CN114628879A - Spatial foldable array device with two expansion forms of plane and curved surface - Google Patents

Spatial foldable array device with two expansion forms of plane and curved surface Download PDF

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Publication number
CN114628879A
CN114628879A CN202210269710.9A CN202210269710A CN114628879A CN 114628879 A CN114628879 A CN 114628879A CN 202210269710 A CN202210269710 A CN 202210269710A CN 114628879 A CN114628879 A CN 114628879A
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unfolding
annular
folding
units
foldable
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CN114628879B (en
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黄海林
邬金杉
王森
李兵
刘荣强
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Shenzhen Graduate School Harbin Institute of Technology
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Shenzhen Graduate School Harbin Institute of Technology
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    • HELECTRICITY
    • H01ELECTRIC ELEMENTS
    • H01QANTENNAS, i.e. RADIO AERIALS
    • H01Q1/00Details of, or arrangements associated with, antennas
    • H01Q1/08Means for collapsing antennas or parts thereof
    • HELECTRICITY
    • H01ELECTRIC ELEMENTS
    • H01QANTENNAS, i.e. RADIO AERIALS
    • H01Q1/00Details of, or arrangements associated with, antennas
    • H01Q1/08Means for collapsing antennas or parts thereof
    • H01Q1/081Inflatable antennas
    • HELECTRICITY
    • H01ELECTRIC ELEMENTS
    • H01QANTENNAS, i.e. RADIO AERIALS
    • H01Q1/00Details of, or arrangements associated with, antennas
    • H01Q1/08Means for collapsing antennas or parts thereof
    • H01Q1/085Flexible aerials; Whip aerials with a resilient base
    • HELECTRICITY
    • H01ELECTRIC ELEMENTS
    • H01QANTENNAS, i.e. RADIO AERIALS
    • H01Q15/00Devices for reflection, refraction, diffraction or polarisation of waves radiated from an antenna, e.g. quasi-optical devices
    • H01Q15/14Reflecting surfaces; Equivalent structures
    • H01Q15/16Reflecting surfaces; Equivalent structures curved in two dimensions, e.g. paraboloidal
    • H01Q15/161Collapsible reflectors
    • HELECTRICITY
    • H01ELECTRIC ELEMENTS
    • H01QANTENNAS, i.e. RADIO AERIALS
    • H01Q15/00Devices for reflection, refraction, diffraction or polarisation of waves radiated from an antenna, e.g. quasi-optical devices
    • H01Q15/14Reflecting surfaces; Equivalent structures
    • H01Q15/16Reflecting surfaces; Equivalent structures curved in two dimensions, e.g. paraboloidal
    • H01Q15/161Collapsible reflectors
    • H01Q15/163Collapsible reflectors inflatable
    • HELECTRICITY
    • H01ELECTRIC ELEMENTS
    • H01QANTENNAS, i.e. RADIO AERIALS
    • H01Q15/00Devices for reflection, refraction, diffraction or polarisation of waves radiated from an antenna, e.g. quasi-optical devices
    • H01Q15/14Reflecting surfaces; Equivalent structures
    • H01Q15/18Reflecting surfaces; Equivalent structures comprising plurality of mutually inclined plane surfaces, e.g. corner reflector
    • H01Q15/20Collapsible reflectors
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02SGENERATION OF ELECTRIC POWER BY CONVERSION OF INFRARED RADIATION, VISIBLE LIGHT OR ULTRAVIOLET LIGHT, e.g. USING PHOTOVOLTAIC [PV] MODULES
    • H02S20/00Supporting structures for PV modules
    • H02S20/30Supporting structures being movable or adjustable, e.g. for angle adjustment
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02SGENERATION OF ELECTRIC POWER BY CONVERSION OF INFRARED RADIATION, VISIBLE LIGHT OR ULTRAVIOLET LIGHT, e.g. USING PHOTOVOLTAIC [PV] MODULES
    • H02S30/00Structural details of PV modules other than those related to light conversion
    • H02S30/20Collapsible or foldable PV modules
    • YGENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02EREDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E10/00Energy generation through renewable energy sources
    • Y02E10/50Photovoltaic [PV] energy

