CN117709071A - Method and system for constructing compact space folding array model based on three-pump folding paper - Google Patents
Method and system for constructing compact space folding array model based on three-pump folding paper Download PDFInfo
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Abstract
本发明涉及折展模型构建技术领域,具体公开一种基于三浦折纸的紧凑空间折展阵列模型构建方法及系统,该方法包括:基于四组相同的三浦折纸,构建零厚度折纸模型;对所述零厚度折纸模型进行厚板化处理,得到厚板化的折展阵列模型;根据所述厚板化的折展阵列模型的构型,设计四连杆联动装置,并利用所述四连杆联动装置,将所述厚板化的折展阵列模型的自由度从5调整至1,得到紧凑空间折展阵列模型。本发明所构建的折展阵列模型适用于各种需要大面积平面阵列的航天器,并具有高空间利用率与高折展比,能够有效降低太空任务的成本。
The present invention relates to the technical field of folding model construction, and specifically discloses a compact space folding array model construction method and system based on Miura origami. The method includes: building a zero-thickness origami model based on four groups of identical Miura origami; The zero-thickness origami model is processed into a thickened plate to obtain a thickened folding array model; according to the configuration of the thickened folding array model, a four-link linkage device is designed, and the four-linkage linkage is used The device adjusts the degree of freedom of the thickened folding array model from 5 to 1 to obtain a compact space folding array model. The folding array model constructed by the present invention is suitable for various spacecrafts that require large-area planar arrays, has high space utilization and high folding ratio, and can effectively reduce the cost of space missions.
Description
技术领域Technical field
本发明涉及折展模型构建技术领域,尤其涉及一种基于三浦折纸的紧凑空间折展阵列模型构建方法及系统。The present invention relates to the technical field of folding and unfolding model construction, and in particular to a compact space folding and unfolding array model construction method and system based on Miura origami.
背景技术Background technique
从空间太阳能利用到卫星通信,从空间站建设到深空探测任务,可展开结构在航天工程中发挥着愈发重要的作用。在各类可展开结构中,刚性厚板折纸机构因为其动力学建模方便、运动自由度少、型面精度高、展开过程中和展开后具有良好的刚性和稳定性等优势,近年来备受研究人员关注,具有广阔的应用前景和设计潜力。刚性厚板折纸机构继承了数学上理想零厚度折纸模型的两个特征性质:等距性,即面板上两点之间的最短距离不会随着折叠改变,在工程上体现为面板在设计载荷下的变形可以忽略不计;单射性,即在折叠过程中面板之间不能发生相交。在这样的假设下,面板只允许沿折痕线转动。然而与零厚度折纸模型不同的是,刚性厚板折纸机构认为面板具有有限厚度,直接套用零厚度折纸模型的运动形式可能会造成物理干涉。因此,刚性厚板折纸机构通常是在零厚度折纸图案的基础上应用合适的厚板化技术得到的。例如Resch折纸、Flasher折纸、Waterboom折纸和三浦折纸。具体地:From space solar energy utilization to satellite communications, from space station construction to deep space exploration missions, deployable structures play an increasingly important role in aerospace engineering. Among various types of deployable structures, rigid thick plate origami mechanisms have been developed in recent years due to their advantages such as convenient dynamic modeling, less freedom of movement, high surface accuracy, and good rigidity and stability during and after deployment. It has attracted the attention of researchers and has broad application prospects and design potential. The rigid thick plate origami mechanism inherits two characteristic properties of the mathematically ideal zero-thickness origami model: isometricity, that is, the shortest distance between two points on the panel does not change with folding, which is reflected in the design load of the panel in engineering The deformation under is negligible; injectivity, that is, no intersection between panels can occur during the folding process. Under this assumption, the panel is only allowed to rotate along the crease line. However, unlike the zero-thickness origami model, the rigid thick-plate origami mechanism considers the panel to have a limited thickness, and directly applying the motion form of the zero-thickness origami model may cause physical interference. Therefore, rigid thick plate origami mechanisms are usually obtained by applying appropriate thick plate technology on the basis of zero-thickness origami patterns. For example, Resch origami, Flasher origami, Waterboom origami and Miura origami. specifically:
1)畅博彦等人基于三浦折纸图案构造出两种厚板折展单元——Bennett机构单元和球面四杆机构单元,在保证机构可以从展开状态运动到收拢状态且不发生物理干涉的前提下,以折展单元可无限次叠加组网为设计目标,分析构件几何参数应满足的约束条件,阐述模块化组成大尺度厚板三浦折展机构的原理和过程,提出Bennett组网和混合组网两种模块扩展方式。使用该模型设计的空间大型可展太阳翼安装在航天器两侧。在展开平面内,完全收合与展开两种状态下单个太阳翼的尺寸分别为1.07m×0.144m和1.9m×5.2m,太阳翼展开后的总工作面积为18.34m2,折展比为60。然而,该模型存在以下缺点:1) Chang Boyan and others constructed two thick plate folding and unfolding units based on Miura origami patterns - Bennett mechanism unit and spherical four-bar mechanism unit, on the premise of ensuring that the mechanism can move from the unfolded state to the collapsed state without physical interference. , with the design goal that the folding and unfolding units can be stacked infinitely, analyze the constraints that the geometric parameters of the components should meet, explain the principles and processes of modularly forming large-scale thick plate Miura folding and unfolding mechanisms, and propose Bennett networking and hybrid networking Two module expansion methods. Large-scale deployable solar wings designed using this model are installed on both sides of the spacecraft. In the unfolded plane, the dimensions of a single solar wing in the fully folded and unfolded states are 1.07m×0.144m and 1.9m×5.2m respectively. The total working area of the solar wing after unfolding is 18.34m2, and the folding ratio is 60 . However, this model suffers from the following shortcomings:
①外形不规则:在该模型中,折叠后的太阳翼模块大致呈扁长的梯形柱状,并以长边方向挂载在航天器两侧。航天器整体外形凹凸不平且长边方向远大于其他两边,这为运输与装载带来了困难。①Irregular shape: In this model, the folded solar wing module is roughly in the shape of a long and flat trapezoidal column, and is mounted on both sides of the spacecraft in the long-side direction. The overall shape of the spacecraft is uneven and its long side is much larger than the other two sides, which makes transportation and loading difficult.
