. A loading protocol consisting of six loading phases has been devised in order to predict the static vertical and horizontal load resistance, and horizontal hysteretic response of the RGHLS by keeping the amplitudes of the vertical load constantly as 1.0, 1.4 and 1.6 times the vertical design load of the reduced-scale test model, respectively. The experimental results obtained indicate that the test model remains elastic under 1.8 times its design loads, which is commonly adopted as static structural strength limit in practical design in China. In addition, horizontal cyclic load test indicated that the reduced-scale test model demonstrated sufficiently large horizontal load-carrying capacity as well as exhibited stable and ample hysteretic curves even under 1.6 times vertical load actions without any obvious stiffness reductions. This study comprehensively introduces the experimental test schemes and deeply analyzes the experimental results, thus forming an important basis for designing the load-carrying capacity of such RGHLSs. Ultimately, according to the experimental loading protocol, numerical simulations and analyses of the test model have been conducted by adopting ANSYS 12.1. The interaction strength design curve of the test model under a combination of vertical and horizontal loads is also proposed by carrying out additional numerical simulations of the model. The FE and experimental results have been compared, and they correspond well to one another, indicating that the results of the reduced-scale test model are accurate enough and reliable.

The optimal parameters and operating modes of vibratory roller for soil compaction after sowing winter wheat were substantiated. For objective function - the optimum coefficient of variation of density of soil during operation of vibratory roller for compacting winter wheat regression equation was obtained in the planning according to the BK plan of the experiment. The adequacy of model according to Fisher criterion, the significance and reliability of coefficients of regression equation was established. The response surface obtained by the shape of hyperboloid rotation was studied, two-dimensional sections of three factors were constructed on optimization criterion. With its minimum value, the optimal parameters of vibratory roller were established: the mass of roller is 293 kg, the spring stiffness is 11.95 kN/m, the working speed of roller is 9.6 km/h. The minimum value of optimization criterion is 10.43%.

Here we propose a novel 2-stage dish concentrator system for concentrating solar power plants based on the so-called overlap method, which improves both the radial flux concentration ratio (β) and the intercept factor (γ) of the concentrator. The 2-stage dish is composed of paraboloid primary and hyperboloid secondary mirrors having a special hollow structure enabling the mirrors to overlap, but avoiding excess shading. Geometric and optical analyses with ray-tracing show maximum values of β = 15,498 and γ = 0.78. Also, the size of the focal spot could be reduced. The concept is applicable for solar tower concepts enabling more compact unit mirrors and reducing the receiver size.

The study illustrates the mathematical model, applied to the synthesis of hyperboloid gear drives with taking into account the singularity appearance on the contacting active tooth surfaces. A kinematic approach for registration of the singularity on the tooth surfaces of the synthesized spatial transmissions is shown. The analytical dependencies applicable for defining and controlling of the singularities on the conjugates active surfaces are illustrated. Key words: Hyperboloid gear drives, kinematic synthesis, mathematical modeling, region of mesh, singularity.

In this paper, three monitoring stages of detection, localization, and extent determination of radial deformation in power transformer winding using stationary ultra-wideband antennas, are investigated. For this purpose, two types of radial deformation are implemented on the actual transformer high-voltage winding. The first type is a modeled bulgy mechanical deformation, which its extent and reversibility may be changed and it can occur in different positions. The second type is an actual radial deformation applied to the winding. Hyperboloid method and 2-D locus of the winding are adopted in the localization stage. To perform a precise analysis of the received signals, matched filter technique is employed. The extent of the deformation is also determined by magnitude Euclidean distance index. The experimental results prove the effectiveness of the proposed method.

High-frequency diffraction of a plane acoustic wave incident at a small angle to the axis of a narrow hyperboloid of revolution is considered. By the parabolic equation method in spheroidal coordinates, the leading term of field asymptotics in the near-surface boundary layer is constructed in the form of an integral involving Whittaker functions. Difficulties associated with its calculation are considered. Results obtained for the field at the surface of a perfectly rigid hyperboloid are presented. They reproduce the predicted high-frequency diffraction effects.

