Curved surface configuration design method, device and equipment based on non-flat origami unit

Abstract

Embodiments of the present application provide a curved surface configuration design method, device and equipment based on a non-flat origami unit, relate to the technical field of curved surface configuration, and the method comprises: obtaining a first mathematical model constructed for a rigid origami structure; the rigid origami structure is formed by a plurality of first basic units being spliced with each other in an array form, the first basic unit is a single-vertex multi-fold structure, and the sum of all interior angles of rigid surfaces in a first basic unit at a vertex is not equal to 2pi; the first mathematical model is used to describe the mathematical relationship between the geometric design parameters of the first basic unit and the morphological characteristics of a first curved surface, and the first curved surface is a curved surface presented by the rigid origami structure in a maximum unfolded state; determining a target value of the morphological characteristics; and determining a target design value of the geometric design parameters by substituting the target value into the first mathematical model. By applying the embodiments of the present application, the shape stability of the deployable structure applying the curved surface configuration can be improved.

Description

Technical Field

[0001] This application relates to the field of curved surface configuration technology, and in particular to a method, apparatus and equipment for curved surface configuration design based on non-flat origami units. Background Technology

[0002] Expandable structures are widely used in many scenarios, and in some of these scenarios, it is necessary to ensure that the expandable structure remains in a curved state after being expanded.

[0003] Taking the aerospace field as an example, with the rapid development of Earth observation, deep space exploration, and satellite communication technologies, the demand for large-aperture, high-precision deployable space antennas is becoming increasingly urgent. These antennas need to be retracted into a small rocket fairing during spacecraft launch and reliably deployed after the spacecraft is in orbit, maintaining extremely high surface accuracy to ensure electromagnetic performance. While traditional solid-plane deployable antennas can provide a stable reflector, their compactness is limited by the thickness of the rigid panel and complex mechanical hinge mechanisms, resulting in large system mass and challenges to deployment reliability, making them unsuitable for the future trend of ultra-large aperture antennas.

[0004] Against this backdrop, origami engineering, based on the concept of thin-plate folding, offers promising solutions for the design of spatially deployable structures. Among these, deployable structures based on rigid origami theory have attracted considerable attention due to their extremely high storage ratio and reliable unfolding process.

[0005] However, when designing curved surface configurations based on rigid origami theory, the resulting unfoldable structures generally suffer from insufficient surface stability and high control difficulty. Summary of the Invention

[0006] The purpose of this application is to provide a method, apparatus, and device for designing curved surface configurations based on non-flat origami units, so as to improve the dimensional stability of unfoldable structures using curved surface configurations. The specific technical solution is as follows: In a first aspect, embodiments of this application provide a method for designing curved surface configurations based on non-flat origami units, including: Obtain a first mathematical model for constructing a rigid origami structure; the rigid origami structure is formed by splicing multiple first basic units together in an array, the first basic unit is a single-vertex multi-crease structure, and the sum of the interior angles of all rigid surfaces at the vertex in a first basic unit is not equal to 2π; the first mathematical model is used to describe the mathematical relationship between the geometric design parameters of the first basic unit and the morphological characteristics of the first surface, the first surface is the surface presented by the rigid origami structure in its maximum unfolded state, and the morphological characteristics include the radius of curvature; determine the target value of the morphological characteristics; by substituting the target value into the first mathematical model, obtain the first numerical condition that the geometric design parameters should meet under the target value of the morphological characteristics; based on the first numerical condition, determine the target design value of the geometric design parameters.

[0007] Optionally, the first basic unit is a single-vertex four-fold structure; a first basic unit includes a vertex, and a first rigid surface, a second rigid surface, a third rigid surface and a fourth rigid surface that surround the vertex in a counterclockwise direction.

[0008] Optionally, the size of the interior angle of the first rigid surface at a vertex is the same as the size of the interior angle of the fourth rigid surface at a vertex, and the size of the interior angle of the second rigid surface at a vertex is the same as the size of the interior angle of the third rigid surface at a vertex.

[0009] Optionally, in a first basic unit, the second crease between the first rigid surface and the second rigid surface, the fourth crease between the third rigid surface and the fourth rigid surface, and the first crease between the fourth rigid surface and the first rigid surface are valley creases, and the third crease between the second rigid surface and the third rigid surface is a mountain crease; or, in a first basic unit, the second crease, the fourth crease, and the first crease are mountain creases, and the third crease is a valley crease.

[0010] Optionally, the first basic unit is designed by adjusting the Miura origami unit as follows: the Miura origami unit includes a first parallelogram and a second parallelogram arranged sequentially in the first row, and a third parallelogram and a fourth parallelogram arranged sequentially in the second row, wherein the tilt direction of the parallelograms in the first row is opposite to that of the parallelograms in the second row: the first vertex of the first parallelogram is adjusted away from the second row along its side; the first vertex is a vertex of the first parallelogram that is away from the second parallelogram and close to the third parallelogram; The second vertex of the second parallelogram is adjusted along its side towards the second row; the second vertex is a vertex of the second parallelogram that is far from the first parallelogram and far from the fourth parallelogram. The third vertex of the third parallelogram is adjusted along its side towards the first row; the third vertex is a vertex of the third parallelogram that is far from the fourth parallelogram and close to the first parallelogram. The fourth vertex of the fourth parallelogram is adjusted along its side towards the first row; the fourth vertex is a vertex of the fourth parallelogram that is far from the third parallelogram and far from the second parallelogram.

[0011] Optionally, the first mathematical model is constructed as follows: Based on the theory of spherical triangles, a first expression is determined for the spatial angle between every two non-adjacent folds within the first basic unit during its unfolding process. The first expression uses geometric design parameters and the folding angle between adjacent rigid surfaces within the first basic unit as variables. A target curvature arc is determined on the first surface to estimate the morphological feature values. Based on the first expression and the geometric design parameters, a second expression for the morphological parameter values ​​on the target curvature arc is determined to obtain a first mathematical model.

