CN115817853A - Self-locking unit with programming function and self-locking array system formed by self-locking units - Google Patents
Self-locking unit with programming function and self-locking array system formed by self-locking units Download PDFInfo
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Abstract
The invention discloses a self-locking unit with a programming function and a self-locking array system formed by the self-locking unit, wherein the self-locking unit comprises a first creasing plate and a second creasing plate which are of symmetrical structures, a plurality of creases are respectively arranged on the first creasing plate and the second creasing plate, the first creasing plate and the second creasing plate are bonded together to form a bonding part, the rest non-bonding parts form a folding part, and the bonding part and the folding part can be folded and unfolded along the creases, so that the self-locking unit has a fully-unfolded configuration, a fully-folded configuration and a partially-folded configuration, and has a self-locking characteristic in the horizontal direction or the vertical direction under the fully-folded configuration. The programmable self-locking array system realizes the programmability of the self-locking characteristic in two orthogonal directions of the unit on the premise of not changing the structure geometry and physical parameters.
Description
Technical Field
The invention relates to the technical field of metamaterials, in particular to a self-locking unit with a programming function and a self-locking array system formed by the self-locking unit. Can be applied to large-scale planes in spacecrafts such as: solar sails, antennas, reflectors, etc.
Background
The performance of the mechanical metamaterial mainly depends on a manually designed microstructure, and the units are periodically arranged in a rotating mode, an array mode or a mirror image mode, so that special mechanical properties which are difficult to achieve by a traditional material are achieved, such as negative Poisson's ratio, negative rigidity or adjustable rigidity. The exotic property of the metamaterial enables the metamaterial to have wide application prospect, and particularly can be used for designing and manufacturing high-receiving-rate antennas, radar reflectors and the like. At present, the adjustment of macroscopic mechanical behavior of an array structure is realized by changing geometric parameters, material properties, boundary conditions, external constraint constraints and the like of the array structure, and the adjustment becomes a research hotspot increasingly. However, once formed, the geometry and material properties of the individual cells within the array are determined, and thus the mechanical properties of the array structure are determined. The invention provides a bistable guided programmable self-locking unit, which realizes the programmability of self-locking characteristics in two orthogonal directions of the unit on the premise of not changing the structure geometry and physical parameters. Based on the programmable self-locking unit, a mechanical coding array structure can be further constructed, and the controllability of mechanical characteristics of the array structure (metamaterial) after processing and forming is realized.
Most deformable materials are limited to one-to-one deformation processes, i.e. one design corresponds to one target shape, limited by the design constraints already formed, and difficult to perform other various deformation modes. For example, for a typical paper folding/cutting structure, a specific folding or cutting pattern corresponds to a target shape, and the corresponding mechanical properties are also unique. The programmability of the array structure is enhanced, and a structural design is utilized to realize various deformation modes and mechanical characteristics, namely a one-to-many mapping relation, so that the array structure is increasingly a key problem to be solved urgently at present.
Generally, the most intuitive method for regulating and controlling the deformation model and the mechanical behavior of the metamaterial is to change the geometric dimension, topology, material or boundary of the structure.
At present, the mode of realizing paper folding self-locking is mainly to construct a multi-stable paper folding structure. The paper folding structure is provided with two or more stable balance positions, the structure can be switched among the positions under the action of external force, and when the external force is removed, the structure can be stably maintained at the positions, namely, the self-locking effect is realized. For a multistable structure, the minimum external force required to jump from a current stable configuration to an adjacent stable configuration is defined as the steady state margin. However, once the multi-stable origami structure is formed, the stable configuration and the stable margin are generally determined, and the programmable design cannot be realized.
Disclosure of Invention
Aiming at the problems in the prior art, the invention aims to provide a self-locking unit with a programming function and a self-locking array system composed of the self-locking unit. Based on the programmable self-locking unit, a mechanical coding array structure can be further constructed, and the controllability of mechanical characteristics of the array structure after processing and forming is realized.
In order to achieve the above object, the present invention provides a self-locking unit with a programming function, the self-locking unit includes a first creasing plate and a second creasing plate which are symmetrical to each other, the first creasing plate and the second creasing plate are respectively provided with a plurality of creases, the first creasing plate and the second creasing plate are bonded together to form a bonding portion, the rest non-bonding portions form a folding portion, the bonding portion and the folding portion can be folded and unfolded along the creases, so that the self-locking unit has a fully unfolded configuration, a fully folded configuration and a partially folded configuration, and the self-locking unit has a self-locking characteristic in a horizontal direction or a vertical direction in the fully folded configuration.
