CN113378391B - Configuration method of space curved foldable array mechanism and foldable array mechanism - Google Patents

Abstract

The invention provides a configuration method of a space curved foldable array mechanism based on Flasher origami and a space curved foldable array mechanism. The configuration method includes: 1) determining an array center, an array mechanism of the space curved foldable array mechanism The number of layers, the number of array loops, and the shape of the space surface are used to establish a plane foldable array mechanism model based on Flasher origami as a benchmark; 2) It is calculated that the established plane foldable array mechanism model forms a plane when it is in a fully expanded state. The fold valley/peak vertices on the midline crease of each folded and unfolded partition of the array and the ridge vertices on the connection creases of the adjacent folded and unfolded partitions; 3) Perform parallel projection to the space surface; 4) Obtain the feasible solution that satisfies the constraints. Fitting error; 5) Repeat the calculation for many times to obtain the vertex positions of all the curved surface arrays of the curved surface foldable array mechanism model, and complete the configuration of the curved surface foldable array mechanism model. The invention has the advantages of light weight, large and variable folding ratio, and high curve fitting accuracy.

Description

Configuration method of space curved foldable array mechanism and foldable array mechanism

technical field

The invention belongs to the technical field of space foldable and expandable mechanisms, relates to a space curved surface foldable and expandable mechanism, and more particularly relates to a configuration method of a space curved foldable and expandable array mechanism based on Flasher origami and a spatial curved surface foldable obtained by adopting the configuration thereof. Exhibition array.

Background technique

Space curved reflectors and curved antennas, as important components of the spacecraft, provide communication guarantees for the spacecraft. The foldable array of space curved surface has the characteristics of foldable and expandable, and has been widely used and studied. Due to the increasing demand for foldable curved arrays in applications such as deep space exploration and interstellar communication, it is necessary to design curved foldable arrays with lighter weight, larger folding ratio and higher precision. The traditional curved surface foldable array has a complex mechanism, a large folded volume, and a fixed fold-to-expand ratio, which can no longer meet higher application requirements. The Flasher origami model has the characteristics of large folding ratio, definite degree of motion and good ductility, and has been widely used in the design of large-scale flat foldable mechanisms in space.

Chinese patent 201910269483.8 discloses a hinge realization method of a Flasher expandable mechanism. The mechanism is mainly assembled by several groups of rigid plates, central plates, flexible springs, hinge hinges and bolts, and several groups of rigid plates are all of the same structure. The whole mechanism is in a rotationally symmetrical configuration.

The above-mentioned prior art belongs to the plane mechanism.

Based on this, a configuration method of a space curved foldable array mechanism based on Flasher origami and a space curved foldable array mechanism obtained by adopting its configuration are proposed to realize the application of the Flasher origami model in the space curved foldable mechanism. application.

The shape of the center base and the number of folded layers can be adjusted according to the requirements of use, and the space surface foldable array with light weight, large and variable folding ratio, and high surface fitting accuracy can be designed according to the surface fitting of spherical targets with different radii. Adapt to application needs.

SUMMARY OF THE INVENTION

In view of the defects of the prior art, the present invention provides a configuration method of a space curved foldable array mechanism based on Flasher origami and a space curved foldable array mechanism obtained by adopting the configuration, which has the advantages of light weight, high folding ratio It is large and variable, and has the advantages of high surface fitting accuracy.

In order to achieve the above object, on the one hand, the present invention provides a configuration method of a space curved foldable array mechanism based on Flasher origami, which includes:

1) Determine the array center, the number of array layers, the number of array rings and the shape of the space curved surface of the space curved surface foldable array mechanism, in which the regular polygonal prism base is used as the array center, and the array of the space curved surface foldable array mechanism is determined. The center, the number of array layers and the number of array rings are used as a benchmark to establish a planar foldable array mechanism model based on Flasher origami;

2) Calculate the fold valley/peak apex on the midline crease of each foldable and unfolded area of the plane array and the folds on the connection creases of the adjacent folded and unfolded areas when the established planar foldable array mechanism model is in a fully unfolded state. ridge vertex;