[0012] Optionally, before determining the target design values ​​of the geometric design parameters based on the first numerical conditions, the method further includes: Determine the folding angle between adjacent rigid surfaces within the first basic unit in its maximum unfolded state; substitute the determined angle value into the first mathematical model.

[0013] Secondly, embodiments of this application provide a curved surface configuration design device based on non-flat origami units, including: The model acquisition module is used to acquire a first mathematical model for constructing a rigid origami structure. The rigid origami structure is formed by splicing multiple first basic units together in an array. The first basic unit is a single-vertex multi-crease structure, and the sum of the interior angles of all rigid surfaces at the vertex in a first basic unit is not equal to 2π. The first mathematical model is used to describe the mathematical relationship between the geometric design parameters of the first basic unit and the morphological features of the first surface. The first surface is the surface presented by the rigid origami structure in its maximum unfolded state, and the morphological features include the radius of curvature. The morphological feature determination module is used to determine the target value of the morphological features. The condition determination module is used to obtain the first numerical condition that the geometric design parameters should meet under the target value of the morphological features by substituting the target value into the first mathematical model. The design value determination module is used to determine the target design value of the geometric design parameters based on the first numerical condition.

[0014] Thirdly, embodiments of this application provide an electronic device, including a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other through the communication bus; the memory is used to store computer programs; and the processor is used to implement the curved surface configuration design method based on non-flat origami units of the first aspect when executing the program stored in the memory.

[0015] This application embodiment also provides a deployable structure with a curved surface configuration, which is formed by splicing together multiple first basic units. The geometric design parameters of the first basic units are described in the curved surface configuration design method based on non-flat origami units of the first aspect.

[0016] Beneficial effects of the embodiments in this application: The surface configuration design method, apparatus, and device based on non-flat origami units provided in this application, by setting the sum of the interior angles of all rigid surfaces at the vertices of a first basic unit within a rigid origami structure to be no greater than 2π, enables the first basic unit to possess controllable non-flat characteristics. In other words, a first basic unit can exhibit a controllable inherent curvature in its maximum unfolded state. Therefore, for a rigid origami structure formed by splicing multiple first basic units in an array, the inherent curvatures of each first basic unit can be coordinated within the array. Consequently, the rigid origami structure can spontaneously present a smooth first curved surface after reaching its maximum unfolded state, and the morphological characteristics of this first curved surface can be precisely controlled by adjusting the geometric design parameters of the first basic unit.

[0017] Based on the above principles, this application constructs a first mathematical model to describe the mathematical relationship between the geometric design parameters of the first basic unit and the morphological features of the first surface. When designing the surface configuration, by determining the target value of the expected morphological features presented by the first surface, and then substituting the target value into the first mathematical model, the target design value of the geometric design parameters corresponding to that target value can be determined. Therefore, when assembling the actual configuration of the first basic unit and the rigid origami structure based on the determined target design value, the rigid origami structure can be precisely formed into a first surface with the expected morphological features upon final unfolding.

[0018] As can be seen from the above, the embodiments of this application, by designing the first basic unit to possess controllable non-flattening characteristics, enable the rigid origami structure to spontaneously present a first curved surface with the expected morphological characteristics after stable unfolding. Compared with the traditional design scheme that focuses on the curved surface configuration of the intermediate folded state of the rigid origami structure that meets the flattening condition, this approach can ensure the surface stability of the first curved surface at the essential level of geometric configuration, fundamentally avoiding the problems of control complexity and difficulty in maintaining surface accuracy caused by the reliance on unstable intermediate folded states in traditional design schemes. Furthermore, the embodiments of this application, based on the constructed first mathematical model, set target design values ​​for geometric design parameters corresponding to the expected morphological characteristics of the first curved surface. Through the directional design of geometric design parameters, a first curved surface configuration with arbitrary target curvature radius can be achieved, thereby providing a general and computationally efficient design framework for realizing a series of customized curved surfaces with different curvature radii.

[0019] Of course, implementing any product or method of this application does not necessarily require achieving all of the advantages described above at the same time. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other embodiments can be obtained based on these drawings.

[0021] Figure 1 A flowchart illustrating the surface configuration design method based on non-flat origami units provided in this application embodiment; Figure 2 A schematic diagram of a single-vertex four-fold structure with non-flat characteristics provided in an embodiment of this application; Figure 3 A schematic diagram of another single-vertex four-fold structure with non-flat characteristics provided in an embodiment of this application; Figure 4A schematic diagram of the first basic unit provided in an embodiment of this application; Figure 5 A schematic diagram of the Miura origami unit; Figure 6 A planar crease distribution diagram of the first basic unit provided in the embodiments of this application; Figure 7 This is a schematic diagram of the assembly array of the rigid origami structure provided in the embodiments of this application; Figure 8 A schematic diagram of the three-dimensional configuration of the single-vertex four-fold structure provided in the embodiments of this application during its unfolding process; Figure 9 A schematic diagram of the rigid origami structure provided in the embodiments of this application in its maximum unfolded state; Figure 10 A spatial perspective view of the curved surface configuration of the rigid origami structure provided in the embodiment of this application in its maximum unfolded state; Figure 11 A schematic diagram of the geometric relationship of the curved surface configuration of the rigid origami structure provided in the embodiment of this application in its maximum unfolded state within the projection plane; Figure 12 A schematic diagram of a curved surface configuration design device based on a non-flat origami unit provided in an embodiment of this application; Figure 13 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. Detailed Implementation

[0022] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art based on this application are within the scope of protection of this application.

