CN104775519A - Quasi-cuboctahedron tensegrity structure - Google Patents
Quasi-cuboctahedron tensegrity structure Download PDFInfo
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- CN104775519A CN104775519A CN201510166382.XA CN201510166382A CN104775519A CN 104775519 A CN104775519 A CN 104775519A CN 201510166382 A CN201510166382 A CN 201510166382A CN 104775519 A CN104775519 A CN 104775519A
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- node
- drag
- line
- cuboctahedron
- depression bar
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- E—FIXED CONSTRUCTIONS
- E04—BUILDING
- E04B—GENERAL BUILDING CONSTRUCTIONS; WALLS, e.g. PARTITIONS; ROOFS; FLOORS; CEILINGS; INSULATION OR OTHER PROTECTION OF BUILDINGS
- E04B1/00—Constructions in general; Structures which are not restricted either to walls, e.g. partitions, or floors or ceilings or roofs
- E04B1/18—Structures comprising elongated load-supporting parts, e.g. columns, girders, skeletons
- E04B1/19—Three-dimensional framework structures
- E04B2001/1996—Tensile-integrity structures, i.e. structures comprising compression struts connected through flexible tension members, e.g. cables
Abstract
The invention aims to provide a quasi-cuboctahedron tensegrity structure. The shape of the quasi-cuboctahedron tensegrity structure is obtained by connecting midpoints of every two adjacent edges and removing eight corners on the basis of a cube. The quasi-cuboctahedron tensegrity structure is formed by twelve nodes, twenty-four pulling cables and twelve pressing rods, wherein the twelve nodes are respectively positioned on vertexes of a cuboctahedron and are distributed on one spherical surface, i.e., a circumscribed sphere of the cuboctahedron; the radius of the circumscribed sphere is equal to the length of each pulling cable, namely, the side length; four equilateral triangles are formed by distributing the twenty-four pulling cables on edges of the cuboctahedron and the twelve pressing rods in the cuboctahedron and are nested to one another. The quasi-cuboctahedron tensegrity structure provided by the invention has the characteristics of a regular tetrahedron and a regular hexahedron and is symmetrical and attractive in structure; compared with a first-order tensegrity structure, rods of a second-order tensegrity structure are in contact with each other, the rigidity is larger, and the requirement on larger rigidity can be met; compared with the first-order tensegrity structure, the bearing capacity is also larger.
Description
Technical field
What the present invention relates to is a kind of tension integral structure.
Background technology
" stretching integral " concept is the invention of famous American architect Fu Le (R.B.Fuller), the condensation that this refers to " stretch-draw " (tensile) and " entirety " (integrity).Fu Le thinks that the operation in universe is only analysed principle according to stretch-draw one and carried out, and namely gravitation is the tension web of a balance, and each celestial body is the isolated point one by one in this net.Due to tension integral structure intrinsic meet the natural law, maximally utilised the characteristic of material and cross section, super-span building can have been built with as far as possible few steel.
Tension integral structure is a kind of prestressing force self equilibrium systems be made up of drag-line and depression bar, and the rigidity of this class formation is provided by prestressing force, and component internal force oneself balance mutually, once lose prestressing force, structure will no longer be set up.Tension integral structure has the advantages such as quality is light, span large, beautiful design, receives the extensive concern of science and engineering circles.Because tension integral structure is a kind of prestressing force self equilibrium systems, the annexation of its node location and component must meet prestressing force self-balancing condition, can not as other structural systems at random Tectonic Geometry.Therefore, existing tension integral structure is generally irregular geometry.
Summary of the invention
The object of the present invention is to provide the class cuboctahedron tension integral structure with positive tetrahedron and regular hexahedron characteristic.