②空间利用率低:在该模型中,研究人员使用太阳翼本身的展开面积和折叠面积来计算折展比,这种算法缺乏实际意义。因为发射过程中太阳翼与航天器主体是连接在一起的,所以应该计算二者总体积。而该方案中航天器不规则的整体外形导致,装载时无论选择何种形状的包络几何体,都会造成很大比例的运输空间被浪费。这与折展机构的根本目的是相悖的。② Low space utilization: In this model, researchers use the unfolded area and folded area of the solar wing itself to calculate the folding ratio. This algorithm lacks practical significance. Because the solar wing and the main body of the spacecraft are connected together during the launch process, the total volume of the two should be calculated. The irregular overall shape of the spacecraft in this plan results in a large proportion of transportation space being wasted no matter what shape of envelope geometry is chosen during loading. This is contrary to the fundamental purpose of the folding and unfolding mechanism.
2)Zirbel等人与Bolanos等人对Flasher折纸进行了厚板化,成功创建了具有高折展面积比和高折展直径比的折展阵列模型。Flasher折纸在展开后形成规则的正多边形,折叠后则可以紧密地包裹在一个圆柱体中,非常适合应用于空间成本高昂的航天领域。目前,该模型已被用于NASA系外行星探测任务中的遮星罩设计。然而,该模型存在以下缺点:2) Zirbel et al. and Bolanos et al. thickened Flasher origami and successfully created a folding array model with a high folding area ratio and a high folding diameter ratio. Flasher origami forms a regular polygon after unfolding, and can be tightly wrapped in a cylinder after folding, making it very suitable for use in aerospace fields where space costs are high. Currently, this model has been used in the design of star shields in NASA’s exoplanet exploration missions. However, this model suffers from the following shortcomings:
①计算困难,设计灵活性差:厚板化Flasher折纸的几何模型非常复杂,约束条件众多,节点坐标必须经过复杂的运算得出,无法为设计提供直观参考。另一方面,许多设计参数只能取为离散值,中间状态无法得出符合约束的模型,使得设计自由度与灵活性大大下降。① Difficult calculation and poor design flexibility: The geometric model of thick-plate Flasher origami is very complex and has many constraints. The node coordinates must be obtained through complex calculations, which cannot provide an intuitive reference for design. On the other hand, many design parameters can only be taken as discrete values, and a model that meets the constraints cannot be derived from the intermediate state, which greatly reduces the design freedom and flexibility.
②自由度过多,展开路径缺乏机械约束:Zirbel等人提出的Flasher折纸厚板化方法需要在四边形面板上添加折痕,使机构变为若干三角面板的组合。这种方法使得机构的自由度成倍增加,展开路径不唯一,必须设计合适的驱动方案才能正确展开平面。然而过于复杂的驱动控制存在风险,如果施力大小和顺序出现偏差,就可能将机构卡死或撕裂。② Too much freedom and lack of mechanical constraints on the expansion path: The Flasher origami thickening method proposed by Zirbel et al. requires adding creases to the quadrilateral panels, turning the mechanism into a combination of several triangular panels. This method doubles the degree of freedom of the mechanism, and the expansion path is not unique. A suitable driving scheme must be designed to correctly expand the plane. However, there are risks in overly complex drive control. If there is a deviation in the size and sequence of force application, the mechanism may be stuck or torn.
发明内容Contents of the invention
为解决上述技术问题,本发明提供了一种基于三浦折纸的紧凑空间折展阵列模型构建方法及系统。In order to solve the above technical problems, the present invention provides a compact space folding array model construction method and system based on Miura origami.
第一方面,本发明提供一种基于三浦折纸的紧凑空间折展阵列模型构建方法,该方法的技术方案如下:In the first aspect, the present invention provides a method for constructing a compact space folding array model based on Miura origami. The technical solution of the method is as follows:
基于四组相同的三浦折纸,构建零厚度折纸模型;Based on four sets of identical Miura origami, a zero-thickness origami model is constructed;
对所述零厚度折纸模型进行厚板化处理,得到厚板化的折展阵列模型;Perform thickening processing on the zero-thickness origami model to obtain a thickened folding array model;
根据所述厚板化的折展阵列模型的构型,设计四连杆联动装置,并利用所述四连杆联动装置,将所述厚板化的折展阵列模型的自由度从5调整至1,得到紧凑空间折展阵列模型。According to the configuration of the thickened folding array model, a four-link linkage device is designed, and the four-link linkage device is used to adjust the degree of freedom of the thickened folding array model from 5 to 1. Obtain the compact space folding array model.
本发明的一种基于三浦折纸的紧凑空间折展阵列模型构建方法的有益效果如下:The beneficial effects of the compact space folding array model construction method based on Miura origami of the present invention are as follows:
本发明的方法所构建的折展阵列模型适用于各种需要大面积平面阵列的航天器,并具有高空间利用率与高折展比,能够有效降低太空任务的成本。The folding array model constructed by the method of the present invention is suitable for various spacecrafts that require large-area planar arrays, has high space utilization and high folding ratio, and can effectively reduce the cost of space missions.
在上述方案的基础上,本发明的一种基于三浦折纸的紧凑空间折展阵列模型构建方法还可以做如下改进。On the basis of the above solution, the method of constructing a compact space folding array model based on Miura origami of the present invention can also be improved as follows.
在一种可选的方式中,基于四组相同的三浦折纸,构建零厚度折纸模型的步骤,包括:In an optional way, the steps to build a zero-thickness origami model based on four sets of identical Miura origami include:
按照旋转对称的方式,对四组相同的三浦折纸进行拼接,得到所述零厚度折纸模型。According to the method of rotational symmetry, four groups of identical Miura origami are spliced to obtain the zero-thickness origami model.