[0023] Deployable structures designed based on origami theory have wide applications in many scenarios, and in some applications, it is necessary to maintain the curved surface state of the deployable structure after deployment. Taking the aerospace field as an example, deployable structures based on rigid origami theory have attracted much attention in the design of space deployable curved surface antennas due to their extremely high packing ratio and reliable deployment process.

[0024] However, as the target application of rigid origami theory shifts from planar structures to high-precision curved surfaces, the inherent limitations of traditional rigid origami schemes become increasingly apparent.

[0025] Currently, the main approach to constructing the target curved surface shape of an unfoldable structure using rigid origami theory involves utilizing the transient configuration of the origami structure during its continuous movement from fully folded to fully unfolded. Specifically, this approach involves carefully designing crease patterns to allow the origami structure to present the shape of the target curved surface at a certain intermediate folding state, and relying on a control system to precisely lock the structure in that state.

[0026] While the aforementioned schemes can theoretically achieve smooth curved surfaces, the target tooling state of the origami structure, as the desired curve, is not a mechanically stable state, resulting in insufficient surface stability and significant control challenges. Specifically, the fully unfolded and fully folded states of an origami structure typically correspond to stable energy equilibrium points, while intermediate folded states are often unstable or metastable equilibrium points. Taking the curved configuration of a space-deployable antenna as an example, this means that maintaining the surface shape of such antennas during on-orbit operation heavily relies on precise active control or complex mechanical locking mechanisms. However, in practical applications, microgravity, thermal cycling, and minor disturbances in the space environment can all cause structural surface drift or jitter, severely impacting the antenna's final performance. Furthermore, maintaining this non-naturally stable state typically requires precise and complex control and locking mechanisms, which not only increases system mass, control complexity, and manufacturing costs but also introduces potential failure risks, reducing the overall on-orbit reliability of the antenna system.

[0027] In summary, current methods for designing curved surfaces face a core challenge: how to ensure that the unfolded structure maintains a pre-defined, high-precision target curved surface after unfolding, without relying on complex and unreliable intermediate folding locking mechanisms, while achieving an extremely high folding ratio. The solutions mentioned earlier, by essentially relying on a specific intermediate folding state during the unfolding process of the origami structure, not only increase the difficulty of system control and the risk of failure, but also fail to fundamentally achieve stable maintenance of the high-precision target curved surface, thus failing to resolve this core challenge.

[0028] In view of this, embodiments of this application provide a method for designing curved surface configurations based on non-flat origami units, see [link to relevant documentation]. Figure 1 The method matrix includes the following steps: Step S101: Obtain the first mathematical model for the rigid origami structure; the rigid origami structure is formed by splicing multiple first basic units together in an array. The first basic unit is a single-vertex multi-fold structure, and the sum of the interior angles of all rigid surfaces at the vertex in a first basic unit is not equal to 2π; the first mathematical model is used to describe the mathematical relationship between the geometric design parameters of the first basic unit and the morphological characteristics of the first surface. The first surface is the surface presented by the rigid origami structure in its maximum unfolded state, and the morphological characteristics include the radius of curvature.

[0029] A single-vertex multi-crease structure refers to an origami structure formed by multiple creases converging at one vertex, where each pair of adjacent creases forms a separate rigid surface. In traditional rigid origami mechanisms, the single-vertex multi-crease structure constituting the basic unit generally satisfies the flatness condition. That is, the sum of the interior angles of all rigid surfaces at the vertex in a basic unit equals 2π, thus a basic unit in its fully unfolded state is planar. However, in the embodiments of this application, the sum of the interior angles of all rigid surfaces at the vertex in a first basic unit is not equal to 2π. This setting breaks the flatness condition, allowing the first basic unit to exhibit a specific curvature in its fully unfolded state.

[0030] The following example illustrates a single-vertex, four-fold structure. See [link / reference]. Figure 2 and Figure 3 The single-vertex four-fold structure shown in the figure , , and These represent four creases, with a rigid surface formed between each pair of adjacent creases, resulting in a total of four rigid surfaces. , , and These represent the interior angles of the four rigid surfaces at their vertices. Figure 2 The figure shows the sum of the interior angles of all rigid surfaces at their vertices. A planar crease distribution diagram of a single-vertex four-crease structure. Figure 3 The middle section shows the sum of the interior angles of all rigid surfaces at their vertices. A planar crease distribution diagram of a single-vertex four-crease structure. Figure 3 The dashed part in the middle represents the interior angle. The rigid surface is blocked by the interior angle The portion that is blocked by the rigid surface. In the... Figure 2 and Figure 3 When assembling and using the single-vertex four-fold structure illustrated in the diagram, it is necessary to follow the folds. internal angle Rigid surface and interior angle Connect to the rigid surface. This is easily understood by referring to the diagram. Figure 2 and Figure 3 The single-vertex four-fold structure illustrated in the diagram, after being assembled, presents a non-flat shape in its fully unfolded state.

[0031] In this embodiment, a first basic unit exhibits a fixed curvature in its fully unfolded state. Therefore, for a rigid origami structure formed by splicing multiple first basic units together, the rigid origami structure will spontaneously form a smooth surface (first surface) with a specific curvature after stable unfolding. In practical applications, this can be achieved by periodically expanding and assembling the first basic units along the longitudinal and transverse directions to form a rigid origami structure that macroscopically presents as a first surface.

[0032] Those skilled in the art will understand that the morphological characteristics (such as curvature) of the first surface exhibited by a rigid origami structure in its fully unfolded state are determined by the geometric design parameters of the first basic unit constituting the rigid origami structure (the geometric design parameters of the first basic unit may include the size of the interior angles of each rigid surface in the first basic unit at the vertices, and the length of each crease in the first basic unit). In other words, there is a specific mathematical relationship between the morphological characteristics of the first surface and the geometric design parameters of the first basic unit. Therefore, in this embodiment, to reasonably set the geometric design parameters of the first basic unit so that the rigid origami structure formed by splicing the first basic units exhibits the expected target curvature in its fully unfolded state, a first mathematical model describing the mathematical relationship between the geometric design parameters of the first basic unit and the morphological characteristics of the first surface can be determined. In one example, the first mathematical model can be derived based on the relevant knowledge of spherical trigonometry. This embodiment does not limit the specific implementation method for obtaining the first mathematical model.