3) Obtain the radius and sphere center of the sphere where the space surface is located, set the center of the plane foldable array mechanism model in the fully expanded state at the center of the sphere of the space surface, and perform parallel projection toward the space surface to obtain A series of curved surface array ridge vertices corresponding to plane ridge vertices and a series of surface array valley/fold peak vertices to be optimized corresponding to plane fold valley/fold peak vertices;

4) Use the numerical method to obtain the distance from the valley/peak vertex of the curved surface array to be optimized to the spherical surface that satisfies the folding geometric constraints and the surface equation constraints, and takes this distance as the fitting error of the feasible solution, and the fitting error is the smallest among all feasible solutions. The solution of the surface array as valley/peak vertices;

5) Repeat the calculation for many times to obtain the vertex positions of all the curved surface arrays of the curved surface foldable array mechanism model, and complete the configuration of the curved surface foldable array mechanism model.

The space curved surface in the present invention is a space curved surface on a designated spherical surface.

As another specific embodiment of the present invention, the apex of the valley/peak of the curved surface array to be optimized and the two adjacent ridge vertices of the curved surface array on the same connecting crease form a triangular folded sheet, and the valley/peak of the curved surface array to be optimized Collapsing geometric constraints that vertices need to satisfy include:

An angle constraint, wherein the angle constraint defines that two triangular folded sheets with a common side have two sides that overlap each other after folding, and the common side is located on the midline crease;

Side length constraint, where the side length constraint defines that one of the non-common sides of a triangular folded sheet coincides with the side edge of the regular polygonal prism base after being folded, and the non-common side is the inner angle of the fold valley/fold peak vertex of the surface array to be optimized the opposite side;

Surface Constraints, where the surface constrains the valley/peak vertices of the surface array to be optimized lie on the determined space surface.

As another specific embodiment of the present invention, when the number of array rings is a single ring, the midline crease of each folding and unfolding subsection is in the same direction, that is, a folded valley or a folding peak; Creases exist in two opposite directions, namely valleys and peaks.

On the other hand, the present invention also provides a space curved foldable array mechanism using the above-mentioned configuration method of the space curved foldable array mechanism based on Flasher origami, which includes a regular polygonal prism base and a plurality of foldable arrays. Expandable array unit, a plurality of foldable and expandable array unit arrays are distributed on the outer circumference of the regular polygonal prism base.

As another specific embodiment of the present invention, the foldable array unit includes a number of triangular folded sheets distributed based on the Flasher origami mechanism, wherein the folds located at the side edges of the regular polygonal prism base after folding are provided with torsion and displacement Functional two-degree-of-freedom flexure hinges, and single-degree-of-freedom flexure hinges with torsion function at other creases.

The present invention has the following beneficial effects:

The invention creatively abstracts the parametric design problem of the target space curved surface foldable array into an optimization problem, integrates the surface equation constraints and the folding geometric constraints into one, conducts a three-dimensional search through an iterative method and determines the appropriate vertex positions, so that the The space curved surface foldable and expandable array mechanism configured in the invention can be expanded into a high-precision designated curved surface, and can be folded and folded, and has the advantages of light weight, large and variable folding ratio, and high surface fitting accuracy.

In the present invention, different base shapes can be designed, and curved surface folding arrays with different radius spheres and different layers can be designed. When folded, the volume is small, and it has the advantages of easy loading and transportation.

The two different hinge connections used between the triangular folded sheets in the space curved foldable array mechanism of the present invention can adapt to the thickness of the triangular unfolded sheets when the spatial curved foldable array mechanism is folded to ensure complete folding.

The present invention will be further described in detail below in conjunction with the accompanying drawings.