Furthermore, the four corners of the first indentation plate are marked as A 1 、B 1 、C 1 、D 1 The square panel is internally provided with a square hollow area, and the four corners of the hollow area are respectively marked as E 1 、F 1 、G 1 、H 1 Wherein, square A 1 B 1 C 1 D 1 And square E 1 F 1 G 1 H 1 Having the same center point, and point A 1 、E 1 、G 1 、C 1 Distributed on the same diagonal, point E 1 To edge A 1 B 1 Is marked as A 2 Point E 1 To edge A 1 D 1 Is marked as D 4 Point F 1 To edge A 1 B 1 Is marked with A 4 Point F 1 To side B 1 C 1 Is marked as B 2 Point G of 1 To side B 1 C 1 Is marked as B 4 Point G 1 To edge C 1 D 1 Is marked as C 2 Point H 1 To edge C 1 D 1 Is marked as C 4 Point H 1 To edge A 1 D 1 Is marked as D 2 ；
In length, set to A 1 A 2 =A 4 B 1 =B 1 B 2 =B 4 C 1 =C 1 C 2 =C 4 D 1 =D 1 D 2 =A 1 D 4 =a，
Set point A 3 、B 3 、C 3 、D 3 、E 2 、F 2 、G 2 、H 2 So as to be in length
A 2 A 3 =B 2 B 3 =C 3 C 4 =D 3 D 4 =E 1 E 2 =F 1 F 2 =G 2 H 1 =E 1 H 2 =b，
And A is 3 A 4 =B 3 B 4 =C 2 C 3 =D 2 D 3 =E 2 F 1 =F 2 G 1 =G 1 G 2 =H 1 H 2 =c；
To achieve bistability in both the fully expanded and fully folded configurations, the geometry is such that
。
Further, the creases of the first creasing plate 1 are respectively
Correspondingly, the creases of the second creasing plate 2 are respectively
The bonding parts of the first creasing plate and the second creasing plate are respectively square areas
And square area
Bonded, square area
And square area
Bonded, square area
And square area
Bonded, square area
And a square region
And (6) bonding.
Further, the crease of the first creasing plate
Respectively with the crease of the second creasing plate
Bonding; crease of first creasing plate
With the corresponding crease of the second creasing plate 2
The self-locking unit is provided with non-adhesive creases, and the non-adhesive creases at corresponding positions on the first creasing plate and the second creasing plate move along the direction perpendicular to the panel and far away from each other when pressure is applied on the self-locking unit, so that the self-locking unit is folded.
Furthermore, the self-locking unit has a folding sequence of 'horizontal folding and then vertical folding', pressure along the horizontal direction is respectively applied to the left end and the right end of the self-locking unit in the horizontal direction of the completely unfolded configuration, the self-locking unit is folded in the horizontal direction, and the rectangular area is formed
And
are respectively folded in a rectangle
And a rectangle
In the middle of; rectangular area
And
are respectively folded in a rectangle
And a rectangle
To (c) to (d); square area
And square area
Is also folded; after folding, the self-locking unit is unfolded from the fully unfolded configuration A 1 B 1 C 1 D 1 Modified into a partially folded configuration A 1 B 1 B 3 D 3 (ii) a Then, respectively applying a pressure along the vertical direction at the upper end and the lower end of the self-locking unit in the vertical direction; with the application of pressure, the self-locking unit is folded in the vertical direction from a partially folded configuration A 1 B 1 B 3 D 3 Modified to a fully folded configuration A 1 A 3 C 1 D 3 (ii) a At this time, the self-locking unit is in a self-locking state in the horizontal direction.
Furthermore, the self-locking unit has a folding sequence of 'vertical folding and then horizontal folding', pressure along the vertical direction is respectively applied to the upper end and the lower end of the unfolding configuration of the self-locking unit in the vertical direction, so that the self-locking unit is folded in the vertical direction, and after the self-locking unit is folded, the self-locking unit is folded from a completely unfolded configuration A 1 B 1 C 1 D 1 Modified into a partially folded configuration A 1 A 3 C 3 D 1 (ii) a Then, a horizontal pressure is applied to the left and right ends of the self-locking unit respectively, so that the self-locking unit is folded in the horizontal direction and is partially folded to form a partially folded configuration A 1 A 3 C 3 D 1 Modified to a fully folded configuration A 1 A 3 C 1 D 3 (ii) a At this time, the self-locking unit is in a self-locking state in the vertical direction.
On the other hand, the invention provides a self-locking array system, which consists of a plurality of self-locking units, wherein the self-locking units are self-locking units with a programming function according to the invention, the self-locking array system performs two-dimensional array on the plurality of self-locking units so that the self-locking units can perform programming design on folding and unfolding sequences, the number of arrays in the horizontal direction is M, and the number of arrays in the vertical direction is N.
Further, the self-locking array system is described for programming using the following method: the fully collapsed configuration of the self-locking array system may be represented as
(ii) a The array structure needs to be completely self-locked in the horizontal direction, and when the array structure has expandability in the vertical direction, the folding sequence of the self-locking array system is designed as follows: firstly, sequentially folding the units in the 1 st to M th rows from left to right in the horizontal direction, and then sequentially folding the units in the 1 st to N th rows from top to bottom in the vertical direction; wherein, X represents the horizontal direction, Y represents the vertical direction, the numbers behind X represent the folding or unfolding state of each row of units from left to right, and the three-digit numbers behind Y represent the folding or unfolding state of each row of units from top to bottom, wherein the folding state is represented by the number 1, and the unfolding state is represented by the number 0;
when the array structure is completely self-locked in the horizontal direction and has expandability in the vertical direction, the completely folded configuration of the self-locking array system can be expressed as follows:
further, the self-locking array system is described for programming using the following method: when the array structure needs to be completely self-locked in the vertical direction and has expandability in the horizontal direction, the completely folded configuration of the self-locking array system can be expressed as follows:
。
the number of the units in each row in the horizontal direction is M, the number of the units in each column in the vertical direction is N, the mechanical properties of the array structures obtained by different folding methods are different, and the mechanical programmability of the array structures can be realized by utilizing the properties;
the sequence was folded as follows:
the sequence was folded as follows:
the sequence was folded as follows:
in the obtained self-locking array system, only two groups of units can be unfolded under the action of horizontal tension, and then the structure is self-locked and cannot be unfolded continuously under the action of the horizontal tension;
the sequence was folded as follows:
in the obtained self-locking array system, only three groups of units can be unfolded under the action of horizontal tension, then the structure is self-locked, and the structure cannot be unfolded continuously under the action of the horizontal tension;
therefore, under different folding sequences, the corresponding structure configuration can be regulated and controlled when the structure self-locking occurs, so that the structure has mechanical programmable characteristics.
