CN1779144A

CN1779144A - Externally turnover and openalbe expandable structure and production thereof

Info

Publication number: CN1779144A
Application number: CN 200510060849
Authority: CN
Inventors: 罗尧治; 刘晶晶
Original assignee: Zhejiang University ZJU
Current assignee: Zhejiang University ZJU
Priority date: 2005-09-22
Filing date: 2005-09-22
Publication date: 2006-05-31
Anticipated expiration: 2025-09-22
Also published as: CN100346043C

Abstract

This invention is an outward retroflexion deployable structure and its process method. The structure comprises a movable connecting rod device, which is composed by several tetrahedrons that are connected by rotating joint to form a three- dimensional ring structure. At moving, the structure could deploy into an outspread structure. The process method is as followed: (1) decide the structure form and the basic geometry size and design the basic geometry parameters; (2) calculate out the tetrahedrons size according to the geometry size; (3) link the tetrahedrons through connecting joint at proper positions and design the wheel's position; (4) design the slide-rail's form and size; (5) link the structure and the slide-rail together. This structure's top part could be totally closed at closing and easy for control.

Description

Outward turning open type deployable structure and manufacturing method thereof

Technical Field

The invention relates to an outward turning open type deployable structure and a manufacturing method thereof. It comprises a movable linkage mechanism consisting of a plurality of rigid members connected by rotational connections to form a three-dimensional ring mechanism that is opened by movement of the mechanism.

Background

The expandable structure is a novel engineering structure in recent years, the geometric shape of the expandable structure can be changed according to actual conditions, and the expandable structure can be folded and expanded by means of large displacement and movement of the expandable structure. The structure formed by the mechanism has internal freedom, the folding and unfolding processes of the mechanism are rigid motion, strain can not be generated in the parts of the mechanism, and the mechanism is favorable for being used as a repeatedly opened structure. The types of existing openable roof structures in the world can be divided into horizontal movement opening, rigid rotation opening, up-and-down movement opening and radial opening according to the roof opening movement mode. The invention provides an outward turning open type deployable structure which adopts a link mechanism^[1-2]And a tetrahedral rotary ring^[3-4]Is the basis of the theory of (1).

[1]Bricard.R.(1897).Mémoire sur la théorie de l’octacdre articulé.Journal demathématiques pures et appliquées，Liouville 3，113-148.

[2]Bricard.R.(1927).Lecons de cinématique.Tome II cinématique Appliquée，Gauthier-Villars，Paris，7-12.

[3]Schattschneider，D.and Walker，W.(1977).M.C.Escher Kalerdocycles，Ballantin Books，New York.

[4]Schatz，P.(1998).Rhythmusforschung und Technik，2.Auflage.Verlag FreiesGeistesleben，Stuttgart.

Disclosure of Invention

The invention aims to provide an outward turning open type deployable structure and a manufacturing method thereof.

The outward-turning open type deployable structure comprises a movable link mechanism, wherein the link mechanism consists of N (N is more than or equal to 6, and N is an even number) tetrahedral rigid components, the tetrahedral rigid components are connected through rotary connecting pieces of a roof shaft and a support shaft to form a three-dimensional annular mechanism, the bottom end of the support shaft is a support, when the support moves from inside to outside along a sliding rail simultaneously, tetrahedrons rotate around the rotary connecting pieces of the tetrahedrons, the inner side surfaces of adjacent tetrahedrons of the structure can be in contact with each other, and the upper part of the structure is closed; when the support moves from outside to inside along the slide rail, the tetrahedron rotates around the rotating connecting piece, and the upper part of the structure is turned outwards and opened.

The geometry of the outwards-turned open-type deployable structure consisting of N tetrahedral rigid members can adopt various forms. When the structure is closed, the projection of the top surface in the horizontal direction can be a regular N-shaped polygon, the triangles serving as the top surfaces of the structure in the four surfaces of each tetrahedron are identical isosceles triangles, and the vertex of each triangle is coincided with one point when the structure is closed; when the structure is closed, the projection of the top surface in the horizontal direction can also be triangular, square, rectangular or polygonal.