Description of drawings

1 is a schematic diagram of a planar foldable and expandable array mechanism model serving as a reference in a fully expanded state according to an embodiment of the configuration method of the present invention;

Fig. 2 is the schematic diagram after Fig. 1 is folded;

3 is a schematic diagram of a parallel projection of a plane foldable array mechanism model in a fully expanded state toward a space curved surface in an embodiment of the configuration method of the present invention;

4 is a schematic diagram of a spatial curved surface foldable array mechanism model configured by an embodiment of the configuration method of the present invention;

Fig. 5 is the unfolded model schematic diagram of the single-ring array single foldable array unit in Fig. 4;

6 is a schematic diagram of another spatial curved surface foldable array mechanism model configured by an embodiment of the configuration method of the present invention;

Fig. 7 is the unfolded model schematic diagram of single-ring array single foldable array unit in Fig. 6;

8 is a schematic diagram of the constraint relationship of the first folding layer of a single foldable array unit during folding in an embodiment of the configuration method of the present invention;

9 is a schematic diagram of the constraint relationship of the second folding layer of a single foldable array unit during folding in an embodiment of the configuration method of the present invention;

FIG. 10 is a schematic diagram showing a space curved foldable array mechanism of a single ring array in an embodiment of the configuration method of the present invention;

11 is a schematic diagram showing a space curved foldable array mechanism of a double-ring array in an embodiment of the configuration method of the present invention;

12 is a schematic diagram of connection and cooperation of a single foldable array unit in an embodiment of the space curved foldable array mechanism of the present invention.

Detailed ways

In order to understand the above objects, features and advantages of the present invention more clearly, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that the embodiments of the present application and the features in the embodiments may be combined with each other in the case of no conflict.

Many specific details are set forth in the following description to facilitate a full understanding of the present invention. However, the present invention can also be implemented in other ways different from those described herein. Therefore, the protection scope of the present invention is not limited to the specific details disclosed below. Example limitations.

A configuration method of a space curved foldable array mechanism based on Flasher origami, comprising:

1) Determine the array center, the number of array layers, the number of array rings and the shape of the space curved surface of the space curved surface foldable array mechanism, in which the regular polygonal prism base is used as the array center, such as regular triangular prism, regular quadrangular prism, regular hexagonal prism, regular eight prism The number of prismatic array layers is N≥2, and the number of array rings is M≥1. According to the determined array center, number of array layers and number of array rings of the spatial curved surface foldable array mechanism, a Flasher-based origami is established as a benchmark. The plane foldable array mechanism model of , as shown in Figure 1-2;

Among them, the method for establishing a planar foldable array mechanism model is applicable to the prior art, such as the literature published by the authors Zirbel Shannon A, Robert J. Lang and others in the journal titled "Transactions of the A SME: Journal of Mechanical Design" Introduced in Accommodating Thickness in Origami-BasedDeployable Arrays.

2) Calculate the plane fold valley/fold peak apex on the midline crease of each fold-and-expand area and the adjacent fold-out area connection crease when the established plane foldable array mechanism model is in the fully expanded state. plane ridge vertex;

3) Obtain the radius and spherical center of the spherical surface where the space curved surface is located, set the center of the plane foldable array mechanism model in the fully expanded state at the spherical center of the space curved surface, and perform parallel projection toward the space curved surface, such as As shown in Fig. 3, a series of curved surface array ridge vertices corresponding to the plane ridge vertices and a series of curved valley/fold peak vertices to be optimized corresponding to the plane folded valley/folded peak vertices are obtained;

The obtained series of surface array ridge vertices can be directly used as surface array ridge vertices, and the obtained series of curved valley/fold peak vertices of the surface array to be optimized need to satisfy the optimization of folding geometric constraints and surface equation constraints, and then be used as surface arrays Valley/Crest apex.

As shown in Figures 4-5, an example of a regular hexagonal prism base, the number of array layers is 4, and the number of array rings is 1, which includes six foldable array units, and each foldable array unit includes four layers, wherein the first layer includes two triangular folds and the other three layers each include four triangular folds.

