Deployable antenna mechanism based on decagonal and hexagonal heterogeneous module networking and paraboloid profile division method thereof

Abstract

The invention discloses a deployable antenna mechanism based on decagonal and hexagonal heterogeneous module networking and a paraboloid profile division method thereof. The deployable antenna mechanism is formed by combining a plurality of pyramid combination units in a networking mode. Each pyramid combination unit comprises a ten-pyramid basic deployable unit and five hexagonal-pyramid basic deployable units which surround the periphery of the ten-pyramid basic deployable unit, are distributed in an annular array mode and are movably connected with the ten-pyramid basic deployable unit, and every two adjacent hexagonal-pyramid basic deployable units are movably connected through a foldable connecting rod piece. The ten-pyramid and hexagonal-pyramid multi-rod-piece structure has the good symmetry characteristic and the tight splicing characteristic, rapid expansion and combination can be achieved through circumferential array arrangement, the requirements of paraboloid deployable antennas of different sizes and different curvatures can be met on the premise that the excellent rigidity performance is kept, and the design is reasonable. An effective technical path is provided for the design of a large-caliber and high-precision antenna, and the antenna can be suitable for different working environments.

Description

Technical Field

[0001] This invention relates to the field of deployable antenna mechanisms, and more particularly to a deployable antenna mechanism based on a network of decagonal and hexagonal heterogeneous modules and its parabolic surface division method. Background Technology

[0002] Deployable frame antennas have become a research hotspot due to their high fold-to-spread ratio and high stiffness. Since the parabolic properties meet the requirements of deployable frame antennas for transmitting and receiving electromagnetic signals, their parabolic shape needs to be modularly designed and deployed with high precision through a reasonable surface division method. In aerospace communications, deep space exploration, and other fields, deployable antennas have become key technological equipment due to their high packing ratio, high stiffness, and large aperture characteristics. The core challenge lies in how to achieve high-precision surface deployment within a limited launch space. Surface division, as a fundamental step determining the accuracy of the reflector and the stability of the structure, has significant limitations. Traditional design methods, such as using triangular or hexagonal grids for reflector division, require repeated adjustments to the length of the rods and the position of the nodes to approximate the ideal parabolic surface. For example, the Chinese patent "Single-Degree-of-Freedom Parabolic Cylindrical Deployable Antenna Mechanism Based on Oblique Pentahedral Unit Array" (patent application number: CN2022112225674) describes a mechanism composed of multiple single-degree-of-freedom oblique pentahedral deployable units. Each oblique pentahedron consists of five central node disks, four sets of folding rods, and four diagonal tie rods. The mechanism is composed of multiple identical units connected together in the horizontal direction and units with different degrees of inclination connected together in the vertical direction to form a parabolic feature. While this mechanism has only one degree of freedom and offers high deployment reliability, it relies on a limited number of rod units for antenna mechanism expansion and networking, resulting in limited overall stiffness and making it unsuitable for complex working environments. Summary of the Invention

[0003] Purpose of the invention: The first purpose of this invention is to provide a method for parabolic surface partitioning based on decagonal and hexagonal heterogeneous module networking.

[0004] The second objective of this invention is to provide a deployable antenna mechanism based on a network of decagonal and hexagonal heterogeneous modules that is rigid and suitable for complex working environments.

[0005] Technical solution: This invention discloses a parabolic surface partitioning method based on decagonal and hexagonal heterogeneous module networking, comprising the following steps:

[0006] S1: Construct a composite surface division unit composed of regular decagons, regular hexagons and isosceles trapezoids on a two-dimensional plane from a top-down perspective;

[0007] S2: The two-dimensional planar diagram of the parabolic surface formed by the deployable antenna mechanism is divided using composite surface division units to obtain a combined graphic with the combined features of regular decagons, regular hexagons and isosceles trapezoids, and a coordinate system xoy is established at the center of the combined graphic.

[0008] S3: Calculate the side length of the polygon in the composite surface division unit based on the pre-set diameter of the composite surface division unit, and calculate the coordinates of the center point of the polygon in the coordinate system xoy based on the side length of the polygon, so as to obtain the coordinates of the center point of the polygon.

[0009] S4: Construct a transformation equation based on the angular relationship between the nodes of the polygon and its center point using the rotation coordinate transformation method. Calculate the polygon node coordinates based on the transformation equation and the polygon center point coordinates obtained in step S3; and calculate the coordinates of the polygon nodes based on the pre-defined parabolic surface parametric equations. Calculate the coordinates of the polygon nodes in the three-dimensional coordinate system xyz, where f is the focal length of the parabolic surface;

[0010] S5: Curvature and Parametric Equations Based on Parabolic Surfaces The three-dimensional node coordinates obtained in step S4 are curve-fitted and connected to obtain the parabolic surface of the deployable antenna mechanism in three-dimensional space.

[0011] S6: Based on the parabolic surface in three-dimensional space obtained in step S5, construct a pyramidal combination unit formed by combining the basic deployable pentagonal pyramidal unit and the basic deployable quadrangular pyramidal unit. The obtained three-dimensional node coordinates of the regular hexagon and isosceles trapezoid refer to the center point of the bottom center node disk of the deployable antenna mechanism, and the length of the line connecting adjacent three-dimensional node coordinates refers to the rod length of the deployable antenna mechanism.

[0012] Based on the same inventive concept, this invention also discloses a deployable antenna mechanism based on a network of decagonal and hexagonal heterogeneous modules. The deployable antenna mechanism is composed of several pyramidal combination units arranged in a network configuration. Each pyramidal combination unit includes a basic decagonal pyramidal deployable unit and five hexagonal pyramidal basic deployable units arranged in a circular array around the basic decagonal pyramidal deployable unit and movably connected to it. Adjacent hexagonal pyramidal basic deployable units are movably connected by foldable connecting rods. The orthographic projection of the bottom surface of the basic decagonal pyramidal deployable unit forms a regular decagon, and the hexagonal pyramidal basic deployable unit... The orthographic projection of the base of the pyramidal unit forms a regular hexagon, and the side lengths of the regular decagon and the regular hexagon are equal. The orthographic projection of the base of the pyramidal unit forms a closed ring structure, which is composed of a regular decagon at the center, five regular hexagons arranged in a ring around the decagon, and five isosceles trapezoids arranged in a ring around the decagon. The regular hexagons and isosceles trapezoids are arranged alternately. One side of each of the five regular hexagons coincides with a side of the regular decagon, one side of each isosceles trapezoid coincides with a side of the regular decagon, and the two opposite sides of each isosceles trapezoid coincide with the sides of the two adjacent regular hexagons.