An outward turning open type deployable structure composed of N tetrahedral rigid members takes the projection of a top surface in the horizontal direction as a regular N-shaped edge as an example when the structure is closed, and the manufacturing method comprises the following steps:

(1) the basic geometrical parameters for designing a developable structure consisting of N tetrahedral rigid members are as follows: when the structure is closed, the side length a of the regular N-shaped polygon projected in the horizontal direction of the roof is larger than 0; when the structure is closed, the upper rise c is larger than 0, and the relative rise xi is c/a; when the structure is closed, the included angle phi between the support shaft and the horizontal direction,

<math> <mrow> <mn>0</mn> <mo><</mo> <mi>φ</mi> <mo><</mo> <mi>π</mi> <mo>-</mo> <mi>arccos</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>/</mo> <msqrt> <mn>1</mn> <mo>+</mo> <msup> <mi>ξ</mi> <mn>2</mn> </msup> </msqrt> <mo>)</mo> </mrow> <mo>;</mo> </mrow> </math>

the length d of the support shaft is more than 0 and less than a/cos phi, and the relative length eta of the support shaft is d/a; the angle between the roof axis and the horizontal direction when the structure is completely unfolded

<math> <mrow> <msup> <mi>γ</mi> <mo>′</mo> </msup> <mrow> <mo>(</mo> <mi>arccos</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>/</mo> <msqrt> <mn>1</mn> <mo>+</mo> <msup> <mi>ξ</mi> <mn>2</mn> </msup> </msqrt> <mo>)</mo> </mrow> <mo><</mo> <msup> <mi>γ</mi> <mo>′</mo> </msup> <mo><</mo> <mi>π</mi> <mo>/</mo> <mn>2</mn> <mo>)</mo> </mrow> <mo>;</mo> </mrow> </math>

(2) Determining the dimensions of N tetrahedral rigid members constituting the structure, wherein one tetrahedron A is represented₁The formula for the length of the six sides of ABG is as follows:

BG＝ηa；

the geometry and dimensions of the remaining (N-1) tetrahedra can also be determined according to the above formula;

(3) determining a connection form between tetrahedral rigid members, wherein adjacent tetrahedral rigid members are respectively connected at the positions of a roof shaft and a support shaft through replaceable rotary connecting pieces to form a three-dimensional annular mechanism, the bottom end of the support shaft is a support, a pulley is arranged at the position of the support, and the slidable direction of the pulley is along the radial direction of a regular N-edge circumscribed circle;

(4) the form of the slide rail is designed, and the (N/2) slide rails are positioned on the same plane, the mutual included angle is (4 pi/N), and the extension lines can intersect at a point which is used as the center point of the slide rail. The position of the outermost point of the slide rail is equivalent to the position of the support when the structure is closed, and the distance formula from the central point

J₁＝a-dcosφ

The position of the innermost point of the slide rail is equivalent to the position of the support when the structure is completely unfolded, and the distance formula from the center

Wherein,

<math> <mrow> <mi>α</mi> <mo>=</mo> <mi>arccos</mi> <mfrac> <mrow> <mn>2</mn> <mi>ξ</mi> <mi>sin</mi> <mi>φ</mi> <mo>-</mo> <mn>2</mn> <mi>cos</mi> <mi></mi> <mi>φ</mi> <mi>cos</mi> <mrow> <mo>(</mo> <mn>2</mn> <mi>π</mi> <mo>/</mo> <mi>N</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mn>2</mn> <msqrt> <mn>1</mn> <mo>+</mo> <msup> <mi>ξ</mi> <mn>2</mn> </msup> </msqrt> <mi>cos</mi> <mrow> <mo>(</mo> <mn>2</mn> <mi>π</mi> <mo>/</mo> <mi>N</mi> <mo>)</mo> </mrow> </mrow> </mfrac> </mrow> </math>

<math> <mrow> <msup> <mi>τ</mi> <mo>′</mo> </msup> <mo>=</mo> <mi>arccos</mi> <mfrac> <mrow> <mo>-</mo> <mi>cos</mi> <msup> <mi>γ</mi> <mo>′</mo> </msup> <mi>cos</mi> <mi></mi> <mi>α</mi> <mi>cos</mi> <mrow> <mo>(</mo> <mn>2</mn> <mi>π</mi> <mo>/</mo> <mi>N</mi> <mo>)</mo> </mrow> <mo>+</mo> <mi>sin</mi> <msup> <mi>γ</mi> <mo>′</mo> </msup> <msqrt> <msup> <mi>sin</mi> <mn>2</mn> </msup> <mi>α</mi> <mo>-</mo> <msup> <mi>cos</mi> <mn>2</mn> </msup> <msup> <mi>γ</mi> <mo>′</mo> </msup> <msup> <mi>sin</mi> <mn>2</mn> </msup> <mrow> <mo>(</mo> <mn>2</mn> <mi>π</mi> <mo>/</mo> <mi>N</mi> <mo>)</mo> </mrow> </msqrt> </mrow> <mrow> <mn>1</mn> <mo>-</mo> <msup> <mi>cos</mi> <mn>2</mn> </msup> <msup> <mi>γ</mi> <mo>′</mo> </msup> <msup> <mi>sin</mi> <mn>2</mn> </msup> <mrow> <mo>(</mo> <mn>2</mn> <mi>π</mi> <mo>/</mo> <mi>N</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>;</mo> </mrow> </math>

(5) the pulley and the slide rail are correspondingly installed, so that the central shaft of the structure is ensured to pass through the central point of the slide rail, and the pulley can slide in the track of the slide rail.

