CN100338319C - Manufacturing method of plate type ellipsoid like structure capable of opening - Google Patents

Abstract

The present invention discloses a manufacture method for openable plate type ellipsoid like structures, which has the following procedures: firstly, an openable plate type ellipsoid like structure which is composed of a triangular plate covering unit of an arc line boundary class and a quadrangular plate covering unit of an arc line boundary class or an openable plate type ellipsoid like structure which is composed of a triangular plate covering unit of a broken line boundary class and a quadrangular plate covering unit of a broken line boundary class is selected, and design parameters are set according to the selected structure; secondly, four kinds of plate covering units of the openable plate type ellipsoid like structure can be designed; thirdly, the positions of hinging holes on the four plate covering units are determined; fourthly, the plate covering units of the two kinds of openable plate type ellipsoid like structures are connected through scissor type hinging joints according to a combining mode. The present invention has the advantages that the structure made by the manufacture method has the advantages of graceful and rich shape, artful conception, flexible design and large structural opening rate, the center is completely closed without holes when the structure is closed, and all plate covering units make simultaneous motion when the structure is opened, which is easy to control.

Description

The preparation method of plate type ellipsoid like structure capable of opening

Technical field

The present invention relates to a kind of preparation method of plate type ellipsoid like structure capable of opening.

Background technology

Up to now, existing in the world type of opening roof structure can be divided into according to roof system opening movement mode: 1. horizontal movement is opened, for example Ri Ben Ariake Colosseum; 2. Rigid Body in Rotation With is opened, for example the loyal tennis of Shanghai flag center; 3. unlatching, for example sports palace, Olympics, Montreal move up and down.The novel roof structure opened of one class is arranged in the current research, and it has used the notion of scissors hinges.The scissors hinged joint is a kind of hinged joint that is similar to the scissors node, and its characteristics are can freely rotate each other by each member that the scissors hinged joint connects.Spain engineer Pinero ^[1]The earliest the scissors hinge is applied in the middle of the open-type building, afterwards Escrig and Zeigler ^[2]It is improved.The Hoberman of the U.S. ^[3,4]Invent unit, simple angle (Simple Angulated Element), and designed Aris Dome.

List of references

[1].Pinero，E.P.，1961.Spain?Patent?Number?266801.

[2].Zeigler，T.R.，1981.Collapsible?self-supporting?structures?andpanels?and?hub?therefore，US?Patent?4,290,244.

[3].Hoberman，C.，1990.Reversibly?expandable?doubly-curved?trussstructures.US?Patent?4,942,700.

[4].Hoberman，C.，1991.Radial?expansion?retraction?truss?structure.US?Patent?5,024,031.

Summary of the invention

The preparation method that the purpose of this invention is to provide a kind of plate type ellipsoid like structure capable of opening.

Its step is as follows:

1) selects plate type ellipsoid like structure capable of opening that becomes with camber line border class quadrangle cladding plate unit combination by class triangle cladding plate unit, camber line border or the plate type ellipsoid like structure capable of opening that becomes with broken line border class quadrangle cladding plate unit combination by class triangle cladding plate unit, broken line border, and determine design parameters according to selected structure;

2) four kinds of cladding plate unit of design plate type ellipsoid like structure capable of opening: class triangle cladding plate unit, camber line border, class triangle cladding plate unit, broken line border, class quadrangle cladding plate unit, camber line border, class quadrangle cladding plate unit, broken line border, main formulas is as follows:

$r_{\max }=\frac{l}{\sin \frac{\mathrm{\π}}{n}}\·\cos [\frac{\mathrm{\π}}{n}+\frac{{\mathrm{\ψ}}_1+{\mathrm{\ψ}}_2}{2}],$

$\mathrm{\Φ}=\mathrm{\π}-\frac{2\mathrm{\π}}{n}-({\mathrm{\ψ}}_1+{\mathrm{\ψ}}_2);$

3) determine hinge connection hole site on four kinds of cladding plate unit, at first set up polar coordinate system, for class triangle cladding plate unit, camber line border and class triangle cladding plate unit, broken line border, the coordinate at hinge connection center, hole is (ρ _i, θ _i), (i=1,2,3), main formulas is as follows

${\mathrm{\ρ}}_i=\frac{l}{\sin \frac{\mathrm{\π}}{n}}\·\sin [(i-1)\frac{\mathrm{\π}}{n}+\frac{{\mathrm{\ψ}}_1}{2}](i=\mathrm{1,2,3}),$

${\mathrm{\θ}}_i=(3-i)\frac{\mathrm{\π}}{n}+\frac{{\mathrm{\ψ}}_2}{2}(i=\mathrm{1,2,3}),$

For class quadrangle cladding plate unit, camber line border, class quadrangle cladding plate unit, broken line border, the coordinate at three hinge connection centers, hole is respectively

$(\frac{2l\·\sin (\frac{\mathrm{\π}}{n}+\frac{{\mathrm{\ψ}}_1}{2})}{\cos \mathrm{\γ}},\frac{\mathrm{\π}}{2}+\frac{{\mathrm{\ψ}}_2}{2}-\mathrm{\γ}),(\frac{l\·\sin (\frac{\mathrm{\π}}{n}+\frac{{\mathrm{\ψ}}_1}{2})}{\sin \frac{\mathrm{\π}}{n}},\frac{\mathrm{\π}}{n}+\frac{{\mathrm{\ψ}}_2}{2}),$

$(2l\·\sin (\frac{\mathrm{\π}}{2}-\frac{\mathrm{\π}}{n}-\frac{{\mathrm{\ψ}}_1}{2})+\frac{l}{\sin \frac{\mathrm{\π}}{n}}\sin \frac{{\mathrm{\ψ}}_1}{2},\frac{{\mathrm{\ψ}}_2}{2}),\mathrm{\γ}=\arctan \left(\frac{\sin \frac{{\mathrm{\ψ}}_1}{2}}{2\sin \frac{\mathrm{\π}}{n}\·\sin (\frac{\mathrm{\π}}{n}+\frac{{\mathrm{\ψ}}_1}{2})}\right);$

4) the cladding plate unit of two kinds of plate type ellipsoid like structure capable of opening connects by the scissors hinged joint according to compound mode.