在一种可选的方式中,对所述零厚度折纸模型进行厚板化处理,得到厚板化的折展阵列模型的步骤,包括:In an optional manner, the step of thickening the zero-thickness origami model to obtain a thickened folded array model includes:
对所述零厚度折纸模型依次进行三浦折纸厚板化处理与五折痕顶点厚板化处理,得到所述厚板化的折展阵列模型。The zero-thickness origami model is sequentially subjected to Miura origami thickening processing and five-fold vertex thickening processing to obtain the thickened folding and unfolding array model.
在一种可选的方式中,还包括:In an optional approach, it also includes:
基于目标航天器的类型,确定所述紧凑空间折展阵列模型的目标设计参数,以根据所述目标设计参数,生成符合所述目标航天器的目标紧凑空间折展机构。Based on the type of the target spacecraft, target design parameters of the compact space folding array model are determined, so as to generate a target compact space folding mechanism that conforms to the target spacecraft according to the target design parameters.
第二方面,本发明提供一种基于三浦折纸的紧凑空间折展阵列模型构建系统,该系统的技术方案如下:In the second aspect, the present invention provides a compact space folding array model construction system based on Miura origami. The technical solution of the system is as follows:
包括:第一处理模块、第二处理模块和第三处理模块;It includes: a first processing module, a second processing module and a third processing module;
所述第一处理模块用于:基于四组相同的三浦折纸,构建零厚度折纸模型;The first processing module is used to: build a zero-thickness origami model based on four groups of identical Miura origami;
所述第二处理模块用于:对所述零厚度折纸模型进行厚板化处理,得到厚板化的折展阵列模型;The second processing module is used to: perform thickening processing on the zero-thickness origami model to obtain a thickened folding and unfolding array model;
所述第三处理模块用于:根据所述厚板化的折展阵列模型的构型,设计四连杆联动装置,并利用所述四连杆联动装置,将所述厚板化的折展阵列模型的自由度从5调整至1,得到紧凑空间折展阵列模型。The third processing module is used to: design a four-link linkage device according to the configuration of the thickened folding array model, and use the four-link linkage device to fold and unfold the thickened plate. The degree of freedom of the array model is adjusted from 5 to 1 to obtain a compact space folding array model.
本发明的一种基于三浦折纸的紧凑空间折展阵列模型构建系统的有益效果如下:The beneficial effects of the compact space folding array model construction system based on Miura origami of the present invention are as follows:
本发明的系统所构建的折展阵列模型适用于各种需要大面积平面阵列的航天器,并具有高空间利用率与高折展比,能够有效降低太空任务的成本。The folding array model constructed by the system of the present invention is suitable for various spacecrafts that require large-area planar arrays, has high space utilization and high folding ratio, and can effectively reduce the cost of space missions.
在上述方案的基础上,本发明的一种基于三浦折纸的紧凑空间折展阵列模型构建系统还可以做如下改进。Based on the above solution, the compact space folding array model construction system based on Miura origami of the present invention can also be improved as follows.
在一种可选的方式中,所述第一处理模块具体用于:In an optional manner, the first processing module is specifically used to:
按照旋转对称的方式,对四组相同的三浦折纸进行拼接,得到所述零厚度折纸模型。According to the method of rotational symmetry, four groups of identical Miura origami are spliced to obtain the zero-thickness origami model.
在一种可选的方式中,所述第二处理模块具体用于:In an optional manner, the second processing module is specifically used to:
对所述零厚度折纸模型依次进行三浦折纸厚板化处理与五折痕顶点厚板化处理,得到所述厚板化的折展阵列模型。The zero-thickness origami model is sequentially subjected to Miura origami thickening processing and five-fold vertex thickening processing to obtain the thickened folding and unfolding array model.
在一种可选的方式中,还包括:生成模块;In an optional manner, it also includes: generating module;
所述生成模块用于:基于目标航天器的类型,确定所述紧凑空间折展阵列模型的目标设计参数,以根据所述目标设计参数,生成符合所述目标航天器的目标紧凑空间折展机构。The generation module is configured to: determine the target design parameters of the compact space folding array model based on the type of the target spacecraft, so as to generate a target compact space folding mechanism that conforms to the target spacecraft according to the target design parameters. .
第三方面,本发明提供的一种存储介质的技术方案如下:In the third aspect, the technical solution of a storage medium provided by the present invention is as follows:
存储介质中存储有指令,当计算机读取所述指令时,使所述计算机执行如本发明的一种基于三浦折纸的紧凑空间折展阵列模型构建方法的步骤。Instructions are stored in the storage medium. When the computer reads the instructions, the computer is caused to execute the steps of the Miura origami-based compact space folding array model construction method of the present invention.
第四方面,本发明的一种电子设备的技术方案如下:In the fourth aspect, the technical solution of an electronic device of the present invention is as follows:
包括存储器、处理器及存储在所述存储器上并在所述处理器上运行的程序,所述处理器执行所述程序时实现如本发明的一种基于三浦折纸的紧凑空间折展阵列模型构建方法的步骤。It includes a memory, a processor, and a program stored in the memory and run on the processor. When the processor executes the program, it implements the construction of a compact space folding array model based on Miura origami according to the present invention. Method steps.
上述说明仅是本发明技术方案的概述,为了能够更清楚了解本发明的技术手段,而可依照说明书的内容予以实施,并且为了让本发明的上述和其它目的、特征和优点能够更明显易懂,以下特举本发明的具体实施方式。The above description is only an overview of the technical solution of the present invention. In order to have a clearer understanding of the technical means of the present invention, it can be implemented according to the content of the description, and in order to make the above and other objects, features and advantages of the present invention more obvious and understandable. , the specific embodiments of the present invention are listed below.
