CN117852146A

CN117852146A - Design method of uniform convex polyhedron device with variable volume

Info

Publication number: CN117852146A
Application number: CN202410044551.1A
Authority: CN
Inventors: 王晖; 刘梦嫚
Original assignee: Zhejiang University ZJU
Current assignee: Zhejiang University ZJU
Priority date: 2024-01-11
Filing date: 2024-01-11
Publication date: 2024-04-09

Abstract

The invention discloses a design method of a uniform convex polyhedron device with variable volume, which uses plane hinge mosaic to construct each surface of the uniform convex polyhedron, applies force with centroid pointing to the vertex direction on each surface vertex, and leads each vertex to be unfolded at the same speed, thus obtaining an innovative and systematic design method of the expandable body. The method can quickly construct a series of uniform convex polyhedrons with variable volumes. The uniform convex polyhedron has wide application scenes in actual work and life due to the high symmetry and the regular polygon characteristic of each surface. The design method has the advantages of simple form, no need of additional frames, specific volume and expandability, and artistic expression, and has higher application potential in the fields of artwork design, movable building design, mechanical design and industrial design.

Description

Design method of uniform convex polyhedron device with variable volume

Technical Field

The invention belongs to the field of movable device design, and particularly relates to a design method of a uniform convex polyhedron device with a variable volume.

Background

The movable structure has great application potential and aesthetic value in building design, curtain wall design and artistic device design, and has wide research and practice cases at home and abroad. The prior research results of the volume-variable device can be roughly divided into four types from the exercise mechanism: (1) The rod units rotate and fold mutually under the traction of external force, such as a scissor-type unit structure, a link mechanism and the like; (2) The units are stretched and shortened under the drive of springs or motors, such as a tension integrated system, a grid-shaped parabolic antenna and the like; (3) Flexible materials which are unfolded under the action of external force, such as inflatable structures, thin-wall pipe stretching arms and the like; (4) The rigid board unit is folded and unfolded under the action of the node, or the rigid board unit is rotated and unfolded, such as a board antenna, an extension arm and the like. There is a relatively lack of research into the design of variants consisting of rigid dough sheet combinations.

Disclosure of Invention

In view of this, an object of the embodiments of the present application is to provide a design method of a uniform convex polyhedron device with a variable volume, in which a hinge mosaic is a mosaic pattern formed by hinging rigid members at vertices, and closing and expanding can be achieved by rotating the members around hinge points. Compared with the existing inflatable body structure, the invention has the characteristics of no outer frame and simple driving mechanism.

The embodiment of the application provides a design method of a uniform convex polyhedron device with a variable volume, which comprises the following steps:

determining the type and the side length of a uniform convex polyhedron to be designed;

selecting proper mosaic patterns and sizes according to the shape of each regular polygon surface of the polyhedron, and filling each regular polygon surface;

layering the surface sheets of the mosaic patterns, adding hinge points, deflecting the hinge points by a certain angle, and mutually staggering to avoid collision of the hinge points;

calculating the linear expansion rate of each surface, and taking the minimum value as the linear expansion rate of the maximum expansion state of the uniform convex polyhedron;

according to the linear expansion rate of the maximum expansion state of the uniform convex polyhedron, determining the moving distance of the top point after expansion relative to the starting point, and selecting a corresponding driving component;

according to the closed size of the polyhedron, the size and the driving direction of the driving member, the shape and the size of the internal frame are designed to ensure that the vertexes move synchronously at equal speed along the vector direction pointing to each vertex from the centroid of the uniform convex polyhedron;

the surface piece at the edge of each surface is cut into angles, so that the surface piece collision between the adjacent surfaces is avoided;

if the driving point is on the triangular patch, adding a measure for preventing over rotation on the triangular patch;

the induction system is arranged according to the requirements to control the driving components, so that the movement synchronization of the driving points is ensured, and the required movement response is realized.

Further, the uniform convex polyhedron type is one of a regular polyhedron or an archimedes polyhedron.

