CN113378391B - Configuration method of space curved surface foldable array mechanism and foldable array mechanism - Google Patents
Configuration method of space curved surface foldable array mechanism and foldable array mechanism Download PDFInfo
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Abstract
The invention provides a configuration method of a space curved surface foldable and expandable array mechanism based on Flasher origami and the space curved surface foldable and expandable array mechanism, wherein the configuration method comprises the following steps: 1) determining the array center, the array layer number, the array ring number and the shape of the space curved surface foldable array mechanism, and establishing a plane foldable array mechanism model based on flash origami as a reference; 2) calculating to obtain valley/peak points on the crease of the central line of each folding and unfolding subarea of the plane array and peak points on the connecting crease of the adjacent folding and unfolding subareas when the established plane foldable and unfoldable array mechanism model is in a fully unfolded state; 3) performing parallel projection towards the space curved surface; 4) solving fitting errors of feasible solutions which meet the constraints; 5) and repeating the calculation for multiple times to obtain the vertex positions of all the curved surface arrays of the curved surface foldable and expandable array mechanism model, thereby completing the configuration of the curved surface foldable and expandable array mechanism model. The invention has the advantages of light weight, large and variable folding-unfolding ratio, high curved surface fitting precision and the like.
Description
Technical Field
The invention belongs to the technical field of space foldable and unfoldable mechanisms, and relates to a space curved surface foldable and unfoldable mechanism, in particular to a configuration method of a space curved surface foldable and unfoldable array mechanism based on Flasher folded paper and the space curved surface foldable and unfoldable array mechanism obtained by adopting the configuration method.
Background
The space curved surface reflector and the curved surface antenna are used as important components of the spacecraft, and communication guarantee is provided for the spacecraft. The space curved surface foldable array has the characteristic of being foldable and unfoldable and is widely applied and researched. Due to the increasingly high demand of applications such as deep space exploration and interplanetary communication on the foldable curved array, the foldable curved array with lighter mass, larger folding-unfolding ratio and higher precision needs to be designed. The traditional curved surface foldable array mechanism is complex, large in folding volume and fixed in folding and unfolding ratio, and cannot meet higher application requirements. The Flasher paper folding model has the characteristics of large folding-unfolding ratio, definite motion degree, good extensibility and the like, and is widely applied to the design of a large-space plane folding-unfolding mechanism.
Chinese patent 201910269483.8 discloses a hinge implementation method for a Flasher deployable mechanism, which is mainly assembled by a plurality of sets of rigid plates, a central plate, flexible reeds, hinge hinges and bolts, wherein the plurality of sets of rigid plates are all in a consistent configuration, and the whole mechanism is in a rotational symmetry configuration.
The above prior art belongs to a planar mechanism.
Based on the above, a configuration method of the space curved surface foldable and expandable array mechanism based on the Flasher folded paper and the space curved surface foldable and expandable array mechanism obtained by adopting the configuration method are especially provided, so that the application of a Flasher folded paper model in the space curved surface foldable and expandable mechanism is realized.
The shape of the central base and the number of folding layers can be adjusted according to the use requirement, and the space curved surface foldable array has the advantages of light weight, large and variable folding-unfolding ratio and high curved surface fitting precision, and can be designed according to spherical target fitting curved surfaces with different radiuses, and can meet the application requirements.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a configuration method of a space curved surface foldable array mechanism based on Flasher folding paper and the space curved surface foldable array mechanism obtained by adopting the configuration method, and the space curved surface foldable array mechanism has the advantages of light weight, large and variable folding-unfolding ratio, high curved surface fitting precision and the like.