附图说明Description of the drawings
附图仅用于示出实施方式,而并不认为是对本发明的限制。而且在整个附图中,用相同的参考符号表示相同的部件。在附图中:The drawings are only used to illustrate the embodiments and are not considered to be limitations of the present invention. Also throughout the drawings, the same reference characters are used to designate the same components. In the attached picture:
图1为本发明的一种基于三浦折纸的紧凑空间折展阵列模型构建方法的实施例的流程示意图;Figure 1 is a schematic flow chart of an embodiment of a compact space folding array model construction method based on Miura origami according to the present invention;
图2为零厚度折纸模型的示意图;Figure 2 is a schematic diagram of the zero-thickness origami model;
图3为旋转轴偏移量的定义示意图;Figure 3 is a schematic diagram of the definition of rotation axis offset;
图4为厚板化五折痕顶点参数示意图;Figure 4 is a schematic diagram of the vertex parameters of the five creases of thick plate;
图5为四连杆联动装置的剖面图;Figure 5 is a cross-sectional view of the four-bar linkage device;
图6为四连杆联动装置的运动示意图;Figure 6 is a schematic diagram of the movement of the four-bar linkage device;
图7为紧凑空间折展阵列模型的整体折叠状态的示意图;Figure 7 is a schematic diagram of the overall folding state of the compact space folding array model;
图8为紧凑空间折展阵列模型的整体展开状态的示意图;Figure 8 is a schematic diagram of the overall unfolded state of the compact space folding array model;
图9为本发明的一种基于三浦折纸的紧凑空间折展阵列模型构建系统的实施例的结构示意图。Figure 9 is a schematic structural diagram of an embodiment of a compact space folding array model construction system based on Miura origami according to the present invention.
具体实施方式Detailed ways
下面将参照附图更详细地描述本发明的示例性实施例。虽然附图中显示了本发明的示例性实施例,然而应当理解,可以以各种形式实现本发明而不应被这里阐述的实施例所限制。Exemplary embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. Although exemplary embodiments of the invention are shown in the drawings, it should be understood that the invention may be embodied in various forms and should not be limited to the embodiments set forth herein.
图1示出了本发明提供的一种基于三浦折纸的紧凑空间折展阵列模型构建方法的实施例的流程示意图。如图1所示,包括如下步骤:Figure 1 shows a schematic flow chart of an embodiment of a compact space folding array model construction method based on Miura origami provided by the present invention. As shown in Figure 1, it includes the following steps:
S1、基于四组相同的三浦折纸,构建零厚度折纸模型。S1. Based on four groups of identical Miura origami, construct a zero-thickness origami model.
具体地,按照旋转对称的方式,对四组相同的三浦折纸进行拼接,得到零厚度折纸模型。Specifically, four groups of identical Miura origami were spliced in a rotationally symmetric manner to obtain a zero-thickness origami model.
其中,图2示出了零厚度折纸模型的示意图,该零厚度折纸模型形成一个中心对称的平面,机架能够轻松地连接到中心面板上而不会对展开过程产生干扰。四个三浦折纸的叶片各占据一个象限,且互不重叠。机架指代航天器除了折展平面以外的部分,该部分对折展平面有支撑与固定的作用。除此之外,机架也会有其他功能,根据航天器的任务目标进行确定。例如通信卫星会在机架中安装相应的通信设备,实验卫星安装相应的科学仪器。Among them, Figure 2 shows a schematic diagram of the zero-thickness origami model, which forms a centrally symmetrical plane, and the frame can be easily connected to the center panel without disturbing the unfolding process. The four Miura origami leaves each occupy a quadrant and do not overlap each other. The frame refers to the part of the spacecraft other than the folding and unfolding plane, which supports and fixes the folding and unfolding plane. In addition, the rack will also have other functions, which are determined according to the mission objectives of the spacecraft. For example, communication satellites will install corresponding communication equipment in the rack, and experimental satellites will install corresponding scientific instruments.
在S1中,需要说明的是:In S1, what needs to be explained is:
1)三浦折纸叶片和中心面板存在两种不同的连接方式。三浦折纸的折痕在一个方向上排列为直线(图2中以m方向标注),在另一个方向上排列为之字形(图2中以n方向标注)。若三浦折纸叶片的角面板用m方向上的折痕和中心面板连接,则得到零厚度折纸模型的构型A;如果角面板用n方向上的折痕和中心面板连接,则得到零厚度折纸模型的构型B。两个方向上的面板数量都是可变的,分别记为M和N,且二者不需要相等。1) There are two different ways of connecting the Miura origami blades and the center panel. The folds of Miura origami are arranged in a straight line in one direction (marked in the m direction in Figure 2) and in a zigzag pattern in the other direction (marked in the n direction in Figure 2). If the corner panels of the Miura origami blade are connected to the center panel by creases in the m direction, then the configuration A of the zero-thickness origami model is obtained; if the corner panels are connected to the center panel by creases in the n direction, a zero-thickness origami model is obtained. Configuration B of the model. The number of panels in both directions is variable, denoted M and N respectively, and they do not need to be equal.
2)两种构型(构型A和构型B)的折痕类型分布是一致的。角面板始终通过山折痕(折痕向纸面外突出)和中心面板连接,而角面板和其他三浦面板都以谷折痕连接(折痕向纸面内凹陷)。三浦折纸上其他的折痕类型可以根据以下规律依次确定:2) The distribution of crease types in the two configurations (configuration A and configuration B) is consistent. The corner panels are always connected to the center panel by a mountain crease (a crease that protrudes outward from the paper), while the corner panels and other Miura panels are connected by a valley crease (a crease that is sunk inward from the paper). Other crease types on Miura origami can be determined according to the following rules:
①m方向上山折痕和谷折痕交错分布;①The uphill creases and valley creases are staggered in the m direction;
②n方向上折痕类型保持一致;②The crease type remains consistent in the n direction;
③同一个面板的对边折痕类型相反。之所以要规定折痕类型,是因为只有在这种折叠形式下,才能保证其他面板在折叠后都排布在角面板的外侧,为中心面板下方留出长方体空间以安装机架或者放置其他仪器。③The opposite crease types of the same panel are opposite. The reason why the crease type is specified is that only in this folding form can other panels be arranged outside the corner panels after folding, leaving a cuboid space under the center panel to install racks or place other instruments. .