The invention has the advantages that the expandable structure is directly constructed by utilizing the three-dimensional annular mechanism, the structural form is beautiful, the center of the structural roof is completely closed when the structure is closed, the motion symmetry of the support is ensured, and the expansion to the required structural form is realized. When the expandable structure is formed by six tetrahedral members, the mechanism is a single-degree-of-freedom over-constrained three-dimensional mechanism, the single degree of freedom enables the structure motion to be very easy to control, and the complex operation required by expansion is avoided. Furthermore, the over-constrained nature of the mechanism provides relatively high rigidity and structural strength, which make the deployable structure particularly useful.

Drawings

The invention will be further explained with reference to the drawings. In the attached drawings

FIGS. 1(a) - (c) are schematic views of the structure of the outward flip open deployable structure in the closed state;

FIGS. 2(a) - (c) are schematic views of the structure of the outwardly flipped open deployable structure during deployment;

fig. 3 is a schematic view of the geometrical relationship of the expandable structure with bar members perpendicular to and intersecting adjacent axes replacing a tetrahedral linkage when N is 6;

FIGS. 4(a) and (b) are diagrammatic views of an alternative connector form for connecting two tetrahedral members;

FIGS. 5(a) - (c) are plan, elevation and isometric views of the structural model in a closed, deployed and fully deployed configuration in a flip-out open deployable structure;

FIG. 6 is a tetrahedron A in the closed state of an outwardly flipped open deployable structure₁ABG calculation schematic diagram;

FIG. 7 is a tetrahedron A during deployment of an outwardly flipped open deployable structure₁ABG calculation schematic diagram;

fig. 8(a), (b), (c), (d) and (e) are schematic plan views of the top surface projected in the horizontal direction as a regular hexagon, a triangle, a regular octagon, a square and a rectangle when the flip-out open deployable structure is closed, respectively;

fig. 9(a), (b), (c) and (d) are mesh structure diagrams of the closed and open state of the flip-out open deployable structure.

Detailed Description

The invention provides an outward-turnable open-type deployable structure, which is based on the theories of a link mechanism and a tetrahedral rotating ring. A link is a special form of mechanism that consists of several interconnected rigid members, the connection between the two members being called a hinge. The hinge has various types, the invention adopts a rotary hinge, and the hinge has only one rotational degree of freedom; the rigid member may be a straight rod, a curved rod or even a body.

The tetrahedral rotating ring may be seen as a link mechanism with tetrahedrons as rigid members. The N identical tetrahedrons are composed of 4N (N is more than or equal to 6, and N is an even number) identical equilateral or isosceles triangles, two opposite sides of each tetrahedron are respectively connected with the sides of other tetrahedrons to form a ring, the tetrahedrons can rotate around the adjacent common sides to form a three-dimensional mechanism, and the ring-shaped mechanism can continuously rotate inwards or outwards. Note that the motion of the tetrahedral ring has a single degree of freedom when N is 6, and if a regular tetrahedron is used to form the ring, when the mechanism moves to a certain state, the two surfaces contact each other to stop the motion.

Two adjacent common edges in the tetrahedral rotating ring are perpendicular to each other, and (N/2) symmetric planes exist when the tetrahedral rotating ring moves to any state. If the symmetrical plane of the mechanism is ensured to be unchanged, the shape of the tetrahedron is changed, so that the adjacent common edges are not necessarily vertical and are not parallel or intersected, and the tetrahedron ring can still move. It is characterized in thatThus, comprising N tetrahedral elements and movable in a specific direction by means of hinges having a rotation axis, and ensuring, during the movement, that the mechanism has (N/2) planes of symmetry in any state of movement, with a single degree of freedom of movement, limited by certain geometrical conditions. Setting a straight line perpendicular to and intersecting with the two adjacent shafts, using the connecting line of the two adjacent intersection points as a rigid rod, and keeping the axial direction of the hinges unchanged, so that the axial distance of the adjacent hinges is the rod length a_i(i+1)Axial included angle alpha of adjacent hinges_i(i+1)And the distance R between the end points of two adjacent rods at the hinge i along the axis_iSatisfying the following geometrical conditions (fig. 3 shows a geometrical relationship diagram of the link mechanism when N ═ 6)

a₁₂＝a₂₃＝……＝a_N1＝l

α₁₂＝α₃₄＝……＝α_(N-1)N＝α，α₂₃＝α₄₅＝……＝α_N1＝2π-α (1)

R₁＝R₂＝……＝R_N＝0

The research on the tetrahedral rotating ring has attracted many people for research and analysis, but so far, the research on the tetrahedral rotating ring has been mainly focused on the case where the tetrahedron is a regular tetrahedron (two opposite sides of the tetrahedron as common sides are perpendicular) and the ring mechanism can be continuously rotated, mainly for the toy design and the like, and rarely applied to the structure.