[0013] Furthermore, the basic deployable unit of the deca-pyramid includes ten bottom center node disks located at the ten vertices of a regular decagon, ten first lower center node disk folding linkage rods located at the ten sides of the regular decagon, a top center node disk located directly above the center point of the regular decagon, and ten side edges rotatably connected between the top center node disk and the corresponding bottom center node disk via revolute joints. The two ends of the first lower center node disk folding linkage rods are rotatably connected to two adjacent bottom center node disks via revolute joints. The ten first lower center node disk folding linkage rods fold synchronously and link the top center node disk and the bottom center node disk towards the center point, forming a frustum structure surrounded by the ten first lower center node disk folding linkage rods around the ten side edges.

[0014] Furthermore, the basic deployable unit of the hexagonal pyramid includes six bottom center node disks located at the six vertices of a regular hexagon, six first lower center node disk folding linkage rods located at the six sides of the regular hexagon, a top center node disk located directly above the center point of the regular hexagon, and six side edges rotatably connected between the top center node disk and the corresponding bottom center node disk via revolute joints. The two ends of the first lower center node disk folding linkage rods are rotatably connected to two adjacent bottom center node disks via revolute joints. The six first lower center node disk folding linkage rods fold synchronously and link the top center node disk and the bottom center node disks toward the center point, forming a conical structure in which the six first lower center node disk folding linkage rods surround the six side edges.

[0015] Furthermore, the connecting rods include five upper center node disk folding linkage rods and a second and fifth lower center node disk folding linkage rod. The upper center node disk folding linkage rods are rotatably connected between the top center node disks of two adjacent hexagonal pyramidal deployable basic units via a revolute joint. The five and the second and fifth lower center node disk folding linkage rods are respectively located on the sides of five isosceles trapezoids that do not share sides with the regular decagon and regular hexagon. The two ends of the second and fifth lower center node disk folding linkage rods are rotatably connected to the bottom center node disks of two adjacent hexagonal pyramidal deployable basic units via revolute joints.

[0016] Furthermore, all the first lower center node disk folding linkage rods and the five second lower center node disk folding linkage rods fold in the same direction, facing inwards towards the parabolic surface; the folding direction of the upper center node disk folding linkage rods is opposite to that of the first lower center node disk folding linkage rods; the five and thirty-five first lower center node disk folding linkage rods and the five second-fifth lower center node disk folding linkage rods fold synchronously and link the top center node disk and the bottom center node disk towards the center point, forming a cylindrical structure in which fifteen first lower center node disk folding linkage rods and five second lower center node disk folding linkage rods of the hexagonal pyramid deployable basic unit are located on the outermost layer, the remaining twenty first lower center node disk folding linkage rods and thirty side edges of the hexagonal pyramid deployable basic unit are located in the middle layer, and the ten side edges of the deca-pyramid deployable basic unit are located in the innermost layer.

[0017] Furthermore, when the pyramidal composite unit is fully unfolded, the top central node disks of the deca-pyramidal basic developable unit and the hexagonal pyramidal basic developable unit are at different heights.

[0018] Furthermore, when the pyramidal assembly unit is fully unfolded, it exhibits a parabolic surface, with each base center node disk resting on the parabolic surface, and the parametric equation of the parabolic surface is as follows:

[0019]

[0020] Where x, y, and z form a three-dimensional coordinate system, and f is the focal length of the parabolic surface.

[0021] Furthermore, the ratio of the spatial volume occupied by the pyramidal assembly unit when fully expanded to when fully collapsed is called the collapse ratio, and the formula for calculating the collapse ratio is as follows:

[0022]

[0023] Where V0 is the volume of the pyramidal unit when fully expanded, D0 is the diameter of the envelope circle of the central node disk of the reflecting surface when the pyramidal unit is fully expanded, d0 is the diameter of the envelope circle of the central node disk of the back frame when the pyramidal unit is fully expanded, and h0 is the vertical distance between the central node disk of the reflecting surface and the central node disk of the back frame when the pyramidal unit is fully expanded; V1 is the volume of the pyramidal unit when fully collapsed, D1 is the diameter of the envelope circle of the central node disk of the reflecting surface when the pyramidal unit is fully collapsed, d1 is the diameter of the envelope circle of the central node disk of the back frame when the pyramidal unit is fully collapsed, and h0 is the vertical distance between the central node disk of the reflecting surface and the central node disk of the back frame when the pyramidal unit is fully collapsed.

[0024] Furthermore, among the multiple pyramidal combination units, one pyramidal combination unit is selected to form a central combination unit, and the remaining pyramidal combination units are arranged in a circular grid according to the number of regular hexagons in the central combination unit, and one edge of the outer regular hexagon in the remaining pyramidal combination units coincides with one edge of the outer regular hexagon in the central combination unit.

[0025] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages: The multi-bar structure of the deca-pyramid and hexagonal pyramid of the present invention has good symmetry and tight splicing characteristics. It can be rapidly expanded and combined through circumferential array arrangement. While maintaining excellent stiffness performance, it can adapt to the needs of parabolic deployable antennas of different sizes and curvatures, providing an effective technical path for the design of large-aperture, high-precision antennas, and is applicable to different working environments.

[0026] This invention uses deca-pyramids and hexagonal pyramids as basic deployment units. Compared to traditional single triangular pyramid modules, deca-pyramids and hexagonal pyramids have more members and more node connections, forming a multi-member spatial truss structure with higher redundancy. The multi-member configuration gives the deployable antenna higher structural stiffness and load-bearing capacity in the deployed state, effectively resisting external loads and vibration interference, and ensuring higher stability of the deployable antenna mechanism.

[0027] This invention, based on the rotation coordinate transformation method and the parametric equations of parabolic surfaces, can realize the transformation from two-dimensional plane division to three-dimensional surface division, and has high computational efficiency in the division process. It can not only reduce the complexity of the shape finding process, but also help improve the matching accuracy of the curvature and focal length of the parabolic surface. Attached Figure Description

[0028] Figure 1 This is an orthographic projection of the bottom surface of the pyramidal assembly unit of the present invention;

[0029] Figure 2 This is a frontal projection of the bottom surface of the multiple pyramidal combination units of the present invention when they are combined.