3)通过添加两个独立的三角面板,能够把相邻的两个三浦折纸的角面板和中心面板连接起来,构成五折痕顶点。从中心板开始,按顺时针遍历五折痕顶点面板,扇形角(两条相邻折痕围绕其相交顶点的角度)分别是:90°,45°,45°,90°,90°。Kawasaki–Justin定理指出,只有当扇形角的交错和等于0时,折痕图案才能平折。因此这里的五折痕顶点不会使两个三浦折纸的角面板重合在一起。另一方面,该顶点由形成交叉线的四条山折痕和一条谷折痕构成,符合Abel等人指出的鸟足条件,因此可以证明该顶点是刚性可折的。事实上,五顶点折痕允许三浦折纸的角面板和中心面板之间的二面角在90°-180°之间变化,而且始终保持两个角面板关于中心板的对角面对称运动。因此,四个五折痕顶点构成了联动装置,让四个三浦折纸的叶片能以相同的速度同步展开。3) By adding two independent triangular panels, the corner panels and center panels of two adjacent Miura origami can be connected to form the five-fold vertex. Starting from the center panel and traversing the five-fold vertex panel clockwise, the fan angles (the angles of two adjacent creases around their intersection vertices) are: 90°, 45°, 45°, 90°, 90°. The Kawasaki–Justin theorem states that the crease pattern can be folded flat only when the staggered sum of the sector angles is equal to 0. So the five crease vertices here won't bring the two Miura origami corner panels together. On the other hand, this vertex is composed of four mountain creases and one valley crease that form cross lines, which conforms to the bird's foot condition pointed out by Abel et al., so it can be proved that this vertex is rigidly foldable. In fact, the five-vertex crease allows the dihedral angle between the corner panels and the center panel of Miura's origami to vary between 90°-180°, while always maintaining diagonal symmetrical movement of the two corner panels with respect to the center panel. Therefore, the four five-fold vertices form a linkage that allows the four Miura origami blades to unfold simultaneously at the same speed.
4)五折痕顶点要求两个角面板和三角面板之间的扇形角是直角,而三浦折纸单元(三浦折纸是由若干个大小相同的平行四边形平面组成的,每个平行四边形可以视为一个三浦折纸单元)由平行四边形构成,因此需要对靠近其他叶片的第一列三浦面板的形状进行修改。可以通过扩张面板来让叶片的边缘垂直于折痕。在图2中,扩张之前的三浦折纸边缘用虚线表示,而扩张后的边缘用黑色实线表示。4) The five-fold vertex requires that the sector angle between the two corner panels and the triangular panel is a right angle, and the Miura origami unit (Miura origami is composed of several parallelogram planes of the same size, and each parallelogram can be regarded as a The Miura origami unit) is composed of a parallelogram, so the shape of the first row of Miura panels near the other blades needed to be modified. The edge of the blade can be brought perpendicular to the crease by expanding the panel. In Figure 2, the edge of the Miura origami before expansion is represented by a dotted line, while the edge after expansion is represented by a solid black line.
5)在图2中,左侧为展开状态下的折痕图,短虚线表示山折痕,点线表示谷折痕,长虚线表示三浦折纸图案原本的边界线,实线表示组合图案的实际边缘线(无运动约束)。中间为半折叠状态。右侧为完全折叠状态。5) In Figure 2, the left side shows the fold diagram in the unfolded state. The short dotted line represents the mountain crease, the dotted line represents the valley crease, the long dotted line represents the original boundary line of the Miura origami pattern, and the solid line represents the actual edge of the combined pattern. Line (no motion constraints). The middle is in a half-folded state. The right side is fully folded.
S2、对所述零厚度折纸模型进行厚板化处理,得到厚板化的折展阵列模型。S2. Perform thickening processing on the zero-thickness origami model to obtain a thickened folding and unfolding array model.
具体地,对零厚度折纸模型依次进行三浦折纸厚板化处理与五折痕顶点厚板化处理,得到厚板化的折展阵列模型。Specifically, the zero-thickness origami model is sequentially subjected to Miura origami thickening processing and five-fold vertex thickening processing to obtain a thickened folding and unfolding array model.
1)在S2中,三浦折纸厚板化处理的过程为:1) In S2, the process of Miura origami thickening is as follows:
如图3所示,在三浦折纸的m和n方向建立顶点网格Vm,n,顶点Vm,n和Vm′,n′之间的折痕线记为假设各个面板具有相同的厚度d,则在完全展开状态下,所有面板的上表面和下表面分别共面。因此可以定义平行于上下表面,且到两平面距离相等的平面为中平面。旋转轴/>到中平面的距离即为旋转轴偏移量/> As shown in Figure 3, a vertex grid V m,n is established in the m and n directions of Miura origami, and the crease line between the vertices V m,n and V m′,n′ is recorded as Assuming that each panel has the same thickness d, the upper and lower surfaces of all panels are respectively coplanar in the fully unfolded state. Therefore, the plane parallel to the upper and lower surfaces and equidistant from the two planes can be defined as the midplane. Rotation axis/> The distance to the midplane is the rotation axis offset/>
当符合按照下述规律排布时,厚板化的三浦折纸就能保持零厚度状态下的运动特征,即单自由度运动且不发生干涉:when When arranged according to the following rules, the thickened Miura origami can maintain the motion characteristics of the zero-thickness state, that is, single-degree-of-freedom motion without interference:
2)在S2中,五折痕顶点厚板化处理的过程为:2) In S2, the process of thickening the five-fold vertex is:
运用机构运动学易证明,轴对称的五折痕顶点在厚板化时可以等效为Myard连杆机构。Myard连杆机构是一种闭环5R过约束空间机构,Myard连杆机构的构型与运动也同样是轴对称的,并且具有单自由度。It is easy to prove by using mechanism kinematics that the axially symmetrical five-fold apex can be equivalent to a Myard connecting rod mechanism when the plate is thickened. The Myard link mechanism is a closed-loop 5R over-constrained space mechanism. The configuration and motion of the Myard link mechanism are also axially symmetric and have a single degree of freedom.