The invention designs an outward turning open type deployable structure by combining the concepts of a tetrahedral rotating ring and a link mechanism, and provides a manufacturing method thereof. The method comprises the following steps:

first, the geometry and opening mode of the flip-out open deployable structure of the present invention are described.

The deployable structure comprises a linkage mechanism consisting of a plurality of rigid tetrahedral members (1), the tetrahedral members (1) being connected by rotary connectors (e.g. the alternative connectors 2 in fig. 4(a) and 4(b) respectively).

When the outwardly-turned open-type deployable structure is a ring-shaped structure composed of N (N is equal to or greater than 6, and N is an even number) tetrahedrons, fig. 5 shows a structural model when N is equal to 6. The N tetrahedrons are spaced at the same interval, and the edges of the adjacent tetrahedron members (1) are connected through a rotary connector (2) to form a ring (the connection mode is shown in figure 4). Adjacent common edges are not necessarily perpendicular and are not parallel nor intersecting. When the structure is closed, the inner side surfaces (6) of adjacent tetrahedrons are contacted, and the structure can be kept stable under the action of self weight and external force. The (N/2) public sides are used as roof shafts (3), the (N/2) public sides are used as support shafts (4), the support shafts (4) are inclined inwards by a certain angle, and the (N/2) supports (7) are respectively positioned at the bottom ends of the support shafts (4). The roof shaft (3) and the support shaft (4) are alternately positioned in N vertical planes with an included angle of (2 pi/N), and the roof shaft (3) and the support shaft (4) move in the planes when the structure is closed and unfolded.

The geometry of the outwards-turned open-type deployable structure consisting of N tetrahedral rigid members can adopt various forms. When the structure is closed, the projection of the top surface in the horizontal direction can be a regular N-polygon (such as ABCDEF in fig. 1 (a)), the triangle as the top surface (5) of the structure in the four faces of each tetrahedron is the same isosceles triangle, and the vertex of each triangle is coincided with one point (8) when the structure is closed; when the structure is closed, the projection of the top surface in the horizontal direction can also be a triangle, a square, a rectangle or a polygon (as shown in fig. 8).

When the support moves from inside to outside along the sliding rail (9), the tetrahedron (1) rotates around the rotary connecting piece (2) of the tetrahedron, so that the inner side surfaces (6) of the adjacent tetrahedron of the structure are contacted with each other, and the upper part of the structure is closed; when the support moves from outside to inside along the sliding rail (9), the tetrahedron (1) rotates around the rotating connecting piece (2), and the upper part of the structure is turned outwards and opened.

And secondly, the geometric parameters involved in the outwards-turning open type deployable structure are adopted.

The structure geometry was set as follows:

(1) a represents the side length of a regular N-shaped polygon projected in the horizontal direction when the structure is closed (as shown in FIG. 1(a), a is more than 0);

(2) c represents the upper rise when the structure is closed (as in fig. 1(b), OO' ═ c, c > 0), and relative rise ξ ═ c/a;

(3) phi represents the angle between the axis of the support and the horizontal when the structure is closed

<math> <mrow> <mo>(</mo> <mn>0</mn> <mo><</mo> <mi>φ</mi> <mo><</mo> <mi>π</mi> <mo>-</mo> <mi>arccos</mi> <mo>(</mo> <mn>1</mn> <mo>/</mo> <msqrt> <mn>1</mn> <mo>+</mo> <msup> <mi>ξ</mi> <mn>2</mn> </msup> </msqrt> <mo>)</mo> </mrow> </math>

As in fig. 6);

(4) d represents the length of the support shaft (as shown in fig. 1(c), BG ═ DM ═ FN ═ d, 0 < d < a/cos phi), and the relative length η of the support shaft is d/a;

(5) gamma' indicates the angle between the roof axis and the horizontal when the structure is fully deployed