[0030] Figure 3 For the present invention Figure 2 Diagram showing the included angles of the regular hexagon numbered ①;

[0031] Figure 4 For the present invention Figure 2 Diagram showing the included angles of isosceles trapezoid numbered ②;

[0032] Figure 5 This is a schematic diagram illustrating the transformation of a pyramidal composite unit from a two-dimensional plane to a parabolic surface in an embodiment of the present invention;

[0033] Figure 6 This is a schematic diagram illustrating the transformation of multiple pyramidal combination units from a two-dimensional plane to a parabolic surface in an embodiment of the present invention;

[0034] Figure 7 This is a view of dividing a composite surface into units using a Python program in an embodiment of the present invention;

[0035] Figure 8 This is a view of the process of dividing a composite surface into units using a Python program in an embodiment of the present invention;

[0036] Figure 9 For the present invention Figure 1 Label diagrams for regular hexagons and isosceles trapezoids;

[0037] Figure 10 This is a schematic diagram of the structure of the basic deployable unit of the deca-pyramid of the present invention when fully unfolded;

[0038] Figure 11 This is a top view of the fully unfolded basic deployable unit of the deca-pyramidal structure of the present invention.

[0039] Figure 12 This is a front view of the basic expandable unit of the deca-pyramid of the present invention when it is fully collapsed.

[0040] Figure 13 This is a top view of the basic expandable unit of the deca-pyramid of the present invention when it is fully collapsed.

[0041] Figure 14 This is a schematic diagram of the structure of the basic deployable hexagonal pyramidal unit of the present invention when fully unfolded.

[0042] Figure 15 This is a top view of the hexagonal pyramid basic deployable unit of the present invention when fully unfolded.

[0043] Figure 16 This is a front view of the basic expandable hexagonal pyramidal unit of the present invention when fully collapsed.

[0044] Figure 17This is a top view of the hexagonal pyramidal basic expandable unit of the present invention when it is fully collapsed.

[0045] Figure 18 This is a schematic diagram of the pyramidal assembly unit of the present invention when fully unfolded;

[0046] Figure 19 This is a schematic diagram of the pyramidal assembly unit of the present invention when fully collapsed;

[0047] Figure 20 This is the front view of the pyramidal assembly unit when it is fully collapsed.

[0048] Figure 21 This is a top view of the pyramidal assembly unit of the present invention when fully retracted.

[0049] Figure 22 This is a schematic diagram of the pyramidal assembly unit when fully unfolded in an embodiment of the present invention. Figure 1 ;

[0050] Figure 23 This is a schematic diagram of the pyramidal assembly unit when fully unfolded in an embodiment of the present invention. Figure 2 ;

[0051] Figure 24 This is a schematic diagram of the pyramidal assembly unit when fully unfolded in an embodiment of the present invention. Figure 3 ;

[0052] Figure 25 This is a diagram showing the diameter of the pyramidal assembly unit of the present invention when fully expanded;

[0053] Figure 26 This is a diagram showing the diameter of the pyramidal assembly unit of the present invention when it is fully collapsed. Detailed Implementation

[0054] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0055] Example 1

[0056] This invention discloses a method for constructing parabolic surfaces based on decagons and hexagons, comprising the following steps:

[0057] S1: Construct a composite surface division unit on a two-dimensional plane from a top-down perspective, consisting of regular decagons, regular hexagons, and isosceles trapezoids.

[0058] Among them, such as Figure 1The parabolic reflector surface of the deployable antenna is defined by a combination of regular decagons, regular hexagons, and isosceles trapezoids. On a plane viewed from above, a regular decagon is drawn, and regular hexagons are arranged in a circular array around the center of the decagon's circumcircle. Five more regular hexagons are then connected sequentially, forming a planar view of the antenna surface combining decagons, hexagons, and isosceles trapezoids. In this configuration, one side of each of the five regular hexagons coincides with a side of the decagon. Adjacent regular hexagons are connected by isosceles trapezoids. One side of each of the five regular hexagons coincides with a side of the decagon, and two sides coincide with sides of the two regular hexagons they connect to, ultimately forming a polygonal unit composed of regular decagons, hexagons, and isosceles trapezoids. Using this composite surface division unit as the surface center, a circular array network is formed according to the number of its side lengths, and finally the deployment antenna surface with the combined features of regular decagon, regular hexagon and isosceles trapezoid is completed on the plane.

[0059] S2: The two-dimensional planar diagram of the parabolic surface formed by the deployable antenna mechanism is divided using composite surface division units to obtain a combined graphic with the combined features of regular decagons, regular hexagons and isosceles trapezoids, and a coordinate system xoy is established at the center of the combined graphic.

[0060] like Figure 2 As shown, taking the composite surface dividing unit O as the center of the parabolic surface, a circular array is formed according to the number of side lengths of the composite surface dividing unit O. Finally, a two-dimensional planar diagram of a parabolic surface with combined features of regular decagons, regular hexagons, and isosceles trapezoids is obtained on the plane, thus yielding the composite graphic. Each composite graphic consisting of one regular decagon, five regular hexagons, and five isosceles trapezoids is systematically numbered. Specifically, as... Figure 2 The clearly shown composite unit located at the center point of the parabolic surface is designated as number O. The remaining composite figures arranged in a circular array around the center point are assigned numbers A through E in a clockwise direction. Furthermore, the regular hexagons and isosceles trapezoids within each composite figure are meticulously numbered, again following a clockwise order. The regular hexagons and isosceles trapezoids in composite figures O, A, B, C, D, and E are numbered o1~o10, a1~a10, b1~b10, c1~c10, d1~d10, and e1~e10, respectively. Figure 2 The numbered circles represent lowercase letters indicating different image combination numbers. Following a clockwise order, the coordinates of the center point of the polygon in each image combination are set as follows: , , , , , .

[0061] S3: Calculate the side length of the polygons in the composite surface division unit based on the pre-defined aperture of the composite surface division unit. Based on the side length of the polygons, calculate the coordinates of the center point of the polygon in the xoy coordinate system of all composite surface division units to obtain the coordinates of the center point of the polygon. The polygon refers to a regular hexagon and an isosceles trapezoid.

[0062] The aperture, curvature, and focal length of the parabolic surface are set according to the actual situation. Based on the aperture of the composite surface unit, the side lengths of the regular decagons, regular hexagons, and isosceles trapezoids in the composite surface unit can be calculated. Based on the calculated side lengths of the regular decagons, regular hexagons, and isosceles trapezoids, and the position of each composite surface unit on the xoy coordinate system, the coordinates of the center points of all regular hexagons and isosceles trapezoids in all composite surface units are calculated, that is, the coordinates of the center points of the regular decagons, regular hexagons, and isosceles trapezoids are obtained, which is equivalent to calculating... , , , , , .