The plate type ellipsoid like structure capable of opening that is become with camber line border class quadrangle cladding plate unit combination by class triangle cladding plate unit, camber line border is by n class triangle cladding plate unit, heads camber line border, individual class quadrangle cladding plate unit, heads camber line border of m and class triangle cladding plate unit, camber line border up, n the back side, class quadrangle cladding plate unit, camber line border up, m the back side according to compound mode connect by the scissors hinged joint and form, node connection relation is that the inner ring node is corresponding links to each other, inferior inner ring node is corresponding to link to each other, and the like, the outmost turns node is corresponding to link to each other.

The plate type ellipsoid like structure capable of opening that is become with broken line border class quadrangle cladding plate unit combination by class triangle cladding plate unit, broken line border is by n class triangle cladding plate unit, heads broken line border, individual class quadrangle cladding plate unit, heads broken line border of m and class triangle cladding plate unit, broken line border up, n the back side, class quadrangle cladding plate unit, broken line border up, m the back side according to compound mode connect by the scissors hinged joint and form, node connection relation is that the inner ring node is corresponding links to each other, inferior inner ring node is corresponding to link to each other, and the like, the outmost turns node is corresponding to link to each other.

Advantage of the present invention is that the beautiful design of the structure made according to this preparation method enriches, is skillfully constructed, the unlatching rate of flexible design, structure is big; Central authorities' complete closed when structure is closed, the hole of not boxing out; All cladding plate unit all are synchronized with the movement during unlatching, are easy to control.

Description of drawings

The present invention is further described below in conjunction with accompanying drawing

Fig. 1 (a) is the plate type ellipsoid like structure capable of opening closure state schematic diagram that the present invention is become with camber line border class quadrangle cladding plate unit combination by class triangle cladding plate unit, camber line border;

Fig. 1 (b) is the plate type ellipsoid like structure capable of opening opening schematic diagram that the present invention is become with camber line border class quadrangle cladding plate unit combination by class triangle cladding plate unit, camber line border;

Fig. 2 (a) is the plate type ellipsoid like structure capable of opening closure state schematic diagram that the present invention is become with broken line border class quadrangle cladding plate unit combination by class triangle cladding plate unit, broken line border;

Fig. 2 (b) is the plate type ellipsoid like structure capable of opening opening schematic diagram that the present invention is become with broken line border class quadrangle cladding plate unit combination by class triangle cladding plate unit, broken line border;

Fig. 3 (a)～(d) is class triangle cladding plate unit, a camber line of the present invention border design flow diagram;

Fig. 3 (e) is that figure is determined in hinge connection hole site on the class triangle cladding plate unit, camber line of the present invention border;

Fig. 4 (a)～(d) is class triangle cladding plate unit, a broken line of the present invention border design flow diagram;

Fig. 4 (e) is that figure is determined in hinge connection hole site on the class triangle cladding plate unit, broken line of the present invention border;

Fig. 5 (a)～(c) is class quadrangle cladding plate unit, a camber line of the present invention border design flow diagram;

Fig. 5 (d) is that figure is determined in hinge connection hole site on the class quadrangle cladding plate unit, camber line of the present invention border;

Fig. 6 (a)～(c) is class quadrangle cladding plate unit, a broken line of the present invention border design flow diagram;

Fig. 6 (d) is that figure is determined in hinge connection hole site on the class quadrangle cladding plate unit, broken line of the present invention border;

Fig. 7 (a) is the plate type ellipsoid like structure capable of opening front cladding plate element number figure that the present invention is become with camber line border class quadrangle cladding plate unit combination by class triangle cladding plate unit, camber line border;

Fig. 7 (b) is the plate type ellipsoid like structure capable of opening back side cladding plate element number figure that the present invention is become with camber line border class quadrangle cladding plate unit combination by class triangle cladding plate unit, camber line border;

Fig. 7 (c) is the plate type ellipsoid like structure capable of opening cladding plate unit combination mode schematic diagram that the present invention is become with camber line border class quadrangle cladding plate unit combination by class triangle cladding plate unit, camber line border;

Fig. 7 (d) is that the present invention finishes figure by the plate type ellipsoid like structure capable of opening cladding plate unit assembling that class triangle cladding plate unit, camber line border becomes with camber line border class quadrangle cladding plate unit combination;

Fig. 8 (a) is the plate type ellipsoid like structure capable of opening front cladding plate element number figure that the present invention is become with broken line border class quadrangle cladding plate unit combination by class triangle cladding plate unit, broken line border;

Fig. 8 (b) is the plate type ellipsoid like structure capable of opening back side cladding plate element number figure that the present invention is become with broken line border class quadrangle cladding plate unit combination by class triangle cladding plate unit, broken line border;

Fig. 8 (c) is the plate type ellipsoid like structure capable of opening cladding plate unit combination mode schematic diagram that the present invention is become with broken line border class quadrangle cladding plate unit combination by class triangle cladding plate unit, broken line border;

Fig. 8 (d) is that the present invention finishes figure by the plate type ellipsoid like structure capable of opening cladding plate unit assembling that class triangle cladding plate unit, broken line border becomes with broken line border class quadrangle cladding plate unit combination.