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  • Electromagnetism (AREA)
  • Toys (AREA)
  • Aerials With Secondary Devices (AREA)

Abstract

The invention provides a space foldable array device with two unfolding forms of a plane and a curved surface, which comprises a central base, a plurality of annular foldable units which are mutually nested, a substrate for carrying the plurality of annular foldable units and a flexible part for providing support and drive, wherein the central base is provided with a plurality of annular foldable units; the annular folding and unfolding units are single-degree-of-freedom paper folding mechanisms and comprise a plurality of identical quadrilateral folding and unfolding bodies, the closed quadrilateral folding and unfolding bodies are distributed in an annular array mode and are arranged in a ridge and valley staggered arrangement mode, and the corresponding quadrilateral folding and unfolding bodies in the annular folding and unfolding units are arranged in a ridge and valley staggered arrangement mode in the radial direction; the flexible part is arranged on the lower side of the substrate and is simultaneously connected with the corresponding quadrilateral folding and unfolding bodies in the plurality of annular folding and unfolding units, and an air passage in the radial direction is arranged in the flexible part; the invention can be correspondingly used in a plane configuration or a curved surface configuration according to different use requirements, and has the characteristics of multiple purposes, strong flexibility and the like.

Description

Spatial foldable array device with two expansion forms of plane and curved surface
Technical Field
The invention belongs to the technical field of space foldable and expandable mechanisms, and particularly relates to a space foldable and expandable array device with two expansion forms of a plane and a curved surface.
Background
The spatial foldable array has two types of plane type and curved surface type, the plane type foldable array forms a large plane after being unfolded and can be used for a solar cell array or a plane antenna array, the curved surface type foldable array forms a three-dimensional film structure after being unfolded, and the three-dimensional film structure can form a parabolic surface, a spherical surface and other spatial curved surfaces and can be used as a feedback type antenna reflecting surface.
The traditional curved surface foldable and unfoldable mechanism has the defects of complex structure, large folding volume and fixed folding and unfolding ratio, and cannot meet higher application requirements; meanwhile, the folding and unfolding mechanism in the prior art cannot realize two unfolding forms of a plane and a curved surface at the same time.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a space foldable array device with two unfolding states of a plane and a curved surface, which can be correspondingly used in a plane configuration or a curved surface configuration according to different use requirements and has the characteristics of multiple purposes, strong flexibility and the like.
In order to achieve the above object, the present invention provides a spatial foldable array device with two unfolding forms of a plane and a curved surface, comprising a central base, a plurality of annular foldable units nested with each other, a substrate for carrying the plurality of annular foldable units, and a flexible member for providing support and drive;
the annular folding and unfolding units are single-degree-of-freedom paper folding mechanisms and comprise a plurality of identical quadrilateral folding and unfolding bodies, the closed quadrilateral folding and unfolding bodies are distributed in an annular array mode and are arranged in a ridge and valley staggered arrangement mode, and the corresponding quadrilateral folding and unfolding bodies in the annular folding and unfolding units are arranged in a ridge and valley staggered arrangement mode in the radial direction;
the substrate is a flexible film which can be folded, unfolded and deformed along with the annular folding and unfolding unit;
the flexible part is arranged on the lower side of the substrate and is simultaneously connected with the corresponding quadrilateral folding and unfolding bodies in the plurality of annular folding and unfolding units, and an air passage in the radial direction is arranged in the flexible part;