[0063] S4: Construct a transformation equation based on the angular relationship between the nodes of the polygon and its center point using the rotation coordinate transformation method. Calculate the polygon node coordinates based on the transformation equation and the polygon center point coordinates obtained in step S3; and calculate the coordinates of the polygon nodes based on the pre-defined parabolic surface parametric equations. Calculate the coordinates of the polygon nodes in the three-dimensional coordinate system xyz, where f is the focal length of the parabolic surface.

[0064] Based on the coordinates of the polygon center point obtained in step S3, a transformation equation based on the relationship between polygon vertices and angles is constructed using a rotational coordinate transformation method. This transformation equation aims to accurately calculate the vertex coordinates of the plane containing each polygon within the partition surface of the combined graphic. Subsequently, according to the pre-defined parabolic curvature and its parametric equations, the calculated two-dimensional vertex coordinates are substituted into the parabolic equation to determine the precise position of the polygon nodes in three-dimensional space.

[0065] When using the polygon center node coordinate transformation method to extend the parabolic surface of the deployable antenna mechanism into a combination of regular decagons, regular hexagons, and isosceles trapezoids, it is necessary to know the angle between the line connecting each vertex of each regular hexagon and isosceles trapezoid to its center coordinate point and the positive x-axis of the coordinate system established with the center point. For example... Figure 3 and 4 As shown, the angle between the line connecting each vertex of the regular hexagon to the center point of its combined shape and the positive x-axis is calculated using the geometric relationships of the figures. The angle between the line connecting the vertex of the isosceles trapezoid to the center point of its composite figure and the positive x-axis. At the same time, calculate the circumradius of the regular hexagon based on its side length. radius of the circumcircle of the isosceles trapezoid ,in Based on the above calculation of the center point coordinates and angles, the center point coordinate matrices of the regular hexagon and isosceles trapezoid in each combined image are constructed using the following formulas (1) and (2). The positive x-axis angle matrix of the graph combined with its vertices ,in :

[0066] (1)

[0067] (2)

[0068]

[0069] Based on the above formulas (1), (2), and (3), the vertex coordinate transformation formula for the relationship between the center point and the angle of a polygon is established using the rotation coordinate transformation method, as shown in formula (3):

[0070] (4)

[0071] In the formula, This represents the x-value of the i-th coordinate in matrix P. This represents the y-value of the i-th coordinate in matrix P. This represents the included angle matrix corresponding to the i-th coordinate in matrix P. The radius of the circumcircle of the polygon.

[0072] Substitute the coordinates of all the center points obtained in step S2 into the established formula (3), and obtain the vertex coordinates of the regular hexagon and trapezoid through coordinate transformation. Simultaneously, the calculated planar coordinates of the combined graphic division surface are substituted into the pre-defined parabolic surface parametric equations to calculate the coordinate degree z of each vertex on the parabolic surface, thus converting the two-dimensional graphic vertex coordinates into three-dimensional spatial coordinates. In this process, different combinations of x and y coordinates will produce different z values, thereby forming different shapes on the parabolic surface. In this way, we can map points in three-dimensional space onto a parabolic surface, thus obtaining a schematic diagram of the transformation from a plane to a parabolic surface for decagonal, hexagonal, and trapezoidal combined units and extended units, as shown in the diagram. Figure 5 and Figure 6 As shown.

[0073] S5: Curvature and Parametric Equations Based on Parabolic Surfaces The three-dimensional node coordinates obtained in step S4 are curve-fitted and connected to obtain the parabolic surface of the deployable antenna mechanism in three-dimensional space.

[0074] In practical use, Python software is used to perform curve fitting and connection processing on the 3D node coordinate data generated in step S4, thereby achieving accurate conversion from the 2D surface based on the combined graphic division to the deployable antenna parabolic surface, and performing visualization of the divided surface and efficient data extraction. Code was written for the parabolic surface divided by the combined graphic of regular decagons, regular hexagons, and isosceles trapezoids. The relevant parameters, parabolic surface equations, and formulas from step S4 were parameterized and input together. A for loop was used to convert the center coordinates of each regular hexagon and isosceles trapezoid into vertex coordinates according to angular relationships and coordinate transformation methods. Python was then used to visualize the combined and extended surfaces, such as... Figure 7 and Figure 8 As shown. Finally, the node data of the combined parabolic surface are saved.

[0075] S6: Based on the parabolic surface in three-dimensional space obtained in step S5, construct a pyramidal combination unit formed by combining the basic deployable pentagonal pyramidal unit and the basic deployable quadrangular pyramidal unit. The obtained three-dimensional node coordinates of the regular hexagon and isosceles trapezoid refer to the center point of the bottom center node disk of the deployable antenna mechanism, and the length of the line connecting adjacent three-dimensional node coordinates refers to the rod length of the deployable antenna mechanism.

[0076] Following the shape rules of the combined graphic division, multiple pyramidal combination units are arranged in an orderly manner according to the layout principle of the circular array, and finally a deployable antenna mechanism with a parabolic surface based on a deca-pyramid and a hexagonal pyramid is formed.

[0077] This invention relates to a deployable antenna mechanism based on decapsulated and hexagonal pyramids and its parabolic surface networking method. The resulting pyramidal modular deployable antenna mechanism not only breaks away from the traditional single-unit division method, ensuring the consistency of the antenna's shape during deployment and retraction, but also establishes a highly redundant spatial multi-member truss system by increasing the number of members and strengthening node connections in the decapsulated and hexagonal pyramidal configurations. This design architecture enables the deployable antenna to achieve superior structural stiffness and load-bearing characteristics in the deployed state.

[0078] Example 2

[0079] This invention discloses a deployable antenna mechanism based on a network of decagonal and hexagonal heterogeneous modules. The deployable antenna mechanism is composed of several pyramidal combination units arranged in a network configuration. Each pyramidal combination unit includes a basic decagonal pyramidal deployable unit and five hexagonal pyramidal basic deployable units arranged in a circular array around the basic decagonal pyramidal deployable unit and movably connected to it. Adjacent hexagonal pyramidal basic deployable units are movably connected by foldable connecting rods. Figure 1 As shown, the orthographic projection of the base of the basic developable unit of the deca-pyramid forms a regular decagon 1, and the orthographic projection of the base of the basic developable unit of the hexagon forms a regular hexagon 2. The side lengths of regular decagon 1 and regular hexagon 2 are equal. The orthographic projection of the base of the pyramidal composite unit forms a closed ring structure, which consists of a central regular decagon 1, five regular hexagons 2 arranged in a ring around the outer perimeter of the regular decagon 1, and five isosceles trapezoids 3 arranged in a ring around the outer perimeter of the regular decagon 1. Regular hexagons 2 and isosceles trapezoids 3 are arranged alternately. One side of each of the five regular hexagons 2 coincides with a side of the regular decagon 1, one side of each isosceles trapezoid 3 coincides with a side of the regular decagon 1, and the two opposite sides of each isosceles trapezoid 3 coincide with the sides of two adjacent regular hexagons 2. Furthermore, the outermost side of the isosceles trapezoid 3 is longer than the side coinciding with the regular decagon 1. Figure 9 As shown, the regular hexagons with odd numbers are the orthographic projections of the base of the basic developable unit of the hexagonal pyramid, which are also known as regular hexagon 2; the ones with even numbers are isosceles trapezoids 3.