<math> <mrow> <mo>(</mo> <mi>arccos</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>/</mo> <msqrt> <mn>1</mn> <mo>+</mo> <msup> <mi>ξ</mi> <mn>2</mn> </msup> </msqrt> <mo>)</mo> </mrow> <mo><</mo> <msup> <mi>γ</mi> <mo>′</mo> </msup> <mo><</mo> <mi>π</mi> <mo>/</mo> <mn>2</mn> <mo>)</mo> </mrow> </math>

(6) Gamma represents the included angle between the support shaft and the horizontal direction when the structure moves (as shown in figure 7);

(7) tau represents the angle between the roof axis and the horizontal direction when the structure moves (as shown in figure 7);

(8) alpha represents the included angle between the axes of the adjacent hinges (as in the formula (1));

(9) l represents the distance between the axes of adjacent hinges (as shown in equation (1));

(10) e, f and h represent the distances in the direction of the axis from the end points of the rods perpendicular to the axes of the two adjacent hinges of the structure and intersecting the two axes to the end points of the common edges of the tetrahedron (see fig. 6 and 7, a)₁A₀＝e，AA₀＝f，BB₀＝h，GB₀＝d-h)。

(1) "5" is a basic geometric parameter of the structure, which determines the geometry and dimensions of the structure, and other geometric parameters of the structure can be obtained from the basic geometric parameter. (6) And (7) parameters representing the structure deployment process, which vary as the structure moves. (8) "10" are indirect geometrical parameters of the structure, representing the relationship between the axes of the tetrahedron and the relationship between the tetrahedron and the rod perpendicular to and intersecting the two axes.

And thirdly, the formula involved in the outward turning open type deployable structure is provided.

The invention can adopt various geometric forms, and takes the situation that an expandable structure consisting of N tetrahedrons is adopted, and the projection of the top surface of the structure in the horizontal direction is a regular N-shaped polygon when the structure is closed as an example.

1. Determination of geometrical dimensions of tetrahedral elements in a structure

The N tetrahedrons are identical or symmetrical, and only the tetrahedron A needs to be calculated₁The geometry of the ABG, as in fig. 6. A rectangular coordinate system O ' XYZ is established by taking O ' as an origin, O ' B as an X axis, O ' Q (O ' Q vertical plane OO ' B) as a Y axis and O ' O as a Z axis. When the structure is closed, the coordinates of each point are respectively A₁(0, 0, c), B (a, 0, 0), A (acos (2 π/N), asin (2 π/N), 0), G (a-dcos φ, 0, -dsin φ). Tetrahedron A₁The six sides of the ABG have a length of

BG＝ηa；

2. Determining values of structure indirect geometric parameters alpha, l, e, f and h

As shown in FIG. 6, a straight line A is set₀B₀With two tetrahedron axes A₁A and BG are perpendicular and intersect at A₀And B₀When the included angle between the axes of adjacent shafts is alpha and the distance is l, A is₀B₀L; extension A of the rods into a tetrahedron₁A₀＝e，AA₀＝f，BB₀H. When A is used as AR/BG and the intersecting plane O' XY is used as R, the point of R is (0, asin (2 pi/N), -atan phi cos (2 pi/N)), so as to satisfy the geometric relationship

And is

Substituting formula (3) into formula (4)

<math> <mrow> <mi>α</mi> <mo>=</mo> <mi>arccos</mi> <mfrac> <mrow> <mn>2</mn> <mi>ξ</mi> <mi>sin</mi> <mi>φ</mi> <mo>-</mo> <mn>2</mn> <mi>cos</mi> <mi></mi> <mi>φ</mi> <mi>cos</mi> <mrow> <mo>(</mo> <mn>2</mn> <mi>π</mi> <mo>/</mo> <mi>Ν</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mn>2</mn> <msqrt> <mn>1</mn> <mo>+</mo> <msup> <mi>ξ</mi> <mn>2</mn> </msup> </msqrt> <mi>cos</mi> <mrow> <mo>(</mo> <mn>2</mn> <mi>π</mi> <mo>/</mo> <mi>Ν</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow> </math>

Axis A₁The angle alpha between A and BG, the distance l, then the tetrahedron A₁Volume of ABG

Passing through A as straight line AH ^ plane OBG and crossing O' B at H, tetrahedron A₁Volume of ABG

<math> <mrow> <mi>V</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mn>3</mn> </mfrac> <mi>AH</mi> <mo>·</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mi>BG</mi> <mo>·</mo> <msub> <mi>A</mi> <mn>1</mn> </msub> <mi>B</mi> <mo>·</mo> <mi>sin</mi> <mo>&angle;</mo> <mi>OBG</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow> </math>