The invention provides a programmable self-locking array structure combining paper folding and paper cutting, which realizes the programmability of self-locking characteristics in two orthogonal directions of a unit on the premise of not changing the geometrical and physical parameters of the structure. Based on the programmable self-locking unit, a mechanical coding array structure can be further constructed, and the controllability of mechanical characteristics of the array structure after processing and forming is realized.
Drawings
FIG. 1 is a schematic diagram showing an expanded state of a self-locking unit with a programming function according to an embodiment of the invention;
FIG. 2 is a schematic diagram showing the dimensions of a self-locking cell with programming functionality according to an embodiment of the present invention;
FIG. 3 is a schematic diagram showing two folding sequences of a self-locking unit with programming function according to an embodiment of the present invention, wherein FIG. 3 (a) is folded horizontally and then vertically; FIG. 3 (b) is a vertical fold followed by a horizontal fold;
FIG. 4 shows a schematic diagram of the folded configuration I of FIG. 3 (a);
FIG. 5 shows a schematic view of the folded configuration II of FIG. 3 (b);
FIG. 6 shows the anisotropy diagrams of configuration I and configuration II with respect to deployment and self-locking, wherein FIG. 6 (a) is a schematic diagram of configuration I and FIG. 6 (b) is a schematic diagram of configuration II;
FIG. 7 is a schematic diagram of a self-latching array architecture with a programmable design for a fold/unfold sequence in accordance with an embodiment of the present invention;
FIG. 8 shows a schematic diagram of a fully deployed configuration of a self-locking array structure in accordance with an embodiment of the present invention;
FIG. 9 is a schematic diagram illustrating a fully folded configuration of a self-locking array structure in a horizontal direction according to an embodiment of the present invention;
FIG. 10 shows a schematic view of a fully folded configuration I in both directions according to an embodiment of the invention;
FIG. 11 shows a schematic view of a fully folded configuration II in both directions according to an embodiment of the present invention;
FIG. 12 is a schematic diagram illustrating a fully collapsed configuration of a programmable self-locking array structure in accordance with an embodiment of the present invention;
FIG. 13 shows pull-displacement curves for different configurations of a programmable self-locking array structure according to an embodiment of the present invention.
Detailed Description
The technical solutions of the present invention will be described clearly and completely with reference to the accompanying drawings, and it should be understood that the described embodiments are some, but not all embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In the description of the present invention, it should be noted that the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc., indicate orientations or positional relationships based on the orientations or positional relationships shown in the drawings, and are only for convenience of description and simplicity of description, but do not indicate or imply that the device or element being referred to must have a particular orientation, be constructed and operated in a particular orientation, and thus, should not be construed as limiting the present invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance.
In the description of the present invention, it should be noted that, unless otherwise explicitly specified or limited, the terms "mounted," "connected," and "connected" are to be construed broadly and may be, for example, fixedly connected, detachably connected, or integrally connected; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meanings of the above terms in the present invention can be understood by those skilled in the art according to specific situations.
The following describes in detail a specific embodiment of the present invention with reference to fig. 1 to 13. It should be understood that the detailed description and specific examples, while indicating the present invention, are given by way of illustration and explanation only, not limitation.
The invention provides a self-locking unit with a programming function and a self-locking array system composed of the self-locking unit. Based on the programmable self-locking unit, a mechanical coding array structure can be further constructed, and the controllability of mechanical characteristics of the array structure after processing and forming is realized. The invention discloses a self-locking unit with a programming function and a self-locking array system composed of the self-locking unit, belongs to the technical field of mechanical metamaterials, and can be applied to satellite antennas and radar reflectors.
The self-locking unit with the programming function is formed by bonding two creasing plates in partial areas through a design concept of combining paper folding and paper cutting, and the configuration of the unit when the unit is completely unfolded is shown as figure 1. Specifically, the self-locking unit comprises a first creasing plate 1 and a second creasing plate 2 which are of symmetrical structures, a plurality of creases are respectively arranged on the first creasing plate 1 and the second creasing plate 2, the first creasing plate 1 and the second creasing plate 2 are partially bonded together to form a bonding part, the rest non-bonding parts form a folding part, the bonding part and the folding part can be folded and unfolded along the creases, so that the self-locking unit has a fully-unfolded configuration, a fully-folded configuration and a partially-folded configuration, and the self-locking unit has a self-locking characteristic in the horizontal direction or the vertical direction under the fully-folded configuration.