[0080] like Figures 10 to 13 As shown, the basic deployable unit of the deca-pyramid includes ten base center node disks 4, ten first lower center node disk folding linkage rods 5, one top center node disk 6, and ten side edges 7. The ten base center node disks 4 are located at the ten vertices of the regular decagon 1, and the ten first lower center node disk folding linkage rods 5 are located at the ten sides of the regular decagon 1. The two ends of the first lower center node disk folding linkage rods 5 are rotatably connected to the two adjacent base center node disks 4 through a revolute joint. The top center node disk 6 is located directly above the center point of the regular decagon 1, and the center point refers to the center of the circumcircle of the regular decagon 1. The ten side edges 7 are rotatably connected between the top center node disk 6 and the corresponding base center node disk 4 through a revolute joint.

[0081] When the basic expandable unit of the ten-sided pyramid is folded up, the ten side edges 7 move closer to the parabolic surface, and the ten first lower center node disk folding linkage rods 5 fold up simultaneously and move the top center node disk 6 and the bottom center node disk 4 closer to the center point, folding up into a frustum structure surrounded by the ten first lower center node disk folding linkage rods 5 around the ten side edges 7.

[0082] like Figures 14 to 17As shown, the basic deployable unit of the hexagonal pyramid includes six base center node disks 4, six first lower center node disk folding linkage rods 5, one top center node disk 6, and six side edges 7. The six base center node disks 4 are located at the six vertices of the regular hexagon 2, and the six first lower center node disk folding linkage rods 5 are located at the six sides of the regular hexagon 2. The two ends of the first lower center node disk folding linkage rods 5 are rotatably connected to the two adjacent base center node disks 4 through a swivel joint. The six side edges 7 are rotatably connected between the top center node disk 6 and the corresponding base center node disk 4 through a swivel joint.

[0083] When the basic expandable unit of the hexagonal pyramid is folded up, the six side edges 7 move closer to the parabolic surface, and the six first lower center node disk folding linkage rods 5 fold simultaneously and link the top center node disk 6 and the bottom center node disk 4 to move closer to the center point, folding up into a conical structure surrounded by the six first lower center node disk folding linkage rods 5 around the six side edges 7.

[0084] like Figure 18 As shown, the side edges 7 of the basic deployable unit of the deca-pyramid and the basic deployable unit of the hexagonal pyramid have the same length, but the included angle between the side edges 7 of the basic deployable unit of the deca-pyramid and the basic deployable unit of the hexagonal pyramid and the bottom center node disk 4 is different. This makes the height of the top center node disk 6 of the basic deployable unit of the deca-pyramid and the basic deployable unit of the hexagonal pyramid different when the pyramid combination unit is fully unfolded. However, when the pyramid combination unit is fully closed, the height of the top center node disk 6 of the basic deployable unit of the deca-pyramid and the basic deployable unit of the hexagonal pyramid is the same. The included angle between the side edges 7 of the basic deployable unit of the deca-pyramid and the basic deployable unit of the hexagonal pyramid and the bottom center node disk 4 is set according to actual needs.

[0085] The connecting rods include five upper center node disk folding linkage rods 8 and a second fifth lower center node disk folding linkage rod 9. The upper center node disk folding linkage rods 8 are rotatably connected between the top center node disks 6 of two adjacent hexagonal pyramidal deployable basic units via revolute joints. The five second fifth lower center node disk folding linkage rods 9 are respectively located on the sides of five isosceles trapezoids 3 that do not share sides with regular decagons 1 and regular hexagons 2. The two ends of the second fifth lower center node disk folding linkage rods 9 are rotatably connected to the bottom center node disks 4 of two adjacent hexagonal pyramidal deployable basic units via revolute joints. The second fifth lower center node disk folding linkage rod 9 is longer than the first lower center node disk folding linkage rod 5.

[0086] When the pyramidal assembly unit is folded up, all the first lower central node disk folding linkage rods 5 and the five second lower central node disk folding linkage rods 9 fold in the same direction, facing inwards towards the parabolic surface; the folding direction of the upper central node disk folding linkage rods 8 is opposite to that of the first lower central node disk folding linkage rods 5, facing outwards towards the parabolic surface; the five upper central node disk folding linkage rods 8, the thirty-five first lower central node disk folding linkage rods 5 and the five second lower central node disk folding linkage rods 9 fold synchronously and link the top central node disk 6 and the bottom central node disk 4 to move towards the center point, folding up into a cylindrical structure where the fifteen first lower central node disk folding linkage rods 5 and the five second lower central node disk folding linkage rods 9 of the hexagonal pyramidal deployable basic unit are located on the outermost layer, the remaining twenty first lower central node disk folding linkage rods 5 and the thirty side edges 7 of the hexagonal pyramidal basic deployable unit are located in the middle layer, and the ten side edges 7 of the ten-sided pyramidal basic deployable unit are located in the innermost layer.

[0087] like Figures 19 to 21 As shown, when the pyramidal assembly unit is fully retracted, the forty equal-length side edges move towards the center of the parabolic surface. Simultaneously, the lower center node disk folding linkage rods 047-76 fold inwards towards the parabolic surface, and the upper center node disk folding linkage rods 077-081 fold outwards towards the parabolic surface, simultaneously driving the bottom and top center node disks to move towards the parabolic surface. After retraction, each folding linkage rod is in a folded state. The outer lower center node disk folding linkage rod is in the outer layer, while the ten lower center node disk folding linkage rods connecting the outer and inner bottom center node disks, the thirty side edges of the five basic deployable hexagonal pyramidal units, and the ten lower center node disk folding linkage rods connecting the inner bottom center node disk—a total of fifty rods—are in the middle layer. The lower center node disk folding linkage rods of the inner ten-sided pyramid are in the innermost layer. The top five upper center node disk folding linkage rods 077-081 are also in a folded state, with the folding direction opposite to that of the lower center node disk folding linkage rods 047-76. During the closing process, each side edge, the lower center node disk folding linkage rod, and the upper center node disk folding linkage rod simultaneously drive the connected top center node disk and bottom center node disk to move towards the center point, closing into a cylindrical structure. Among them, the twenty outer bottom center node disks 017~036 and the five outer top center node disks 02~06 are in the outermost circle, and the ten inner bottom center node disks 07~016 and one inner top center node disk 01 of the ten-sided pyramid basic expandable unit are in the innermost circle, finally achieving the fully closed state of the pyramid combination unit.