Further, selecting a proper mosaic pattern according to each regular polygon surface of the polyhedron to fill up each regular polygon surface, including:

and selecting a mosaic graph according to the shape of the regular polygon surface, determining the side length of each surface piece, and spreading each regular polygon, wherein the side length of each surface piece is equal.

Further, the linear expansion coefficient P1 of the square face is calculated as follows:

P1＝L/l

wherein the overall side length of the closed state is L, the overall side length of the maximum unfolded state is L, each side of the square surface comprises n pieces of surface pieces, and the distance between adjacent points after the hinge point rotates is L ₁ The rotation angle is alpha.

Further, the linear expansion coefficient P2 of the regular triangle face is calculated by:

P2＝L/l

wherein the overall side length in the closed state is L, the overall side length in the maximum unfolding state is L, each side of the regular triangle surface comprises a regular hexagonal surface piece and the total number of the triangular surface pieces is n (n is more than or equal to 3), the number of the regular hexagonal surface pieces is (n-1)/2, the number of the regular triangle surface pieces is (n+1)/2, and the distance between adjacent points after the rotation of the hinging point is L ₂ The rotation angle is alpha.

Further, the linear expansion coefficient P3 of the regular hexagonal surface is calculated as follows:

P3＝L/l

wherein the overall side length in the closed state is L, the overall side length in the maximum unfolding state is L, the total number of the regular hexagonal surface pieces and the regular triangle surface pieces contained in each side of the regular hexagonal surface is n (n is more than or equal to 3), the number of the regular hexagonal surface pieces is (n+1)/2, the number of the regular triangle surface pieces is (n-1)/2, and the distance between adjacent points after the rotation of the hinge point is L ₃ The rotation angle is alpha.

Further, the shape and size of the internal frame are designed according to the closed size of the polyhedron and the size and driving direction of the driving member to ensure constant velocity expansion of the vertices in the vector direction pointing from the centroid of the uniformly convex polyhedron to each vertex, comprising:

at least 3 groups of support rods are arranged for each vertex, and the frame and the driving push rod are connected through the connecting piece, so that the movement track of the starting point is ensured to point to the direction of the vertex along the centroid.

Further, the corner cutting of the dough sheet at the edge position of each face comprises:

according to the motion simulation of a computer, the surface pieces protruding out of each side of the polyhedron in the rotation process are cut into round angles or oblique angles so as to avoid collision of the adjacent surface pieces in the unfolding process.

If the driving point is on the triangular patch, then adding means to prevent over-rotation on the triangular patch, including:

by adding a locking mechanism at the maximum unfolding position of the triangular surface piece, the triangular surface is prevented from being closed beyond the maximum unfolding state.

Further, an induction system is arranged according to the requirements to control the driving component, so that the movement synchronization of the driving point is ensured, and the required movement response is realized. Comprising the following steps:

the control system including the sensor and the signal control element is added, so that the polyhedral device can change the volume according to the requirements of light, temperature, movement or other kinds of interaction response, the synchronous movement of the driving rod is ensured, and the maximum extension length does not exceed a limit value.

The technical scheme provided by the embodiment of the application can comprise the following beneficial effects:

the method uses plane hinge mosaic to construct each surface of uniform convex polyhedron, and applies force with centroid pointing to vertex direction on each surface vertex at the same time, so that each vertex is unfolded at the same speed, and the design method of the expandable body with innovation and systematicness is obtained. The method uses the rigid surface sheet to form the main component of the inflatable body, which is beneficial to overcoming the technical problem that the design aspect of the prior inflatable structure is more outstanding: (1) The problems of large occupied space, complex mechanism, high energy consumption, high manufacturing cost, lower stability and the like caused by the shearing type rod piece or folding are solved; (2) The design is limited to a few types, and has no problems of universality, systemicity and the like; (3) Most variable volume devices have an external frame or structural system exposed, affecting the purely and artistic nature of the morphology.

The technical scheme of the application can quickly construct a series of uniform convex polyhedrons with variable volumes. The uniform convex polyhedron has wide application scenes in actual work and life due to the high symmetry and the regular polygon characteristic of each surface. The design method has the advantages of simple form, no need of additional frames, specific volume and expandability, and artistic expression, and has higher application potential in the fields of artwork design, movable building design, mechanical design and industrial design.

