Relative Rotation Angle Research Articles

The method of manipulability control of a robot

The paper presents the results of a numerical experiment that demonstrates the effectiveness of a control algo-rithm that maintains a sufficiently high numerical value of the robot's manipulability function , which ensures «remoteness» from a singular configuration. The problem of approaching the end effector of the space manipula-tor Canadarm2, which has seven degrees of freedom (one redundant generalized coordinate), with an object mov-ing along a known trajectory, is considered. To the six parameters that determine the position and orientation of the gripper in absolute space, a «kinematic» function , depending on the relative rotation angles of the links, has been added. In this case, the kinematics equations became closed with respect to the rotation angles. The control law includes a condition for maintaining a certain numerical value that exceeds the minimum allowable value. Illustrations in the form of three-dimensional animation obtained on the basis of numerical integration of the equa-tions of controlled motion of the manipulator and the object were built using the Mathematica computer algebra system.

Mechanical properties analysis of joints for prefabricated metro station structure based on Whole-process in-situ monitoring

Changchun Metro Line 2 implemented the whole-process monitoring and measurement of prefabricated metro station for the first time. This paper analyzes the mechanical behavior and deformation of the joints of vault and arch springing, which bear high bending moments, in order to study the mechanical properties of these joints, which play a key role in the bearing capacity of prefabricated structure. In addition, it also discusses the trend of the joint stress, relative deformation and relative rotation angle as it changes with the construction process and after opening for traffic. Furthermore, it analyzes the performance of the joints in different construction stages, and compares it with the numerical calculation results based on the long-term in-situ monitoring and survey data carried out at the prefabricated station of Changchun Metro during the whole construction period. As indicated by the result, at the beginning of the assembly and arching into a ring of the components at the top, the structure undergoes a self-adaptation period, where the joints are subject to heavy stress and deformation. After backfilling and water level recovery, the joints are subject to increased axial force and reduced stress and deformation, resulting in a positive effect on the bearing capacity of the joints. The overall change range in joint stress is rather small. During the construction period, the two tenons of double-tenon joint of vault bear external force by mutual engagement, which are subject to two types of stresses, namely, tensile stress and compressive stress. The concave-convex tenon of single-tenon joint at the arch springing is markedly engaged with each other, with the tenon subject to a bending effect. The test results are relatively stable, and the overall deformation at the joint of vault and arch springing is relatively small, with sufficient safety margin from the end of construction disturbance through the operation stage till today. The research results demonstrate great practical guiding significance for the joint and structure design of prefabricated metro station.

Динамика плоского движения космического крана-манипулятора типа руки с учетом изгиба звеньев

The paper considers the plane motion dynamics of a three-link crane-manipulator consisting of two rods elastic in bending and a massive solid body attached to them at their end (load capture). All links are interconnected by hinge joints with the given (controlled) relative rotation angles. The first link is also connected to the mobile base. The system mathematical model was developed to calculate its non-stationary oscillations and dynamic loading of links at arbitrary in time and large relative angles of the links rotation as the solid bodies. The rods bending deformations (elastic transverse displacements and rotation angles of the axes) were considered to be insignificant (linear). Each rod ending was represented by the Ritz method using two given shape functions with the unknown coefficients, which were taken as the generalized coordinates. In this case, the “cantilever” bending forms of each rod with the given transverse displacement and angle of rotation at their ends were used. A simplified version was considered: each rod bending was represented by only one given form of its bending by a single moment applied at the end. System oscillation equations were obtained based on the principle of probable displacements in the generalized coordinates (four equations or two in a simplified form). Since rotation angles at the ends of the elastic rods were added to the given rotation angles of the non-deformable rods, total angles were left under the signs of sines and cosines without linearization for convenience of calculations and increasing accuracy. As a result, such equations of non-stationary oscillations remained non-linear. They were integrated by numerical methods using standard programs in one of the computer algebra systems. Examples are provided with the comparative results estimates obtained in the two-term and one-term approximations of the function in regard to the bending form of the system bending rod joints.