The specific embodiment

One, the plate type ellipsoid like structure capable of opening of the present invention's making is described

The class ellipse is to add at the two ends of minor face that by a rectangle two semicircles combine, and is similar to the shape of international standard 400m runway.This structure can be divided into two big classes, and a class is the plate type ellipsoid like structure capable of opening (as shown in Figure 1) that is become with camber line border class quadrangle cladding plate unit combination by class triangle cladding plate unit, camber line border.It is a kind of structure of two layers, each layer forms by the connection of scissors hinged joint according to certain compound mode by class triangle cladding plate unit, n camber line border and class quadrangle cladding plate unit, m camber line border, each class triangle cladding plate unit, camber line border is all identical, and each class quadrangle cladding plate unit, camber line border is all identical.Integral body was configured as the class ellipse when architectural feature was closure, the central authorities hole of not boxing out; Each cladding plate unit does not collide each other during unlatching, and total only has one degree of freedom in the moving process; The shape of opening back structure central opening is an a kind of closed figures by multistage camber line and line segment combination.Another kind of is the plate type ellipsoid like structure capable of opening (as shown in Figure 2) that is become with broken line border class quadrangle cladding plate unit combination by class triangle cladding plate unit, broken line border.It is a kind of structure of two layers, each layer forms by the connection of scissors hinged joint according to certain compound mode by class triangle cladding plate unit, n broken line border and class quadrangle cladding plate unit, m broken line border, each class triangle cladding plate unit, broken line border is all identical, and each class quadrangle cladding plate unit, broken line border is all identical.Integral body was configured as the class ellipse when architectural feature was closure, the central authorities hole of not boxing out; Each cladding plate unit does not collide each other during unlatching, and total only has one degree of freedom in the moving process; The shape of opening back structure central opening is an a kind of closed figures by many line segment combinations.

Two, primary variables that relates to of the present invention and formula

${\mathrm{\ρ}}_i=\frac{l}{\sin \frac{\mathrm{\π}}{n}}\·\sin [(i-1)\frac{\mathrm{\π}}{n}+\frac{{\mathrm{\ψ}}_1}{2}](i=\mathrm{1,2,3})---\left(1\right)$

${\mathrm{\θ}}_i=(3-i)\frac{\mathrm{\π}}{n}+\frac{{\mathrm{\ψ}}_2}{2}(i=\mathrm{1,2,3})---\left(2\right)$

$r_{\max }=\frac{l}{\sin \frac{\mathrm{\π}}{n}}\·\cos [\frac{\mathrm{\π}}{n}+\frac{{\mathrm{\ψ}}_1+{\mathrm{\ψ}}_2}{2}]---\left(3\right)$

$\mathrm{\Φ}=\mathrm{\π}-\frac{2\mathrm{\π}}{n}-({\mathrm{\ψ}}_1+{\mathrm{\ψ}}_2)---\left(4\right)$

N represents class triangle cladding plate number of unit (among Fig. 1 and Fig. 2, n=8) in each layer of plate type ellipsoid like structure capable of opening;

M represents class quadrangle cladding plate number of unit (among Fig. 1 and Fig. 2, m=4) in each layer of plate type ellipsoid like structure capable of opening;

K represents the hinge connection hole count that comprises in the single cladding plate unit, for plate type ellipsoid like structure capable of opening, and k=3;

ψ ₁Represent dwell angle;

ψ ₂Represent opening angle;

r _jRepresentative hinge connection pore radius;

L represents the distance at adjacent hinge connection center, hole on the same cladding plate unit;

R _STotal is at the radius of short-axis direction when representing closure;

R _LTotal is at the radius of long axis direction when representing closure.

Three, making step of the present invention is as follows:

(1) selects plate type ellipsoid like structure capable of opening that becomes with camber line border class quadrangle cladding plate unit combination by class triangle cladding plate unit, camber line border or the plate type ellipsoid like structure capable of opening that becomes with broken line border class quadrangle cladding plate unit combination by class triangle cladding plate unit, broken line border, and determine design parameters n, ψ according to the moulding of selected structure ₁And ψ ₂

1) equal sign is not got in n 〉=6 as far as possible.

2) ψ ₁And ψ ₂Value can not differ too big, equate as far as possible.

3) ψ ₁And ψ ₂Value is advisable between 5 °～20 °.

According to choice structure minor axis radius, major axis radius, the size of scissors hinge, determine R respectively _SWith l, R _LWith m, hinge connection pore radius r _j

R _S＞ρ ₃+ r _j, R _SValue not excessive, as long as than value lower limit bigger slightly;

$R_L\≈R_S+\frac{m}{2}l\·\sin (\frac{\mathrm{\π}}{n}+\frac{{\mathrm{\ψ}}_1}{2}).$

Attention: the plate type ellipsoid like structure capable of opening overwhelming majority that the design parameters of choosing according to above-mentioned requirements designs is feasible.Just in case the design failure, alternative is got one group of design parameters, till design effectively.

(2) design of camber line border class triangle cladding plate unit, class triangle cladding plate unit, broken line border, class quadrangle cladding plate unit, camber line border, class quadrangle cladding plate unit, broken line border

1) camber line border class triangle cladding plate unit design procedure

A) shown in Fig. 3 (a), set up polar coordinate system, with limit O as circular arc starting point, (ρ ₀,-θ ₀) be the center of circle, make circular arc OF, hand over pole axis in the F point. ${\mathrm{\ρ}}_0\·\cos {\mathrm{\θ}}_0=l\·\sin \frac{\mathrm{\Φ}}{2},$ Note ρ ₀And θ ₀Span.

${\mathrm{\ρ}}_0\∈[l,\∞),{\mathrm{\θ}}_0\∈[\frac{\mathrm{\π}}{2}-\frac{\mathrm{\Φ}}{2},\frac{\mathrm{\π}}{2})(k=3)$

B) shown in Fig. 3 (b), be second section circular arc starting point with F, on pole axis, periodically repeat picture and equate circular arc FG.As a rule, repeating the picture circular arc gets final product for 1 to 2 time.

C) shown in Fig. 3 (c), circular arc OF and FG are turned over counterclockwise

Angle repeats a, b step once again, draws circular arc OP and PQ.

D) shown in Fig. 3 (d), be the center of circle with limit O, R _SBe radius, make circular arc ST and hand over circular arc FG, hand over circular arc PQ in S in T.

2) broken line border class triangle cladding plate unit design procedure

A) shown in Fig. 4 (a), setting up polar coordinate system, is the circular arc starting point with limit O, (ρ ₀,-θ ₀) be the center of circle, make circular arc OF, hand over pole axis in the F point. ${\mathrm{\ρ}}_0\·\cos {\mathrm{\θ}}_0=l\·\sin \frac{\mathrm{\Φ}}{2},$ Note ρ ₀And θ ₀Span.Replace circular arc with the multistage broken line.For example among Fig. 4 (a), arcuate midway point is A, replaces circular arc OF with broken line OAF

${\mathrm{\ρ}}_0\∈[l,\∞),{\mathrm{\θ}}_0\∈[\frac{\mathrm{\π}}{2}-\frac{\mathrm{\Φ}}{2},\frac{\mathrm{\π}}{2})(k=3)$

B) shown in Fig. 4 (b), as being second section broken line starting point, on pole axis, periodically repeating picture and equate broken line FBG with the F point.As a rule, repeating the picture broken line gets final product for 1 to 2 time.