through aerifing in the air flue, the flexible piece expands in radial direction in order to push away a plurality of annular folding and unfolding units, and a plurality of annular folding and unfolding units expand in step around central base until being in plane development form simultaneously, and wherein, when a plurality of annular folding and unfolding units are in plane development form, through continuing to aerify to the air flue, the below side of flexible piece is long along its axial makes the flexible piece wholly upwards crooked, makes a plurality of annular folding and unfolding units upwards crooked and be in curved surface development form.
As another specific embodiment of the present invention, the central base is a regular prism, and the number of the side lengths of the bottom surface of the central base is the same as the number of the quadrilateral folding bodies in the annular folding and unfolding unit.
As another embodiment of the present invention, the plurality of annular folding units are configured using a Miura-ori paper folding structure.
As another specific embodiment of the invention, the number of the flexible parts is two or more, and the two or more flexible parts are arranged at intervals.
As another specific embodiment of the invention, the central base is provided with an air inlet channel, and the air channel in the flexible part is communicated with the air inlet channel.
As another specific embodiment of the invention, the central base is provided with an annular groove, the air inlet channel is communicated with the air passage through an air pipe, and the air pipe penetrates through the annular groove and can slide in the annular groove.
As another embodiment of the invention, the pliable component is bonded to the underside of the substrate.
As another embodiment of the present invention, a gap for keeping the annular folding and unfolding units from deforming when the annular folding and unfolding units are bent is provided between adjacent annular folding and unfolding units.
The invention has the following beneficial effects:
the invention can be further deformed into a curved surface configuration on the basis of the expansion of the annular plane, has more flexible use modes according to different use scenes, realizes multiple expansion modes on the same array structure, can correspondingly use the plane configuration or the curved surface configuration according to different use requirements, and has the characteristics of multiple purposes, strong flexibility and the like.
The invention can be folded into a smaller volume, saves transportation space, can be unfolded into a large-area plane or curved surface according to different requirements when unfolded, and can be applied to a plane solar cell array, a curved surface antenna or a curved surface reflector of a satellite and the like.
The present invention will be described in further detail with reference to the accompanying drawings.
Drawings
FIG. 1 is a schematic model of example 1 of the apparatus of the present invention;
FIG. 2 is a crease profile of a substrate of example 1 of the apparatus of the present invention;
FIG. 3 is a schematic diagram of the structure of the central base of embodiment 1 of the apparatus of the present invention;
FIG. 4 is a schematic view of the apparatus of embodiment 1 of the present invention in a folded state;
FIG. 5 is a schematic illustration of the deployment process of embodiment 1 of the apparatus of the present invention;
FIG. 6 is a schematic illustration of embodiment 1 of the apparatus of the present invention in a flat, expanded state;
FIG. 7 is a schematic view of embodiment 1 of the apparatus of the present invention in a curved deployed state;
FIG. 8 is a schematic representation of the configuration of the apparatus of example 1 of the present invention using the Miura-ori paper structure;
FIG. 9 is a schematic view showing the "one-dot-four-wire" unwinding motion in example 1 of the apparatus of the present invention;
FIG. 10 is a schematic representation of the dihedral angle relationship during deployment in example 1 of the apparatus of the present invention.
Detailed Description
In order that the above objects, features and advantages of the present invention can be more clearly understood, a more particular description of the invention will be rendered by reference to the appended drawings. It should be noted that the embodiments and features of the embodiments of the present application may be combined with each other without conflict.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, however, the present invention may be practiced otherwise than as specifically described herein and, therefore, the scope of the present invention is not limited by the specific embodiments disclosed below.
Example 1