A Method for Electric Tractor Molding Based on Terminal Sliding Mode Control Algorithm

Smart transformation and green development are the core research directions of electric vehicles. An electric tractor is powered by the vehicle battery. The motor converts electric energy into mechanical energy and drives the wheels through the drive train. Therefore, the electric tractor model is a modular mathematical model for the battery, motor, drive train, and drive wheel. A class of high-order terminal sliding mode control strategies is adopted to establish the relative rotational angles of drive wheels, driving angular speeds, and motor angular speeds as input, and driving angular speeds and motor angular speeds as output. This process ensures stable operating speed and good working quality under the operating conditions and achieves small-scale unattended driving. The output is a nonlinear system state equation. An n-order derivative continuous function is introduced to design the terminal sliding surface of the sliding mode. A control function to reduce chattering is also designed to ensure that the output function converges at the finite time and the existing sliding stage achieves zero steady-state error. Simulation results of the whole electric tractor model show that the speed remains stable under the condition of outside interference, and experiments verify the feasibility of the control strategy.

The evolution of the out-of-phase dipole beams in the repulsive defect photonic moiré lattice with saturable self-focusing nonlinearity media

We demonstrate in a numerical manner the intriguing transmission of the out-of-phase (OOP) dipole beams in the repulsive defect photonic moiré lattice with rotation angle and defect depth under saturable self-focusing nonlinearity. Photonic moiré lattices, that are created by two mutually rotated square patterns with a relative rotation angle . We introduce a single-site repulsive defect in periodic photonic moiré lattices, and excite this site with the OOP dipole beams. We reveal that the OOP dipole beams undergoes two evolution stages during propagation, for the first time to our knowledge. It is shown that the OOP dipole beams maintain stable propagation over a certain distance in the first stage, which depends on the defect depth. Then the energy of the OOP dipole beams flows between its two spots, exhibiting periodic-like oscillation in the second stage, along with discussion about the effect of defect depth on the stable propagation distance of the OOP dipole beams, one finds that the stable propagation distance decreases linearly with increasing defect depth . At the same time, we perform a polynomial fit between the oscillation period of the OOP dipole beams and the defect depth . These two fitting curves fully demonstrate that the repulsive defect can profoundly affect the propagation behavior of the OOP dipole beams. Our results may provide novel insights into the localization and oscillation of beams in defect structures.

The association between unilateral high-riding vertebral artery and atlantoaxial joint morphology: a multi-slice spiral computed tomography study of 396 patients and a finite element analysis

Background ContextA high-riding vertebral artery (HRVA) can deviate too medially, too posteriorly, or too superiorly to allow the safe insertion of screws. However, it is unknown whether the presence of a HRVA is associated with morphological changes of the atlantoaxial joint. PurposeTo investigate the association between HRVA and atlantoaxial joint morphology in patients with and without HRVA. Study DesignA retrospective case–control study and finite element (FE) analysis. Patient SampleA total of 396 patients with cervical spondylosis underwent multi-slice spiral computed tomography (MSCT) of cervical spine at our institutions from 2020 to 2022. Outcome MeasuresA series of atlantoaxial joint morphological parameters, including C2 lateral mass settlement (C2 LMS), C1–2 sagittal joint inclination (C1–2 SI), C1–2 coronal joint inclination (C1–2 CI), atlanto-dental interval (ADI), lateral atlanto-dental interval (LADI), and C1–2 relative rotation angle (C1–2 RRA) were measured, and lateral atlantoaxial joints osteoarthritis (LAJs-OA) was recorded. The stress distribution on the C2 facet surface under different torques of flexion-extension, lateral bending, and axial rotation was analyzed by FE models. A 2-Nm moment was applied to all models to determine the range of motion (ROM). MethodsA total of 132 consecutive cervical spondylosis patients with unilateral HRVA were enrolled in the HRVA group, and 264 patients without HRVA matched for age and sex were enrolled in the normal (NL) group. Atlantoaxial joint morphological parameters were compared between two sides of C2 lateral mass within HRVA or NL group, and between HRVA and NL groups. A 48-year-old woman with cervical spondylosis without HRVA was selected for cervical MSCT. A three-dimensional (3D) FE intact model of the normal upper cervical spine (C0-C2) was created. We established the HRVA model by simulating atlantoaxial morphological changes of unilateral HRVA with FE method. ResultsThe C2 LMS was significantly smaller on the HRVA side than that on the non-HRVA side in the HRVA group, but C1–2 SI, C1–2 CI, and LADI on HRVA side were significantly larger than those on non-HRVA side. There was no significant difference between left and right sides in the NL group. The difference in C2 LMS (d-C2 LMS) between HRVA side and non-HRVA side in the HRVA group was larger than that in the NL group (P < 0.05). Meanwhile, the differences in C1–2 SI (d-C1/2 SI), C1–2 CI (d-C1/2 CI), and LADI (d-LADI) in the HRVA group were significantly larger than those in the NL group. The C1–2 RRA in the HRVA group was significantly larger than that in the NL group. Pearson correlations showed that d-C1/2 SI, d-C1/2 CI, and d-LADI were positively associated with d-C2 LMS (r=0.428, 0.649, 0.498, respectively, p<.05 for all). The incidence of LAJs-OA in the HRVA group (27.3%) was significantly larger than that in the NL group (11.7%). Compared with the normal model, the ROM of C1-2 segment declined in all postures of the HRVA FE model. We found a larger distribution of stress on the C2 lateral mass surface of the HRVA side under different moment conditions. ConclusionsWe suggest that HRVA affects the integrity of the C2 lateral mass. This change in patients with unilateral HRVA is associated with the nonuniform settlement of the lateral mass and an increase in the lateral mass inclination, which may further affect the degeneration of the atlantoaxial joint because of the stress concentration on the C2 lateral mass surface.