Equations (6) and (7) are equal and have

<math> <mrow> <mi>sin</mi> <mo>&angle;</mo> <mi>OBG</mi> <mo>=</mo> <mfrac> <mrow> <mi>ξ</mi> <mi>cos</mi> <mi>φ</mi> <mo>+</mo> <mi>sin</mi> <mi>φ</mi> </mrow> <msqrt> <mn>1</mn> <mo>+</mo> <msup> <mi>ξ</mi> <mn>2</mn> </msup> </msqrt> </mfrac> <mo>,</mo> </mrow> </math>

AH＝asin(2π/N)，A₁A＝A₁B

To obtain

Per A₀As AP/BB₀And AP ═ BB₀H, then BP ═ A₀B₀＝l，∠A₁A₀P ═ α, satisfy

A_{1} A = e + f = \sqrt{a^{2} + c^{2}}

Get it solved

3. Determining the relation between the included angle gamma between the roof axis and the horizontal direction and the included angle tau between the support axis and the horizontal direction in the process of unfolding the structure

The schematic view of the structure in the process of unfolding is shown in figure 2, a roof shaft A₁A、C₁C and E₁The extension line of E is crossed with O₁The extension lines of the support axes BG, DM and FN intersect at O₂Plane A₀C₀E₀Quadrature axis O₁O₂In O₀₁Plane B₀D₀F₀Quadrature axis O₁O₂In O₀₂. The structure N tetrahedrons are identical or symmetrical, taking the tetrahedron A₁The ABG calculates the geometry of the structure as it is deployed, as shown in fig. 7.

Translating the origin of the rectangular coordinate system to O₀₁Point and establish a rectangular coordinate system O₀₁X₀₁Y₀₁Z₀₁. Per A₀As A₀S∥BB₀Intersecting plane O₀₁Y₀₁Z₀₁At S, set A₀O₁E', each point coordinate is A₀(e′cosγcos(2π/N)，e′cosγsin(2π/N)，0)，O₁(0, 0, e ' sin gamma), S (0, e ' cos gamma sin (2 pi/N), -e ' cos gamma cos (2 pi/N) tan tau) satisfying the geometric relationship

O₁A₀＝e′

And is

Substituting the formula (11) into the formula (12) to obtain the geometric parameter relationship in the structure unfolding process

sinγsinτ-cosγcosτcos(2π/N)＝cosα (13)

When the structure is closed, the air inlet pipe is connected with the air inlet pipe,

<math> <mrow> <msub> <mi>τ</mi> <mn>0</mn> </msub> <mo>=</mo> <mi>φ</mi> <mo>,</mo> <msub> <mi>γ</mi> <mn>0</mn> </msub> <mo>=</mo> <mi>arccos</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>/</mo> <msqrt> <mn>1</mn> <mo>+</mo> <msup> <mi>ξ</mi> <mn>2</mn> </msup> </msqrt> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>14</mn> <mo>)</mo> </mrow> </mrow> </math>

when the structure is fully unfolded, γ ═ γ', then

<math> <mrow> <msup> <mi>τ</mi> <mo>′</mo> </msup> <mo>=</mo> <mi>arccos</mi> <mfrac> <mrow> <mo>-</mo> <mi>cos</mi> <msup> <mi>γ</mi> <mo>′</mo> </msup> <mi>cos</mi> <mi></mi> <mi>α</mi> <mi>cos</mi> <mrow> <mo>(</mo> <mn>2</mn> <mi>π</mi> <mo>/</mo> <mi>N</mi> <mo>)</mo> </mrow> <mo>+</mo> <mi>sin</mi> <msup> <mi>γ</mi> <mo>′</mo> </msup> <msqrt> <msup> <mi>sin</mi> <mn>2</mn> </msup> <mi>α</mi> <mo>-</mo> <msup> <mi>cos</mi> <mn>2</mn> </msup> <msup> <mi>γ</mi> <mo>′</mo> </msup> <msup> <mi>sin</mi> <mn>2</mn> </msup> <mrow> <mo>(</mo> <mn>2</mn> <mi>π</mi> <mo>/</mo> <mi>N</mi> <mo>)</mo> </mrow> </msqrt> </mrow> <mrow> <mn>1</mn> <mo>-</mo> <msup> <mi>cos</mi> <mn>2</mn> </msup> <msup> <mi>γ</mi> <mo>′</mo> </msup> <msup> <mi>sin</mi> <mn>2</mn> </msup> <mrow> <mo>(</mo> <mn>2</mn> <mi>π</mi> <mo>/</mo> <mi>N</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>15</mn> <mo>)</mo> </mrow> </mrow> </math>

Equation (13) describes the relationship of the variables τ and γ during the structure unfolding process. When the structure is unfolded from the closed state, the included angle gamma between the roof axis and the horizontal plane is from gamma₀Increasing gradually to gamma', and the included angle tau between the support shaft and the horizontal plane is from tau₀And gradually decreases to tau'.

