Parabolic Cylindrical Surface Research Articles

Waldron linkage-inspired deployable cylindrical mechanisms with smooth surfaces

Deployable mechanisms with solid surfaces, which possess the advantage of high accuracy, have great potential in engineering applications. This paper proposes a design method to construct a deployable cylindrical mechanism with smooth solid surfaces based on Waldron hybrid linkage. Joints above the desired surface are replaced by remote central mechanisms. The equivalence of joints ensures the surface smooth and keeps the motion characteristics unchanged. A largescale deployable mechanism is obtained by networking the proposed units along axial and radial directions, while the characteristics of 1-DOF, smooth surface, and compact folding remain. A correlation model is established to describe the relationship among design parameters. A design method is proposed to obtain the optimal mechanism parameters for constructing various types of cylindrical surfaces with maximum deployment ratio. Three cases of a circular cylindrical surface, a parabolic cylindrical surface and an elliptical cylindrical surface are developed. The effectiveness of the proposed method is verified by the deployment function and precision tests of the prototype.

Thick-panel origami-based parabolic cylindrical antenna

This paper proposes a novel parabolic cylindrical antenna with great folding efficiency based on two symmetrically arranged Miura-ori thick-panel origami patterns and the removal of partial material from each panel. A design rule for the transition from the given parabolic equation to the geometric parameters of the thick-panel origami is defined. To ensure that the deployable structure has one degree of freedom (DOF), specific connectors between the two thick-panel origami patterns are designed from spherical 4R linkages and Bennett linkages, which are verified by kinematic analysis based on the assembly of linkages corresponding to the thick-panel origami pattern. Two joint-removing techniques based on the kinematic equivalence of linkages are constructed to obtain the continuous and smooth parabolic cylindrical surface and maintain the one-DOF property. The deployed/folded ratio influencing factors are fully studied, finding that a small panel thickness and a large origami pattern sector angle are necessary to obtain a high deployed/folded ratio. Finally, a prototype of the deployable structure is manufactured to verify and demonstrate its excellent performance.

Modelling and analysis for a cylindrical net-shell deployable mechanism

Existing cylindrical deployable structures have poor controllability of deployment or weak bearing capacity. In order to satisfy the application needs of cylindrical deployable structures in the space industry, a cylindrical net-shell deployable mechanism is established in this article. The proposed cylindrical net-shell deployable mechanism has a regular cuboid shape in the folded state and a truss structure in the deployed state, and it can fit cylindrical surface, parabolic cylindrical surface, sine cylindrical surface and so on. Furthermore, based on reciprocal screw theory and screw synthesis theory, the mobility of cylindrical net-shell deployable mechanism in the whole motion cycle is analysed by the proposed equivalent model method. Results show that the cylindrical net-shell deployable mechanism is a single-degree-of-freedom mechanism. Moreover, a prototype is manufactured, and its motion performance is tested. The experiment shows that the cylindrical net-shell deployable mechanism has a smooth motion performance, and the mobility analysis method for complex coupled mechanism in this study is valid. This study has a certain significance in expanding the application field of cylindrical shell structure.

Partial electromagnetic wave guidance by a parabolic cylindrical chiroboundary with small flare angle

Summary Propagation of electromagnetic (EM) waves through an unbounded medium with two regions, having different values of chirality admittances separated by a parabolic cylindrical surface, is dealt with. The dispersion relations and cutoff conditions for such a chiroguide are described under the assumption of small flare angle of the parabolic cylindrical boundary. More emphasis is, however, given on the field cutoffs. A kind of mode bunching phenomenon is reported which is, however, partially localized in this case.

Partial Guidance of Electromagnetic Waves by a Parabolic Cylindrical Boundary Separating Two Chiral Media

An investigation has been made of the electromagnetic wave propagation in a medium with two regions, having different chiral admittances, separated by a parabolic cylindrical surface. The resulting guide is analogous to a circular chirowaveguide when the circle is degenerated into a parabola. The eigenvalue equation and the cutoff conditions of such a chirowaveguide have been derived for different special cases.

Analysis of the guidance of electromagnetic waves by a deformed planar waveguide with parabolic cylindrical boundaries

An analytical study of a waveguide with two parabolic cylindrical surfaces separating the guiding region of refractive index n1 from two cladding regions of common refractive index n2 with n1≳n2 is presented. The cutoff conditions for modes are derived as equations containing trigonometric functions. The modes show a bunching tendency instead of well-defined discreteness, and several mode bunches occur because the distance of separation between the two interfaces does not remain constant but continues to increase as one moves away from the region near the vertices of the parabolas. Unlike the planar waveguide, a nonzero cutoff is deduced which may be attributed to the curvature of the boundaries, and the flare.

Parabolic cylindrical surfaces employed as line sources and their use for illuminating conical reflectors

The properties of line sources simulated by a parabolic cylindrical surface utilizing a point source are investigated. The factors controlling the cross-polarization and the means for elimination of the aperture blockage are also identified and studied. The line source is then used to illuminate a conical reflector with a 90° vertex angle. The performance of the resulting dual reflector system and the effects of various design parameters on its radiation patterns are investigated and presented.

Scattering by a conformal array of metallic patches

AbstractThe scattering characteristics of metallic patches arranged on a parabolic cylindrical surface are investigated. The induced surface current on each patch is identified as the current induced on the center patch of a planar array, which is tangent to the parabolic cylindrical surface at the patch. Each of these planar‐array problems is solved by the spectral‐Galerkin method. The scattering pattern from the conformal array is obtained by superposition.

Surface ray analysis of mutually coupled arrays on variable curvature cylindrical surfaces

Two previously developed ray methods for conformal arrays on surfaces with variable curvature are further systematized and applied to arrays of equispaced identical slits on perfectly conducting parabolic cylindrical surfaces. The two methods differ in their definition of the canonical problems that are fundamental to the scattering process. In the first method, multiple scattering on the smooth cylinder surface accounts for interaction between isolated elements, while in the second, surface rays are defined on a local periodically loaded surface. The first method is valid under quite general conditions and yields reliable numerical results for mutual-coupling coefficients and radiation patterns. The second provides a simple explanation of a variety of coupling and radiation phenomena when the array possesses aspects of periodicity, and it is preferable for numerical calculation of mutual coupling in large arrays. These features are illustrated in detail on a particular example. The results obtained confirm the utility of the ray analysis in furnishing solutions for coupling coefficients and element patterns in conformal arrays, and they also demonstrate the fundamental insight gained by the local periodic-structure approach.