[0088] When the pyramidal composite unit is fully unfolded, it presents a parabolic surface. Each base center node disk 4 falls on the parabolic surface, and the parametric equation of the parabolic surface is as follows:

[0089]

[0090] Where x, y, and z form a three-dimensional coordinate system, and f is the focal length of the parabolic surface.

[0091] Taking a pyramidal combination unit as an example, the pyramidal combination unit is composed of a deca-pyramid and five identical hexagons formed by regularly numbered hexagons. For example... Figure 22 As shown, the pyramid assembly includes twenty outer base center node disks, ten inner base center node disks, five outer top center node disks and one inner top center node disk, forty equal-length side edges, thirty-five folding linkages for the first lower center node disks, five folding linkages for the second lower center node disks, and five folding linkages for the upper center node disks. Figure 22 As shown, an internal top center node disk is located directly above the center point of regular decagon 1, and is designated as top center node disk 01; five external top center node disks are... Figure 9 Above the center points of regular hexagons 2 (numbered odd numbers ①, ③, ⑤, ⑦, ⑨), the top center node disks are set in clockwise order as follows: 02, 03, 04, 05, and 06. The twenty outer bottom center node disks correspond to the outer nodes of the five regular hexagons 2, and are set in clockwise order as bottom center node disks 017 to 036. The ten inner bottom center node disks are located at the ten nodes of regular decagon 1, and are set as bottom center node disks 07 to 016.

[0092] like Figure 23As shown, ten of the thirty-five first lower center node disk folding linkage rods are located at the ten sides of a regular decagon 1. These ten first lower center node disk folding linkage rods are lower center node disk folding linkage rods 037 to 046. Specifically, the two ends of lower center node disk folding linkage rod 037 are rotatably connected to bottom center node disks 07 and 08 via revolute joints, the two ends of lower center node disk folding linkage rod 038 are rotatably connected to bottom center node disks 08 and 09 via revolute joints, the two ends of lower center node disk folding linkage rod 039 are rotatably connected to bottom center node disks 09 and 010 via revolute joints, and the two ends of lower center node disk folding linkage rod 040 are rotatably connected to bottom center node disks 010 and 011 via revolute joints. The two ends of the folding linkage rod 041 are rotatably connected to the bottom center node disk 011 and the bottom center node disk 012 respectively via a rotary joint. The two ends of the folding linkage rod 042 of the lower center node disk are rotatably connected to the bottom center node disk 012 and the bottom center node disk 013 respectively via a rotary joint. The two ends of the folding linkage rod 043 of the lower center node disk are rotatably connected to the bottom center node disk 013 and the bottom center node disk 014 respectively via a rotary joint. The two ends of the folding linkage rod 044 of the lower center node disk are rotatably connected to the bottom center node disk 014 and the bottom center node disk 015 respectively via a rotary joint. The two ends of the folding linkage rod 045 of the lower center node disk are rotatably connected to the bottom center node disk 015 and the bottom center node disk 016 respectively via a rotary joint. The two ends of the folding linkage rod 046 of the lower center node disk are rotatably connected to the bottom center node disk 016 and the bottom center node disk 07 respectively via a rotary joint. The other twenty-five first lower center node disk folding linkage rods are located on the sides of five regular hexagons 2 that do not share sides with regular decagons 1. These twenty-five first lower center node disk folding linkage rods are lower center node disk folding linkage rods 047 to 071. Specifically, the two ends of lower center node disk folding linkage rod 047 are rotatably connected to bottom center node disk 07 and bottom center node disk 036 respectively through a revolute joint. The two ends of lower center node disk folding linkage rod 048 are rotatably connected to bottom center node disk 036 and bottom center node disk 017 respectively through a revolute joint. Lower center node disk folding linkage rod 049... Both ends are rotatably connected to the bottom center node disk 017 and bottom center node disk 018 via revolute joints, respectively. Both ends of the lower center node disk folding linkage rod 050 are rotatably connected to the bottom center node disk 018 and bottom center node disk 019 via revolute joints, respectively. Both ends of the lower center node disk folding linkage rod 051 are rotatably connected to the bottom center node disk 019 and bottom center node disk 08 via revolute joints, respectively. Similarly, the connection relationships between the lower center node disk folding linkage rods 052~071 and the bottom center node disks 09~016 and 020~035 are as follows: Figure 22and Figure 23 As shown, I will not go into too much detail here.

[0093] The five second lower center node disk folding linkage rods are located on the outer sides of the five isosceles trapezoids 3. The five second lower center node disk folding linkage rods are lower center node disk folding linkage rods 072 to 076. Specifically, the two ends of the lower center node disk folding linkage rod 072 are rotatably connected to the bottom center node disks 019 and 020 through a rotary joint, the two ends of the lower center node disk folding linkage rod 073 are rotatably connected to the bottom center node disks 023 and 024 through a rotary joint, the two ends of the lower center node disk folding linkage rod 074 are rotatably connected to the bottom center node disks 027 and 028 through a rotary joint, the two ends of the lower center node disk folding linkage rod 075 are rotatably connected to the bottom center node disks 031 and 032 through a rotary joint, and the two ends of the lower center node disk folding linkage rod 076 are rotatably connected to the bottom center node disks 035 and 036 through a rotary joint.

[0094] The five upper center node disk folding linkage rods are upper center node disk folding linkage rods 077 to 081. Specifically, the two ends of upper center node disk folding linkage rod 077 are rotatably connected to top center node disk 02 and top center node disk 03 through a rotary joint, the two ends of upper center node disk folding linkage rod 078 are rotatably connected to top center node disk 03 and top center node disk 04 through a rotary joint, the two ends of upper center node disk folding linkage rod 079 are rotatably connected to top center node disk 04 and top center node disk 05 through a rotary joint, the two ends of upper center node disk folding linkage rod 080 are rotatably connected to top center node disk 05 and top center node disk 06 through a rotary joint, and the two ends of upper center node disk folding linkage rod 081 are rotatably connected to top center node disk 06 and top center node disk 02 through a rotary joint.