Tunable bilayer photonic quasicrystal

The unique properties of incommensurate two-dimensional bilayer structures, a wide class of optical materials, are largely determined by the relative rotation angle between the layers. Here, we present a comprehensive theoretical analysis of the optical properties of a dodecagonal quasicrystal based on twisted bilayer material with hexagonal layers rotated by 30°. By assuming that the quasicrystal is tuned to the Bragg condition, we calculate its reflectance spectra and reveal the Wood anomalies therein, which are characteristics of structures with a long-range order. It is also shown that the reflectance spectra can be dynamically controlled by the external electric field applied perpendicular to the quasicrystal's surface. This feature can be used to create tunable photonic devices such as optical switches and sharp M-shape bandpass filters.

Dynamically synergistic transition mechanism and modified nonlinear magnetic force modeling for multistable rotation energy harvester

Multistable energy harvesters with magnetic interaction have received increasing attention. However, the synergistic transition mechanism of the different oscillation states for rotation harvesters remains uninvestigated, and there is lack of precise magnetic force model for investigating the effect of the external magnetic force on dynamic characteristics and harvesting performance. This study proposes a synergistic transition and regulation mechanism for rotation energy harvesting and a modified model of the magnetic force is derived by taking the relative displacement and rotational angle into consideration. The transition mechanism of different oscillation states for the rotation system is studied under the guidance of static bifurcation, potential diagram, and dynamic behaviors, respectively. Based on the extended Hamilton’s principle, the theoretical model is established and the complexity dynamic characteristics are simulated. A prototype of multistable energy harvesters with magnetic interaction was fabricated and the effectiveness of the theoretical model was validated by experiments. The experimental results exhibit good agreement with the numerical results. The proposed harvester can harvest energy effectively in a wide rotation speed range of 280–500 rpm, and the output voltage and power can reach 6.4 V and 4 mW.

Chemical covalent connection of carbon nanotubes for related structural manufacturing: A molecular dynamics study

Carbon nanotubes (CNTs) with junction plays an important role in nanomaterial and nano-devices, especially the junction constructed by covalent bonds. However, the connection process between single-walled carbon nanotubes (SWCNTs) could hardly be observed experimentally on an atomic scale and its connection strength is difficult to accurately measure. Hence, this work investigates the atomic reconstruction and evolution of the structure of SWCNTs at joint area and the connection strength of the joined SWCNTs by molecular dynamics (MD) simulation. Various connection effects between two types of typical SWCNTs, i.e. metallic SWCNTs and semiconducting SWCNTs, are investigated for the smooth covalent connection with high mechanical strength. The simulation results indicate that energy parameters (pulse-widths, pulse number, and temperature) and structure parameters (relative rotation angles, end type and chirality of SWCNTs) have great influence on the connection process. However, the size of energy zone and diameter for both armchair and zigzag SWCNTs make little difference to its connection process and connection strength under certain conditions. This study reveals that whether armchair or zigzag SWCNTs, there is an optimal set of energy and structure parameters to connect them into an ideal hexagonal junction with high mechanical strength. The critical technical parameters are obtained in this study for the optimal covalent connection of SWCNTs, which provides enlightening significance to manufacture the covalent SWCNTs junctions.