The material, thickness and size of the first creasing plate 1 and the second creasing plate 2 are identical to the location of the crease. Wherein, the four corners of the first indentation plate are marked as A 1 、B 1 、C 1 、D 1 The square panel is internally provided with a square hollow area, and the four corners of the hollow area are respectively marked as E 1 、F 1 、G 1 、H 1 Similar to a small square cut at the center of a square of paper. Wherein, the square A 1 B 1 C 1 D 1 And square E 1 F 1 G 1 H 1 Having the same center point, and point A 1 、E 1 、G 1 、C 1 Distributed on the same diagonal, point E 1 To edge A 1 B 1 Is marked as A 2 Point E 1 To edge A 1 D 1 Is marked as D 4 Point F 1 To edge A 1 B 1 Is marked as A 4 Point F 1 To edge B 1 C 1 Is marked as B 2 Point G 1 To edge B 1 C 1 Is marked as B 4 Point G 1 To edge C 1 D 1 Is marked as C 2 Point H 1 To edge C 1 D 1 Is marked as C 4 Point H 1 To edge A 1 D 1 Is marked as D 2 。
The self-locking unit is dimensioned as shown in figure 2,
A 1 A 2 =A 4 B 1 =B 1 B 2 =B 4 C 1 =C 1 C 2 =C 4 D 1 =D 1 D 2 =A 1 D 4 =a
set point A 3 、B 3 、C 3 、D 3 、E 2 、F 2 、G 2 、H 2 So that
A 2 A 3 =B 2 B 3 =C 3 C 4 =D 3 D 4 =E 1 E 2 =F 1 F 2 =G 2 H 1 =E 1 H 2 =b，
And A is 3 A 4 =B 3 B 4 =C 2 C 3 =D 2 D 3 =E 2 F 1 =F 2 G 1 =G 1 G 2 =H 1 H 2 =c。
The thickness of each creasing plate (including the first creasing plate 1 and the second creasing plate 2) is denoted w. To achieve full unfolding and folding of the bistable cell, the following are geometrically satisfied:
wherein, in order to realize the complete folding of the bistable unit, it is necessary to ensure
. Furthermore, to achieve the sheet folding effect, the indentation plate thickness w is required to be much less than the minimum of the dimensions a and c, preferably w does not exceed 1/10 of the dimensions a or c.
The first creasing plate 1 has creases of
Correspondingly, the creases of the second creasing plate 2 are respectively
The partial areas of the first creasing plate 1 and the second creasing plate 2 are adhered into a whole and are respectively square areas
And square area
Bonded, square area
And square area
Bonded, square area
And square area
Bonded, square area
And square area
And (6) bonding. Crease of first creasing plate
Respectively with the crease of the second creasing plate
And (6) bonding. Crease of first creasing plate
With corresponding crease of the second creasing plate 2
Do not adhere to each other and the creasing plate corresponds to a crease when pressure is applied to it
Move in a direction away from each other, as do the other non-bonded corresponding folds.
As shown in fig. 3 (a), the folding sequence of "horizontal folding first-vertical folding next" is described visually by illustration. Horizontal pressing forces are applied to the left and right ends of the self-locking unit in the fully expanded configuration in the horizontal direction. The self-locking unit is folded in the horizontal direction along with the application of pressure, and the rectangular area
And
are respectively folded in a rectangle
And a rectangle
To (c) to (d); similarly, a rectangular region
And
are respectively folded in a rectangle
And a rectangle
In between. In addition, a square region
And square area
Is also folded. After folding, the self-locking unit is unfolded from the fully unfolded configuration A 1 B 1 C 1 D 1 Modified into a partially folded configuration A 1 B 1 B 3 D 3 . Then, a pressure along the vertical direction is respectively applied to the upper end and the lower end of the self-locking unit in the vertical direction. With the application of pressure, the self-locking unit is folded in the vertical direction from a partially folded configuration A 1 B 1 B 3 D 3 Modified to a fully folded configuration A 1 A 3 C 1 D 3 。
Similarly, for the deployed configuration shown in fig. 2, it is also possible to perform "fold vertically first-fold horizontally" on it, as shown in fig. 3 (b). And applying pressure along the vertical direction to the upper end and the lower end of the unfolding configuration of the self-locking unit in the vertical direction respectively. With the application of pressure, the self-locking unit is folded in the vertical direction, after folding, from a fully unfolded configuration A 1 B 1 C 1 D 1 Modified into a partially folded configuration A 1 A 3 C 3 D 1 . Then, a horizontal pressure is applied to the left and right ends of the self-locking unit in the horizontal direction. With the application of pressure, the self-locking unit is folded in the horizontal direction from a partially folded configuration A 1 A 3 C 3 D 1 Modified to a fully folded configuration A 1 A 3 C 1 D 3 。
For the programmable self-locking unit described above, there is a difference in the resulting fully folded configuration of the two folding sequences. Wherein the fully folded configuration obtained by the "horizontal folding first and then vertical folding" is the configuration I shown in FIG. 4, and the fully folded configuration obtained by the "vertical folding first and then horizontal folding" is the configuration II shown in FIG. 5.