In the figure, 101-106 are six foldable array unit partitions, 111-114 are four folded layers of a single partition 101, 115 is the inner triangular folded sheet fold, and 116 is the center line fold in the foldable and expandable array unit partition , 117 is the crease of the triangular folded sheet between layers, and 118 is the crease of the connection between the sub-divisions of the foldable array unit.

Wherein, when a foldable array unit with an array ring number of 1 is folded along the midline crease, the midline crease is in the same direction, that is, the folded peak or the folded valley;

As shown in Figures 6-7, the hexagonal prism base, the number of array layers is 4, and the number of array rings is 2 as an example for illustration, including six foldable and expandable array units, of which the number of foldable array rings is 2. The difference between the expandable array unit and the foldable array unit with an array ring number of 1 is that the foldable array unit with an array ring number of 2 also includes a first ring and a second ring, and the first ring and the second ring are connected. After folding, the crease must be parallel to the bottom edge of the regular polygonal prism base. In order to meet its foldable characteristics, the folding direction of the second ring centerline crease is opposite to that of the first ring centerline crease, and at the same time, the second ring centerline crease is folded in the opposite direction. The mark is the axis of symmetry, and the triangular folds on both sides are congruent;

Specifically, when a foldable array unit with an array ring number of 2 is folded along the midline crease, the midline crease has two opposite directions, namely the fold valley and the fold peak, so that the height of the partitions after being tightly folded will not gradually increase. It plays the role of controlling the loading height after folding.

In the figure, 201-206 are six foldable array unit partitions, 211 is the first ring part of a single foldable array unit partition, 212 is the second ring part, 221 is the midline crease of the second ring, 222 is The first loop and the second loop connect the crease; 301 and 302 are the two triangular folded sheets in the first layer, and 303 is the base of the regular hexagonal prism.

4) Use the numerical method to obtain the distance from the valley/peak vertex of the curved surface array to be optimized that satisfies the folding geometric constraints and the surface equation constraints to the spherical surface. As shown in Figure 8-9, this distance is used as the fitting error of the feasible solution, and the The solution with the smallest fitting error among all feasible solutions is regarded as the vertex of the valley/peak of the surface array;

5) Repeat the calculation several times to obtain the vertex positions of all the surface arrays of the surface foldable array mechanism model, and complete the configuration of the surface foldable array mechanism model, as shown in Figure 10-11.

Further, the folded valley/peak apex of the curved surface array to be optimized and the two adjacent curved ridge vertices on the same connecting crease form a triangular folded sheet, and the folding geometric constraints that the folded valley/folded peak apex of the curved surface array to be optimized need to satisfy. include:

An angle constraint, wherein the angle constraint defines that two triangular folded sheets with a common side have two sides that overlap each other after folding, and the common side is located on the midline crease;

Side length constraint, where the side length constraint defines that one of the non-common sides of a triangular folded sheet coincides with the side edge of the regular polygonal prism base after being folded, and the non-common side is the inner angle of the fold valley/fold peak vertex of the surface array to be optimized the opposite side;

Surface Constraints, where the surface constrains the valley/peak vertices of the surface array to be optimized lie on the determined space surface.

Specifically, the geometric constraints of the first layer of a single foldable array unit shown in FIG. 8 , wherein the first layer includes a first triangular folded sheet 301 and a second triangular folded sheet 302, and the angle constraints to be satisfied by the two are:

The above angle constraints guarantee that the first triangular folded sheet P' _1,1,1 P' _1,2,1 and the second triangular folded sheet P' _1,1,1 P' _1,2,1 after folding on the same straight line;

At the same time, the edge length constraints that both need to be satisfied are:

||P' _0,0,1 P' _1,1,1 ||cosβ ₁ =a

In the above formula, a is the length of the bottom side of the base. Combined with the angle relationship, it can ensure that the _sides P' 1, 1, 1 P' 1, 2, ₁ and the sides P' _{1, 2, 1} P' ₀ , 0, 2 are in the After being folded, it can be coincident with the side edges of the regular hexagonal prism base, so as to realize tight folding.