[0033] Step S102: Determine the target value of the morphological features.

[0034] Specifically, the target values ​​for the morphological features can be determined based on actual design requirements. As mentioned earlier, the morphological features of the first surface generally include its curvature. In practical applications, the expected curvature value of the first surface can be determined based on actual requirements, and the determined curvature value can be used as the target value for curvature.

[0035] Step S103: By substituting the target value into the first mathematical model, the first numerical condition that the geometric design parameters should meet when the morphological features are the target values ​​is obtained.

[0036] As mentioned earlier, the first mathematical model describes the mathematical relationship between the geometric design parameters of the first basic unit and the morphological characteristics of the first surface. Therefore, after determining the target values ​​for the morphological characteristics, the first numerical conditions that the geometric design parameters should meet can be obtained by substituting these target values ​​into the first mathematical model.

[0037] Step S104: Based on the first numerical condition, determine the target design value of the geometric design parameters.

[0038] Specifically, the target design value can be taken as the value of the geometric design parameters that meets the first numerical condition.

[0039] It is understandable that since the target design value of the geometric design parameter in step S104 is obtained by substituting the target value of the morphological feature into the first mathematical model, when designing the production of the unfoldable structure with the surface configuration in the subsequent process, by designing the first basic unit according to the determined target design value, it can be ensured that the morphological feature of the surface presented by the finally obtained unfoldable structure in its maximum unfolded state conforms to the target value determined in step S102.

[0040] The surface configuration design method based on non-flat origami units provided in this application's embodiments, by setting the sum of the interior angles at the vertices of all rigid surfaces in a first basic unit within a rigid origami structure to be no greater than 2π, enables the first basic unit to possess controllable non-flat characteristics. In other words, a first basic unit can exhibit a controllable inherent curvature in its maximum unfolded state. Therefore, for a rigid origami structure formed by splicing multiple first basic units in an array, the inherent curvatures of each first basic unit can be coordinated within the array. Consequently, the rigid origami structure can spontaneously present a smooth first curved surface after reaching its maximum unfolded state, and the morphological characteristics of this first curved surface can be precisely controlled by adjusting the geometric design parameters of the first basic unit.

[0041] Based on the above principles, this application constructs a first mathematical model to describe the mathematical relationship between the geometric design parameters of the first basic unit and the morphological features of the first surface. When designing the surface configuration, by determining the target value of the expected morphological features presented by the first surface, and then substituting the target value into the first mathematical model, the target design value of the geometric design parameters corresponding to that target value can be determined. Therefore, when assembling the actual configuration of the first basic unit and the rigid origami structure based on the determined target design value, the rigid origami structure can be precisely formed into a first surface with the expected morphological features upon final unfolding.

[0042] As can be seen from the above, the embodiments of this application, by designing the first basic unit to possess controllable non-flattening characteristics, enable the rigid origami structure to spontaneously present a first curved surface with the expected morphological characteristics after stable unfolding. Compared with the traditional design scheme that focuses on the curved surface configuration of the intermediate folded state of the rigid origami structure that meets the flattening condition, this approach can ensure the surface stability of the first curved surface at the essential level of geometric configuration. It fundamentally avoids the problems of control complexity and difficulty in maintaining surface accuracy caused by the reliance on unstable intermediate folded states in traditional design schemes. This provides a new technical path for the design of deployable structures with curved surface configurations for other applications, such as deployable curved surface antennas in the aerospace field. Furthermore, the embodiments of this application, based on the constructed first mathematical model, set target design values ​​for geometric design parameters corresponding to the expected morphological characteristics of the first curved surface. Through the directional design of the geometric design parameters, a first curved surface configuration with arbitrary target curvature radius can be achieved, thus providing a general and computationally efficient design framework for realizing a series of customized curved surfaces with different curvature radii.

[0043] In one embodiment of this application, the first basic unit may specifically be a single-vertex four-fold structure. Figure 4 An example of the first basic unit of a single-vertex four-fold structure is provided; see [link to relevant documentation]. Figure 4 A first basic unit includes a vertex, and a first rigid surface along the counterclockwise direction and surrounding that vertex (the interior angle at the vertex is denoted as ). The first rigid surface), the second rigid surface (the interior angle at the vertex is denoted as...) The rigid surface), the third rigid surface (the interior angle at the vertex is denoted as ). The rigid surface of the first rigid surface and the fourth rigid surface (the interior angle at the vertex is denoted as ) The rigid surface), the fourth rigid surface and the first rigid surface are separated by the first crease ( The second crease is located between the first rigid surface and the second rigid surface. The third crease is between the second rigid surface and the third rigid surface. The fourth crease is located between the third rigid surface and the fourth rigid surface. ).

[0044] In one embodiment of this application, for Figure 4 The first basic unit of the single-vertex four-fold structure is illustrated in the diagram. To reduce the structural complexity and solution difficulty of the first mathematical model, the first basic unit can be designed with vertical symmetry, that is, making... , Furthermore, it can also make , .in, Finger crease Length, Finger crease Length, Finger crease Length, Finger crease The length.

[0045] In one example, the design for the first basic unit can be achieved by modifying the traditional Miura origami unit.