In this paper a bifocal lens for wide angle beam scanning system in submillimeter wave band radar imaging system is presented. With this bifocal lens, the quasi-optical antenna can ameliorate the deterioration of multiple beams focusing with wide angle scanning in submillimeter imaging system. The paper describes the design and process of the bifocal lens at 100GHz. The simulation and measurement results demonstrate that a scanning angle of 42° (±21°) with increased difference between main lobe and side lobe by about 5dB and a flat beam waist can be achieved compared with the conventional hyperboloid lens or some aspherical lenses.

Existing axial support for segments mostly adopts the Whiffletree support mode. The location of the support point will have a great influence on the surface precision of the primary mirror, and then influence the final imaging quality of the telescope. At present, there is no special support technology for traditional and thin mirror.In this paper, the research is based on LOT’s hexagonal segment (the surface is hyperboloid, diagonal line is 1.2m, thickness is 45mm, material is Zerodur), which is designed by Huazhong university of science and technology. The optimization of the Whiffletree axial support point of the segment is carried out. Efficient optimization algorithm is used in the research. After building parameterized model of segment support point location, FEM is used to obtain segment surface deformation. Taking the minimum RMS of deformation on segment surface under gravity as the goal, optimized software ISIGHT is applied to find the best support point location. Zernike orthonormal polynomials for hexagonal pupils is used to remove rigid-body motion. Finally, the best support point location point is obtained, the RMS of the segment surface deformation is 11.56nm and the PV is 63.98nm. The result can meets the requirement of LOT design well.

Illuminance uniformity and illuminating efficiency are always the key problems of Light Emitting Diode (LED) lighting system design. This study focuses on designing a suitable aspherical surface to create a rectangular and uniform illumination by studying the influence of optical aspheric parameters for a 3D microscopic measurement system. The 3D microscopic measurement system is constructed based on Scheimpflug condition. Then the optical design of LED source to obtain a rectangular-shaped illumination pattern on the DMD chip is simulated and optimized by optical tracing simulation software (TracePro). Our research focuses on the design of the second surface, where the key point of the design is to find appropriate conic constant K2 and the paraxial radius of curvature R2 of the lens, while the first surface of lens is considered as a plane. The conic constant K2 is researched by using the normal equation for conic aspheric and is discussed respectively when the conicoid is parabolic, elliptic and hyperboloidal. The result indicates that paraboloid can get a better uniform rectangular illumination within region than ellipsoid and hyperboloid. The illumination uniformity of the predetermined illumination area on the DMD chip reaches 86.83%.

In this paper, a new model of univalent hyperboloid space cable system suspension bridge is proposed, and a comparative test model of 15 m space suspension bridge and parallel suspension bridge is made. Vertical load test, horizontal load test, partial load test and moving load test were carried out. The results show that compared with the parallel and space cable suspension bridge, the vertical stiffness of the suspension bridge increases slightly, the lateral stiffness is greatly improved and the torsional rigidity is tremendously improved. The space suspension bridge has good wind resisting stability.

An effective computational method for the non-prestressed cable net structure with large deformation problem is proposed in the present study. This computational method is based on the vector form intrinsic finite element (VFIFE) method, which is a novel method to analyze structural behavior. Firstly, we proposed the basic principle and calculation process for analyzing the deformation mechanism of various cable net structures and compiled a finite element analysis program. Then, the numerical examples such as the rod chain mechanism and the space hyperboloid cable net are analyzed in detail. In addition, the accurate tracking of the motion status at different times was realized and the experiment in previous study was also used to verify the calculation results. A space cable net model experiment was designed and performed. The feasibility and correctness of this method were verified by the comparison of the measured deformation and internal force to the numerical results. The computational method proposed in this paper can effectively calculate the whole process of large deformation and internal force distribution of the non-prestressed cable net structure or similar structures, which provides an important method reference for the numerical analysis of such large deformations and strongly nonlinear engineering problems.