Дослідження та вдосконалення запобіжних механізмів шнекових конвеєрів

Many different types of safety mechanisms that are used for mechanical processing machines, such as screw conveyors, to one degree or another provide the requirements set for them regarding the process of functioning during the occurrence of critical loads on the conveyor screws. However, traditional safety ball and cam couplings, when triggered, cause significant shock dynamic loads, and this subsequently causes the destruction of both couplings and conveyor drives. Friction safety clutches have low operating accuracy and do not allow reliable protection of working bodies and drives of machines. Therefore, in order to ensure reliable protection of the working bodies and drives of conveyors, with minor shock loads during the operation of the safety mechanisms, it is advisable to develop new designs of safety ball couplings with closed circular profiles of the engagement elements. The purpose of the work is to increase the operational performance and reliability of the safety clutch by developing a new design of the safety mechanism, which will make it possible to create a wide range of elastic mode of operation before the safety one in the event of an overload of the conveyor screw. The research was carried out using the methods of the theory of mathematical and computer modeling. the method of mathematical planning of the experiment. The article presents new developments of the protective mechanism of the conveyor, which will provide protection of the working bodies against overloads in the axial direction. The article presents theoretical equations for determining the change in torque during clutch activation depending on the angle of relative rotation of the half-couplings and the design and technological parameters of the coupling elements. The work presents graphical dependencies and analyzes the intensity of influence of various parameters on the nature and magnitude of the torque, developed appropriate stands and methods for conducting experimental studies to determine the recommended parameters of safety clutches, as well as presented the results of the conducted experiments

Dual-Band Shared-Aperture Variable Inclination Continuous Transverse Stub Antenna

This article presents a dual-band shared-aperture variable inclination continuous transverse stub (VICTS) antenna with large beam coverage for both frequency bands. A novel hybrid radiating structure is introduced to enable approximately consistent initial beam direction at the boresight for both bands and therefore large beam coverage, by exciting different sets of the radiation elements at each of the two bands. The hybrid structure is formed of interlaced conventional CTS elements and those backed by double-ridge waveguide slots. The latter suppresses the lower band while allowing the high band to radiate. This configuration allows maximum aperture reuse. A parallel-plate waveguide (PPW) diplexer combines the generated plane waves from the two bands to enable one-side excitation. Combined with the nonuniform slow wave structure (SWS), optimized amplitude distribution is achieved across the two frequency bands, thereby improving the antenna efficiency. A prototype is designed, fabricated, and measured for 12.25–12.75 GHz (Ku-band) and 19.6–21.2 GHz (K-band). The measured reflection coefficients are kept less than −11.5 dB during the beam steering. At the center frequencies of 12.5 and 20.4 GHz, the measured beam coverage of over ±49° and ±59° in elevation plane is demonstrated from a relative rotation angle of 40°. During the beam steering, the measured peak gain varies in the range of 26.1–21.1 dBi/30.4–25.2 dBi at these two frequencies.

In Situ Encapsulated Moiré Perovskite for Stable Photodetectors with Ultrahigh Polarization Sensitivity.

Nanostructures provide a simple, effective, and low-cost route to enhance the light-trapping capability of optoelectronic devices. In recent years, nano-optical structures have been widely used in perovskite optoelectronic devices to greatly enhance the device performance. However, the inherent instability of perovskite materials hinders the practical application of these nanostructured optoelectronic devices. Here, in situ encapsulated moiré lattice perovskite photodetectors (PDs) by two nanograting-structured soft templates with relative rotation angles is fabricated. The confinement growth of the two nanograting templates leads to crystal growth with moiré lattice structure, which improves the light-harvesting ability of the perovskite crystal, thereby improving the device performance. The PDexhibits responsivity to 1026.5AW-1 . The Moiré lattice-perovskite-based PD maintained 95% of the initial performance after 223days. After being continuously sprayed with water moist for 180min, the performance is maintained at 95.7% of its initial level. The nanograting structure endows the device with high polarization sensitivity of Imax /Imin as high as 9.1.