In order to achieve the above object, in one aspect, the present invention provides a configuration method of a spatial curved surface foldable and expandable array mechanism based on Flasher folding paper, which includes:
1) determining the array center, the array layer number, the array ring number and the shape of a space curved surface of the foldable and expandable array mechanism with the space curved surface, wherein a regular multi-prism base is adopted as the array center, and a plane foldable and expandable array mechanism model based on Flasher origami as a reference is established according to the array center, the array layer number and the array ring number of the foldable and expandable array mechanism with the space curved surface;
2) calculating to obtain valley/peak points on the crease of the central line of each folding and unfolding subarea of the plane array and peak points on the connecting crease of the adjacent folding and unfolding subareas when the established plane foldable and unfoldable array mechanism model is in a fully unfolded state;
3) acquiring the radius and the spherical center of a spherical surface where the space curved surface is located, arranging the center of the plane foldable array mechanism model in a completely unfolded state at the spherical center of the space curved surface, and performing parallel projection towards the space curved surface to obtain a series of curved surface array folding ridge vertexes corresponding to the flat folding ridge vertexes and a series of curved surface array folding valley/folding peak vertexes to be optimized corresponding to the flat folding valley/folding peak vertexes;
4) calculating the distance from the valley-folding/peak-folding peak of the curved surface array to be optimized to the spherical surface, which meets the folding geometric constraint and the curved surface equation constraint, by adopting a numerical method, taking the distance as the fitting error of a feasible solution, and taking the solution with the minimum fitting error in all feasible solutions as the peak of the valley-folding/peak-folding of the curved surface array;
5) and repeating the calculation for multiple times to obtain the vertex positions of all the curved surface arrays of the curved surface foldable and expandable array mechanism model, thereby completing the configuration of the curved surface foldable and expandable array mechanism model.
The space curved surface in the invention is a space curved surface on a designated spherical surface.
As another specific embodiment of the present invention, the curved array valley/peak to be optimized and the two curved array ridge vertices on the same connecting fold that are close to the curved array valley/peak to be optimized form a triangular folded sheet, and the folding geometric constraints that the curved array valley/peak to be optimized needs to satisfy include:
an angle constraint, wherein the angle constraint defines that two triangular folded sheets having a common edge have two edges coinciding with each other after folding, the common edge being located on the midline fold;
the method comprises the following steps of side length constraint, wherein the side length constraint limits one non-common side of a triangular folding sheet to coincide with a side edge of a regular polygon prism base after being folded, and the non-common side is the opposite side of an inner angle where a valley/peak vertex of a curved surface array to be optimized is located;
and (4) curved surface constraint, wherein the curved surface constraint to be optimized curved surface array valley folding/peak folding vertex is positioned on the determined space curved surface.
As another specific embodiment of the present invention, when the number of the array rings is a single ring, the central line creases of each folding and unfolding sub-area are in the same direction, i.e. a valley or a peak; when the number of the array rings is double, the central line crease of each folding and unfolding subarea has two opposite directions, namely a valley fold and a peak fold.
On the other hand, the invention also provides a spatial curved surface foldable and unfoldable array mechanism adopting the configuration method of the spatial curved surface foldable and unfoldable array mechanism based on the Flasher origami, which comprises a regular multi-prism base and a plurality of foldable and unfoldable array units, wherein the plurality of foldable and unfoldable array units are distributed on the periphery of the regular multi-prism base in an array manner.
As another specific embodiment of the invention, the foldable and expandable array unit comprises a plurality of triangular folding sheets distributed based on a Flasher paper folding mechanism, wherein a double-freedom-degree flexible hinge with torsion and displacement functions is arranged on a folding line positioned at the side edge of the regular polygonal base after being folded, and a single-freedom-degree flexible hinge with torsion function is arranged at other folding lines.
The invention has the following beneficial effects:
the invention creatively refines the parameterization design problem of the target space curved surface foldable array into an optimization problem, integrates the curved surface equation constraint and the folding geometric constraint, carries out three-dimensional search in an iteration mode and determines a proper vertex position, so that the space curved surface foldable array mechanism formed in the invention can be unfolded into a high-precision designated curved surface and folded, and has the advantages of light weight, large folding-unfolding ratio, variability, high curved surface fitting precision and the like.
The space curved surface foldable array mechanism can be designed into curved surface foldable arrays with different base shapes, spherical surfaces with different radiuses and different layers, has large folding and unfolding ratio, large area during unfolding and small volume during folding, and has the advantage of convenient loading and transportation.
The two different hinges adopted for connecting the triangular folding pieces in the spatial curved surface foldable array mechanism can adapt to the thickness of the triangular unfolding pieces when the spatial curved surface foldable array mechanism is folded, so that the complete folding of the spatial curved surface foldable array mechanism is ensured.
The present invention will be described in further detail with reference to the accompanying drawings.