4. Determining the size and position of a sliding track

When the structure is unfolded to a certain state, the positive (N/2) edge A₀C₀E₀… … side length a₀Regular (N/2) polygonal shape B₀D₀F₀… … side length b₀Plane A₀C₀E₀And B₀D₀F₀A distance of c₀I.e. O₀₁O₀₂＝c₀。

In a rectangular coordinate systemO₀₁X₀₁Y₀₁Z₀₁In, each point coordinate is

Satisfy the geometric relationship

Equation (16) is solved

Substituting the formula (13) into the formula (17) to obtain

The expandable structure is composed of N tetrahedral rigid members, and the (N/2) slide rails (9) are in the same plane, have an included angle of (4 pi/N) and have extension lines intersected at one point, and the point is used as the center point of the slide rail. The position of the outermost points (G, M and N in figures 1(a) and (b)) of the sliding rail (9) corresponds to the position of the support (7) when the structure is closed, and the distance formula from the center point

J₁＝a-dcosφ (19)

The innermost points of the slide rail (9) (S in fig. 1(a) and (b) and fig. 2(a) and (b))_G、S_MAnd S_N) Corresponding to the position of the support (7) when the structure is fully unfolded, formula of the distance from the center

Substituting the formula (18) into the formula (20) to obtain

Fourthly, the invention discloses a manufacturing method of an outward turning open type deployable structure

1. From the foregoing, the basic shape of the deployable structure of the present invention has been determined. Selecting proper geometric parameters: the side length a of the regular N-shaped projection of the top surface in the horizontal direction when the structure is closed, the rise c of the upper part when the structure is closed, the included angle phi between the support shaft (4) and the horizontal direction when the structure is closed, the length d of the support shaft (4) and the included angle gamma' between the roof shaft (3) and the horizontal direction when the structure is completely unfolded.

2. According to formula (2), the geometrical dimensions of the N tetrahedral rigid members making up the structure are determined, the N tetrahedral members being designed according to the dimensions.

3. The annular position relation between N tetrahedron components (1) is correctly arranged, the connection form between the tetrahedron rigid components is determined, the adjacent tetrahedron components (1) are respectively connected at the positions of a roof shaft (3) and a support shaft (4) through replaceable rotary connectors (2), the bottom end of the support shaft is provided with a support (4), a pulley is arranged at the position of the support, and the slidable direction of the pulley is along the radial direction of a circumscribed circle of a regular N-edge. Attention is paid to confirm the correct positions of the roof axis (3) and the support axis (4) of the tetrahedral member (1).

4. According to the formulas (19) and (21), the outermost points (G, M and N in FIGS. 1(a) and (b)) of the slide rail (9) and the innermost points (S in FIGS. 1(a), (b) and FIGS. 2(a), (b)) of the slide rail (9) are determined_G、S_MAnd S_N) The distance from the center is designed according to the basic schematic diagram of the sliding rail (9) in the figures 1 and 2, the (N/2) sliding rails are in the same plane, the mutual included angle is (4 pi/N), and the extension lines can intersect at a point which is used as the center point of the sliding rail.

5. The pulley and the slide rail are correspondingly installed, so that the central shaft of the structure is ensured to pass through the central point of the slide rail, and the pulley can slide in the track of the slide rail.

In the foregoing, the N tetrahedral members of the deployable structure are considered as N entities. In fact, the N tetrahedrons in the present invention can also be tetrahedrons formed by a grid formed by rods (as shown in fig. 9), and can also be combined with a film material, so that the density and the weight of the structure can be greatly reduced, which is very beneficial to engineering application.

The invention has the advantages that the expandable structure is directly constructed by utilizing the three-dimensional annular mechanism, the structural form is attractive, the center of the structural roof is completely closed when the structure is closed, the motion symmetry of the support is ensured, and the expansion to the required structural form is realized. When the expandable structure is formed by six tetrahedral members, the mechanism is a single-degree-of-freedom over-constrained three-dimensional mechanism, the single degree of freedom enables the structure motion to be very easy to control, and the complex operation required by expansion is avoided. Furthermore, the over-constrained nature of the mechanism provides relatively high rigidity and structural strength, which make the deployable structure particularly useful.

The invention can be applied to openable roof structures with various sizes, and the opening mode of the openable roof structure is an outward turning opening mode.