Anisotropy with respect to deployment and self-locking of configuration I and configuration II. As shown in fig. 6 (a), for the configuration I, when external force is applied to the left and right ends of the configuration I to stretch the configuration I to the two sides, the horizontal folded creasing plate is clamped by the vertical folded creasing plate, so that the self-locking unit cannot be unfolded in the horizontal direction and takes on a self-locking state; if external force is applied to the upper end and the lower end of the structure to stretch towards the two sides, the structure I is firstly unfolded in the vertical direction, then external force is applied to the left end and the right end of the structure to stretch towards the two sides, and finally the structure is completely unfolded. As shown in fig. 6 (b), for the configuration II, when external force is applied to the left and right ends of the configuration II to stretch the configuration II to the two sides, the configuration II is firstly unfolded in the horizontal direction, then external force is applied to the upper and lower ends of the configuration II to stretch the configuration II to the two sides, and the self-locking unit is completely unfolded finally; external force is applied to the upper end and the lower end of the structure II to stretch the structure II towards the two sides, and the indentation plates folded in the vertical direction are clamped by the indentation plates folded in the horizontal direction, so that the structure II cannot be unfolded in the vertical direction and is in a self-locking state.
It can be seen that although configuration I and configuration II are both fully folded configurations, there is a significant difference in the malleability in two orthogonal directions (horizontal and vertical) due to the difference in their folding sequences. Specifically, if the unfolded configuration is converted into the folded configuration according to a certain folding sequence, the folding to the unfolding is realized according to the reverse order of the folding sequence. By utilizing the characteristics, the programmable self-locking array structure can be further designed.
The programmable self-locking unit provided by this embodiment is used for two-dimensional array to obtain a self-locking array structure with a folding/unfolding sequence programmable design, where the number of arrays in the horizontal direction is M, and the number of arrays in the vertical direction is N, as shown in fig. 7. Since each self-locking unit is stable in both the expanded and folded configurations, the structure formed by the plurality of bistable unit arrays has a plurality of stable planar configurations.
A typical self-locking array structure is described as an example, where the number of horizontal arrays is M =3, and the number of vertical arrays is N =2. The fully unfolded configuration is shown in fig. 8, and the horizontally fully folded configuration is shown in fig. 9, on which basis it is folded vertically, and the resulting two-way fully folded configuration is shown in fig. 10.
For the above array structure, the following two description methods are given for characterizing the current state of the array structure. First, a first description method is introduced, taking fig. 8-10 as an example, and the current states thereof can be described as: "X:0, Y", "X:1, 1. Wherein, X represents the horizontal direction, Y represents the vertical direction, three digits after X represent the folding/unfolding state of three rows of units from left to right respectively, three digits after Y represent the folding/unfolding state of two rows of units from top to bottom respectively, wherein 0 represents unfolding, and 1 represents folding. However, the described method is limited in that the folding sequence of the array structure cannot be characterized. Using FIGS. 4 and 5 as examples, the methods described herein can be described as "X: 1Y".
Therefore, on the basis of the above description of the current state of the array structure, the folding sequence of the array structure needs to be supplemented. A second description is given below, again taking fig. 8-10 as examples, of the folding sequences which can be described as: "X:0, Y", "X:1,2,3, Y. Wherein, X represents the horizontal direction, Y represents the vertical direction, the numbers after X/Y represent the folding sequence of three columns of units from left to right, 0 represents the unfolded state, 1 represents the first folding of the column/row, and 2 represents the second folding of the column/row, so as to recur. For example, "X:0, Y; "X:1,2,3, Y0, 0" indicates that the folding order of the array structure is in the order of columns 1,2,3; "X:1,2,3, Y4, 5" indicates that the folding order of the array structure is first the 1,2,3 column sequential folding and second the 1,2 row sequential folding. For the configurations shown in FIGS. 4 and 5, the second description method can be described as "X: 1Y", "X:2, Y.
In summary, for completely describing the configuration of the array structure, it is necessary to describe both the folding/unfolding state of each row and each column of the array structure and to give the folding sequence of the array structure. The first description method can only represent the folding state of each unit of the array structure, and does not contain folding sequence information; the second description method can represent both the folded state of each cell of the array structure and also contains folding sequence information.
Taking fig. 10 and fig. 11 as an example, the difference between the two description methods is illustrated. The folding sequence of the array structure shown in fig. 10 is: the 1 st to 3 rd rows are folded from left to right, and the 1 st to 2 nd rows are folded from top to bottom. The array structure can be represented by a first descriptive method as "X:1, y". The folding sequence of the array structure shown in fig. 11 is: first, the 1 st column and the 2 nd column are folded sequentially from left to right, then the 1 st-2 nd rows are folded sequentially from top to bottom, and finally the rightmost column (the 3 rd column) is folded. The array structure can be represented by "X:1, Y. Comparing fig. 10 and 11, it can be seen that although each cell in the two array structures is folded, there is a difference in configuration due to the difference in folding sequence. The first expression method can only express the folded/unfolded state of each cell constituting the array structure, and thus the array structures shown in fig. 10 and 11 have the same expression method. The second description method contains folding sequence information, and thus the array structures shown in fig. 10 and 11 are described differently. The programmable design of the self-locking array structure using the second described method is preferred because of the obvious advantages of the second described method.