At the same time, the two also need to meet the surface constraints, that is, the points to be found in the unfolded state (the vertices of the valleys/peaks of the surface array to be optimized) should be on the space surface.

More specifically, the geometric constraints of the second layer of a single foldable array unit shown in FIG. 9 , wherein the second layer includes four triangular folded sheets, and the angle constraints that the four triangular folded sheets need to satisfy are:

The above angle constraints guarantee that the sides P' _2,1,1 P' _2,2,1 and P' _2,2,1 P' _1,1,2 of the two triangular folds on either side of the midline crease of the second layer On the same line after folding.

The edge length constraints that need to be satisfied at the same time are:

||P' _1,1,1 P' _2,1,1 ||cosβ ₂ =a

Ensure that the two sides P' _2,1,1 P' _2,2,1 and P' _2,2,1 P' _1,1,2 are located on the side edges of the regular hexagonal prism base 303 after folding, so that the space curved surface The collapsible array mechanism can be folded around the side edges.

At the same time, the surface constraints must be satisfied, that is, the points to be found in the unfolded state (the fold valley/peak vertices of the surface array to be optimized) should be on the space surface.

When the other layers after the second layer are designed, the geometric constraints to be satisfied are similar to those of the second layer, which will not be explained in detail here.

In this embodiment, when configuring a foldable array unit with an array ring number of 2, the design constraints of the first ring part are the same as the configuration of a foldable array unit with an array ring number of 2. The first ring and the second ring The connecting crease must be parallel to the bottom edge of the regular polygon base after folding. In order to meet its foldable characteristics, the folding direction of the centerline crease of the second ring is opposite to that of the centerline crease of the first ring, and at the same time, the centerline crease of the second ring is used as the axis of symmetry, and the triangular folded sheets on both sides are congruent; Satisfy the surface constraints. In this way, the vertices of the entire space curved surface foldable array mechanism are located on the target curved surface when unfolded, which is very good for surface fitting; when folded and folded, the first ring part is folded upward, and the second ring part is folded downward, which is very good. The array height in the folded state is limited, as shown in the folded area in Figure 11.

A space curved foldable array mechanism using the above-mentioned configuration method of the space curved foldable array mechanism based on Flasher origami, which comprises a regular polygonal prism base and a plurality of foldable array units, and a plurality of foldable and unfoldable array units. The array unit array is distributed on the outer periphery of the regular polygonal prism base.

The foldable array unit includes a number of triangular folded sheets distributed based on the Flasher origami mechanism. The folds located at the side edges of the regular polygonal prism base after folding are provided with dual-degree-of-freedom flexible hinges with torsion and displacement functions. Other folds There is a single degree of freedom flexible hinge with torsion function.

In the engineering application of the curved surface foldable array, due to the thickness of each triangular folded sheet, and since the curved surface foldable array is unfolded to fit the curved surface, it needs to be tightly wound around the base of the regular polygonal prism when folded, and the flexible hinges at different positions The performance requirements are different. As shown in FIG. 12, the centerline crease 116 (the centerline crease 221 of the second ring) within the foldable array unit partition, the connecting fold 118 between the foldable array unit partitions, the first ring and the second ring The loop connection crease 222 needs to be fully folded when folded, and the I-type flexible hinge with only torsion function is used in these places, and the triangular folded sheet crease 115 in the layer only needs to be slightly bent when folded, and only the torsion function is provided in these places. The I-type flexible hinge, the interlayer triangular folded sheet crease 117 is located at the edge of the regular hexagonal prism when it is folded. It needs to adapt to the thickness of the folded triangular folded sheet. In addition to the need for torsion, it will also be stretched to produce a gap. These joints are used to provide torsion. and displacement of the Type II flexible hinge 402 .

Using two different flexible hinges at different crease positions can ensure that the curved foldable array maintains the curved shape when unfolded, and wraps tightly around the base of the regular hexagonal prism when folded.