Research on a Sowing Depth Detection System Based on an Improved Adaptive Kalman Filtering Method

The current real-time detection of sowing depth has the problems of low detection accuracy and poor reliability. After analyzing the movement mechanism of the sowing monomer parallel four-bar linkage, an improved adaptive Kalman filtering method for sowing depth detection is proposed. The method uses two MPU6050 attitude sensors. The difference between the rotation angle of the parallel four-bar linkage and the attitude angle of the sowing monomer is used as the relative rotation angle of the parallel four-bar linkage relative to the sowing monomer. The sowing monomer parallel four-bar linkage has the characteristics of up–down translation, and sowing depth changes can be obtained by converting the angle data. By using moving average filter, particle filter, Kalman filter, and improved adaptive Kalman filter to fuse the data of MPU6050 in two positions and perform MATLAB simulation, the average mean squared errors of the above four filtering algorithms are 0.12645, 0.05545, 0.03785, and 0.0189, respectively. In the end, the experiment of sowing depth detection was carried out, and it was found that the improved adaptive Kalman filter algorithm detects the smallest sowing depth mean squared error, which is 0.0636, and the algorithm can track data changes better. At the same time, it is more adaptable to noise and obtains an ideal filtering effect.

Improvement of two-dimensional dynamic modeling of cable based on strain modification

<p indent="0mm">In this paper, based on the nonlinear continuum mechanics and curve theory in differential geometry, we comprehensively consider the nonlinear strain of Perkins’ model and the dynamic curvature of Howell’s model for model establishment. Under the updated Lagrangian formulation, we establish the plane dynamic equations of the cable structure, including dynamic curvature and large strain based on the current configuration. The expression of shear force is simplified using dimensionless parameter analysis, and the nonlinear geometric equation and the relative rotation angle equation are supplemented in the plane dynamic equations to form the modified Howell model. We illustrate the difference between the original and modified Howell model by analyzing the tension and shear coefficients. Moreover, we illustrate the superiority of the modified Howell model in terms of computational accuracy and efficiency through examples.

Dual-Band Combined-Aperture Variable Inclination Continuous Transverse Stub Antenna With Consistent Beam Direction

This article presents a Tx/Rx dual-band combined-aperture variable inclination continuous transverse stub (VICTS) antenna for low-earth-orbit (LEO) satellite-on-the-move (SOTM) applications. The beam directions for the Tx and Rx bands are kept consistent during beam scanning, so that the antenna allows a duplex link. The topology of the combined-aperture VICTS antenna is derived from the requirement for consistent beam directions. Nonuniform slow wave structures (SWSs) are used to achieve the required phase difference and phase-changing rate (PCR) between the radiation slots in the two bands, while maximizing the antenna efficiency. Predeflection technique is applied to the radiation slots to reduce the gain drop at a wide beam scanning angle. A prototype operating at K- and Ka-bands is designed, fabricated, and measured. Experimental results show that the antenna has a consistent beam direction during scanning in the frequency ranges of 19–21 GHz (Rx band) and 29–31 GHz (Tx band). The maximum beam directions in Tx and Rx bands exceeds ±47° at a relative rotation angle of 40°, and the gain drop during the beam scanning is reduced within 2.3 and 3.5 dB.

Moiré-driven electromagnetic responses and magic angles in a sandwiched hyperbolic metasurface

Recent moiré configurations provide a new platform for tunable and sensitive photonic responses, as their enhanced light–matter interactions originate from the relative displacement or rotation angle in a stacking bilayer or multilayer periodic array. However, previous findings are mostly focused on atomically thin condensed matter, with limitations on the fabrication of multilayer structures and the control of rotation angles. Structured microwave moiré configurations are still difficult to realize. Here, we design a novel moiré structure, which presents unprecedented capability in the manipulation of light–matter interactions. Based on the effective medium theory and S -parameter retrieval process, the rotation matrix is introduced into the dispersion relation to analyze the underlying physical mechanism, where the permittivity tensor transforms from a diagonal matrix to a fully populated one, whereas the permeability tensor evolves from a unit matrix to a diagonal one and finally becomes fully filled, so that the electromagnetic responses change drastically as a result of stacking and rotation. Besides, the experiment and simulation results reveal hybridization of eigenmodes, drastic manipulation of surface states, and magic angle properties by controlling the mutual rotation angles between two isolated layers. Here, not only a more precisely controllable bilayer hyperbolic metasurface is introduced to moiré physics, the findings also open up a new avenue to realize flat bands at arbitrary frequencies, which shows great potential in active engineering of surface waves and designing multifunctional plasmonic devices.