C) shown in Fig. 4 (c), broken line OAF and FBG are turned over counterclockwise

Angle repeats a, b step once again, draws broken line OCP and broken line PDQ

D) shown in Fig. 4 (d), be the center of circle with limit O, R _SBe radius, make circular arc ST broken line FBG, hand over broken line PDQ in S in T.

3) camber line border class quadrangle cladding plate unit design procedure

A) a in the specification of repetition class triangle cladding plate unit, camber line border, two steps of b.

B) shown in Fig. 5 (a), connect ON, the coordinate of N is

Crossing the N point makes boost line MN and is parallel to pole axis.

C) shown in Fig. 5 (b), be starting point with the N point, on MN, make circular arc NP and circular arc PQ, they and circular arc OF and circular arc FG are identical.

D) shown in Fig. 5 (c), be the center of circle with limit O, R _SMake circular arc for radius and hand over circular arc FG, cross some T and make ON parallel lines ST friendship circular arc PQ in S in T.

4) broken line border class quadrangle cladding plate unit design procedure

A) a in the specification of repetition class triangle cladding plate unit, broken line border, two steps of b.

B) shown in Fig. 6 (a), connect ON, the coordinate of N is

Crossing the N point makes boost line MN and is parallel to pole axis.

C) shown in Fig. 6 (b), be starting point with the N point, on MN, make broken line NCP and circular arc PDQ, they and broken line OAF and broken line FBG are identical.

D) shown in Fig. 6 (c), be the center of circle with limit O, R _SMake circular arc for radius and hand over broken line FBG, cross some T and make ON parallel lines ST friendship broken line PDQ in S in T.

(3) determine hinge connection hole site on two kinds of cladding plate unit

1) hinge joins determining of hole site on the camber line border class triangle cladding plate unit

Shown in Fig. 3 (e), clip the redundance of each circular arc, with (ρ _i, θ _i) be the center of circle, r _jBe radius, do hinge connection hole,, join distance order number consecutively hole 1, hole 2, hole 3 from small to large to the extreme, hole with hinge respectively to hinge connection hole numbering.So far, the design of class triangle cladding plate unit, camber line border is all finished, and from the appearance, it is the closed figures that is combined by circular arc OF, circular arc FT, circular arc OP, circular arc PS, circular arc ST, and it is r that there are 3 radiuses the centre _jHinge connection hole.The key of design is that hinge connection hole must be within each border, cladding plate unit.

2) hinge joins determining of hole site on the broken line border class triangle cladding plate unit

Shown in Fig. 4 (e), clip the redundance of each broken line, with (ρ _i, θ _i) be the center of circle, r _jBe radius, do hinge connection hole,, join distance order number consecutively hole 1, hole 2, hole 3 from small to large to the extreme, hole with hinge respectively to hinge connection hole numbering.So far, the design of class triangle cladding plate unit, broken line border is finished, and from the appearance, it is the closed figures that is combined by broken line OAF, broken line FBT, broken line OCP, broken line PDS, circular arc ST, and it is r that there are 3 radiuses the centre _jHinge connection hole.The key of design is that hinge connection hole must be within each border, cladding plate unit.

3) hinge joins determining of hole site on the camber line border class quadrangle cladding plate unit

Shown in Fig. 5 (d), clip each circular arc redundance, respectively with

$(\frac{2l\·\sin (\frac{\mathrm{\π}}{n}+\frac{{\mathrm{\ψ}}_1}{2})}{\cos \mathrm{\γ}},\frac{\mathrm{\π}}{2}+\frac{{\mathrm{\ψ}}_2}{2}-\mathrm{\γ}),(\frac{l\·\sin (\frac{\mathrm{\π}}{n}+\frac{{\mathrm{\ψ}}_1}{2})}{\sin \frac{\mathrm{\π}}{n}},\frac{\mathrm{\π}}{n}+\frac{{\mathrm{\ψ}}_2}{2}),$

$(2l\·\sin (\frac{\mathrm{\π}}{2}-\frac{\mathrm{\π}}{n}-\frac{{\mathrm{\ψ}}_1}{2})+\frac{l}{\sin \frac{\mathrm{\π}}{n}}\sin \frac{{\mathrm{\ψ}}_1}{2},\frac{{\mathrm{\ψ}}_2}{2}),$ $\mathrm{\γ}=\arctan \left(\frac{\sin \frac{{\mathrm{\ψ}}_1}{2}}{2\sin \frac{\mathrm{\π}}{n}\·\sin (\frac{\mathrm{\π}}{n}+\frac{{\mathrm{\ψ}}_1}{2})}\right)$ These 3 is the center of circle, r _jBe radius, do hinge connection hole, give hinge connection hole numbering respectively, with polar angle order number consecutively hole 1, hole 2 from big to small, hole 3.So far, the design of class quadrangle cladding plate unit, camber line border is finished, and from the appearance, it is the closed figures that is combined by circular arc OF, circular arc FT, circular arc NP, circular arc PS, line segment ON, line segment ST, and it is r that there are 3 radiuses the centre _jHinge connection hole.The key of design is that hinge connection hole must be within each border, cladding plate unit.