[0095] like Figure 24 As shown, the ten equal-length lateral edges of the basic developable unit of the deca-pyramid are arranged in clockwise order as lateral edges 082 to 091. The tops of lateral edges 082 to 091 are rotatably connected to the top center node disk 01 via a revolute joint, and the bottoms of lateral edges 082 to 091 are rotatably connected to the bottom center node disks 07 to 016 via revolute joints, respectively. The remaining thirty equal-length lateral edges are composed of the connecting rods of five basic developable units of the hexagonal pyramid, arranged according to... Figure 9The quadrilaterals are numbered sequentially, dividing the basic developable units of the hexagonal pyramid into five groups. The first group consists of lateral edges 092 to 097; the second group consists of lateral edges 098 to 102; the third group consists of lateral edges 103 to 108; the fourth group consists of lateral edges 109 to 114; and the fifth group consists of lateral edges 115 to 119. The upper end of each group of hexagonal pyramids is connected to the top center node disk 02 via a revolute joint. Center node disk 03, top center node disk 04, top center node disk 05, and top center node disk 06 are rotatably connected. The lower ends of side edges 092, 093, 094, 095, 096, and 097 are rotatably connected to bottom center node disks 07, 036, 017, 018, 019, and 08 respectively via revolute joints. The lower ends of side edges 098, 099, 100, 101, and 102 are rotatably connected to bottom center node disks 08 via revolute joints. Center node disk 09, bottom center node disk 020, bottom center node disk 021, bottom center node disk 023, and bottom center node disk 010 are rotatably connected. The lower ends of side edges 103, 104, 105, 106, 107, and 108 are rotatably connected to bottom center node disks 011, 024, 025, 026, 027, and 012 respectively via revolute joints. Side edges 109, 110, 111, 112, and 113 are also rotatably connected. The lower ends of side ribs 113 and 114 are rotatably connected to bottom center node disks 013, 028, 029, 030, 031, and 014 respectively via swivel joints. The lower ends of side ribs 115, 116, 117, 118, and 119 are rotatably connected to bottom center node disks 015, 033, 032, 033, 034, and 035 respectively via swivel joints.

[0096] like Figure 25 and Figure 26As shown, V0 is the volume of the pyramidal unit when fully expanded, D0 is the diameter of the envelope circle of the central node disk of the reflecting surface when the pyramidal unit is fully expanded, d0 is the diameter of the envelope circle of the central node disk of the back frame when the pyramidal unit is fully expanded, and h0 is the vertical distance between the central node disk of the reflecting surface and the central node disk of the back frame when the pyramidal unit is fully expanded; V1 is the volume of the pyramidal unit when fully collapsed, D1 is the diameter of the envelope circle of the central node disk of the reflecting surface when the pyramidal unit is fully collapsed, d1 is the diameter of the envelope circle of the central node disk of the back frame when the pyramidal unit is fully collapsed, and h0 is the vertical distance between the central node disk of the reflecting surface and the central node disk of the back frame when the pyramidal unit is fully collapsed. The ratio of the volume occupied by the pyramidal unit when fully expanded to when fully collapsed is the collapse ratio, and the formula for calculating the collapse ratio is as follows:

[0097] ;

[0098] In this embodiment, the diameter of the pyramidal assembly unit is 1600mm, and the equation of the parabola is... and focal length The pyramidal composite unit in its fully collapsed state , , The pyramidal assembly unit in its fully unfolded state , , After the convergence rate calculation formula The calculated ratio of the space volume occupied by the pyramidal composite unit in its fully expanded and fully collapsed states is 83.03.

[0099] Multiple pyramidal combination units are selected, one of which forms the central combination unit. The remaining pyramidal combination units are arranged in a circular grid according to the number of regular hexagons 2 in the central combination unit, and one edge of the outermost regular hexagon 2 in each of the remaining pyramidal combination units coincides with one edge of the outermost regular hexagon 2 in the central combination unit. For example... Figure 2 As shown, pyramid combination unit O is set as the central combination unit, and pyramid combination units A, B, C, D, and E are arranged in a circular array network with pyramid combination unit O as the center.

Claims

1. A method for parabolic surface partitioning based on decagonal and hexagonal heterogeneous module networking, characterized in that: The method comprises the following steps, S1: constructing a composite profile division unit composed of regular decagon, regular hexagon and isosceles trapezoid in a two-dimensional plane of a top view perspective; S2: dividing a two-dimensional plan view of a parabolic surface formed by the deployable antenna mechanism by using the composite profile division unit to obtain a divided combined pattern having the characteristics of regular decagon, regular hexagon and isosceles trapezoid, and establishing a coordinate system xoy at the center position of the combined pattern; S3: calculating the side length of the polygon in the composite profile division unit based on the caliber of the composite profile division unit set in advance, calculating the coordinates of the center point of the polygon of all composite profile division units in the coordinate system xoy based on the side length of the polygon, and obtaining the center point coordinates of the polygon; S4: using the rotation coordinate transformation method to construct a transformation equation based on the angle relationship between the polygon nodes and the center points of the polygon, calculating the polygon node coordinates based on the transformation equation and the polygon center point coordinates obtained in step S3; calculating the three-dimensional node coordinates of the polygon node coordinates in the three-dimensional coordinate system xyz based on the parameter equation of the parabolic surface set in advance , wherein f refers to the focal length of the parabolic surface; S5: based on the curvature and the parametric equation of the parabolic surface The parabolic surface of the deployable antenna mechanism in the three-dimensional space is obtained by curve fitting and connecting the three-dimensional node coordinates obtained in step S4. S6: based on the parabolic surface in the three-dimensional space obtained in step S5, constructing a pyramid combination unit composed of a five-pyramid basic deployable unit and a four-pyramid basic deployable unit, and obtaining the three-dimensional node coordinates of the regular hexagon and the isosceles trapezoid, which indicate the center point of the bottom center node disc of the deployable antenna mechanism, and the length of the connecting line between adjacent three-dimensional node coordinates, which indicates the length of the rod of the deployable antenna mechanism.