Drawings
FIG. 1 is a schematic illustration of a reference planar collapsible array mechanism model in a fully expanded configuration according to an embodiment of the configuration method of the present invention;
FIG. 2 is a schematic view of FIG. 1 after folding;
FIG. 3 is a schematic diagram of parallel projection of a planar foldable array mechanism model in a fully unfolded state towards a spatial curved surface according to an embodiment of the configuration method of the present invention;
FIG. 4 is a schematic diagram of a spatial curved surface foldable array mechanism model configured by an embodiment of the configuration method of the invention;
FIG. 5 is a schematic diagram of an expanded model of a single collapsible array cell of the single ring array of FIG. 4;
FIG. 6 is a schematic diagram of another spatial curved surface foldable array mechanism model configured by the embodiment of the configuration method of the invention;
FIG. 7 is a schematic diagram of an expanded model of a single collapsible array cell of the single ring array of FIG. 6;
FIG. 8 is a schematic diagram of the constraint relationship of the first layer of folded layer of the single foldable array unit during folding in the embodiment of the configuration method of the present invention;
FIG. 9 is a schematic diagram of the constraint relationship of the second layer of folded layer of single foldable array unit when folded in the configuration method of the present invention;
FIG. 10 is a schematic diagram of a spatially curved deployable array mechanism showing a single loop array in an embodiment of a method of configuration of the invention;
FIG. 11 is a schematic diagram of a spatial curved surface foldable array mechanism showing a double-ring array in an embodiment of the configuration method of the present invention;
FIG. 12 is a schematic diagram of the connection and matching of a single foldable array unit in the embodiment of the spatial curved surface foldable array mechanism of the present invention.
Detailed Description
In order that the above objects, features and advantages of the present invention can be more clearly understood, a more particular description of the invention will be rendered by reference to the appended drawings. It should be noted that the embodiments and features of the embodiments of the present application may be combined with each other without conflict.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, however, the present invention may be practiced in other ways than those specifically described herein, and therefore the scope of the present invention is not limited to the specific embodiments disclosed below.
A configuration method of a space curved surface foldable and unfoldable array mechanism based on Flasher folded paper comprises the following steps:
1) determining the array center, the array layer number, the array ring number and the shape of a space curved surface of the foldable array mechanism with the space curved surface, wherein a regular multi-prism base is adopted as the array center, such as a regular triangular prism, a regular quadrangular prism, a regular hexagonal prism, a regular octagonal prism, the array layer number N is more than or equal to 2, the array ring number M is more than or equal to 1, and a plane foldable array mechanism model based on Flasher folded paper is established as a reference according to the determined array center, array layer number and array ring number of the foldable array mechanism with the space curved surface, as shown in figure 1-2;
the method for establishing the planar foldable array mechanism model is applicable to the prior art, for example, the authors are ZirbelShannon A, Robert J.Lang et al, published Transactions of the A SM E: described in the literature of the integrating simulation and knowledge in organic-Based applied development Arrays, which is disclosed in the Journal of Mechanical Design.
2) Calculating to obtain the plane valley/peak of the crease on the central line of each folding and unfolding subarea of the plane array and the plane ridge peak of the connecting crease of the adjacent folding and unfolding subareas when the established plane folding and unfolding array mechanism model is in a fully unfolded state;
3) obtaining the radius and the spherical center of the spherical surface where the space curved surface is located, arranging the center of the plane foldable array mechanism model in the completely unfolded state at the spherical center of the space curved surface, and performing parallel projection towards the space curved surface, as shown in fig. 3, to obtain a series of curved surface array folding ridge vertexes corresponding to the flat folding ridge vertexes and a series of curved surface array folding valley/folding peak vertexes to be optimized corresponding to the flat folding valley/folding peak vertexes;
the obtained series of curved surface array crest points can be directly used as curved surface array crest points, and the obtained series of curved surface array crest points to be optimized are used as curved surface array crest points after the obtained series of curved surface array crest points to be optimized need to meet the optimization of folding geometric constraint and curved surface equation constraint.
As shown in fig. 4-5, the regular hexagonal prism base, the number of array layers being 4, and the number of array rings being 1 are taken as an example for illustration, and the regular hexagonal prism base comprises six foldable array units, each foldable array unit comprises four layers, wherein the first layer comprises two triangular folded sheets, and the other three layers comprise four triangular folded sheets.