[0046] Figure 5 This illustration shows an example of a Miura origami unit, which features a symmetrical design. , , and Four creases separate four rigid parallelogram-shaped surfaces, and all four creases are of equal length. For ease of explanation, the two parallelograms in the first row of the Miura origami unit will be referred to as the first parallelogram and the second parallelogram, respectively; the two parallelograms below will be referred to as the third parallelogram and the fourth parallelogram, respectively; the outer vertex of the first parallelogram closest to the second row will be called the first vertex; the outer vertex of the second parallelogram furthest from the second row will be called the second vertex; the outer vertex of the third parallelogram closest to the first row will be called the third vertex; and the outer vertex of the fourth parallelogram furthest from the first row will be called the fourth vertex. In the embodiments of this application, it is possible to... Figure 5 The Miura origami unit shown is adjusted as follows to design the first basic unit: Adjust the first vertex of the first parallelogram away from the second row along its side; adjust the second vertex of the second parallelogram closer to the second row along its side; adjust the third vertex of the third parallelogram away from the first row along its side; adjust the fourth vertex of the fourth parallelogram closer to the first row along its side.

[0047] Simply put, it means creases The left end point is simultaneously tilted up and down at a certain angle, and the origami unit is positioned at the crease. The right endpoints of the two outer sides are simultaneously recessed inward by the same angle.

[0048] An example of the planar crease distribution diagram of the first basic unit obtained after the above adjustments can be found here. Figure 6 , Figure 6 The first basic unit shown is in Figure 5 Based on the Miura origami unit shown, by creases The left end point deflects synchronously up and down. and fold the origami unit along the crease. The right endpoints of the two outer sides indent inwards simultaneously. Obtained. In Figure 6 Within the first basic unit shown, the sizes of the four interior corners of the upper left rigid surface are as follows: , , and The rigid surface at the bottom left is symmetrical to the rigid surface at the top left. The sizes of the four interior angles of the rigid surface at the top right are respectively... , , and The rigid surface at the bottom right is symmetrical to the rigid surface at the top right.

[0049] It can be seen that, through reference Figure 6 Designing the geometry of the first basic unit in a schematic manner simplifies it to a form consisting only of [missing information - likely components]. , and The unit cell geometry can be fully defined with just three parameters.

[0050] for Figure 6 Regarding the first basic unit illustrated in the diagram, its geometric design parameters specifically include: to and to Because the first basic unit adopts a top-bottom symmetrical design, therefore , , Furthermore, to simplify the design of the geometric parameters of the first basic unit, it is possible to design... Thus, the lengths of each crease within the first basic unit satisfy: , In this case, only the first basic unit needs to be modified. , and By determining the target design values ​​of several parameters, the target design values ​​of all geometric design parameters in the first basic unit can be obtained.

[0051] The following is combined Figure 7 The folding method of rigid origami structures is explained. Figure 7 The diagram illustrates a rigid origami structure formed by piecing together multiple basic units, where the first basic unit is a single-vertex, four-fold structure. It shows the topological expansion from the first basic unit to the curved surface, with solid lines representing valley folds and dashed lines representing mountain folds. For practical applications, please refer to... Figure 7The diagram illustrates the folding method of a rigid origami structure.

[0052] also, Figure 7 The image further identifies the creases in a first basic unit within the rigid origami structure. , , and The position. Therefore, in one possible implementation of this application, referring to this example, a crease can be set within the first basic unit. , and For grain crease, crease For the mountain crease; in another possible implementation of this application, a crease can also be set within the first basic unit in a manner symmetrical to this example. , and For the mountain crease, crease For grain creases.

[0053] In one embodiment of this application, the aforementioned first mathematical model can be constructed through the following steps a1-a3: Step a1: Based on the spherical triangle theory, determine the first expression for the spatial angle between every two non-adjacent folds within the first basic unit during the unfolding process; the first expression uses geometric design parameters and the folding angle between adjacent rigid surfaces within the first basic unit as variables.

[0054] In this embodiment, specifically based on the geometric configuration of the first basic unit, the kinematic model of the first basic unit from its folded state to its unfolded state can be constructed using spherical trigonometry theory to derive the first expression. The process of deriving its kinematic model is illustrated below using a single-vertex, four-fold structure as an example: Figure 8 The three-dimensional configuration of a single-vertex four-fold structure during its unfolding process is shown. Figure 8 In the above, the interior angles of the four rigid faces at the vertices in a single-vertex four-fold structure are respectively denoted as... , , and And record the four creases as follows: , , and ,exist Figure 8 In the configuration shown, the crease The mountain crease is formed by folding counterclockwise. , and This is a valley crease formed by folding clockwise. Figure 8 In the illustration, In addition to marking the location of creases, it is also used to indicate the location of creases. Similarly, the folding angle between two adjacent rigid surfaces that are separated... It is also used to indicate creases The folding angle between two adjacent rigid surfaces that are separated. It is also used to indicate creases The folding angle between two adjacent rigid surfaces that are separated. It is also used to indicate creases The folding angle between two adjacent rigid surfaces. Based on spherical trigonometry, the kinematic relationship between the folding angles in a single-vertex four-crease structure can be derived as follows: (1) crease With creases The spatial angle between them is denoted as crease With creases The spatial angle between them is denoted as Based on the theory of spherical trigonometry, spatial angles can also be derived. and The relationship between the folding angle and the folding angle is as follows: (2) Step a2: Determine the target curvature arc on the first surface for estimating the morphological feature values.

[0055] Specifically, for a rigid origami structure formed by splicing multiple first basic units together in an array, after driving the rigid origami structure to unfold from its folded state to its maximum unfolded state, the inherent curvature of each first basic unit in the rigid origami structure can be coordinated with each other in the array, so that the rigid origami structure as a whole can spontaneously be configured into a continuous smooth surface (first surface).

[0056] In order to establish a first mathematical model by mathematically representing the morphological characteristics of the first surface, in this step, a target curvature arc for estimating the morphological characteristic values ​​can be determined on the first surface.