2. The deployable antenna mechanism based on decagon and hexagon isomerous module networking of claim 1, characterized in that: The deployable antenna mechanism is composed of a plurality of pyramid combination units in a networking manner; the pyramid combination unit comprises one ten-pyramid basic deployable unit and five six-pyramid basic deployable units which are annularly arranged and movably connected to the outer periphery of the ten-pyramid basic deployable unit, and adjacent two six-pyramid basic deployable units are movably connected through a foldable connecting rod; the orthographic projection of the bottom surface of the ten-pyramid basic deployable unit forms a regular decagon (1), the orthographic projection of the bottom surface of the six-pyramid basic deployable unit forms a regular hexagon (2), and the side length of the regular decagon (1) is equal to that of the regular hexagon (2); the orthographic projection of the bottom surface of the pyramid combination unit forms a ring-shaped closed structure, and the ring-shaped closed structure is composed of the regular decagon (1) at the center position, five regular hexagons (2) annularly arranged at the outer periphery of the regular decagon (1), and five isosceles trapezoids (3) annularly arranged at the outer periphery of the regular decagon (1); the regular hexagons (2) and the isosceles trapezoids (3) are arranged alternately, one side of the five regular hexagons (2) coincides with the side of the regular decagon (1), one side of the isosceles trapezoid (3) coincides with the side of the regular decagon (1), and the opposite two sides of the isosceles trapezoid (3) respectively coincide with the sides of the adjacent two regular hexagons (2).

3. The deployable antenna mechanism based on decagonal and hexagonal isomorphic module networking of claim 2, wherein: The ten-prism basic developable unit comprises ten bottom center node discs (4) respectively located at ten vertices of the regular decagon (1), ten first lower center node disc folding linkage rods (5) respectively located at ten sides of the regular decagon (1), a top center node disc (6) located directly above the center point of the regular decagon (1), and ten side edges (7) respectively connected between the top center node disc (6) and the corresponding bottom center node disc (4) through revolute pairs. The two ends of the first lower center node disc folding linkage rod (5) are respectively connected with two adjacent bottom center node discs (4) through revolute pairs. The ten first lower center node disc folding linkage rods (5) are synchronously folded and link the top center node disc (6) and the bottom center node disc (4) to move towards the center point, and are folded into a conical table structure with the ten side edges (7) surrounding the outer periphery of the ten side edges (7).

4. The deployable antenna mechanism based on decagonal and hexagonal isomorphic module networking of claim 3, wherein: The six-prism basic developable unit comprises six bottom center node discs (4) respectively located at six vertices of the regular hexagon (2), six first lower center node disc folding linkage rods (5) respectively located at six sides of the regular hexagon (2), a top center node disc (6) located directly above the center point of the regular hexagon (2), and six side edges (7) respectively connected between the top center node disc (6) and the corresponding bottom center node disc (4) through revolute pairs. The two ends of the first lower center node disc folding linkage rod (5) are respectively connected with two adjacent bottom center node discs (4) through revolute pairs. The six first lower center node disc folding linkage rods (5) are synchronously folded and link the top center node disc (6) and the bottom center node disc (4) to move towards the center point, and are folded into a conical structure with the six side edges (7) surrounding the outer periphery of the six side edges (7).

5. The deployable antenna mechanism based on decagonal and hexagonal isomorphic module networking of claim 4, wherein: The connecting rod comprises five upper center node disc folding linkage rods (8) and five second lower center node disc folding linkage rods (9). The upper center node disc folding linkage rod (8) is connected between the top center node discs (6) of two adjacent six-prism developable basic units through a revolute pair. The five second lower center node disc folding linkage rods (9) are respectively located on the sides of the five isosceles trapezoids (3) which are not shared with the regular decagon (1) and the regular hexagon (2). The two ends of the second lower center node disc folding linkage rod (9) are respectively connected with the bottom center node discs (4) of two adjacent six-prism developable basic units through revolute pairs.

6. The deployable antenna mechanism based on decagonal and hexagonal isomorphic module networking of claim 5, wherein: The folding directions of all the first lower central node plate folding linkage rods (5) and the five second lower central node plate folding linkage rods (9) are consistent and face the parabolic surface; the folding direction of the upper central node plate folding linkage rod (8) is opposite to that of the first lower central node plate folding linkage rod (5); the five upper central node plate folding linkage rods (8), the thirty-five first lower central node plate folding linkage rods (5) and the five second lower central node plate folding linkage rods (9) are synchronously folded and link the top central node plate (6) and the bottom central node plate (4) to converge towards the center point, and are folded into a cylindrical structure of fifteen first lower central node plate folding linkage rods (5) and five second lower central node plate folding linkage rods (9) located at the outermost layer, the remaining twenty first lower central node plate folding linkage rods (5) and thirty side edges (7) of the hexagonal pyramid basic deployable unit located at the middle layer, and ten side edges (7) of the ten-pyramid basic deployable unit located at the innermost layer.

7. The deployable antenna mechanism based on decagonal and hexagonal isomorphic module networking of claim 6, wherein: When the pyramid combination unit is fully unfolded, the top central node plates (6) of the ten-pyramid basic deployable unit and the hexagonal pyramid basic deployable unit are at different heights.

8. The deployable antenna mechanism based on decagonal and hexagonal isomorphic module networking of claim 4, wherein: When the pyramid combination unit is fully unfolded, a parabolic surface is formed, each bottom central node plate (4) falls on the parabolic surface, and the parametric equation of the parabolic surface is as follows: Where x, y and z form a three-dimensional coordinate system, and f is the focal length of the parabolic surface.

9. The deployable antenna mechanism based on decagonal and hexagonal isomorphic module networking of claim 2, wherein: The ratio of the space volume occupied by the pyramid combination unit when fully unfolded to the space volume occupied by the pyramid combination unit when fully folded is the folding rate, and the calculation formula of the folding rate is as follows: Where V0 is the volume of the pyramid combination unit when fully unfolded, D0 is the diameter of the envelope circle of the central node plate of the reflecting surface when the pyramid combination unit is fully unfolded, d0 is the diameter of the envelope circle of the central node plate of the back frame when the pyramid combination unit is fully unfolded, h0 is the vertical distance between the central node plate of the reflecting surface and the central node plate of the back frame when the pyramid combination unit is fully unfolded; V1 is the volume of the pyramid combination unit when fully folded, D1 is the diameter of the envelope circle of the central node plate of the reflecting surface when the pyramid combination unit is fully folded, d1 is the diameter of the envelope circle of the central node plate of the back frame when the pyramid combination unit is fully folded, and h0 is the vertical distance between the central node plate of the reflecting surface and the central node plate of the back frame when the pyramid combination unit is fully folded.

10. The deployable antenna mechanism based on decagonal and hexagonal isomorphic module networking of claim 2, wherein: A plurality of the pyramid combination units, one of which is selected as a central combination unit, and the remaining pyramid combination units are arranged in a circular array according to the number of regular hexagons (2) in the central combination unit, and one edge of a regular hexagon (2) on the periphery of the remaining pyramid combination units coincides with one edge of a regular hexagon (2) on the periphery of the central combination unit.

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