The invention provides a space foldable array device with two unfolding forms of a plane surface and a curved surface, which comprises a central base 100, a plurality of annular foldable units 200 nested with each other, a substrate 300 for carrying the plurality of annular foldable units 200 and a flexible member 400 for providing support and driving, as shown in fig. 1-7.
The annular folding and unfolding units 200 are single-degree-of-freedom paper folding mechanisms and comprise a plurality of identical quadrilateral folding and unfolding bodies 201, specifically sixteen closed quadrilateral folding and unfolding bodies 201 are distributed in an annular array mode and are arranged in a ridge and valley staggered arrangement mode at the same time, the number of the annular folding and unfolding units 200 is three, and the corresponding quadrilateral folding and unfolding bodies 201 in the three annular folding and unfolding units 200 are arranged in a ridge and valley staggered arrangement mode in the radial direction.
Further, the central base 100 is embodied as a regular prism, for example, a sixteen prism, and the number of the side lengths of the bottom surface of the central base 100 is the same as the number of the quadrangular folding bodies 201 in the annular folding unit 200, for example, as shown in fig. 3.
Specifically, the substrate 300 is a flexible film that can be folded, unfolded and deformed along with the annular folding and unfolding unit 200;
the flexible element 400 is disposed on the lower side of the substrate 300 and simultaneously connects the corresponding quadrilateral folding bodies 201 in the plurality of annular folding units 200, that is, the corresponding quadrilateral folding bodies 201 in the three annular folding units 200 in the radial direction share one flexible element 400, and preferably, the flexible element 400 is adhered on the lower side of the substrate 300.
In the flexible member 400, an air passage 401 is provided in a radial direction.
Wherein the three ring-shaped folding and unfolding units 200 in the folded state are folded in a zigzag shape.
By inflating the air duct 401, the flexible member 400 expands in the radial direction to push the plurality of annular folding units 200 open, and simultaneously the plurality of annular folding units 200 are unfolded around the central base 100 until they are in the planar unfolded state, as shown in fig. 6, at which time, the inflation of the air duct 401 is stopped, the pressure inside the air duct 401 is maintained, and at this time, the air duct 401 can serve as a support mechanism for the annular folding units 200, so that the planar configuration is maintained.
When the plurality of annular folded units 200 are in the planar unfolded state, the air duct 401 is continuously inflated, and the inner side of the air duct 201 is bonded to the substrate 300 and cannot be deformed in the axial direction, so that the lower side of the flexible member 400 is increased in the axial direction to bend the flexible member 400 upward as a whole, and the plurality of annular folded units 200 are bent upward and are in the curved unfolded state by the flexibility of the substrate 300, as shown in fig. 7.
Still further, the number of the flexible members 400 is two or more, for example sixteen, and the sixteen flexible members 400 are arranged at intervals, and when the flexible members 400 are unfolded to be a plane, the sixteen flexible members 400 are in a spoke shape of a wheel.
In the embodiment, the central base 100 is provided with an air inlet passage 101, the air passage 401 in the flexible member 400 is communicated with the air inlet passage 101, the central base 100 is provided with an annular groove 102, the air inlet passage 101 is communicated with the air passage 401 through an air pipe (not shown in the figure), the air pipe passes through the annular groove 102 and can slide in the annular groove, and correspondingly, equipment such as an air pump and the like is arranged in the air inlet passage 101 to provide an air source.
Wherein, the flexible member 400 can be connected with the central base 100 in a movable fit manner to provide support for the plurality of annular folding units 200.
In this embodiment, a gap (not shown) for keeping the annular folding and unfolding units 200 from deforming when the annular folding and unfolding units 200 are bent is formed between adjacent annular folding and unfolding units 200, and the flexible member 400 is continuously inflated on the basis that the plurality of annular folding and unfolding units 200 are unfolded in a plane, and the flexible member 400 cannot deform in the axial direction because the flexible member 400 is bonded to the substrate 300, and the outer side of the flexible member can grow in the axial direction, so that the flexible member 400 deforms in an upward bending manner; because the gaps are formed between the annular folding units 200 and the substrate 300 is a flexible film, the deformation generated in the bending deformation process is accumulated in the substrate 300 in the gaps of the annular folding units 200, so that the annular folding units 200 can be ensured not to deform in the bending state.