Steering of Beam Using Cylindrical Arrangements in a Metallic Parallel Plates Structure Operating over Ku-Band

A novel flat beam steering prototype based on the specific arrangement of a cylindrical unit cell is designed, manufactured and tested. The wideband and broad scanning capability is demonstrated at the Ku-band. We have considered two configurations, first with circular rings (CR) of the defined permittivity values for respective radial distance from the center of the aperture, second with cylindrical rods that shall be placed on a respective CR, which mimics the defined permittivity. The structure is generated from Vero CMYK full color wax, which utilizes the Multijet 3D printing method. The proposed prototype is designed in the operating frequency of 12 GHz (λ = 25 mm) and separation distance between the two parallel plates are maintained at 12.5 mm (0.5λ) for the TE10 mode of operation. The diameter of the two parallel plates and the proposed structure is of 100 mm (4λ) where the radius of cylinders varies from 0.5 to 3.5 mm and corresponding relative permittivity varies from 0.6687 to 2.4395. The overall height of the structure is 12.5 mm and is placed between two parallel plates. The minimum separation distance is maintained between the proposed structure and the feed WR-75 waveguide. Irises effect is performed to obtain impedance matching in the operating frequency bands. Beam steering of the radiated waves is observed for relative rotation angles of 0∘, 30∘, 45∘, 75∘ and 90∘ of the WR-75 waveguide along the edge of parallel plates. The overall proposed system weighs 179 g, which signifies the light weight characteristics. Moreover, the proposed structure shows low return loss over 10 GHz to 15 GHz operating frequency band.

C–H⋯S Hydrogen Bond Assisted Supramolecular Encapsulation of Fullerenes with Nanobelts

C–H⋯S Hydrogen Bond Assisted Supramolecular Encapsulation of Fullerenes with Nanobelts

Hybrid machine-learning-assisted stochastic nano-indentation behaviour of twisted bilayer graphene

We present herein a polynomial chaos-Kriging (PC-Kriging)-based molecular dynamics (MD) simulation framework of twisted bilayer graphene (tBLG) structures to investigate the influence of stochastic parametric variations on their nano-indentation behaviour. The relative rotation angle (RRA) and operating temperature were taken as input parameters, which were randomly distributed in the ranges 0–30° and 100–900 K, respectively. Considering Monte Carlo sampling (MCS), a series of MD simulations of nano-indentation was performed to obtain the critical indentation force (Fcr) and critical indentation depth (δcr) in each instance. The dataset generated by MCS-driven MD simulation was employed to train and validate the PC-Kriging-based metamodel. The generalization capability of the constructed model was ensured by implementing a leave-points-out (LpO) cross-validation scheme, and by minimizing prediction errors by adopting a sufficient size of samples for model training and validation. The constructed computationally efficient PC-Kriging-based metamodel has been used to perform data-driven uncertainty and probabilistic analysis. The hybrid machine-learning-based stochastic nano-indentation behaviour of tBLG structures has been described, considering practically relevant uncertain irregularities in RRA and temperature. The present analysis aims to capture the continuous parametric range of input parameters so as to allow detailed probabilistic investigation of the nano-indentation behaviour of tBLG nanostructures.

A Low-Profile Fabry–Pérot Cavity Antenna Using Anisotropic Metasurface

A Fabry–Pérot cavity (FPC) antenna utilizing a new cavity resonance phenomenon based on the polarization standing wave (PSW) is proposed. To produce PSW, two anisotropic metasurfaces acting as the handedness preserving mirror are designed as the two ends of the cavity. Such a cavity possesses a new resonant condition, i.e., the relative rotation angle and distance between two metasurfaces together determine its resonant frequency. Hence, in comparison to conventional FPC antennas, the proposed one possesses a lower profile height of around 0.125 wavelengths. The antenna concept is experimentally demonstrated for the 12 GHz <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X</i> -band application. Measurement results agree well with simulations. A measured peak gain of around 17.28 dBi is obtained within the impedance bandwidth of 11.61–12.21 GHz. The PSW-based antenna brings a new approach for cavity antenna designs.