Since each cell constituting the array structure has the splay/self-lock anisotropy, the array structure as a whole exhibits the splay/self-lock anisotropy. By utilizing this property, a programmable design of the self-locking array structure can be achieved. On the premise of ensuring that the folding/unfolding of each unit in the horizontal direction and the vertical direction of the array structure are the same, the design of different self-locking characteristics of the array structure can be realized by regulating and controlling the folding sequence of the array structure.
Taking the array structure shown in FIG. 12 in which each cell is in a folded state, the number of cells per row in the horizontal direction is M, and the number of cells per row in the vertical direction is MThe number of cells per column in the straight direction is N, and the array structure can be represented by using the first description method
。
If the array structure needs to be completely self-locked in the horizontal direction and has expandability in the vertical direction, the folding sequence of the array structure can be designed as follows: the units in the 1 st to M th rows from left to right are sequentially folded in the horizontal direction, and the units in the 1 st to N th rows from top to bottom are sequentially folded in the vertical direction. If the second method of description is used, i.e.
. If the array structure needs to be completely self-locked in the vertical direction and has extensibility in the horizontal direction, the folding sequence of the array structure can be designed as follows: the units in the 1 st to N th rows are sequentially folded in the vertical direction from top to bottom, and the units in the 1 st to M th rows are sequentially folded in the horizontal direction from left to right. If the second method of description is used, i.e.
. In a broader sense, the array structure may be designed to have an unfolding sequence in two directions, where the unfolding sequence is the reverse of the folding sequence.
With the array structure shown in fig. 13, the number of units in each row in the horizontal direction is M, the number of units in each column in the vertical direction is N, the mechanical characteristics of the array structure obtained by different folding methods are different, and the mechanical programmability of the array structure can be realized by using the characteristics.
(1) If the folding sequence of the array structure is:
(2) If the folding sequence of the array structure is:
(3) If the folding sequence of the array structure is:
the resulting tension-displacement curve in the case of the horizontal direction stretching is shown in the case of (3) in fig. 13. Because of the restriction of the folding sequence, the array structure can only unfold two groups of units under the action of horizontal tension, and then the structure is self-locked, so that the structure can not be unfolded continuously under the action of the horizontal tension.
(4) If the folding sequence of the array structure is:
the resulting tension-displacement curve in the case of the horizontal direction stretching is shown in the (4) th case in fig. 13. Due to the constraint of the folding sequence, the array structure can only unfold three groups of units under the action of horizontal tension, and then the structure is self-locked and cannot be unfolded continuously under the action of horizontal tension.
In addition, the array structure can also realize other forms of tension-displacement curves, which are not necessarily enumerated herein. It can be seen that the array structure can realize different force-displacement curves under different folding sequences, and can regulate and control the corresponding structural configuration when the array structure is subjected to structural self-locking. Therefore, it can be seen that the array structure proposed by the present invention has a mechanically programmable property.
The invention provides a programmable self-locking array structure combining paper folding and paper cutting, which realizes the programmability of self-locking characteristics in two orthogonal directions of a unit on the premise of not changing the geometrical and physical parameters of the structure. Based on the programmable self-locking unit, a mechanical coding array structure can be further constructed, and the controllability of mechanical characteristics of the array structure after processing and forming is realized.
The folding and unfolding unit and the array system provided by the embodiment of the invention are passively operated, and as for the power or transmission device, a motor or other power device known in the art and any known mode capable of realizing the functions thereof can be adopted, such as rope driving, fixing clamp and the like, without limitation.
The invention has the following characteristics:
(1) The programmable self-locking unit combining paper folding and paper cutting is formed by bonding two pieces of indentation paper in certain areas, the configuration of the unit when the unit is completely unfolded is shown as figure 1, and the folding configuration is shown as figures 4 and 5.
(2) The material, thickness and size of the first creasing plate 1 and the second creasing plate 2 are identical to the location of the crease. The first creasing plate 1 has creases respectively
Correspondingly, the creases of the second creasing plate 2 are respectively
(ii) a The partial areas of the first creasing plate 1 and the second creasing plate 2 are bonded into a whole and are respectively square areas
And a square region
Bonded, square area
And square area
Bonded, square area
And a square region
Bonded, square area
And a square region
And (6) bonding.
(3) The size of the self-locking unit is as follows,
，
，
the thickness of each creasing plate (including the first creasing plate 1 and the second creasing plate 2) is denoted w. To achieve full unfolding and folding of the bistable cell, it is geometrically necessary to ensure that:
（1）
wherein, in order to realize the complete folding of the bistable unit, it is necessary to ensure
. For dimension a, there is no relative size requirement with respect to b and c. Furthermore, to achieve the sheet folding effect, the indentation plate thickness w is required to be much less than the minimum of the dimensions a and c, and typically w cannot exceed 1/10 of the dimensions a or c.
(4) For the programmable self-locking unit, the folding sequence can be regulated and controlled to realize the switching of the extensibility/self-locking in two orthogonal directions (horizontal direction and vertical direction). If the unfolded configuration is changed into the folded configuration according to a certain folding sequence, the folding to the unfolding can be realized according to the reverse order of the folding sequence.
(5) In order to realize that the programmable self-locking unit can be unfolded in the horizontal direction and self-locked in the vertical direction, the folding sequence of the self-locking unit is 'vertical folding firstly-horizontal folding secondly'; in order to realize that the programmable self-locking unit can be unfolded in the vertical direction and self-locked in the horizontal direction, the folding sequence of the self-locking unit is 'horizontal folding firstly-vertical folding secondly'.