为了使厚板化后的折纸机构符合Myard连杆机构的特征,本实施例中首先对三浦折纸的角面板进行一些修饰。如图4所示,假设两个角面板以及中间的两个三角板具有相同的板厚。三角板与角面板的上边缘相接,记为转动副z2与z5。而两个三角板之间的转动副安装在下边缘,记为z1。然而角面板并不直接连接到中心面板上,而是需要在原先角面板的上表面再添加一个凸台,再以凸台的上边缘连接中心面板,相接处的轴是z3与z4。在图4中,a12与a51代表原先角面板与三角板的厚度,a23与a45描述凸台的厚度。这些量遵循的关系为:In order to make the thickened origami mechanism conform to the characteristics of the Myyard link mechanism, in this embodiment, some modifications are first made to the corner panels of the Miura origami. As shown in Figure 4, assume that the two corner panels and the two triangular panels in the middle have the same plate thickness. The triangular plate is connected to the upper edge of the corner panel, which are designated as the rotating pairs z 2 and z 5 . The rotating pair between the two triangular plates is installed on the lower edge, recorded as z 1 . However, the corner panel is not directly connected to the center panel. Instead, a boss needs to be added to the upper surface of the original corner panel, and then the upper edge of the boss is connected to the center panel. The axes of the connection are z 3 and z 4 . In Figure 4, a 12 and a 51 represent the thickness of the original corner panels and triangular panels, and a 23 and a 45 describe the thickness of the boss. These quantities follow the relationship:
a12=a51, a 12 = a 51 ,
根据折痕图容易得到上述机构各连杆之间的安装角:According to the crease diagram, it is easy to obtain the installation angle between the connecting rods of the above mechanism:
S3、根据所述厚板化的折展阵列模型的构型,设计四连杆联动装置,并利用所述四连杆联动装置,对所述厚板化的折展阵列模型的自由度进行调整,得到紧凑空间折展阵列模型。S3. According to the configuration of the thickened folding array model, design a four-link linkage device, and use the four-link linkage device to adjust the degree of freedom of the thickened folding array model. , a compact space folded array model is obtained.
S3的具体实现过程为:The specific implementation process of S3 is:
1)厚板化的折展阵列模型的构型B的最内侧面板P1,1与中心面板之间的轴线A,最内侧面板P1,1与次内侧面板P2,1之间的轴线B,在运动过程中始终是平行的。本实施例在P2,1板上在添加一条轴线C,使B与C平行;在中心面板上添加一条轴线D,使A与D平行;再用连杆将C与D相连。这样,中心面板(AD)、最内侧面板P1,1(AB)、次内侧面板P2,1(BC)以及新增连杆CD就构成了平面四连杆机构(四连杆联动装置),如图5所示。本实施例通过使用四连杆联动装置将三浦折纸的叶片转动与叶片展开同步起来,以得到紧凑空间折展阵列模型。1) The axis A between the innermost panel P 1,1 and the center panel of the configuration B of the thickened folding array model, and the axis between the innermost panel P 1,1 and the next innermost panel P 2,1 B, always parallel during movement. In this embodiment, an axis C is added to the P 2,1 board to make B and C parallel; an axis D is added to the center panel to make A and D parallel; and a connecting rod is used to connect C and D. In this way, the center panel (AD), the innermost panel P 1,1 (AB), the second inner panel P 2,1 (BC) and the new connecting rod CD form a planar four-bar linkage mechanism (four-bar linkage device) , as shown in Figure 5. In this embodiment, a four-link linkage device is used to synchronize the blade rotation and blade expansion of Miura origami to obtain a compact space folding array model.
2)AB与AD之间的夹角ρ1表示叶片整体相对于中心面板的转动,AB与BC之间的夹角ρ2表征叶片中各面板的展开情况。从完全折叠状态到完全展开状态,叶片整体相对于中心面板旋转了90°,而叶片内两个面板之间的二面角从0°变为180°。因此,该四连杆联动装置必须具有这样的性质:当ρ1具有90°增量的时候,ρ2应当具有180°增量。2) The angle ρ 1 between AB and AD represents the rotation of the entire blade relative to the center panel, and the angle ρ 2 between AB and BC represents the expansion of each panel in the blade. From the fully folded state to the fully unfolded state, the entire blade rotates 90° relative to the center panel, and the dihedral angle between the two panels within the blade changes from 0° to 180°. Therefore, the four-bar linkage must have such a property that when ρ 1 has an increment of 90°, ρ 2 should have an increment of 180°.
3)本实施例中隐去面板的具体形状,只关注等效连杆的运动,选取AB杆作为固定参照物,得到图6中的四连杆联动装置的运动示意图。ABC1D1表示完全折叠状态下的四连杆,ABC2D2表示完全展开状态下的四连杆。可以看出从BC1到BC2旋转了180°,而从AD1到AD2旋转了90°。从图6中能够列出四连杆各参数应满足的几何关系:3) In this embodiment, the specific shape of the panel is hidden, and only the movement of the equivalent connecting rod is focused. The AB rod is selected as a fixed reference object to obtain the motion diagram of the four-bar linkage device in Figure 6. ABC 1 D 1 represents the four-link in the fully folded state, and ABC 2 D 2 represents the four-link in the fully unfolded state. It can be seen that there is a rotation of 180° from BC 1 to BC 2 , and a rotation of 90° from AD 1 to AD 2 . From Figure 6, the geometric relationships that each parameter of the four-link link should satisfy can be listed:
上述方程的解不唯一。事实上,连杆长度x具有一个取值范围,对于范围内的任意x,都可以解出剩余的r1,r2,s。不同的r1,r2代表轴线D与C的位置不同,在实际设计情境中可以根据工程需要确定D与C的位置,进而选择一组合适的四连杆解。The solution to the above equation is not unique. In fact, the connecting rod length x has a value range, and for any x within the range, the remaining r 1 , r 2 , s can be solved. Different r 1 and r 2 represent different positions of axes D and C. In the actual design situation, the positions of D and C can be determined according to engineering needs, and then a suitable set of four-link solutions can be selected.