In this work, the geometrically nonlinear deflection responses of glass/epoxy composite flat/curved shell panel structure have been analysed theoretically with the help of three different displacement field kinematics and Green–Lagrange strain–displacement relation. In this analysis, the numerical models are developed based on two higher-order shear deformation mid-plane kinematics and one simulation model with the help of commercial finite element package (ANSYS). The present mathematical model is general in the sense that it includes all the nonlinear higher-order terms arising due to Green–Lagrange strain–displacement relation to capture the exact flexural strength of the laminated structure. The present nonlinear model is so generic that it can be easily extended for solving different kinds of geometrical configurations (spherical, cylindrical, elliptical, hyperboloid and plate). The equilibrium equation of the transversely loaded panel is achieved by minimizing total potential energy expression and discretized using the suitable finite element steps. The required deflection values are computed numerically via a homemade MATLAB code in conjunction with Picard’s iterative method. Consequently, the stability of the present numerical solutions has been established through the convergence test and validated by comparing the results with those available published results. In addition, the transverse deflections are obtained experimentally via three-point bend test and utilized for the comparison purpose to demonstrate the significance of the newly developed higher-order finite element model.

The paper deals with the use of a point diffraction interferometer (PDI) to study the surface shape of rotation figures. The relations are given for the correspondence of the coordinates on the surfaces of an ellipsoid, a paraboloid and a hyperboloid as well as on an interferogram. Using PDI and Zygo white-light interferometer (WLI), we experimentally investigated the surface shape of the grazing incidence ellipsoid with the multilayer reflective coating on a wavelength of 0.154 nm with the following parameters: length is 55 mm, half-axis are 6 and 235 mm. The results coincided with an accuracy of 73 nm (RMS) without taking into account the PDI lateral resolution, and with an accuracy of 50 nm (RMS) with taking it into account, which ensures the local angles measurement accuracy of the ellipsoid-shaped reflecting surface at a level of 3 μrad. We think that this difference may be attributed to the limited lateral resolution of PDI and errors of frames stitching of WLI; nevertheless, we do believe t...

The article introduces a novel compliant-body pump, with a high volumetric efficiency: A flexible-matrix-composite hyperboloid structure. The high volumetric efficiency is attributed to the geometry of the pump’s structure (hyperboloid) and the high negative effective Poisson’s ratio of the 3-layer flexible-matrix-composite laminate adopted for the compliant body of the pump. The pumping potential, introduced as a measure of the volumetric efficiency, was determined both analytically, using the finite element method, and experimentally, using a built-in prototype. The results indicate that the proposed pump has a very high volumetric efficiency.

Hyperboloid gear drives with face mating gears are used to transform rotations between shafts with non-parallel and non-intersecting axes. A special case of these transmissions are Spiroid1 and Helicon gear drives. The classical gear drives of this type are Archimedean ones. The objective of this study are hyperboloid gear drives with face meshing, when the pinion has threads of conic convolute, Archimedean and involute types, or the pinion has threads of cylindrical convolute, Archimedean and involute types. For simplicity, all three type transmissions with face mating gears and a conic pinion are titled Spiroid and all three type trans- missions with face mating gears and a cylindrical pinion are titled Helicon. Principles of the mathematical modelling of tooth contact synthesis are discussed in Part 1: Basic theoretical and CAD experience of this study. The second part of this article is a brief overview of the innovations and inventions created in this field at the Institute of Mechanics – Bulgarian Academy of Sciences in the last three decades. This study is also dedicated on elaboration of the specialized face gear sets for implementation into bio-robot hand. It is based on the application of 3D software technology, using 3D print for the realization of the physical models of the gear drives.