It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the application.

Drawings

The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the application and together with the description, serve to explain the principles of the application.

FIG. 1 is a flow chart of a method for designing a uniformly convex polyhedron device with variable volume according to an embodiment of the present invention;

FIG. 2 is a diagram of a uniform convex polyhedron, including regular polyhedrons and archimedes polyhedrons, to which embodiments of the present invention are applicable;

FIG. 3 is an example of a hinged mosaic pattern with square and regular triangle outer contours;

FIG. 4 is a layered schematic of adjacent panels;

the hinge points of the square faces of fig. 5-1 are rotationally staggered and in a maximally unfolded state;

the hinge points of the regular triangle faces of fig. 5-2 are rotationally staggered and in a maximum unfolded state;

FIG. 6 is a detailed view of the frame structure and drive system of the internal support bar according to the first embodiment of the present invention;

FIG. 7 is a schematic view of a cut angle of a dough sheet according to a first embodiment of the present invention;

FIG. 8 is a detailed view of the overall structure of the first embodiment of the present invention;

FIG. 9 is a block diagram showing a closed and open state of a light responsive dough sheet according to a first embodiment of the present invention;

FIG. 10 is a schematic illustration showing a closed and an open configuration of a system according to a second embodiment of the present invention;

fig. 11 is a detailed view of an anti-over-rotation mechanism according to a second embodiment of the present invention;

FIG. 12 is a detailed view of the overall structure of a second embodiment of the present invention;

FIG. 13 is a detailed view of the overall structure of a third embodiment of the present invention;

fig. 14 shows a closed and an open state of the system according to the third embodiment of the present invention.

Detailed Description

Reference will now be made in detail to exemplary embodiments, examples of which are illustrated in the accompanying drawings. When the following description refers to the accompanying drawings, the same numbers in different drawings refer to the same or similar elements, unless otherwise indicated. The implementations described in the following exemplary examples are not representative of all implementations consistent with the present application.

The terminology used in the present application is for the purpose of describing particular embodiments only and is not intended to be limiting of the present application. As used in this application and the appended claims, the singular forms "a," "an," and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It should also be understood that the term "and/or" as used herein refers to and encompasses any or all possible combinations of one or more of the associated listed items.

It should be understood that although the terms first, second, third, etc. may be used herein to describe various information, these information should not be limited by these terms. These terms are only used to distinguish one type of information from another. For example, a first message may also be referred to as a second message, and similarly, a second message may also be referred to as a first message, without departing from the scope of the present application. The word "if" as used herein may be interpreted as "at … …" or "at … …" or "responsive to a determination", depending on the context.

FIG. 1 is a flow chart of a method for designing a uniformly convex polyhedron device with variable volume according to an embodiment of the present invention; according to the embodiment of the application, a systematic generation method based on two-dimensional hinged mosaic and synchronous expansion of all sides of a uniform convex polyhedron is provided. The faces of the uniform convex polyhedron are regular polygons, the side lengths are equal, and the uniform convex polyhedron has wide application scenes in actual work and life. The method is based on a two-dimensional hinged mosaic unfolding mechanism, combines a two-dimensional graph on each surface of a three-dimensional uniform convex polyhedron by using a vertex synchronous driving mode, and establishes a corresponding supporting rod and node system for ensuring the equiangular unfolding of each surface, so that the whole uniform convex polyhedron can be synchronously unfolded along the direction of the centroid to the vertex in equal proportion.

The method comprises the following steps:

step S11, selecting 1 type from 18 uniform convex polyhedrons (figure 2) and determining the side length size;

in particular, due to the high symmetry of a uniform convex polyhedron, a two-dimensional hinged mosaic pattern can be well bonded to each face of the polyhedron, thereby achieving three-dimensional synchronous expansion and volume variability. As shown in fig. 2, the present application provides 18 a uniform convex polyhedron type, which is divided into two major classes of regular polyhedrons including regular tetrahedrons, cubes, regular octahedrons, regular dodecahedrons, regular icosahedrons, and archimedean polyhedrons including truncated regular tetrahedrons, truncated cubes, truncated regular octahedrons, small chamfered cubes, small chamfered dodecagons, truncated regular icosahedrons, large truncated cubes, large truncated dodecagons, truncated half dodecagons, twisted cubes, twisted dodecagons.