4) hinge joins determining of hole site on the broken line border class quadrangle cladding plate unit

Shown in Fig. 6 (d), clip each broken line redundance, respectively with

$(\frac{2l\·\sin (\frac{\mathrm{\π}}{n}+\frac{{\mathrm{\ψ}}_1}{2})}{\cos \mathrm{\γ}},\frac{\mathrm{\π}}{2}+\frac{{\mathrm{\ψ}}_2}{2}-\mathrm{\γ}),(\frac{l\·\sin (\frac{\mathrm{\π}}{n}+\frac{{\mathrm{\ψ}}_1}{2})}{\sin \frac{\mathrm{\π}}{n}},\frac{\mathrm{\π}}{n}+\frac{{\mathrm{\ψ}}_2}{2}),$

$(2l\·\sin (\frac{\mathrm{\π}}{2}-\frac{\mathrm{\π}}{n}-\frac{{\mathrm{\ψ}}_1}{2})+\frac{l}{\sin \frac{\mathrm{\π}}{n}}\sin \frac{{\mathrm{\ψ}}_1}{2},\frac{{\mathrm{\ψ}}_2}{2}),$ $\mathrm{\γ}=\arctan \left(\frac{\sin \frac{{\mathrm{\ψ}}_1}{2}}{2\sin \frac{\mathrm{\π}}{n}\·\sin (\frac{\mathrm{\π}}{n}+\frac{{\mathrm{\ψ}}_1}{2})}\right)$ These 3 is the center of circle, r _jBe radius, do hinge connection hole, give hinge connection hole numbering respectively, with polar angle order number consecutively hole 1, hole 2 from big to small, hole 3.So far, the design of class quadrangle cladding plate unit, broken line border is finished, and from the appearance, it is the closed figures that is combined by broken line OAF, line segment FT, broken line NCP, line segment PS, line segment ON, line segment ST, and it is r that there are 3 radiuses the centre _jHinge connection hole.The key of design is that hinge connection hole must be within each border, cladding plate unit.

(4) the cladding plate unit of the plate type ellipsoid like structure capable of opening that is become with camber line border class quadrangle cladding plate unit combination by class triangle cladding plate unit, camber line border connects by the scissors hinged joint according to compound mode; The cladding plate unit of the plate type ellipsoid like structure capable of opening that is become with broken line border class quadrangle cladding plate unit combination by class triangle cladding plate unit, broken line border connects by the scissors hinged joint according to compound mode.

1) compound mode of the plate type ellipsoid like structure capable of opening that becomes with camber line border class quadrangle cladding plate unit combination by class triangle cladding plate unit, camber line border

A) shown in Fig. 7 (a), class triangle cladding plate unit, n camber line border and the class quadrangle cladding plate unit, m camber line border that designs faced up, number consecutively is EAF ₁, EAF ₂... EAF _M+n

B) shown in Fig. 7 (b), with the class triangle cladding plate unit, other n camber line border that designs and the back side, class quadrangle cladding plate unit, m camber line border up, number consecutively is EAB ₁, EAB ₂... EAB _M+n

C) shown in Fig. 7 (c), EAF ₁No. 1 point and EAB ₁No. 1 point link to each other EAF ₁No. 2 points and EAB ₂No. 2 points link to each other EAF ₁No. 3 points and EAB ₃No. 3 points link to each other; By that analogy, EAF _NNo. 1 point and EAB _NNo. 1 point link to each other EAF _NNo. 2 points and EAB _XNo. 2 points link to each other EAF _NNo. 3 points and EAB _YNo. 3 points link to each other.

$X=\left\{\begin{array}{cc}N+1,& N\≤m+n-1\\ N+1-n-m,& N=m+n\end{array}\right\},Y=\left\{\begin{array}{cc}N+2,& N\≤m+n-2\\ N+2-n-m,& N>m+n-2\end{array}\right\}$

D) plate type ellipsoid like structure capable of opening of making that is become with camber line border class quadrangle cladding plate unit combination by class triangle cladding plate unit, camber line border is shown in Fig. 7 (d).

2) the cladding plate unit of the plate type ellipsoid like structure capable of opening that is become with broken line border class quadrangle cladding plate unit combination by class triangle cladding plate unit, broken line border is according to the compound mode of compound mode

A) shown in Fig. 8 (a), class triangle cladding plate unit, n broken line border and the class quadrangle cladding plate unit, m broken line border that designs faced up, number consecutively is EPF ₁, EPF ₂... EPF _M+n

B) shown in Fig. 8 (b), with the class triangle cladding plate unit, other n broken line border that designs and the back side, class quadrangle cladding plate unit, m broken line border up, number consecutively is EPB ₁, EPB ₂... EPB _M+n

C) shown in Fig. 8 (c), EPF ₁No. 1 point and EPB ₁No. 1 point link to each other EPF ₁No. 2 points and EPB ₂No. 2 points link to each other EPF ₁No. 3 points and EPB ₃No. 3 points link to each other; By that analogy, EPF _NNo. 1 point and EPB _NNo. 1 point link to each other EPF _NNo. 2 points and EPB _XNo. 2 points link to each other EPF _NNo. 3 points and EPB _YNo. 3 points link to each other.

$X=\left\{\begin{array}{cc}N+1,& N\≤m+n-1\\ N+1-n-m,& N=m+n\end{array}\right\},Y=\left\{\begin{array}{cc}N+2,& N\≤m+n-2\\ N+2-n-m,& N>m+n-2\end{array}\right\}$

D) plate type ellipsoid like structure capable of opening of making that is become with broken line border class quadrangle cladding plate unit combination by class triangle cladding plate unit, broken line border is shown in Fig. 8 (d).

Embodiment 1

Proposing minor axis radius of meter is 107mm, and major axis radius is the plate type ellipsoid like structure capable of opening that is become with camber line border class quadrangle cladding plate unit combination by class triangle cladding plate unit, camber line border of 155mm, and the diameter that scissors are cut with scissors is 3.0mm.

1) chooses n=8, k=3, ψ ₁=12 °, ψ ₂=10.5 °, r _j=3.1mm; According to R _S＞ρ ₃+ r _j, with (1) formula substitution, promptly

Solve l＜51.1626mm, get l=50mm; Basis again $R_L\≈R_S+\frac{m}{2}l\·\sin (\frac{\mathrm{\π}}{n}+\frac{{\mathrm{\ψ}}_1}{2}),$ Each is worth substitution:

Solve m ≈ 4.02, get m=4.

2) with in design parameters substitution (3) formula and (4) formula, calculate r _Max=108.6367mm, Φ=112.5 °; Choose ρ ₀=108.6367mm, according to ${\mathrm{\ρ}}_0\·\cos {\mathrm{\θ}}_0=l\·\sin \frac{\mathrm{\Φ}}{2},$ Calculate θ ₀=67.5 °.