A specific folding manner of the plurality of annular folding units in this embodiment is shown in fig. 8 to 10, specifically: the plurality of annular folding units are configured by a Miura-ori folding paper structure, and the crease distribution of only partial annular areas is shown in figure 8, so that the crease distribution design can be carried out on all the annular areas.
The peripheral crease is overlapped with the side length of the polygon, the radial crease and the radius direction form an alpha included angle, but the difference is that the alpha angle of each ring takes different values in order to meet the plane folding rule.
For judging whether the folding method is plane folding, the following two rules are provided:
(1)|Nm-Nv|=2,Nmand NVThe number of the folded ridges and the folded valleys at the same node respectively;
(2) for the folding method of one point and four lines, the theorem of voltage is satisfied, namely the sum of the opposite angles is equal.
When one of the nodes O is analyzed, the broken lines of the nodes O are 3 ridges and 1 valley, and obviously, the rule (1) is satisfied.
For rule (2), the angle AOD + angle BOC needs to be equal to angle COD + angle AOB, namely angle BOC-angle COD is equal to angle AOB-angle AOD.
For folding unit blocks OAFD, let alpha be less than AFDmEasy to verify:
∠AOD=βm=αm+θ (2-1)
∠OAE=∠OEA=αm (2-2)
∠BOE=βm (2-3)
then the angle AOE is equal to pi-2 alpham,∠AOB-∠AOD=π-2αm
And because the angle AOD plus the angle COD plus the angle BOC plus the angle AOB is 2 pi
Then ═ BOC ═ pi-alpham-1-2θ,∠BOC-∠COD=π-2αm-1-2θ
Obviously, when alpha ism-1=αmθ, rule (2) is satisfied.
In the same way have alpham-2=αm-1Theta, and so on, the alpha of each layer can be obtainedi
The following description will be made by taking the most basic "one-dot-four-line" unfolding motion as an example, and the dihedral angle relationship during the unfolding motion of the circular film-folded paper structure based on the Miura-ori can be generalized by the dihedral angle relationship of the single unit, and the unit shown in FIG. 9 can be regarded as a link mechanism with a link length of 0, wherein the unfolding unit should satisfy the most basic plane folding rule, i.e., α12、α23、α34、α14Satisfies alpha1234=α2314Phi, and the dihedral angle of the rigid surface has a certain relationship with the rotation angle of the link mechanism1=π-θ1、φ2=π-θ2、φ3=π-θ3、φ4=π+θ4
According to the conditions:
Figure BDA0003554140710000071
the two paths 1-2-3 and 1-4-3 are used to switch the revolute joint 1 to the revolute joint 3, that is:
1T2·2T31T4·4T3 (2-5)
the same principle is as follows:
1T2·2T3·3T41T4 (2-6)
2T3·3T42T1·1T4 (2-7)
2T1·1T4·4T32T3 (2-8)
the joint type (2-4), the formula (2-5), the formula (2-6), the formula (2-7), and the formula (2-8) can be obtained:
Figure BDA0003554140710000072
Figure BDA0003554140710000073
Figure BDA0003554140710000074
Figure BDA0003554140710000075
at theta3Assigning values to arguments, e.g. setting alpha12=65°、α23Calculate θ at 85 °1、θ2And theta4The results are shown in FIG. 10.
As can be seen from FIG. 10, during the deployment, θ1=θ2,θ2=θ4And θ3And theta2Satisfying the formula (2-11). At the same time, when θ is known3The other three angles can be obtained, namely, the degree of freedom of the 'one-point four-line' unit is 1.
Since the annular film ori-based annular film folded paper structure is formed by splicing and combining a plurality of 'one-point-four-line' units along the circumferential direction and the radial direction, and the adjacent 'one-point-four-line' units all have a common dihedral angle, namely, when the angle of one dihedral angle is known, the angles of all the other dihedral angles can be calculated, and therefore, the degree of freedom of the annular film ori-based annular folded paper structure is 1.
The above is not relevant and is applicable to the prior art.
Although the present invention has been described with reference to the preferred embodiments, it is not intended to limit the scope of the invention. It will be appreciated by those skilled in the art that changes may be made without departing from the scope of the invention, and it is intended that all matter contained in the above description or shown in the accompanying drawings shall be interpreted as illustrative and not in a limiting sense.