Of the 18 homogeneous convex polyhedron types, the homogeneous convex polyhedron composed of regular polygons (e.g., square, regular triangle, regular hexagon) is the most compact and most widely used, namely, the 4 regular polygons underlined in fig. 2 (regular tetrahedron, cube, regular octagon, regular icosahedron) and the 5 archimedes polyhedron (truncated regular tetrahedron, truncated regular octagon, small chamfer cube, truncated half cube, twisted square).

Step S12, selecting proper mosaic patterns and sizes according to the regular polygon surfaces, and filling the regular polygon surfaces;

specifically, a regular mosaic pattern (composed of one or more of regular quadrangles, regular triangles and regular hexagons) is selected, the sizes of the patches in the pattern are set according to design requirements, and the regular polygons are paved.

Step S13, layering the surface sheets of the mosaic patterns, adding hinge points, deflecting the hinge points by a certain angle, and staggering the hinge points to avoid collision of the hinge points;

specifically, each regular polygon in the mosaic pattern is used as a panel, and a hinge point is added between the panels to form a planar hinge mosaic by using the method provided by the patent application of application number 202111490018.0. (FIG. 3). One characteristic of planar hinged inlaying is that the gaps between the dough sheets form a parallelogram when unfolded and form a straight line when closed, and the avoidance treatment of the dough sheets is necessary under the actual physical condition, and the planar hinged inlaying device adopts a layered mode, and each group is divided into 4 layers, so that the shape of the dough sheets can be kept complete (figure 4).

Specifically, to prevent collision between adjacent nodes, for all the hinge points on each panel, the hinge points are shifted from each other when the mosaic pattern is closed by rotating a certain angle about the centroid of the panel (fig. 5-1, fig. 5-2).

Step S14, calculating the linear expansion rate of each surface, and taking the minimum value as the linear expansion rate of the maximum expansion state of the uniform convex polyhedron;

specifically, the maximum expansion size of each regular polygon surface is calculated, and the linear expansion rate (i.e., the side length expansion rate) of each surface is determined. When the shapes of the faces of the uniform polyhedron are different (such as square faces, regular triangle faces and regular hexagon faces), the maximum expansion rate of the faces is also different. In order to avoid structural damage, the minimum value of linear expansion rate of each upper thread is taken as the linear expansion rate of the maximum expansion state of the uniform convex polyhedron.

The linear expansion coefficient P1 of the square face is calculated as follows:

P1＝L/l

wherein the whole side length of the closed state is L, the whole side length of the maximum unfolding state is L, and each side of the square surface is coveredThe number of the contained patches is n, and the distance between adjacent points after the rotation of the hinge point is l ₁ The rotation angle is alpha.

P2＝L/l

wherein, the whole side length of the closed state is L, and the whole side length of the maximum unfolding state is L. Each side of the regular triangle surface comprises a total number of regular hexagonal surface sheets and triangular surface sheets which are n (n is more than or equal to 3), wherein the number of the regular hexagonal surface sheets is (n-1)/2, the number of the regular triangle surface sheets is (n+1)/2, and the distance between adjacent points after the rotation of the hinge point is l ₂ The rotation angle is alpha.

P3＝L/l

wherein, the whole side length of the closed state is L, and the whole side length of the maximum unfolding state is L. The total number of the regular hexagonal surface pieces and the regular triangle surface pieces contained in each side of the regular hexagonal surface is n (n is more than or equal to 3), wherein the number of the regular hexagonal surface pieces is (n+1)/2, the number of the regular triangle surface pieces is (n-1)/2, and the distance between adjacent points after the hinge point rotates is l ₃ The rotation angle is alpha.

If a plurality of cases such as P1, P2, P3 are included in the polyhedron, the minimum value thereof is selected as the linear expansion coefficient of the polyhedron.