需要说明的是,在本实施例中:It should be noted that in this embodiment:
首先,使用偏移轴线法构造四个独立的单自由度三浦折纸叶片。其次,使用五折痕顶点机构保证四个叶片角面板的转动同步。最后,用四连杆联动装置把叶片的展开过程与角面板的转动联系起来。最终,整个紧凑空间折展阵列模型的自由度减少到1。First, four independent single-degree-of-freedom Miura origami blades were constructed using the offset axis method. Secondly, a five-fold apex mechanism is used to ensure that the rotation of the four blade corner panels is synchronized. Finally, a four-bar linkage is used to link the unfolding process of the blades with the rotation of the corner panels. Eventually, the degree of freedom of the entire compact space folding array model is reduced to 1.
较优地,还包括:Preferably, it also includes:
S4、基于目标航天器的类型,确定所述紧凑空间折展阵列模型的目标设计参数,以根据所述目标设计参数,生成符合所述目标航天器的目标紧凑空间折展机构。S4. Based on the type of the target spacecraft, determine the target design parameters of the compact space folding array model, so as to generate a target compact space folding mechanism that conforms to the target spacecraft according to the target design parameters.
其中,目标航天器为各种需要大面积平面阵列的航天器,目标航天器的类型包括但不限于:空间暴露实验平台、空间太阳能电站、望远镜遮星罩以及平面合成孔径雷达等。Among them, the target spacecraft are various spacecrafts that require large-area planar arrays. The types of target spacecraft include but are not limited to: space exposure experiment platforms, space solar power stations, telescope star shields, and planar synthetic aperture radars.
在S4中,紧凑空间折展阵列模型的整体折叠状态如图7所示,紧凑空间折展阵列模型的整体展开状态如图8所示。定义模型折叠状态下总宽为L,总高为H,中心柱边长为c,板厚为d,板宽为b,板高为h,平行四边形面板的锐角内角为φ。结合实际需求,可以确定中心柱边长最小值为cmin。取L,H,d,φ,M,N为自变量(目标设计参数),对于任意一组满足以下不等式约束的自变量参数组:In S4, the overall folded state of the compact space folding array model is shown in Figure 7, and the overall unfolded state of the compact space folding array model is shown in Figure 8. Define the total width of the model in the folded state as L, the total height as H, the side length of the central column as c, the plate thickness as d, the plate width as b, the plate height as h, and the acute internal angle of the parallelogram panel as φ. Combined with actual needs, it can be determined that the minimum side length of the central column is c min . Let L, H, d, φ, M, and N be the independent variables (target design parameters). For any set of independent variable parameters that satisfy the following inequality constraints:
能够构建出符合要求的折展机构,且机构在折叠后能紧密嵌入长宽高为L×L×H的长方体之中。其他设计参数可以用下式解出:A folding and unfolding mechanism that meets the requirements can be constructed, and the mechanism can be tightly embedded into a cuboid with a length, width and height of L×L×H after folding. Other design parameters can be solved using the following equation:
需要说明的是,为了评估不同参数取值下模型的收纳能力,定义折展比ε与空间利用率η如下:It should be noted that in order to evaluate the storage capacity of the model under different parameter values, the folding ratio ε and space utilization eta are defined as follows:
给出两种构型的折展比与空间利用率计算公式:The calculation formulas for the folding ratio and space utilization of the two configurations are given:
对构型A:For configuration A:
对构型B:For configuration B:
通过计算可以发现,对于绝大多数目标设计参数(L,H,d,φ,M,N),对应的机构空间利用率都在一半以上。相比于以往的折展模型,本实施例的设计能更有效地利用运输空间。Through calculation, it can be found that for most of the target design parameters (L, H, d, φ, M, N), the corresponding mechanism space utilization rate is more than half. Compared with previous folding and unfolding models, the design of this embodiment can utilize the transportation space more effectively.
本实施例的紧凑空间折展阵列模型具有规则的外形和高空间利用率,能够有效降低太空任务的成本,而高度灵活的参数化设计使设计者能够根据不同任务需求快速开发定制的太空装备。因此,本实施例的技术方案有望在未来的国家航天发展中发挥重要作用,在太空探索和应用领域拥有广阔的发展前景。The compact space folding array model of this embodiment has a regular shape and high space utilization, which can effectively reduce the cost of space missions, and the highly flexible parametric design enables designers to quickly develop customized space equipment according to different mission requirements. Therefore, the technical solution of this embodiment is expected to play an important role in the future national aerospace development and has broad development prospects in the field of space exploration and application.
图9示出了本发明提供的一种基于三浦折纸的紧凑空间折展阵列模型构建系统200的实施例的结构示意图。如图9所示,该系统200包括:第一处理模块210、第二处理模块220和第三处理模块230;Figure 9 shows a schematic structural diagram of an embodiment of a compact space folding array model building system 200 based on Miura origami provided by the present invention. As shown in Figure 9, the system 200 includes: a first processing module 210, a second processing module 220 and a third processing module 230;
所述第一处理模块210用于:基于四组相同的三浦折纸,构建零厚度折纸模型;The first processing module 210 is used to: build a zero-thickness origami model based on four groups of identical Miura origami;
所述第二处理模块220用于:对所述零厚度折纸模型进行厚板化处理,得到厚板化的折展阵列模型;The second processing module 220 is configured to: perform thickening processing on the zero-thickness origami model to obtain a thickened folding array model;
所述第三处理模块230用于:根据所述厚板化的折展阵列模型的构型,设计四连杆联动装置,并利用所述四连杆联动装置,对所述厚板化的折展阵列模型的自由度进行调整,得到紧凑空间折展阵列模型。The third processing module 230 is configured to: design a four-bar linkage device according to the configuration of the thickened folding array model, and use the four-bar linkage device to perform the thickened folding array model. The degree of freedom of the expansion array model is adjusted to obtain a compact space expansion array model.
较优地,所述第一处理模块210具体用于:Preferably, the first processing module 210 is specifically used for:
按照旋转对称的方式,对四组相同的三浦折纸进行拼接,得到所述零厚度折纸模型。According to the method of rotational symmetry, four groups of identical Miura origami are spliced to obtain the zero-thickness origami model.