In the figure, 101-106 are six foldable array unit partitions, 111-114 are four folding layers of a single partition 101, 115 is an inner triangular folding sheet crease, 116 is an inner middle line crease of the foldable array unit partition, 117 is an interlayer triangular folding sheet crease, and 118 is an inter-foldable array unit partition connecting crease.
When the foldable array units with the array ring number of 1 are folded along the central line crease, the central line crease is in the same direction, namely, the middle line crease is folded in the same direction;
as shown in fig. 6-7, taking a regular hexagonal prism base, an array layer number of 4, and an array ring number of 2 as an example for illustration, the array includes six foldable array units, where the foldable array unit with the array ring number of 2 is different from the foldable array unit with the array ring number of 1, in that the foldable array unit with the array ring number of 2 further includes a first ring and a second ring, after being folded, a connecting crease of the first ring and the second ring needs to be parallel to a bottom edge of the regular polygonal prism base, in order to satisfy the foldable characteristic thereof, a folding direction of a central line crease of the second ring is opposite to that of a central line of the first ring, and meanwhile, taking the central line crease of the second ring as a symmetry axis, triangular folding pieces at two sides are identical;
specifically, when the array ring number is 2, the foldable array unit is folded along the central line crease, the central line crease has two opposite directions, namely valley folding and peak folding, so that the height of the partitioned compact folded device is not gradually increased, and the function of controlling the folded loading height is achieved.
In the figure, 201 and 206 are six foldable array unit partitions, 211 is a first ring part of a single foldable array unit partition, 212 is a second ring part, 221 is a midline crease of the second ring, and 222 is a connecting crease of the first ring and the second ring; 301 and 302 are two triangular folded sheets in the first layer and 303 is a regular hexagonal prism base.
4) Calculating the distance from the valley-folding/peak-folding peak of the curved surface array to be optimized to the spherical surface, which satisfies the folding geometric constraint and the curved surface equation constraint, by adopting a numerical method, as shown in fig. 8-9, taking the distance as the fitting error of the feasible solution, and taking the solution with the minimum fitting error in all the feasible solutions as the peak of the valley-folding/peak-folding of the curved surface array;
5) and repeating the calculation for multiple times to obtain the vertex positions of all the curved array of the curved foldable array mechanism model, and completing the configuration of the curved foldable array mechanism model, as shown in fig. 10-11.
Further, the curved array valley/peak vertex to be optimized and two curved array ridge vertexes close to the curved array valley/peak vertex to be optimized on the same connecting folding line form a triangular folding sheet, and the folding geometric constraint required to be met by the curved array valley/peak vertex to be optimized includes:
an angle constraint, wherein the angle constraint defines that two triangular folded sheets having a common edge have two edges coinciding with each other after folding, the common edge being located on the midline fold;
the method comprises the steps of side length constraint, wherein the side length constraint limits one non-common side of a triangular folding sheet to coincide with a side edge of a regular polygon base after being folded, and the non-common side is the opposite side of an inner angle where a valley/peak vertex of a curved surface array to be optimized is located;
and (4) curved surface constraint, wherein the curved surface constraint to be optimized curved surface array valley folding/peak folding vertex is positioned on the determined space curved surface.
Specifically, fig. 8 illustrates the geometric constraints of a first layer of a single foldable array cell, wherein the first layer includes a first triangular folded sheet 301 and a second triangular folded sheet 302, which satisfy the following angular constraints:
the above-mentioned angle constraint ensures the side P 'of the first triangular folded piece'1,1,1P’1,2,1And side P 'of a second triangular folded piece'1,1,1P’1,2,1The folded parts are positioned on the same straight line;
meanwhile, the side length constraint which needs to be satisfied by the two is as follows:
||P’0,0,1P’1,1,1||cosβ1＝a
in the above formula, a is the side length of the bottom edge of the base, and the combination angle relationship can ensure a side P'1,1,1P’1,2,1And side P'1,2, 1P’0,0,2After being folded, the folding edge can be superposed with the side edge of the base of the regular hexagonal prism, thereby realizing the tight folding.