(6) The programmable self-locking units provided by the invention are subjected to two-dimensional array, so that a self-locking array structure with a folding/unfolding sequence programmable design can be obtained, the number of arrays in the horizontal direction is M, and the number of arrays in the vertical direction is N, as shown in fig. 7. Since each cell is stable in both the expanded and folded configurations, the structure formed by the plurality of bistable cell arrays has a plurality of stable planar configurations.
(7) Since each cell constituting the array structure has the splay/self-lock anisotropy, the array structure as a whole exhibits the splay/self-lock anisotropy.
(8) On the premise of ensuring that the folding/unfolding of each unit in the horizontal direction and the vertical direction of the array structure are the same, the design of different self-locking characteristics of the array structure can be realized by regulating and controlling the folding sequence of the array structure. Taking the array structure shown in fig. 12 in which each cell is in a folded state, the number of cells in each row in the horizontal direction is M, and the number of cells in each column in the vertical direction is N, the array structure can be represented as follows by the first description method
. If the array structure needs to be completely self-locked in the horizontal direction and has expandability in the vertical direction, the folding sequence of the array structure can be designed as follows: the units of the 1 st to M th columns from the left to the right are arranged in the horizontal directionAnd sequentially folding, and then sequentially folding the units in the 1 st to N th rows from top to bottom in the vertical direction. If the second method of description is used, i.e.
. If the array structure needs to be completely self-locked in the vertical direction and has extensibility in the horizontal direction, the folding sequence of the array structure can be designed as follows: the units in the 1 st to N th rows are sequentially folded in the vertical direction from top to bottom, and the units in the 1 st to M th rows are sequentially folded in the horizontal direction from left to right. If the second method of description is used, i.e.
. In a broader sense, the array structure may be designed to have an unfolding sequence in two directions, where the unfolding sequence is the reverse of the folding sequence.
In the description herein, references to the description of the terms "embodiment," "example," etc., mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above are not necessarily intended to refer to the same embodiment or example. Furthermore, various embodiments or examples described in this specification and features thereof may be combined or combined by those skilled in the art without contradiction.
Although embodiments of the present invention have been shown and described, it is understood that the above embodiments are illustrative and not to be construed as limiting the present invention, and that modifications, alterations, substitutions, and alterations may be made to the above embodiments by those of ordinary skill in the art without departing from the scope of the present invention.
Claims (10)
1. The self-locking unit with the programming function is characterized by comprising a first creasing plate and a second creasing plate which are of symmetrical structures, wherein the first creasing plate and the second creasing plate are respectively provided with a plurality of creases, the first creasing plate and the second creasing plate are partially bonded together to form a bonding part, the rest non-bonding parts form folding parts, the bonding part and the folding parts can be folded and unfolded along the creases, so that the self-locking unit has a fully unfolded configuration, a fully folded configuration and a partially folded configuration, and the self-locking unit has the self-locking characteristic in the horizontal direction or the vertical direction under the fully folded configuration.
2. The self-locking unit with programming function of claim 1, wherein the first indentation plate has four corners marked as A 1 、B 1 、C 1 、D 1 The square panel is internally provided with a square hollow area, and the four corners of the hollow area are respectively marked as E 1 、F 1 、G 1 、H 1 Wherein, square A 1 B 1 C 1 D 1 And square E 1 F 1 G 1 H 1 Having the same center point, and point A 1 、E 1 、G 1 、C 1 Distributed on the same diagonal, point E 1 To edge A 1 B 1 Is marked as A 2 Point E 1 To edge A 1 D 1 Is marked as D 4 Point F 1 To edge A 1 B 1 Is marked as A 4 Point F 1 To edge B 1 C 1 Is marked as B 2 Point G 1 To side B 1 C 1 Is marked as B 4 Point G 1 To edge C 1 D 1 Is marked as C 2 Point H 1 To edge C 1 D 1 Is marked as C 4 Point H 1 To edge A 1 D 1 Is marked as D 2 ；
In length, set to A 1 A 2 =A 4 B 1 =B 1 B 2 =B 4 C 1 =C 1 C 2 =C 4 D 1 =D 1 D 2 =A 1 D 4 =a，
Set point A 3 、B 3 、C 3 、D 3 、E 2 、F 2 、G 2 、H 2 So as to be in length
A 2 A 3 =B 2 B 3 =C 3 C 4 =D 3 D 4 =E 1 E 2 =F 1 F 2 =G 2 H 1 =E 1 H 2 =b，
And A is 3 A 4 =B 3 B 4 =C 2 C 3 =D 2 D 3 =E 2 F 1 =F 2 G 1 =G 1 G 2 =H 1 H 2 =c；
To achieve bistability in both the fully expanded and fully folded configurations, the geometry is such that
。
3. Self-locking unit with programming function according to claim 2, characterized in that the creases of the first creasing plate 1 are respectively
(ii) a Correspondingly, the creases of the second creasing plate 2 are respectively
(ii) a The bonding parts of the first creasing plate and the second creasing plate are respectively square areas
And square area
Bonded, square area
And square area
Bonded, square area
And square area
Bonded, square area
And square area
And (6) bonding.