The object of the present invention is achieved like this:
Class cuboctahedron tension integral structure of the present invention, it is characterized in that: comprise by the first-12 node and first-the two ten four cuboctahedron that drag-line forms, first-12 node is respectively 12 summits of cuboctahedron, first-the two ten four drag-line is respectively 24 seamed edges of cuboctahedron, by 6 of cuboctahedron surface positive limit one of them horizontal positioned of shape, 12 summits are divided into three layers from bottom to top, the first-four node of arranged counterclockwise is become to be positioned at first floor, the 5th-eight node of arranged counterclockwise is become to be positioned at the second layer, the 9th-12 node of arranged counterclockwise is become to be positioned at third layer, first drag-line is connected between first node and Section Point, second drag-line is connected between Section Point and the 3rd node, the 3rd drag-line is connected between 3rd node and the 4th node, 4th connects the 4th drag-line between node and first node, 5th node is connected with Section Point with first node with six roots of sensation drag-line respectively by the 5th drag-line, 6th node is connected with the 3rd node with Section Point with the 8th drag-line respectively by the 7th drag-line, 7th node is connected with the 4th node with the 3rd node with the tenth drag-line respectively by the 9th drag-line, 8th node is connected with first node with the 4th node with the 12 drag-line with drag-line respectively by the 11, 9th node is connected with the 8th node with the 5th node with the 14 drag-line respectively by the 13 drag-line, protelum o'clock is connected with the 6th node with the 5th node with the tenth six roots of sensation drag-line respectively by the 15 drag-line, 11 node is connected with the 7th node with the 6th node with the 18 drag-line respectively by the 17 drag-line, 12 node is connected with the 8th node with the 7th node with the 20 drag-line with drag-line respectively by the 19, the first depression bar is connected between first node and protelum point, the second depression bar is connected between first node and the 7th node, the 3rd depression bar is connected between Section Point and the 11 node, the 4th depression bar is connected between Section Point and the 8th node, the 5th depression bar is connected between 3rd node and the 12 node, the 6th depression bar is connected between 3rd node and the 5th node, the 7th depression bar is connected between 4th node and the 9th node, the 8th depression bar is connected between 4th node and the 6th node, the 9th depression bar is connected between 5th node and the 12 node, the tenth depression bar is connected between 6th node and the 9th node, the 11 depression bar is connected between 7th node and protelum point, the 12 depression bar is connected between 8th node and the 11 node.
The present invention can also comprise:
1, the length of all drag-lines is equal, and the length of all depression bars is equal, and the length of depression bar is 1.732 times of guy cable length.
Advantage of the present invention is:
1, the present invention is second order tension integral structure.Due to tension integral structure intrinsic meet the natural law, maximally utilised the characteristic of material and cross section, longspan structure or building can have been built with as far as possible few material.
The length of all bars 2, in structure of the present invention is equal, and the length of all ropes is equal.Make materials processing convenient, be beneficial to production in enormous quantities.
3, this structure is that the stress be made up of by changing self depression bar and drag-line improves stress, thus improves supporting capacity.
4, the characteristic that the present invention has depends primarily on the form of its uniqueness and the performance of bar rope material itself.The design scheme that traditional architecture system cannot realize can be createed by this structure.
Accompanying drawing explanation
Fig. 1 is stereogram of the present invention;
Fig. 2 is top view of the present invention;
Fig. 3 is elevation of the present invention;
Fig. 4 is left view of the present invention.
Detailed description of the invention
Below in conjunction with accompanying drawing citing, the present invention is described in more detail:
Composition graphs 1 ~ 4, the cuboctahedron tension integral structure in the present invention, its shape is on the basis of square, is connected by adjacent both sides mid point, the unit obtained after clipping eight angles.The number of the block construction facing therefore obtained is 6, and its gore number is 8, total 14, face.Because the regular polygon surface rib of same kind is non-intersect, therefore number that its limit number is multiplied by face can be calculated to obtain the number of its rib: 3 × 8=4 × 6=24.