Meanwhile, the two also need to satisfy the curved surface constraint, namely, the point to be solved (the valley point/peak point of the curved surface array to be optimized) in the unfolded state is on the spatial curved surface.
More specifically, FIG. 9 illustrates the geometric constraints of the second layer of the single foldable array unit, wherein the second layer comprises four triangular folded sheets, wherein the angular constraints that the four triangular folded sheets need to satisfy are:
the above angular constraint ensures the sides P 'of the two triangular folded sheets on either side of the line crease in the second layer'2,1,1P’2,2,1And P'2,2,1P’1,1,2Folded on the same straight line.
Meanwhile, the side length constraint which needs to be met is as follows:
||P’1,1,1P’2,1,1||cosβ2＝a
guarantee two sides P'2,1,1P’2,2,1And P'2,2,1P’1,1,2And is positioned on the side edge of the regular hexagonal prism base 303 after being folded, so that the spatial curved surface foldable array mechanism can be folded around the side edge.
And simultaneously, the curved surface constraint is also met, namely the point to be required (the valley point/peak point of the curved surface array to be optimized) in the unfolding state is on the spatial curved surface.
When other layers after the second layer are designed, the geometrical constraint satisfied is similar to the second layer, and a detailed explanation is not provided here.
In this embodiment, when the number of the array rings is 2, the design constraint of the first ring part is the same as that of the array rings 2, and after the first ring and the second ring are folded, the connecting crease needs to be parallel to the bottom edge of the regular polygon base. In order to meet the folding characteristic, the folding direction of the middle line crease of the second ring is opposite to that of the middle line crease of the first ring, and meanwhile, the middle line crease of the second ring is taken as a symmetry axis, and the triangular folding pieces on the two sides are equal; furthermore, surface constraints still need to be satisfied. Therefore, when the whole space curved surface foldable array mechanism is unfolded, each vertex is positioned on the target curved surface, and curved surface fitting is well carried out; when folded, the first loop portion folds upward and the second loop portion folds downward, well limiting the array height in the folded position, as shown in the reverse fold region in fig. 11.
The spatial curved surface foldable and expandable array mechanism comprises a regular multi-prism base and a plurality of foldable and expandable array units, wherein the plurality of foldable and expandable array units are distributed on the periphery of the regular multi-prism base in an array mode.
The foldable array unit comprises a plurality of triangular folding pieces distributed based on a Flasher paper folding mechanism, wherein a double-freedom-degree flexible hinge with twisting and displacement functions is arranged on a crease positioned at the side edge of the regular polygon prism base after being folded, and a single-freedom-degree flexible hinge with twisting function is arranged at other creases.
In the engineering application of the curved surface foldable array, because each triangular folding sheet has thickness and the curved surface foldable array is unfolded into a fitting curved surface, the curved surface foldable array needs to be tightly wound around a regular polygon base when being folded, and the performance requirements of the flexible hinges at different positions are different, as shown in fig. 12, the foldable array unit partitions are provided with an inner central line crease 116 (a central line crease 221 of a second ring), foldable array unit partitions are connected with creases 118 among themselves, and a first ring and a second ring are connected with creases 222 to be folded completely, I-type flexible hinges only with torsion functions are used at the positions, the inner triangular folding sheet creases 115 are only slightly bent when being folded, I-type flexible hinges only with torsion functions are also used at the positions, the interlayer triangular folding sheets 117 are positioned at the edges of a regular hexagon when being folded, and the thickness of the folded triangular folding sheets needs to be adapted, in addition to requiring torsion and also stretching to create a gap, these connections use type II flex hinges 402 that provide both torsion and displacement.
Two different flexible hinges are used at different crease positions, so that the curved surface fitting shape can be kept when the curved surface foldable array is unfolded, and the curved surface foldable array is tightly wound around the regular hexagonal prism base when being folded.
Compared with a plane Flasher model, the spatial curved surface foldable array mechanism in the embodiment has the capability of fitting a curved surface after being unfolded, so that a curved surface array is obtained after being unfolded; all the folding sheets in the layers are triangular folding sheets (the plane Flasher model consists of triangular folding sheets and quadrilateral folding sheets) so that the curved surface folding array can better fit a target curved surface; after the flat flash model is tightly folded, the lower edges of all the partitions are gradually raised on the regular hexagonal prism, and the lower edges of all the partitions of the flat flash model are positioned at the same height (positioned at the lower edge of the base of the regular hexagonal prism).