[0057] The following is combined Figures 9 to 10 An example is provided to illustrate the selection of the target curvature arc. Figure 9 The first basic unit is shown to employ Figure 6 A schematic diagram of the curved surface configuration of a rigid origami structure formed by splicing multiple first basic units in its fully unfolded state, under the design condition. Figure 10This shows a spatial perspective view of the curved surface configuration. For ease of explanation, in Figure 6 The endpoints of each rigid surface within the first basic unit are labeled A, B1, B2, and C, respectively. 11 C 12 C 21 C 22 D1 and D2, and in Figure 9 The text specifically marks the endpoints A, B1, B2, and C of the first basic unit within the rigid origami structure. 11 C 12 C 21 C 22 The specific locations of D1 and D2, and still... Figure 9 The line segment AD1 (crease) is marked in the middle. ) and line segment AD2 (crease) The spatial angle between ) In one example, for Figure 9 For example, you can refer to Figure 11 The diagram illustrates that the arcs containing line segments AD1 and AD2 are defined as the target curvature arcs.

[0058] Step a3: Based on the first expression and the geometric design parameters, determine the second expression for the morphological parameter values ​​on the target curvature arc to obtain the first mathematical model.

[0059] Specifically, by determining the second expression for the values ​​of the morphological parameters on the target curvature arc, and combining it with the first expression determined in step a1, the mathematical relationship between the morphological parameters and the geometric design parameters can be established, thus obtaining the first mathematical model.

[0060] The following continues from step a2. Figure 9 and Figure 11 The provided examples serve as illustrative examples. See also Figure 9 and Figure 11 As illustrated, after determining the target curvature arc and its spatial plane on the spatial curved surface configuration, the target curvature arc can be projected onto the perpendicular bisector of line segment B1B2, and the perpendicular bisector of B1B2 is used as the curvature calculation projection surface for estimating the curvature radius of the target curvature arc. Figure 11 The diagram illustrates the parametric geometric relationships within the perpendicular bisector plane and identifies the center point O corresponding to the target curvature arc, the radius of curvature R of the target curvature arc, and the angle between line segments OA1 and OD1 within the perpendicular bisector plane. The angle between line segment A1D1 and line segment OA1 within the perpendicular bisector plane And the angle between line segment A1D2 and line segment OA1 within the perpendicular bisector plane. .in, For creases With creases The angle between the planes within the perpendicular bisector of the plane.

[0061] according to Figure 9 as well as Figure 11 The geometric relationships shown can lead to the following equations (3)-(7): (3) (4) (5) (6) (7) in, , and These are intermediate variables in the modeling process.

[0062] In summary, when referring to Figure 6 When designing the first basic unit, the above equations (1) to (7) can be used as the first mathematical model to describe the mathematical relationship between the geometric design parameters of the first basic unit and the morphological features of the first surface.

[0063] Based on equations (1) to (7) above, it can be seen that by systematically adjusting and optimizing the symmetry design of the first basic unit... , and By using the same dimensional parameters, the inherent curvature characteristics of the first basic unit can be altered, thereby enabling precise and continuous control over the radius of curvature of the first surface of the rigid origami structure in its fully unfolded state. In practical applications, the target values ​​of the morphological parameters of the first surface of the rigid origami structure in its fully unfolded state can be planned first according to actual needs. Then, based on the determined target values, the numerical conditions that the geometric design parameters of the first basic unit should satisfy are calculated by inversion using the first mathematical model. Based on this, the target design values ​​of the geometric design parameters are determined, thereby ensuring that the rigid origami structure designed based on the target design values ​​can stably and continuously achieve the expected surface shape during the folding process.

[0064] In one example, if the equations (1)-(7) shown above are used as the first mathematical model for a rigid origami structure configuration, the geometric parameters for the first basic unit can be designed based on the following process: First, the radius of curvature of the first surface can be... And the central angle corresponding to a single first basic unit in a rigid origami structure. Two parameters serve as the morphological features of the first surface and are set according to actual requirements. and The target value (equivalent to) and (Target value).

[0065] Furthermore, to solve for the target design values ​​of the geometric design parameters, the folding angle between adjacent rigid surfaces within the first basic element can be further determined under the maximum unfolded state of the first basic element. In other words, the folding angle is determined. , , and The value taken when the first basic unit is in its fully expanded state. For example, in reference... Figure 6 When designing the first basic unit, the diagram can be used to set... The value is 0 when the first basic unit is in its fully expanded state, that is... exist The value at its smallest value (that is, when) , Substituting the result into equation (1) to obtain the minimum value that can be achieved simultaneously, we get the result. , and The value when the first basic unit is in its maximum unfolded state.

[0066] Finally, by setting up... and Substitute the target value into equations (3)-(7), and determine the... , , and Substituting the values ​​of the first basic unit in its maximum unfolded state into equation (2), we can synthesize equations (2)-(7) to obtain the numerical conditions that the geometric design parameters of the first basic unit should satisfy, so as to achieve the setting of the target design values ​​of the geometric design parameters. When the first basic unit adopts Figure 6 In the schematic design, the geometric design parameters can be obtained by combining equations (2) to (7). , and The numerical conditions between them, and based on these numerical conditions, determine , and The target design value; then according to and The value of is determined The value of is determined based on the fact that each rigid surface in the Miura origami unit before adjustment is a parallelogram, and then combined with... , , and By taking these values, the target design values ​​of all geometric design parameters of the first basic unit can be obtained.

[0067] Based on the above-described process for designing the geometric parameters of the first basic element, it can be seen that when determining the geometric design parameters of the first basic element, when referring to... Figure 6 When the design of the first basic unit is carried out according to the diagram, and the first basic unit adopts the design of vertical symmetry, the structural complexity and solution difficulty of the first mathematical model can be significantly reduced, so that the target design values ​​of each geometric design parameter of the first basic unit can be determined more easily and efficiently.