Step S15, determining the distance (limit value) of the top point moving relative to the starting point after expansion according to the linear expansion rate of the maximum expansion state of the uniform convex polyhedron, and selecting a corresponding driving component;

specifically, a driving member such as a telescopic rod satisfying the extension distance is selected according to the distance by which the polygon vertex moves relative to the starting point.

And S16, designing the shape and the size of the internal frame according to the closed size of the polyhedron and the size and the driving direction of the driving member so as to ensure that the vertexes are synchronously unfolded along the vector direction pointing to each vertex from the centroid of the uniform convex polyhedron at equal speed.

Specifically, the shape and size of the inner frame are designed according to the direction, position, etc. of the driving lever. The inner frame is not necessarily the geometric reduction of the outer polyhedron, and the shape with stable stress and convenient installation can be selected according to the direction of the driving push rod. Typically, each vertex of the polyhedron corresponds to a drive rod, and the drive ram requires support from an auxiliary rod to ensure that the direction of the drive ram is directed from the centroid of the polyhedron to each vertex. The support rods can be arranged in groups of three, and the frame is connected with the driving push rod through the connecting piece to form a stable space support structure (figure 6).

And S17, chamfering is carried out on the surface pieces at the edge positions of the surfaces, so that the collision of the adjacent surface pieces is avoided.

Specifically, through computer motion simulation, in the process of three-dimensional expansion of the polyhedron, the adjacent faces can generate the collision of the faces due to the fact that the faces rotationally protrude out of the outline of the polyhedron. Thus, the facets on each facet edge are rounded or beveled (FIG. 7) according to the motion simulation to avoid collisions with adjacent facets.

Step S18, if the driving point is on the triangular surface patch, adding a measure for preventing over rotation on the triangular surface patch;

in particular, due to the continuously varying nature of the hinge inlay, the panel will begin to close after reaching a maximum deployment state if it continues to rotate in the same direction. In particular, the triangular surface has smaller hinging points, so that the hinging points have smaller resistance to rotation, and the excessive rotation of the surface piece is easier to cause closing. By adding a mechanism for preventing rotation (such as an anti-over-rotation rivet) at the maximum expansion point, the triangular surface is prevented from over-rotation.

And step S19, setting an induction system to control the driving component according to the requirement, ensuring the movement synchronization of the driving point and realizing the required movement response.

Specifically, a control system comprising a sensor and a signal control element is arranged according to the requirement, the extension and retraction of the driving rod piece are controlled, the maximum extension is ensured not to exceed the limit value determined in the step S15, and the extension and retraction time and the distance of each vertex are synchronous. And various interactive response modes such as light response, temperature sensing, humidity sensing, motion sensing and the like are realized according to the requirements. The wiring arrangement of the circuit should take into account volume-variable factors to avoid damage during movement.

The above steps are further refined in the following examples.

Example 1

The embodiment designs a cube volume-variable device based on the method provided by the invention. The method specifically comprises the following steps:

step 1, selecting a cube as a basic polyhedron, wherein the outline size of the closed state is 750 multiplied by 750mm.

And 2, selecting regular mosaic patterns formed by squares to fill all sides of the square, wherein each side consists of 5*5 square surface sheets with the side length of about 150mm, and the side length of a closed standard surface (theoretical value) is 750mm.

And 3, connecting the square surface pieces with each other through hinge points, dividing the adjacent surface pieces into four layers, rotating the hinge points by alpha=4.5 degrees, and preventing collision of the hinge points of the adjacent surface pieces.

And 4, determining the maximum linear expansion rate of the polyhedron.

In the present embodiment, the maximum linear expansion coefficient is calculated using the following formula with reference to the driving point of the square corner.

P1＝L/l≈1.208

I.e. the maximum extension of the square side is about 906.24-750-156 mm.

And 5, selecting a telescopic rod with the maximum extension length of about 150mm as a driving component.

Step 6, designing an internal frame for fixing the driving rod into a small cube form according to the closed size of the cube of 750mm, the minimum length of the telescopic rod of about 200mm and other factors, wherein the centroid of the internal frame coincides with the large cube, and the side length of the internal frame is about 500mm;

and 7, setting 8 driving points in total by taking each vertex of the large cube as a driving point, and ensuring constant-speed expansion of the vertex in the vector direction pointing to each vertex from the center of the large cube by using an auxiliary stay bar.