Correspondingly, the space curved surface foldable and extensible array mechanism which takes other regular polygonal prisms as bases besides the curved surface foldable array which takes the regular hexagonal prism as the base can also be designed.
The above mentioned matters are not related, and all the matters are applicable to the prior art.
Although the present invention has been described with reference to the preferred embodiments, it is not intended to limit the scope of the invention. It will be appreciated by those skilled in the art that changes may be made without departing from the scope of the invention, and it is intended that all matter contained in the above description or shown in the accompanying drawings shall be interpreted as illustrative and not in a limiting sense.
Claims (4)
1. A configuration method of a space curved surface foldable array mechanism based on Flasher folded paper is characterized by comprising the following steps:
1) determining the array center, the array layer number, the array ring number and the shape of a space curved surface of the foldable and expandable array mechanism with the space curved surface, wherein a regular multi-prism base is adopted as the array center, and a plane foldable and expandable array mechanism model based on Flasher origami as a reference is established according to the array center, the array layer number and the array ring number of the foldable and expandable array mechanism with the space curved surface;
2) calculating to obtain valley/peak points on the crease of the central line of each folding and unfolding subarea of the plane array and peak points on the connecting crease of the adjacent folding and unfolding subareas when the established plane foldable and unfoldable array mechanism model is in a fully unfolded state;
3) acquiring the radius and the spherical center of a spherical surface where the space curved surface is located, arranging the center of the plane foldable array mechanism model in a completely unfolded state at the spherical center of the space curved surface, and performing parallel projection towards the space curved surface to obtain a series of curved surface array folding ridge vertexes corresponding to the flat folding ridge vertexes and a series of curved surface array folding valley/folding peak vertexes to be optimized corresponding to the flat folding valley/folding peak vertexes;
4) calculating the distance from the valley-folding/peak-folding peak of the curved surface array to be optimized to the spherical surface, which meets the folding geometric constraint and the curved surface equation constraint, by adopting a numerical method, taking the distance as the fitting error of a feasible solution, and taking the solution with the minimum fitting error in all feasible solutions as the peak of the valley-folding/peak-folding of the curved surface array;
5) and repeating the calculation for multiple times to obtain the vertex positions of all the curved surface arrays of the curved surface foldable and expandable array mechanism model, thereby completing the configuration of the curved surface foldable and expandable array mechanism model.
2. The configuration method of the space curved surface foldable and expandable array mechanism based on the Flasher origami as claimed in claim 1, wherein the valley/peak vertex of the curved surface array to be optimized and the two curved surface array peak vertices on the same connecting crease close to the same connecting crease form a triangular folding sheet, and the folding geometric constraint required to be met by the valley/peak vertex of the curved surface array to be optimized comprises:
an angle constraint, wherein the angle constraint defines that two triangular folded sheets with a common edge have two edges coinciding with each other after folding, the common edge being located on the midline crease;
the method comprises the steps of side length constraint, wherein the side length constraint limits one non-common side of a triangular folding sheet to coincide with a side edge of a regular polygon base after being folded, and the non-common side is the opposite side of an inner angle where a valley/peak vertex of a curved surface array to be optimized is located;
and (4) surface constraint, wherein the surface constraint is that the valley-folding/peak-folding vertex of the surface array to be optimized is positioned on the determined space surface.
3. The spatial curved surface foldable and expandable array mechanism adopting the configuration method of the spatial curved surface foldable and expandable array mechanism based on the Flasher origami as claimed in claim 1 is characterized by comprising a regular multi-prism base and a plurality of foldable and expandable array units, wherein the plurality of foldable and expandable array units are distributed on the periphery of the regular multi-prism base in an array mode.
4. The spatial curved surface foldable array mechanism as claimed in claim 3, wherein the foldable array unit comprises a plurality of triangular folding pieces distributed based on a Flasher paper folding mechanism, wherein a double-degree-of-freedom flexible hinge with twisting and displacement functions is arranged on the folding line at the side edge of the regular polygon prism base after folding, and a single-degree-of-freedom flexible hinge with twisting function is arranged at the other folding lines.
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