ρ ₀∈[50，∞)，θ ₀∈[33.75°，90°)(k＝3)

3) design of camber line border class triangle cladding plate unit and hinge connection hole site determines

A) shown in Fig. 3 (a), set up polar coordinate system, with limit O as circular arc starting point, (ρ ₀,-θ ₀) be the center of circle, make circular arc OF, hand over the sub-F point of pole axis.

B) shown in Fig. 3 (b), be second section circular arc starting point with F, on pole axis, periodically repeat picture and equate circular arc FG.

C) shown in Fig. 3 (c), circular arc OF and FG are turned over 45 ° counterclockwise, repeat a, b step more once, draw circular arc OP and PQ.

D) shown in Fig. 3 (d), be the center of circle with limit O, R _SBe radius, make circular arc ST and hand over circular arc FG, hand over circular arc PQ in S in T.

E) with in design parameters substitution (1) formula and (2) formula, calculate respectively

F) shown in Fig. 3 (e), clip the redundance of each circular arc, respectively with (ρ ₁, θ ₁), (ρ ₂, θ ₂), (ρ ₃, θ ₃) be the center of circle, do the hinge connection hole of 3.1mm radius, respectively to hinge connection hole numbering, join distance order number consecutively hole 1, hole 2, hole 3 from small to large to the extreme, hole with hinge.

G) repeat a～f step 16 time.

4) design of camber line border class quadrangle cladding plate unit and hinge connection hole site determines

A) a, the b two that repeats in (3) goes on foot.

B) shown in Fig. 5 (a), connect ON, the coordinate of N is

The coordinate that calculates N is (47.7159,95.25 °), and mistake N point is made boost line MN and is parallel to pole axis.

C) shown in Fig. 5 (b), be starting point with the N point, on MN, make circular arc NP and circular arc PQ, they and circular arc OF and circular arc FG are identical.

D) shown in Fig. 5 (c), be the center of circle with limit O, R _SMake circular arc for radius and hand over circular arc FG, cross some T and make ON parallel lines ST friendship circular arc PQ in S in T.

E) calculate the coordinate that three hinges join the centers, hole

$(\frac{2l\·\sin (\frac{\mathrm{\π}}{n}+\frac{{\mathrm{\ψ}}_1}{2})}{\cos \mathrm{\γ}},\frac{\mathrm{\π}}{2}+\frac{{\mathrm{\ψ}}_2}{2}-\mathrm{\γ}),(\frac{l\·\sin (\frac{\mathrm{\π}}{n}+\frac{{\mathrm{\ψ}}_1}{2})}{\sin \frac{\mathrm{\π}}{n}},\frac{\mathrm{\π}}{n}+\frac{{\mathrm{\ψ}}_2}{2}),$

$(2l\·\sin (\frac{\mathrm{\π}}{2}-\frac{\mathrm{\π}}{n}-\frac{{\mathrm{\ψ}}_1}{2})+\frac{l}{\sin \frac{\mathrm{\π}}{n}}\sin \frac{{\mathrm{\ψ}}_1}{2},\frac{{\mathrm{\ψ}}_2}{2}),$ $\mathrm{\γ}=\arctan \left(\frac{\sin \frac{{\mathrm{\ψ}}_1}{2}}{2\sin \frac{\mathrm{\π}}{n}\·\sin (\frac{\mathrm{\π}}{n}+\frac{{\mathrm{\ψ}}_1}{2})}\right);$ Calculating three coordinates is respectively (49.6319,79.2777 °), (62.3438,27.75 °), and (101.5390,5.25 °),

F) shown in Fig. 5 (d), clip each circular arc redundance, respectively with (49.6319,79.2777 °), (62.3438,27.75 °), (101.5390,5.25 °), these 3 is the center of circle, 3.1mm is a radius, do hinge connection hole, give hinge connection hole numbering respectively, with polar angle order number consecutively hole 1, hole 2 from big to small, hole 3.

G) repeat a～f step 8 time.

5) combination of camber line border class triangle cladding plate unit and class quadrangle cladding plate unit, camber line border.

A) shown in Fig. 7 (a), class triangle cladding plate unit, 8 camber line borders and the class quadrangle cladding plate unit, 4 camber line borders that designs faced up, number consecutively is EAF ₁, EAF ₂... EAF ₁₂

B) shown in Fig. 7 (b), with the other class triangle cladding plate unit, 8 camber line borders that designs and the back side, class quadrangle cladding plate unit, 4 camber line borders up, number consecutively is EAB ₁, EAB ₂... EAB ₁₂

C) shown in Fig. 7 (c), EAF ₁No. 1 point and EAB ₁No. 1 point link to each other EAF _rNo. 2 points and EAB ₂No. 2 points link to each other EAF ₁No. 3 points and EAB ₃No. 3 points link to each other; By that analogy, EAF _NNo. 1 point and EAB _NNo. 1 point link to each other EAF _NNo. 2 points and EAB _XNo. 2 points link to each other EAF _NNo. 3 points and EAB _YNo. 3 points link to each other.

$X=\left\{\begin{array}{cc}N+1,& N\≤m+n-1\\ N+1-n-m,& N=m+n\end{array}\right\},Y=\left\{\begin{array}{cc}N+2,& N\≤m+n-2\\ N+2-n-m,& N>m+n-2\end{array}\right\}$

D) plate type ellipsoid like structure capable of opening of making that is become with camber line border class quadrangle cladding plate unit combination by class triangle cladding plate unit, camber line border is shown in Fig. 7 (d).

Embodiment 2

Proposing minor axis radius of meter is 107mm, and major axis radius is the plate type ellipsoid like structure capable of opening that is become with camber line border class quadrangle cladding plate unit combination by class triangle cladding plate unit, camber line border of 155mm, and the diameter that scissors are cut with scissors is 2.5mm.