In this article, the effect of delamination on the free vibration behaviour of the laminated composite curved panels of different geometries (cylindrical, spherical, elliptical, hyperboloid and flat) is investigated. The laminated structure with seeded delamination is modelled mathematically using two different higher-order shear deformable kinematic models. The desired governing equation is obtained using classical Hamilton's principle and discretised with the help of finite element steps. The frequency responses are computed numerically through an in-house computer code developed in MATLAB environment. The convergence behaviour of the present numerical models have been checked and validated by comparing the frequency responses with those of the available published results. Further, the responses are also computed experimentally using CDAQ-9178 (National Instruments) in conjunction with LABVIEW software for the laminated plate with different delamination (size, location and position) and compared with present numerical results. In addition, the frequencies are also computed for the laminated structure with and without delamination using commercial finite element package ANSYS APDL. Finally, the effect of different materials and geometrical parameters including the size, location and position of the delamination on the free vibration behaviour of laminated composite shell panel has been analysed numerically and discussed in detail.

Purpose– The purpose of this paper is to analyse the nonlinear flexural behaviour of laminated curved panel under uniformly distributed load. The study has been extended to analyse different types of shell panels by employing the newly developed nonlinear mathematical model.Design/methodology/approach– The authors have developed a novel nonlinear mathematical model based on the higher order shear deformation theory for laminated curved panel by taking the geometric nonlinearity in Green-Lagrange sense. In addition to that all the nonlinear higher order terms are considered in the present formulation for more accurate prediction of the flexural behaviour of laminated panels. The sets of nonlinear governing equations are obtained using variational principle and discretised using nonlinear finite element steps. Finally, the nonlinear responses are computed through the direct iterative method for shell panels of various geometries (spherical/cylindrical/hyperboloid/elliptical).Findings– The importance of the present numerical model for small strain large deformation problems has been demonstrated through the convergence and the comparison studies. The results give insight into the laminated composite panel behaviour under mechanical loading and their deformation behaviour. The effects of different design parameters and the shell geometries on the flexural responses of the laminated curved structures are analysed in detailed. It is also observed that the present numerical model are realistic in nature as compared to other available mathematical model for the nonlinear analysis of the laminated structure.Originality/value– A novel nonlinear mathematical model is developed first time to address the severe geometrical nonlinearity for curved laminated structures. The outcome from this paper can be utilized for the design of the laminated structures under real life circumstances.

Special-purpose multi-axis CNC machines are used for the face-milling of hypoid gears. These machines are equipped with specially design cutter-head, consisting of inside and outside blades, to machine the convex and concave sides of the gear teeth. In this research, CAD model of a face-milling cutter-head is developed, in which side cutting edges of inside and outside blades of the cutter system are built on the rake face. Since the side cutting edges are not on the axial plane of the cutter, the sweep surface formed by the cutting edges are hyperboloids, rather than the cylindrical surfaces as assumed in the other researches. Due to the hyperboloid sweep surfaces of the cutter, the gear teeth formed by the face-milling have not only curvature along the length of the teeth but also have curvature along the flank-wise direction. It leads towards the result that the blade angles are not equal to the flank angles of the gear teeth at the mean point. Therefore, a CAD-based cutter geometry determination model is built, to calculate the geometry parameter of the cutter-head, such as blade angles and the average cutter radius, for the given parameters of the gear teeth at the mean point.

An axisymmetric multi-mirror system for neutron and X-ray microscopes is proposed to increase their numerical aperture and collection efficiency. A Wolter type-I mirror is used as the basis of the multi-mirror system at grazing incidence. The addition of an even number of hyperboloid mirrors to the Wolter type-I mirror can satisfy both an equal optical path length and Abbe’s sine condition. The numerical aperture increases in proportion to the number of mirrors. The optical parameters of the system with four tandem mirrors are calculated for neutrons and X-rays with a wavelength of 0.4 nm by assuming that the average grazing angle of incidence is 5.4 mrad and the magnification is 10. The inner diameters of the mirrors are limited to