Cuboctahedron tension integral structure in the present invention is made up of 12 nodes, 24 drag-lines and 12 depression bars, 12 nodes lay respectively at 12 summits of cuboctahedron, and be distributed on same sphere, the i.e. circumsphere of cuboctahedron, it is long that this bounding polygon equals rope, and namely the rib of cuboctahedron is long; 24 drag-lines are distributed on 24 seamed edges of cuboctahedron respectively, and 12 depression bars are positioned at the inside of cuboctahedron.By following distribution: cuboctahedron surface has 6 positive limit shapes, select a positive limit shape to overlap with horizontal plane to place, then 12 points are divided into three layers, every layer has 4 points, first floor is for choosing shape place, positive limit plane, choosing this positive limit shape any point is the first point, sees that be followed successively by the second thirdly the 4th point counterclockwise from top to bottom at other 3.The second layer is side on the first layer, has 4 points, and wherein with first and second point all with Suo Xianglian is the 5th point, and four points of the second layer see that arranged counterclockwise is followed successively by the 5th point, the 6th point, the 7th point, the 8th point from top to bottom.Third layer is side on the second layer, and the some is connected with rope with the 5th in third layer distinguishes the 9th and the tenth point, to see in third layer that four some arranged counterclockwise are followed successively by the nine the ten the ten one the 12 points from top to bottom.Then there are 12 depression bars to be respectively first depression bar and connect the 10th point by the 1st, second depression bar connects the 7th point by the 1st, 3rd depression bar connects the 11st point by the 2nd, 4th depression bar connects the 8th point by the 2nd, 5th depression bar connects the 12nd point by the 3rd, six roots of sensation depression bar connects the 5th point by the 3rd, 7th depression bar connects the 9th point by the 4th, 8th depression bar connects the 6th point by the 4th, 9th depression bar connects the 12nd point by the 5th, tenth depression bar connects the 9th point by the 6th, ten depression bar connects the 10th point by the 7th, 12 depression bar connects the 11st point by the 8th.12 bars form 4 equilateral triangles altogether.And four equilateral triangles are mutually nested, enrich the configuration quadrant space of stretching integral; Wherein, the length of all drag-lines is equal, and the length of all depression bars is equal.Bar is connected at Nodes with rope, and each node connects 4 drag-lines and 2 depression bars, and all drag-lines exist pretension, and all depression bars exist precompression, and the pretension of drag-line and the precompression of depression bar balance mutually.
12 nodes of this structure are respectively first node A, Section Point B, the 3rd node C, the 4th node D, the 5th node E, the 6th node F, the 7th node G, the 8th node H, the 9th node I, protelum point J, the 11 node K, the 12 node M.With two node serial numbers at rope two ends, every root rope is described, 24 drag-lines are respectively first rope AI, second rope BI, 3rd rope BK, 4th rope AK, 5th rope EI, six roots of sensation rope FI, 7th rope FJ, 8th rope EJ, 9th rope GM, tenth rope HM, a ten rope HK, 12 rope GK, 13 rope CJ, 14 rope CM, 15 rope DM, tenth six roots of sensation rope DJ, 17 rope BF, 18 rope DF, 19 rope DH, 20 rope BH, a 20 rope AE, 22 rope CE, 23 rope CG, 24 rope AG.Describe every root bar with two node serial numbers at bar two ends, 12 depression bars are respectively first depression bar AM, second depression bar FM, the 3rd depression bar AF, the 4th depression bar DE, the 5th depression bar DK, six roots of sensation depression bar EK, the 7th depression bar GJ, the 8th depression bar BG, the 9th depression bar BJ, the tenth depression bar CH, the ten depression bar HI, a 12 depression bar CI.
The length of drag-line is identical, is L; The length of described depression bar is identical, is 1.732L.
When being subject to external load effect, by the effect changing the internal force of component, external load is resisted in the position of knot modification, but drag-line is in tension state all the time.
Represent drag-line with fine rule in FIG, totally 24 drag-lines, represent depression bar with thick line in FIG, totally 12 depression bars.
The geometrical length of component.With guy cable length in L representation class rescinded angle tetrahedron tension integral structure.Then have all guy cable lengths to be L, the length of all depression bars is 1.732L.
By the component processed by above-mentioned component geometrical length, fitted together by annexation described in the 1st article by hinged joint, the tension integral structure finally obtained will be cuboctahedron, and all drag-line tensions, total is in self-balancing state.
Claims (2)
1. class cuboctahedron tension integral structure, it is characterized in that: comprise by the first-12 node and first-the two ten four cuboctahedron that drag-line forms, first-12 node is respectively 12 summits of cuboctahedron, first-the two ten four drag-line is respectively 24 seamed edges of cuboctahedron, by 6 of cuboctahedron surface positive limit one of them horizontal positioned of shape, 12 summits are divided into three layers from bottom to top, the first-four node of arranged counterclockwise is become to be positioned at first floor, the 5th-eight node of arranged counterclockwise is become to be positioned at the second layer, the 9th-12 node of arranged counterclockwise is become to be positioned at third layer, first drag-line is connected between first node and Section Point, second drag-line is connected between Section Point and the 3rd node, the 3rd drag-line is connected between 3rd node and the 4th node, 4th connects the 4th drag-line between node and first node, 5th node is connected with Section Point with first node with six roots of sensation drag-line respectively by the 5th drag-line, 6th node is connected with the 3rd node with Section Point with the 8th drag-line respectively by the 7th drag-line, 7th node is connected with the 4th node with the 3rd node with the tenth drag-line respectively by the 9th drag-line, 8th node is connected with first node with the 4th node with the 12 drag-line with drag-line respectively by the 11, 9th node is connected with the 8th node with the 5th node with the 14 drag-line respectively by the 13 drag-line, protelum o'clock is connected with the 6th node with the 5th node with the tenth six roots of sensation drag-line respectively by the 15 drag-line, 11 node is connected with the 7th node with the 6th node with the 18 drag-line respectively by the 17 drag-line, 12 node is connected with the 8th node with the 7th node with the 20 drag-line with drag-line respectively by the 19, the first depression bar is connected between first node and protelum point, the second depression bar is connected between first node and the 7th node, the 3rd depression bar is connected between Section Point and the 11 node, the 4th depression bar is connected between Section Point and the 8th node, the 5th depression bar is connected between 3rd node and the 12 node, the 6th depression bar is connected between 3rd node and the 5th node, the 7th depression bar is connected between 4th node and the 9th node, the 8th depression bar is connected between 4th node and the 6th node, the 9th depression bar is connected between 5th node and the 12 node, the tenth depression bar is connected between 6th node and the 9th node, the 11 depression bar is connected between 7th node and protelum point, the 12 depression bar is connected between 8th node and the 11 node.