Claims

1. An outwards-overturning opening type deployable structure is characterized by comprising a movable link mechanism, wherein the link mechanism consists of N tetrahedral rigid components (1), the tetrahedral rigid components are connected through a roof shaft (3) and a rotary connecting piece (2) of a support shaft (4) to form a three-dimensional annular mechanism, a support (7) is arranged at the bottom end of the support shaft (4), when the support moves from inside to outside along a sliding rail (9), the tetrahedrons (1) rotate around the rotary connecting piece (2) of the tetrahedrons, so that the inner side surfaces (6) of adjacent tetrahedrons of the structure are in contact with each other, and the upper part of the structure is closed; when the support moves from outside to inside along the sliding rail (9), the tetrahedron (1) rotates around the rotating connecting piece (2), and the upper part of the structure is turned outwards and opened.

2. A flip-out open deployable structure according to claim 1, wherein the N tetrahedral rigid members are an even number of tetrahedral rigid members equal to or greater than six.

3. A structure deployable in an outwardly turned open configuration according to claim 1 or 2, wherein when the structure of N tetrahedron-shaped rigid members is closed, the projection of the top surface (5) in the horizontal direction is a regular N-sided polygon, the triangles of the four faces of each tetrahedron as the top surfaces (5) of the structure are identical isosceles triangles, and the vertices (8) of the N triangles of the top surface coincide at a point when the structure is closed.

4. A structure deployable in an outwardly turned open position according to claim 1 or 2, wherein the horizontal projection of the top surface (5) when the structure of N tetrahedral rigid members is closed is triangular, square, rectangular or polygonal.

5. A method of making an outwardly turned open deployable structure according to claim 1, further comprising the steps of:

(1) the basic geometrical parameters for designing a developable structure consisting of N tetrahedral rigid members are as follows: when the structure is closed, the side length a of the regular N-shaped polygon projected in the horizontal direction of the roof is larger than 0; when the structure is closed, the upper rise c is larger than 0, and the relative rise xi is c/a; when the structure is closed, the included angle phi between the support shaft (4) and the horizontal direction,

the length d of the support shaft (4) is more than 0 and less than a/cos phi, and the relative length eta of the support shaft is d/a; when the structure is completely unfolded, the roof axis (3) forms an included angle with the horizontal direction

(3) determining a connection form between tetrahedral rigid members, wherein adjacent tetrahedral rigid members (1) are respectively connected at positions of a roof shaft (3) and a support shaft (4) through replaceable rotary connectors (2) to form a three-dimensional annular mechanism, the bottom end of the support shaft (4) is provided with a support (7), a pulley is arranged at the position of the support (7), and the sliding direction of the pulley is along the radial direction of a circumscribed circle of a regular N-edge;

(4) the form and the size of the slide rail are designed, and (N/2) slide rails (9) are in the same plane, the mutual included angle is (4 pi/N), and the extension lines can intersect at one point which is used as the center point of the slide rail. The position of the outermost point of the slide rail (9) is equivalent to the position of the support (7) when the structure is closed, and the distance formula from the central point

J₁＝a-dcosφ

The position of the innermost point of the slide rail (9) is equivalent to the position of the support (7) when the structure is completely unfolded, and the distance formula from the center

Wherein,

<math> <mrow> <msup> <mi>τ</mi> <mo>′</mo> </msup> <mo>=</mo> <mi>arccos</mi> <mfrac> <mrow> <mo>-</mo> <mi>cos</mi> <msup> <mi>γ</mi> <mo>′</mo> </msup> <mi>cos</mi> <mi></mi> <mi>α</mi> <mi>cos</mi> <mrow> <mo>(</mo> <mn>2</mn> <mi>π</mi> <mo>/</mo> <mi>N</mi> <mo>)</mo> </mrow> <mo>+</mo> <mi>sin</mi> <msup> <mi>γ</mi> <mo>′</mo> </msup> <msqrt> <msup> <mi>sin</mi> <mn>2</mn> </msup> <mi>α</mi> <mo>-</mo> <msup> <mi>cos</mi> <mn>2</mn> </msup> <msup> <mi>γ</mi> <mo>′</mo> </msup> <mi>si</mi> <msup> <mi>n</mi> <mn>2</mn> </msup> <mrow> <mo>(</mo> <mn>2</mn> <mi>π</mi> <mo>/</mo> <mi>N</mi> <mo>)</mo> </mrow> </msqrt> </mrow> <mrow> <mn>1</mn> <mo>-</mo> <msup> <mi>cos</mi> <mn>2</mn> </msup> <msup> <mi>γ</mi> <mo>′</mo> </msup> <mrow> <mo>(</mo> <mn>2</mn> <mi>π</mi> <mo>/</mo> <mi>N</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>;</mo> </mrow> </math>