[0068] Based on the same inventive concept, this application also provides a surface-configurable unfoldable structure, which is formed by splicing together multiple first basic units. The geometric design parameters of the first basic units are determined using the surface-configuration design method based on non-flat origami units provided in the foregoing embodiments of this application.

[0069] For more information on the unfoldable structure of this curved surface configuration and its beneficial effects, please refer to the description of the implementation method of the curved surface configuration above, which will not be repeated here.

[0070] Based on the same inventive concept, this application also provides a curved surface configuration design device based on non-flat origami units, see [link to relevant documentation]. Figure 12 The device includes: a model acquisition module 1201, a morphological feature determination module 1202, a condition determination module 1203, and a design value determination module 1204.

[0071] The model acquisition module 1201 is used to: acquire a first mathematical model for the rigid origami structure; the rigid origami structure is formed by splicing multiple first basic units in an array, the first basic unit is a single-vertex multi-crease structure, and the sum of the interior angles of all rigid surfaces in a first basic unit at the vertex is not equal to 2π; the first mathematical model is used to describe the mathematical relationship between the geometric design parameters of the first basic unit and the morphological features of the first surface, the first surface is the surface presented by the rigid origami structure in its maximum unfolded state, and the morphological features include the radius of curvature. The morphological feature determination module 1202 is used to: determine the target value of the morphological features. The condition determination module 1203 is used to: obtain the first numerical condition that the geometric design parameters should meet under the target value of the morphological features by substituting the target value into the first mathematical model. The design value determination module 1204 is used to: determine the target design value of the geometric design parameters based on the first numerical condition.

[0072] In one embodiment of this application, the first basic unit is specifically a single-vertex four-fold structure; a first basic unit includes a vertex, and a first rigid surface, a second rigid surface, a third rigid surface and a fourth rigid surface that surround the vertex in a counterclockwise direction.

[0073] In one embodiment of this application, the size of the interior angle of the first rigid surface at a vertex is the same as the size of the interior angle of the fourth rigid surface at a vertex, and the size of the interior angle of the second rigid surface at a vertex is the same as the size of the interior angle of the third rigid surface at a vertex.

[0074] In one embodiment of this application, in a first basic unit, the second crease between the first rigid surface and the second rigid surface, the fourth crease between the third rigid surface and the fourth rigid surface, and the first crease between the fourth rigid surface and the first rigid surface are valley creases, and the third crease between the second rigid surface and the third rigid surface is a mountain crease; or, in a first basic unit, the second crease, the fourth crease, and the first crease are mountain creases, and the third crease is a valley crease.

[0075] In one embodiment of this application, the first basic unit is designed by adjusting the Miura origami unit as follows: the Miura origami unit includes a first parallelogram and a second parallelogram arranged sequentially in the first row, and a third parallelogram and a fourth parallelogram arranged sequentially in the second row. The tilt direction of the parallelograms in the first row is opposite to that of the parallelograms in the second row. The first vertex of the first parallelogram is adjusted along its side away from the second row. The first vertex is a point on the first parallelogram that is away from the second parallelogram and close to the third parallelogram. Vertex; Adjust the second vertex of the second parallelogram along its side towards the second row; the second vertex is a vertex of the second parallelogram that is farthest from the first parallelogram and farthest from the fourth parallelogram; Adjust the third vertex of the third parallelogram along its side towards the first row; the third vertex is a vertex of the third parallelogram that is farthest from the fourth parallelogram and close to the first parallelogram; Adjust the fourth vertex of the fourth parallelogram along its side towards the first row; the fourth vertex is a vertex of the fourth parallelogram that is farthest from the third parallelogram and farthest from the second parallelogram.

[0076] In one embodiment of this application, the model acquisition module 1201 is specifically used to: determine a first expression for the size of the spatial angle between every two non-adjacent creases within the first basic unit during the unfolding process of the first basic unit, based on the spherical triangle theory; the first expression uses geometric design parameters and the folding angle between adjacent rigid surfaces within the first basic unit as variables; determine a target curvature arc on the first curved surface for estimating the morphological feature values; and determine a second expression for the morphological parameter values ​​on the target curvature arc according to the first expression and the geometric design parameters, so as to obtain a first mathematical model.

[0077] In one embodiment of this application, the condition determination module 1203 is further configured to: determine the angle value of the folding angle between adjacent rigid surfaces within the first basic unit in the maximum unfolded state of the first basic unit; and substitute the determined angle value into the first mathematical model.

[0078] This application also provides an electronic device, such as... Figure 13 As shown, it includes a processor 1301, a communication interface 1302, a memory 1303, and a communication bus 1304. The processor 1301, the communication interface 1302, and the memory 1303 communicate with each other through the communication bus 1304. Memory 1303 is used to store computer programs; The processor 1301, when executing the program stored in the memory 1303, implements the curved surface configuration design method based on non-flat origami units provided in the foregoing embodiments of this application.

[0079] The communication bus mentioned in the above electronic devices can be a Peripheral Component Interconnect (PCI) bus or an Extended Industry Standard Architecture (EISA) bus, etc. This communication bus can be divided into address bus, data bus, control bus, etc. For ease of illustration, only one thick line is used to represent it in the diagram, but this does not mean that there is only one bus or one type of bus.

[0080] The communication interface is used for communication between the aforementioned electronic devices and other devices.

[0081] The memory may include random access memory (RAM) or non-volatile memory (NVM), such as at least one disk storage device. Optionally, the memory may also be at least one storage device located remotely from the aforementioned processor.

[0082] The processors mentioned above can be general-purpose processors, including central processing units (CPUs), network processors (NPs), etc.; they can also be digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components.

[0083] In another embodiment provided in this application, a computer-readable storage medium is also provided, which stores a computer program that, when executed by a processor, implements the steps of any of the above-described surface configuration design methods based on non-flat origami units.