较优地,所述第二处理模块220具体用于:Preferably, the second processing module 220 is specifically used for:
对所述零厚度折纸模型依次进行三浦折纸厚板化处理与五折痕顶点厚板化处理,得到所述厚板化的折展阵列模型。The zero-thickness origami model is sequentially subjected to Miura origami thickening processing and five-fold vertex thickening processing to obtain the thickened folding and unfolding array model.
较优地,还包括:生成模块;Preferably, it also includes: a generation module;
所述生成模块用于:基于目标航天器的类型,确定所述紧凑空间折展阵列模型的目标设计参数,以根据所述目标设计参数,生成符合所述目标航天器的目标紧凑空间折展机构。The generation module is configured to: determine the target design parameters of the compact space folding array model based on the type of the target spacecraft, so as to generate a target compact space folding mechanism that conforms to the target spacecraft according to the target design parameters. .
本实施例的技术方案所构建的折展阵列模型适用于各种需要大面积平面阵列的航天器,并具有高空间利用率与高折展比,能够有效降低太空任务的成本。The folding array model constructed by the technical solution of this embodiment is suitable for various spacecrafts that require large-area planar arrays, has high space utilization and high folding ratio, and can effectively reduce the cost of space missions.
上述关于本实施例的基于三浦折纸的紧凑空间折展阵列模型构建系统200中的各参数和各个模块实现相应功能的步骤,可参考上文中关于基于三浦折纸的紧凑空间折展阵列模型构建方法的实施例中的各参数和步骤,在此不做赘述。Regarding the steps for implementing the corresponding functions of each parameter and each module in the Miura Origami-based compact space folding array model construction system 200 of this embodiment, please refer to the above article about the Miura Origami-based compact space folding array model construction method. The parameters and steps in the embodiment will not be described again here.
本发明实施例提供的一种存储介质,包括:存储介质中存储有指令,当计算机读取所述指令时,使所述计算机执行如基于三浦折纸的紧凑空间折展阵列模型构建方法的步骤,具体可参考上文中的基于三浦折纸的紧凑空间折展阵列模型构建方法的实施例中的各参数和步骤,在此不做赘述。A storage medium provided by an embodiment of the present invention includes: instructions stored in the storage medium. When a computer reads the instructions, the computer is caused to perform steps such as a compact space folding array model construction method based on Miura origami. For details, reference may be made to the various parameters and steps in the above embodiments of the compact space folding array model construction method based on Miura origami, which will not be described again here.
计算机存储介质例如:优盘、移动硬盘等。Computer storage media such as USB flash drives, mobile hard drives, etc.
本发明实施例提供的一种电子设备,包括存储器、处理器及存储在存储器上并可在处理器上运行的计算机程序,所述处理器执行所述计算机程序时,使所述计算机执行如基于三浦折纸的紧凑空间折展阵列模型构建方法的步骤,具体可参考上文中的基于三浦折纸的紧凑空间折展阵列模型构建方法的实施例中的各参数和步骤,在此不做赘述。An electronic device provided by an embodiment of the present invention includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it causes the computer to execute a computer program based on For details about the steps of Miura Origami's compact space folding array model construction method, please refer to the parameters and steps in the above embodiment of the Miura Origami based compact space folding array model construction method, and will not be described in detail here.
所属技术领域的技术人员知道,本发明可以实现为方法、系统、存储介质和电子设备。Those skilled in the art know that the present invention can be implemented as methods, systems, storage media and electronic devices.
因此,本发明可以具体实现为以下形式,即:可以是完全的硬件、也可以是完全的软件(包括固件、驻留软件、微代码等),还可以是硬件和软件结合的形式,本文一般称为“电路”、“模块”或“系统”。此外,在一些实施例中,本发明还可以实现为在一个或多个计算机可读介质中的计算机程序产品的形式,该计算机可读介质中包含计算机可读的程序代码。可以采用一个或多个计算机可读的介质的任意组合。计算机可读介质可以是计算机可读信号介质或者计算机可读存储介质。计算机可读存储介质例如可以是但不限于——电、磁、光、电磁、红外线、或半导体的系统、装置或器件,或者任意以上的组合。计算机可读存储介质的更具体的例子(非穷举的列表)包括:具有一个或多个导线的电连接、便携式计算机磁盘、硬盘、随机存取存储器(RAM),只读存储器(ROM)、可擦式可编程只读存储器(EPROM或闪存)、光纤、便携式紧凑磁盘只读存储器(CD-ROM)、光存储器件、磁存储器件、或者上述的任意合适的组合。在本文件中,计算机可读存储介质可以是任何包含或存储程序的有形介质,该程序可以被指令执行系统、装置或者器件使用或者与其结合使用。尽管上面已经示出和描述了本发明的实施例,可以理解的是,上述实施例是示例性的,不能理解为对本发明的限制,本领域的普通技术人员在本发明的范围内可以对上述实施例进行变化、修改、替换和变型。Therefore, the present invention can be implemented in the following form, that is, it can be complete hardware, or it can be complete software (including firmware, resident software, microcode, etc.), or it can be a combination of hardware and software. This article generally Called a "circuit", "module" or "system". Furthermore, in some embodiments, the present invention may also be implemented in the form of a computer program product in one or more computer-readable media containing computer-readable program code. Any combination of one or more computer-readable media may be employed. The computer-readable medium may be a computer-readable signal medium or a computer-readable storage medium. The computer-readable storage medium may be, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, device or device, or any combination thereof. More specific examples (non-exhaustive list) of computer readable storage media include: electrical connections having one or more conductors, portable computer disks, hard drives, random access memory (RAM), read only memory (ROM), Erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination of the above. As used herein, a computer-readable storage medium may be any tangible medium that contains or stores a program for use by or in connection with an instruction execution system, apparatus, or device. Although the embodiments of the present invention have been shown and described above, it can be understood that the above-mentioned embodiments are illustrative and should not be construed as limitations of the present invention. Those of ordinary skill in the art can make modifications to the above-mentioned embodiments within the scope of the present invention. The embodiments are subject to changes, modifications, substitutions and variations.
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