1) chooses n=8, k=3, ψ ₁=12 °, ψ ₂=10.5 °, r _j=2.6mm; According to R _S＞ρ ₃+ r _j, with (1) formula substitution, promptly

Solve l＜51.4088mm, get l=50mm; Basis again $R_L\≈R_S+\frac{m}{2}l\·\sin (\frac{\mathrm{\π}}{n}+\frac{{\mathrm{\ψ}}_1}{2}),$ Each is worth substitution:

Solve m ≈ 4.02, get m=4.

2) with in design parameters substitution (3) formula and (4) formula, calculate r _Max=108.6367mm, Φ=112.5 °;

Choose ρ ₀=108.6367mm, according to ${\mathrm{\ρ}}_0\·\cos {\mathrm{\θ}}_0=l\·\sin \frac{\mathrm{\Φ}}{2},$ Calculate θ ₀=67.5 °.

ρ ₀∈[50，∞)，θ ₀∈[33.75°，90°)(k＝3)

3) design of broken line border class triangle cladding plate unit and hinge connection hole site determines

A) shown in Fig. 4 (a), set up polar coordinate system, with limit O as circular arc starting point, (ρ ₀,-θ ₀) be the center of circle, make circular arc OF, hand over pole axis in the F point, replace circular arc with the multistage broken line.For example among Fig. 4 (a), arcuate midway point is A, replaces circular arc OF with broken line OAF.

B) shown in Fig. 4 (b), as being second section broken line starting point, on pole axis, periodically repeating picture and equate broken line FBG with the F point.

C) shown in Fig. 4 (c), broken line OAF and FBG are turned over 45 ° counterclockwise, repeat a, b step more once, draw broken line OCP and broken line PDQ.

D) shown in Fig. 4 (d), be the center of circle with limit O, R is a radius, makes circular arc ST broken line FBG in T, hands over broken line PDQ in S.

E) with in design parameters substitution (1) formula and (2) formula, calculate respectively

F) shown in Fig. 4 (e), clip the redundance of each broken line, respectively with (ρ ₁, θ ₁), (ρ ₂, θ ₂), (ρ ₃, θ ₃) be the center of circle, do the hinge connection hole of 2.6mm radius, respectively to hinge connection hole numbering, join distance order number consecutively hole 1, hole 2, hole 3 from small to large to the extreme, hole with hinge.

G) repeat a～f step 16 time.

4) design of broken line border class quadrangle cladding plate unit and hinge connection hole site determines

A) a, the b two that repeats in (3) goes on foot.

B) shown in Fig. 6 (a), connect ON, the coordinate of N is

The coordinate that calculates N is (47.7159,95.25 °), and mistake N point is made boost line MN and is parallel to pole axis.

C) shown in Fig. 6 (b), be starting point with the N point, on MN, make broken line NCP and circular arc PDQ, they and broken line OAF and broken line FBG are identical.

D) shown in Fig. 6 (c), be the center of circle with limit O, R _SMake circular arc for radius and hand over broken line FBG, cross some T and make ON parallel lines ST friendship broken line PDQ in S in T.

E) calculate the coordinate that three hinges join the centers, hole

$(\frac{2l\·\sin (\frac{\mathrm{\π}}{n}+\frac{{\mathrm{\ψ}}_1}{2})}{\cos \mathrm{\γ}},\frac{\mathrm{\π}}{2}+\frac{{\mathrm{\ψ}}_2}{2}-\mathrm{\γ}),(\frac{l\·\sin (\frac{\mathrm{\π}}{n}+\frac{{\mathrm{\ψ}}_1}{2})}{\sin \frac{\mathrm{\π}}{n}},\frac{\mathrm{\π}}{n}+\frac{{\mathrm{\ψ}}_2}{2}),$

$(2l\·\sin (\frac{\mathrm{\π}}{2}-\frac{\mathrm{\π}}{n}-\frac{{\mathrm{\ψ}}_1}{2})+\frac{l}{\sin \frac{\mathrm{\π}}{n}}\sin \frac{{\mathrm{\ψ}}_1}{2},\frac{{\mathrm{\ψ}}_2}{2}),$ $\mathrm{\γ}=\arctan \left(\frac{\sin \frac{{\mathrm{\ψ}}_1}{2}}{2\sin \frac{\mathrm{\π}}{n}\·\sin (\frac{\mathrm{\π}}{n}+\frac{{\mathrm{\ψ}}_1}{2})}\right),$ Calculating three coordinates is respectively (49.6319,79.2777 °), (62.3438,27.75 °), and (101.6079,5.25 °),

F) shown in Fig. 6 (d), clip each broken line redundance, respectively with (49.6319,79.2777 °), (62.3438,27.75 °), (101.6079,5.25 °), these 3 is the center of circle, 2.6mm is a radius, do hinge connection hole, give hinge connection hole numbering respectively, with polar angle order number consecutively hole 1, hole 2 from big to small, hole 3.

G) repeat a～f step 8 time.

5) combination of broken line border class triangle cladding plate unit and class quadrangle cladding plate unit, broken line border.

A) shown in Fig. 8 (a), class triangle cladding plate unit, 8 broken line borders and the class quadrangle cladding plate unit, 4 broken line borders that designs faced up, number consecutively is EPF1, EPF2......EPF12.

B) shown in Fig. 8 (b), with the other class triangle cladding plate unit, 8 broken line borders that designs and the back side, class quadrangle cladding plate unit, 4 broken line borders up, number consecutively is EPB ₁, EPB ₂... EP ₁₂

C) shown in Fig. 8 (c), EPF ₁No. 1 point and EPB ₁No. 1 point link to each other EPF ₁No. 2 points and EPB ₂No. 2 points link to each other EPF ₁No. 3 points and EPB ₃No. 3 points link to each other; By that analogy, EPF _NNo. 1 point and EPB _NNo. 1 point link to each other EPF _NNo. 2 points and EPB _XNo. 2 points link to each other EPF _NNo. 3 points and EPB _YNo. 3 points link to each other.

$X=\left\{\begin{array}{cc}N+1,& N\≤m+n-1\\ N+1-n-m,& N=m+n\end{array}\right\},Y=\left\{\begin{array}{cc}N+2,& N\≤m+n-2\\ N+2-n-m,& N>m+n-2\end{array}\right\}$

D) plate type ellipsoid like structure capable of opening of making that is become with broken line border class quadrangle cladding plate unit combination by class triangle cladding plate unit, broken line border is shown in Fig. 8 (d).