4. Self-locking unit with programming function according to claim 3, characterized in that the crease of the first creasing plate
Respectively with the crease of the second creasing plate
Bonding; crease of first creasing plate
With corresponding crease of the second creasing plate 2
The self-locking unit is provided with non-adhesive creases, and the non-adhesive creases at corresponding positions on the first creasing plate and the second creasing plate move along the direction perpendicular to the panel and far away from each other when pressure is applied on the self-locking unit, so that the self-locking unit is folded.
5. The self-locking unit with programming function according to claim 4, wherein the self-locking unit has a folding sequence of horizontal folding first and vertical folding, and the self-locking unit is folded in the horizontal direction by applying pressure in the horizontal direction at the left and right ends of the self-locking unit in the horizontal direction in the fully unfolded configuration, and the rectangular area
Are respectively folded in a rectangle
In the middle of; rectangular area
Are respectively folded in a rectangle
To (c) to (d); square area
And square area
Is also folded; after folding, the self-locking unit is unfolded from the fully unfolded configuration A 1 B 1 C 1 D 1 Modified into a partially folded configuration A 1 B 1 B 3 D 3 (ii) a Then, respectively applying a pressure along the vertical direction at the upper end and the lower end of the self-locking unit in the vertical direction; with the application of pressure, the self-locking unit is folded in the vertical direction from a partially folded configuration A 1 B 1 B 3 D 3 Modified to a fully folded configuration A 1 A 3 C 1 D 3 (ii) a At this time, the self-locking unit is in a self-locking state in the horizontal direction.
6. The self-locking unit with programming function according to claim 4, wherein the self-locking unit has a folding sequence of "folding vertically and then folding horizontally", and the self-locking unit is folded vertically by applying a pressure in the vertical direction to the upper and lower ends of the self-locking unit in the unfolded configuration, and after folding, is folded from the fully unfolded configuration A 1 B 1 C 1 D 1 Modified into a partially folded configuration A 1 A 3 C 3 D 1 (ii) a Then, a pressure along the horizontal direction is respectively applied to the left end and the right end of the self-locking unit, so that the self-locking unitThe elements being folded in a horizontal direction from a partially folded configuration A 1 A 3 C 3 D 1 Modified to a fully folded configuration A 1 A 3 C 1 D 3 (ii) a At this time, the self-locking unit is in a self-locking state in the vertical direction.
7. A self-locking array system, which consists of a plurality of self-locking units, wherein the self-locking units are the self-locking units with the programming function according to any one of claims 1 to 6, and the self-locking array system is characterized in that the plurality of self-locking units are subjected to two-dimensional array so that the folding and unfolding sequences can be programmed, the number of arrays in the horizontal direction is M, the number of arrays in the vertical direction is N, and each self-locking unit is stable in a fully unfolded configuration and a fully folded configuration, so that the self-locking array system has a plurality of stable plane configurations.
8. The self-locking array system of claim 7, wherein the self-locking array system is programmed by describing it as follows: the fully folded configuration of the self-locking array system can be expressed as:
(ii) a The array structure needs to be completely self-locked in the horizontal direction, and when the array structure has expandability in the vertical direction, the folding sequence of the self-locking array system is designed as follows: firstly, sequentially folding the units in the 1 st to M th rows from left to right in the horizontal direction, and then sequentially folding the units in the 1 st to N th rows from top to bottom in the vertical direction; wherein, X represents the horizontal direction, Y represents the vertical direction, the numbers after X represent the folding or unfolding state of each column unit from left to right, the three-digit numbers after Y represent the folding or unfolding state of each row unit from top to bottom, the folding state is represented by the number 1, and the unfolding state is represented by the number 0.
9. The self-locking array system of claim 7, wherein the self-locking array system is programmed by describing it as follows: when the array structure is completely self-locked in the horizontal direction and has expandability in the vertical direction, firstly, the units in the 1 st to M th rows from the left to the right are sequentially folded in the horizontal direction, and secondly, the units in the 1 st to N th rows from the top to the bottom are sequentially folded in the vertical direction; the fully folded configuration of the self-locking array system can be expressed as:
when the array structure needs to realize complete self-locking in the vertical direction and has extensibility in the horizontal direction, the units in the 1 st to N th rows are sequentially folded in the vertical direction from top to bottom, and the completely folded configuration of the self-locking array system is sequentially folded in the horizontal direction from the 1 st to M th rows from left to right
10. The self-locking array system of claim 9, wherein the number of units in each row in the horizontal direction is M, the number of units in each column in the vertical direction is N, and the mechanical properties of the array structure obtained by different folding methods are different, and the mechanical programmability of the array structure can be realized by using the properties;
the sequence was folded as follows:
the sequence was folded as follows:
the sequence was folded as follows:
in the obtained self-locking array system, only two groups of units can be unfolded under the action of horizontal tension, and then the structure is self-locked and cannot be unfolded continuously under the action of the horizontal tension;
the sequence was folded as follows:
in the obtained self-locking array system, only three groups of units can be unfolded under the action of horizontal tension, then the structure is self-locked, and the structure cannot be unfolded continuously under the action of the horizontal tension;
therefore, under different folding sequences, the corresponding structure configuration can be regulated and controlled when the structure self-locking occurs, so that the structure has mechanical programmable characteristics.
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