2. class cuboctahedron tension integral structure according to claim 1, it is characterized in that: the length of all drag-lines is equal, the length of all depression bars is equal, and the length of depression bar is 1.732 times of guy cable length.
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| CN201510166382.XA CN104775519A (en) | 2015-04-09 | 2015-04-09 | Quasi-cuboctahedron tensegrity structure |
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Cited By (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105350644A (en) * | 2015-10-23 | 2016-02-24 | 东南大学 | Tensegrity structure unit based on hexahedron geometry |
| CN105350645A (en) * | 2015-10-23 | 2016-02-24 | 东南大学 | Tensegrity structure unit based on truncated tetrahedron geometry |
| CN106522368A (en) * | 2016-10-12 | 2017-03-22 | 浙江大学 | Annular stretch-draw integrated structure |
| CN109558654A (en) * | 2018-11-15 | 2019-04-02 | 北京科技大学 | A kind of plane tension integral structure topology design method |
| CN110703748A (en) * | 2019-10-09 | 2020-01-17 | 浙江大学 | Comprehensive cost optimal path planning method for rolling polyhedron tensioning whole robot |
| CN113463762A (en) * | 2021-07-08 | 2021-10-01 | 浙江大学 | Thirty-rod spherical tension integral structure |
| CN113914470A (en) * | 2021-09-12 | 2022-01-11 | 浙江大学 | Novel cut half cube stretch-draw overall structure |
| CN115095023A (en) * | 2022-07-07 | 2022-09-23 | 浙江工业大学 | Regular tetrahedron tensioning integral structure with rigid body |
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Cited By (11)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105350644A (en) * | 2015-10-23 | 2016-02-24 | 东南大学 | Tensegrity structure unit based on hexahedron geometry |
| CN105350645A (en) * | 2015-10-23 | 2016-02-24 | 东南大学 | Tensegrity structure unit based on truncated tetrahedron geometry |
| CN106522368A (en) * | 2016-10-12 | 2017-03-22 | 浙江大学 | Annular stretch-draw integrated structure |
| CN106522368B (en) * | 2016-10-12 | 2018-10-26 | 浙江大学 | Circular ring shape tension integral structure |
| CN109558654A (en) * | 2018-11-15 | 2019-04-02 | 北京科技大学 | A kind of plane tension integral structure topology design method |
| CN109558654B (en) * | 2018-11-15 | 2022-12-16 | 北京科技大学 | Topology design method for planar tension integral structure |
| CN110703748A (en) * | 2019-10-09 | 2020-01-17 | 浙江大学 | Comprehensive cost optimal path planning method for rolling polyhedron tensioning whole robot |
| CN113463762A (en) * | 2021-07-08 | 2021-10-01 | 浙江大学 | Thirty-rod spherical tension integral structure |
| CN113914470A (en) * | 2021-09-12 | 2022-01-11 | 浙江大学 | Novel cut half cube stretch-draw overall structure |
| CN113914470B (en) * | 2021-09-12 | 2022-09-13 | 浙江大学 | Novel cut half cube stretch-draw overall structure |
| CN115095023A (en) * | 2022-07-07 | 2022-09-23 | 浙江工业大学 | Regular tetrahedron tensioning integral structure with rigid body |
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Application publication date: 20150715 |
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