Claims (3)

1. the preparation method of a plate type ellipsoid like structure capable of opening is characterized in that, its step is as follows;

1) selects plate type ellipsoid like structure capable of opening that becomes with camber line border class quadrangle cladding plate unit combination by class triangle cladding plate unit, camber line border or the plate type ellipsoid like structure capable of opening that becomes with broken line border class quadrangle cladding plate unit combination by class triangle cladding plate unit, broken line border, and determine design parameters: the hinge connection hole count k, the dwell angle ψ that comprise in the single cladding plate unit according to selected structure ₁, opening angle ψ ₂, hinge connection pore radius r _j, adjacent hinge connection center, hole apart from l on the same cladding plate unit;

2) four kinds of cladding plate unit of design plate type ellipsoid like structure capable of opening: class triangle cladding plate unit, camber line border, class triangle cladding plate unit, broken line border, class quadrangle cladding plate unit, camber line border, class quadrangle cladding plate unit, broken line border, main formulas is as follows:

$r_{\max }=\frac{l}{\sin \frac{\mathrm{\π}}{n}}\·\cos [\frac{\mathrm{\π}}{n}+\frac{{\mathrm{\ψ}}_1+{\mathrm{\ψ}}_2}{2}],$

$\mathrm{\Φ}=\mathrm{\π}-\frac{2\mathrm{\π}}{n}-({\mathrm{\ψ}}_1+{\mathrm{\ψ}}_2),$

Wherein, ψ ₁Be dwell angle, ψ ₂For opening angle, l are that distance, the n at adjacent hinge connection center, hole on the same cladding plate unit is class triangle cladding plate number of unit in each layer of plate type ellipsoid like structure capable of opening;

3) determine hinge connection hole site on four kinds of cladding plate unit, at first set up polar coordinate system, for class triangle cladding plate unit, camber line border and class triangle cladding plate unit, broken line border, the coordinate at hinge connection center, hole is (p _i, θ _i), (i=1,2,3), main formulas is as follows

${\mathrm{\ρ}}_i=\frac{l}{\sin \frac{\mathrm{\π}}{n}}\·\sin [(i-1)\frac{\mathrm{\π}}{n}+\frac{{\mathrm{\ψ}}_1}{2}](i=\mathrm{1,2,3}),$

${\mathrm{\θ}}_i=(3-i)\frac{\mathrm{\π}}{n}+\frac{{\mathrm{\ψ}}_2}{2}(i=\mathrm{1,2,3}),$

Wherein, ψ ₁Be dwell angle, ψ ₂For opening angle, l are that distance, the n at adjacent hinge connection center, hole on the same cladding plate unit is class triangle cladding plate number of unit in each layer of plate type ellipsoid like structure capable of opening; For class quadrangle cladding plate unit, camber line border, class quadrangle cladding plate unit, broken line border, the coordinate at three hinge connection centers, hole is respectively:

$(\frac{2l\·\sin (\frac{\mathrm{\π}}{n}+\frac{{\mathrm{\ψ}}_1}{2})}{\cos \mathrm{\γ}},\frac{\mathrm{\π}}{2}+\frac{{\mathrm{\ψ}}_2}{2}-\mathrm{\γ}),$ $(\frac{l\·\sin (\frac{\mathrm{\π}}{n}+\frac{{\mathrm{\ψ}}_1}{2})}{\sin \frac{\mathrm{\π}}{n}},\frac{\mathrm{\π}}{2}+\frac{{\mathrm{\ψ}}_2}{2}),$

$(2l\·\sin (\frac{\mathrm{\π}}{2}-\frac{\mathrm{\π}}{n}-\frac{{\mathrm{\ψ}}_1}{2})+\frac{l}{\sin \frac{\mathrm{\π}}{n}}\sin \frac{{\mathrm{\ψ}}_1}{2},\frac{{\mathrm{\ψ}}_2}{2}),$ $\mathrm{\γ}=\arctan \left(\frac{\sin \frac{{\mathrm{\ψ}}_1}{2}}{2\sin \frac{\mathrm{\π}}{n}\·\sin (\frac{\mathrm{\π}}{n}+\frac{{\mathrm{\ψ}}_1}{2})}\right);.$

4) the cladding plate unit of two kinds of plate type ellipsoid like structure capable of opening connects by the scissors hinged joint according to compound mode.

2. the preparation method of a kind of plate type ellipsoid like structure capable of opening according to claim 1, it is characterized in that, described two kinds of cladding plate unit connect by the scissors hinged joint according to compound mode: the plate type ellipsoid like structure capable of opening that is become with camber line border class quadrangle cladding plate unit combination by class triangle cladding plate unit, camber line border is by the individual class triangle cladding plate unit, heads camber line border of n, individual class quadrangle cladding plate unit, heads camber line border of m and class triangle cladding plate unit, camber line border up, n the back side, class quadrangle cladding plate unit, camber line border up, m the back side according to compound mode connect by the scissors hinged joint and form, node connection relation is that the inner ring node is corresponding links to each other, inferior inner ring node is corresponding to link to each other, and the like, the outmost turns node is corresponding to link to each other.

3. a kind of preparation method that can open the oval board-like structure of class based on the mechanism with single degree of freedom principle according to claim 1, it is characterized in that, described two kinds of cladding plate unit connect by the scissors hinged joint according to compound mode: the plate type ellipsoid like structure capable of opening that is become with broken line border class quadrangle cladding plate unit combination by class triangle cladding plate unit, broken line border is by the individual class triangle cladding plate unit, heads broken line border of n, individual class quadrangle cladding plate unit, heads broken line border of m and class triangle cladding plate unit, broken line border up, n the back side, class quadrangle cladding plate unit, broken line border up, m the back side according to compound mode connect by the scissors hinged joint and form, node connection relation is that the inner ring node is corresponding links to each other, inferior inner ring node is corresponding to link to each other, and the like, the outmost turns node is corresponding to link to each other.

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