[0084] In another embodiment provided in this application, a computer program product containing instructions is also provided, which, when run on a computer, causes the computer to execute any of the curved surface configuration design methods based on non-flat origami units in the above embodiments.

[0085] In the above embodiments, implementation can be achieved entirely or partially through software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented entirely or partially as a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid state disk (SSD)).

[0086] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0087] The various embodiments in this specification are described in a related manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, the embodiments of curved surface configuration design devices, electronic devices, and unfoldable structures based on non-flat origami units are basically similar to the method embodiments, so the descriptions are relatively simple; relevant parts can be referred to the descriptions of the method embodiments.

[0088] The above description is merely a preferred embodiment of this application and is not intended to limit the scope of protection of this application. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application are included within the scope of protection of this application.

Claims

1. A method for designing curved surface configurations based on non-flat origami units, characterized in that, The method includes: A first mathematical model is obtained for the construction of a rigid origami structure. The rigid origami structure is formed by splicing multiple first basic units together in an array. The first basic unit is a single-vertex multi-crease structure, and the sum of the interior angles of all rigid surfaces in a first basic unit at the vertex is not equal to 2π. The first mathematical model is used to describe the mathematical relationship between the geometric design parameters of the first basic unit and the morphological features of the first surface. The first surface is the surface presented by the rigid origami structure in its maximum unfolded state, and the morphological features include the radius of curvature. Determine the target value of the morphological feature; By substituting the target value into the first mathematical model, the first numerical condition that the geometric design parameters should meet when the morphological feature is the target value is obtained; Based on the first numerical condition, the target design value of the geometric design parameter is determined.

2. The method according to claim 1, characterized in that, The first basic unit is specifically a single-vertex four-fold structure; one first basic unit includes a vertex, and a first rigid surface, a second rigid surface, a third rigid surface and a fourth rigid surface that surround the vertex in a counterclockwise direction.

3. The method according to claim 2, characterized in that, The size of the interior angle of the first rigid surface at a vertex is the same as the size of the interior angle of the fourth rigid surface at a vertex, and the size of the interior angle of the second rigid surface at a vertex is the same as the size of the interior angle of the third rigid surface at a vertex.

4. The method according to claim 2, characterized in that, In a first basic unit, the second crease between the first rigid surface and the second rigid surface, the fourth crease between the third rigid surface and the fourth rigid surface, and the first crease between the fourth rigid surface and the first rigid surface are valley creases, and the third crease between the second rigid surface and the third rigid surface is a mountain crease; or, In a first basic unit, the second crease, the fourth crease, and the first crease are mountain creases, and the third crease is a valley crease.

5. The method according to claim 2, characterized in that, The first basic unit is designed by adjusting the Miura origami unit as follows: the Miura origami unit includes a first parallelogram and a second parallelogram arranged sequentially in the first row, and a third parallelogram and a fourth parallelogram arranged sequentially in the second row, wherein the inclination direction of the parallelograms in the first row is opposite to that of the parallelograms in the second row. The first vertex of the first parallelogram is adjusted along its side away from the second row; the first vertex is a vertex of the first parallelogram that is away from the second parallelogram and close to the third parallelogram. The second vertex of the second parallelogram is adjusted along its side toward the second row; the second vertex is a vertex of the second parallelogram that is far from the first parallelogram and far from the fourth parallelogram. The third vertex of the third parallelogram is adjusted along its side away from the first row; the third vertex is a vertex of the third parallelogram that is away from the fourth parallelogram and close to the first parallelogram. The fourth vertex of the fourth parallelogram is adjusted along its side toward the first row; the fourth vertex is a vertex of the fourth parallelogram that is far away from the third parallelogram and far away from the second parallelogram.

6. The method according to claim 1 or 2, characterized in that, The first mathematical model was constructed in the following way: Based on the theory of spherical triangles, a first expression is determined for the size of the spatial angle between every two non-adjacent folds within the first basic unit during the unfolding process; the first expression uses the geometric design parameters and the folding angle between adjacent rigid surfaces within the first basic unit as variables. On the first surface, a target curvature arc is determined for estimating the value of the morphological feature; Based on the first expression and the geometric design parameters, a second expression is determined to take the values ​​of the morphological parameters on the target curvature arc, so as to obtain the first mathematical model.

7. The method according to claim 6, characterized in that, Before determining the target design value of the geometric design parameters based on the first numerical condition, the method further includes: Determine the folding angle between adjacent rigid surfaces within the first basic unit when the first basic unit is in its maximum unfolded state. Substitute the determined angle value into the first mathematical model.

8. A curved surface configuration design device based on non-flat origami units, characterized in that, The device includes: The model acquisition module is used to acquire a first mathematical model for the rigid origami structure. The rigid origami structure is formed by splicing together multiple first basic units. The first basic unit is a single-vertex multi-crease structure, and the sum of the interior angles of all rigid surfaces at the vertex in a first basic unit is not equal to 2π. The first mathematical model is used to describe the mathematical relationship between the geometric design parameters of the first basic unit and the morphological features of the first surface. The first surface is the surface presented by the rigid origami structure in its maximum unfolded state, and the morphological features include the radius of curvature. A morphological feature determination module is used to determine the target value of the morphological feature; The condition determination module is used to obtain a first numerical condition that the geometric design parameters should meet when the morphological feature is the target value by substituting the target value into the first mathematical model. The design value determination module is used to determine the target design value of the geometric design parameters based on the first numerical condition.

9. An electronic device, characterized in that, It includes a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other through the communication bus; Memory, used to store computer programs; A processor, when executing a program stored in memory, implements the steps of the method described in any one of claims 1-7.

10. A deployable structure with a curved surface configuration, characterized in that, The deployable structure is formed by splicing together multiple first basic units, the geometric design parameters of which are determined by the method described in any one of claims 1-7.

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