Claims (8)

1. A space foldable array device with two unfolding forms of a plane and a curved surface is characterized by comprising a central base, a plurality of annular foldable units which are nested with each other, a substrate for carrying the annular foldable units and a flexible piece for providing support and driving;
the annular folding and unfolding units are single-degree-of-freedom paper folding mechanisms and comprise a plurality of same quadrilateral folding and unfolding bodies, the closed quadrilateral folding and unfolding bodies are distributed in an annular array mode and are arranged in a ridge and valley staggered arrangement mode, and the corresponding quadrilateral folding and unfolding bodies in the annular folding and unfolding units are arranged in a ridge and valley staggered arrangement mode in the radial direction;
the substrate is a flexible film which can be folded, unfolded and deformed along with the annular folding and unfolding unit;
the flexible part is arranged on the lower side of the substrate and is simultaneously connected with the corresponding quadrilateral folding and unfolding bodies in the annular folding and unfolding units, and an air passage along the radial direction is arranged in the flexible part;
and when the annular folding and unfolding units are in the plane unfolding state, the lower side of the flexible piece grows along the axial direction of the flexible piece to enable the flexible piece to be integrally bent upwards, so that the annular folding and unfolding units are bent upwards and are in a curved surface unfolding state.
2. The spatial foldable array apparatus with two unfolding configurations of plane and curved surfaces as claimed in claim 1, wherein said central base is a regular prism, and the number of the bottom side length of said central base is the same as the number of said quadrangular foldable bodies in said annular foldable unit.
3. A space foldable array apparatus having two unfolding configurations, a plane and a curved surface, as claimed in claim 1, wherein a plurality of said annular folding units are configured using a Miura-ori paper folding structure.
4. A space foldable array apparatus according to claim 1, wherein the number of the flexible members is two or more, and the two or more flexible members are spaced apart.
5. The array of claim 4, wherein the central base has an air inlet channel, and the air passage in the flexible member is in communication with the air inlet channel.
6. A space foldable array apparatus having two unfolded configurations, planar and curved, as claimed in claim 5, wherein said central base has an annular groove, said air inlet channel is in communication with said air passage through an air tube, said air tube passing through said annular groove and being slidable therein.
7. A collapsible spatial array device having both planar and curved deployment configurations as claimed in claim 1 wherein said flexible member is bonded to the underside of said substrate.
8. The spatial foldable array device with two unfolding configurations, namely a plane and a curved surface, as claimed in claim 1, wherein a gap for keeping the annular foldable units from deforming when bending is arranged between adjacent annular foldable units.
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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115848655A (en) * 2023-02-17 2023-03-28 中国人民解放军军事科学院国防科技创新研究院 Multistable smooth control system
US11791563B1 (en) * 2022-04-24 2023-10-17 Xidian University Deployable mesh antenna based on dome-type tensegrity

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Publication number Priority date Publication date Assignee Title
CN101853986A (en) * 2010-05-24 2010-10-06 哈尔滨工业大学 Manufacturing methods of inflatable deployable antenna reflecting surface based on shape memory polymer and reflecting surface film and skin thereof
CN102110867A (en) * 2011-01-16 2011-06-29 浙江大学 Spherical land-based inflatable antenna
CN106785305A (en) * 2016-11-23 2017-05-31 上海卫星工程研究所 A kind of space cylindro-parabolic thin plate antenna based on inflatable structure
JP2020012381A (en) * 2018-07-13 2020-01-23 日本電産株式会社 Impeller
CN113638498A (en) * 2021-05-31 2021-11-12 东南大学 Double-layer foldable film structure based on generalized Miura folded paper

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101853986A (en) * 2010-05-24 2010-10-06 哈尔滨工业大学 Manufacturing methods of inflatable deployable antenna reflecting surface based on shape memory polymer and reflecting surface film and skin thereof
CN102110867A (en) * 2011-01-16 2011-06-29 浙江大学 Spherical land-based inflatable antenna
CN106785305A (en) * 2016-11-23 2017-05-31 上海卫星工程研究所 A kind of space cylindro-parabolic thin plate antenna based on inflatable structure
JP2020012381A (en) * 2018-07-13 2020-01-23 日本電産株式会社 Impeller
CN113638498A (en) * 2021-05-31 2021-11-12 东南大学 Double-layer foldable film structure based on generalized Miura folded paper

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US11791563B1 (en) * 2022-04-24 2023-10-17 Xidian University Deployable mesh antenna based on dome-type tensegrity
CN115848655A (en) * 2023-02-17 2023-03-28 中国人民解放军军事科学院国防科技创新研究院 Multistable smooth control system

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