Compared with the plane Flasher model, the space curved foldable array mechanism in this embodiment has the ability to fit the curved surface after expansion, so as to obtain a curved surface array; folded sheet and quadrilateral folded sheet) so that the curved surface folded array can better fit the target surface; after its close folding, the lower edge of each partition shows a gradual upward trend in the regular hexagonal prism, while the lower edge of all partitions in the planar Flasher model is located at the same height (located on the lower edge of the base of the regular hexagonal prism).

Correspondingly, in addition to the curved surface foldable array based on a regular hexagonal prism, a space curved foldable array mechanism based on other regular polygonal prisms can also be designed.

Everything not covered above is applicable to the prior art.

Although the present invention is disclosed above with preferred embodiments, it is not intended to limit the scope of implementation of the present invention. Any person of ordinary skill in the art can make some improvements without departing from the scope of the present invention, that is, all equivalent improvements made according to the present invention should be covered by the scope of the present invention.

Claims (4)

1. a configuration method based on the space curved surface foldable array mechanism of Flasher origami, is characterized in that comprising: 1) Determine the array center, the number of array layers, the number of array rings and the shape of the space curved surface of the space curved surface foldable array mechanism, in which the regular polygonal prism base is used as the array center, and the array of the space curved surface foldable array mechanism is determined. The center, the number of array layers and the number of array rings are used as a benchmark to establish a planar foldable array mechanism model based on Flasher origami; 2) Calculate the fold valley/peak apex on the midline crease of each foldable zone and the fold on the connection crease of the adjacent foldable zone when the established planar foldable array mechanism model is in the fully expanded state. ridge vertex; 3) Obtain the radius and center of the sphere where the space surface is located, set the center of the plane foldable array mechanism model in the fully expanded state at the center of the space surface, and perform parallel projection toward the space surface to obtain A series of ridge vertices of a curved surface array corresponding to the vertices of the plane ridges and a series of valley/peak vertices of the surface array to be optimized corresponding to the vertices of the plane folds/peaks; 4) Use the numerical method to find the distance from the fold valley/fold peak vertex of the surface array to be optimized that satisfies the folded geometric constraints and the surface equation constraints to the spherical surface, and use this distance as the fitting error of the feasible solution, and the fitting error is the smallest among all feasible solutions. The solution of the surface array as valley/peak vertices; 5) Repeat the calculation several times to obtain the vertex positions of all the surface arrays of the surface foldable array mechanism model, and complete the configuration of the surface foldable array mechanism model. 2. the configuration method of the space curved surface foldable array mechanism based on Flasher origami as claimed in claim 1, it is characterized in that, the two adjacent to it on the curved surface array fold valley/fold peak vertex to be optimized and the same connection crease The ridge vertices of the curved surface array form triangular folded sheets, and the folding geometric constraints to be satisfied by the folded valley/peak vertices of the curved surface array to be optimized include: An angle constraint, wherein the angle constraint defines that two triangular folded sheets with a common side have two sides that overlap each other after folding, and the common side is located on the midline crease; Side length constraint, where the side length constraint defines that one of the non-common sides of a triangular folded sheet coincides with the side edge of the regular polygonal prism base after being folded, and the non-common side is the inner angle of the fold valley/fold peak vertex of the surface array to be optimized the opposite side; Surface Constraints, where the surface constrains the valley/peak vertices of the surface array to be optimized lie on the determined space surface. 3. A space curved surface foldable array mechanism using the configuration method of the flasher origami-based space curved surface foldable array mechanism according to claim 1 is characterized in that, comprising a regular polygonal prism base and a plurality of foldable Expandable array unit, a plurality of foldable and expandable array unit arrays are distributed on the outer circumference of the regular polygonal prism base. 4. The space curved foldable array mechanism according to claim 3, wherein the foldable array unit comprises a plurality of triangular folded sheets distributed based on the Flasher origami mechanism, wherein after folding, they are located at the side edges of the regular polygonal prism base There are double-DOF flexible hinges with torsion and displacement functions on the crease, and single-DOF flexible hinges with torsion function are located at other creases.

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