And 8, performing motion simulation by a computer, and performing corner cutting treatment on the dough pieces at the edges of the cubes to avoid collision of the adjacent dough pieces (figure 8).

And 9, adding an inductor and a signal control system to realize induction control, ensuring that the maximum extension length of the driving rod is less than 156mm, and completing a device system.

The present embodiment combines a response circuit for feedback with a sensor of illumination intensity. The circuit collects illumination intensity through the sensor, and controls the telescopic rod to extend when illumination is weakened, and automatically retract after the illumination is sensed to be strong, so that the whole device expands in volume and expands the dough sheet when the illumination is weak, contracts in volume and closes the dough sheet when the illumination is strong (figure 9). Flow control is implemented by Arduino circuit board programming.

This embodiment demonstrates that square-based hinged mosaic forms a cube device, which can undergo a volume change according to ambient light intensity. The device mainly comprises square dough sheets, driving rods and an inner frame, has few component types and does not need additional guide rails and frame supports; under the action of the internal driving rod, all the surfaces can be simultaneously unfolded and closed, and the whole body is always kept to be square in the movement process, so that the three-dimensional effect with variable volume is realized.

Example two

The embodiment designs a volume-variable device of an regular octahedron based on the method provided by the invention.

Step 1, selecting a regular octahedron as a basic polyhedron, wherein the reference length of each side is 750mm.

And 2, selecting a hinged mosaic pattern formed by combining regular triangles and regular hexagons, filling each face (regular triangle) of the regular octahedron, and closing the regular triangle until the side length of the reference face is 750m.

Step 3, the surface pieces are connected with each other through hinge points, the adjacent surface pieces are divided into four layers, and the hinge points are rotated by alpha=2 degrees, so that collision of the hinge points of the adjacent surface pieces is prevented;

and 4, calculating the linear expansion rate according to the following formula.

P2＝L/l≈1.211

I.e. the maximum extension of the regular octahedron side length is 908-750=158 mm.

And 6, designing the internal frame of the fixed driving rod into a small regular octahedron form according to the closed size of the regular octahedron of 750mm, the minimum length of the telescopic rod of about 200mm and other factors, wherein the centroid of the internal frame is coincident with the large regular octahedron, and the side length of the internal frame is about 450mm.

And 7, setting 6 driving points in total by taking each vertex of the large regular octahedron as a driving point, and ensuring constant-speed expansion of the vertex along the vector direction of each vertex from the centroid of the large regular octahedron by using an auxiliary stay bar.

And 8, performing motion simulation by a computer, and performing corner cutting treatment on the dough pieces at the edge of the regular octahedron to avoid collision of the adjacent dough pieces (figure 10).

Step 9, adding an anti-over-rotation rivet to prevent the triangular dough piece from over-rotating (fig. 11).

And step 10, hanging the regular octahedron on an external frame in a hanging mode (figure 12).

And 11, adding an inductor and a signal control system to realize induction control, ensuring that the maximum extension length of the driving rod is less than 158mm, and completing a device system.

Example III

The embodiment designs a volume-variable device of a truncated cube based on the method provided by the invention.

Step 1, selecting a half cube as a basic polyhedron, wherein the reference length of each side is 750mm.

And 2, filling each surface of the truncated cube with the mosaic pattern. Square mosaic patterns are selected for the square faces, mosaic patterns of regular triangle and regular hexagon combinations are selected for the regular triangle faces, and the side length of the reference face is 750m when closed (figure 13).

and 4, respectively calculating the expansion rates of the square surface and the regular triangle surface according to the methods of the first embodiment and the second embodiment, selecting smaller values, and determining the maximum extension length with 156mm as the side length.

And 6, designing an internal framework of the fixed driving rod into a cuboid form according to the closed side length of the half-cube of 750mm, the minimum length of the telescopic rod of about 200mm and other factors, wherein the bottom surface of the internal framework is 500mm by 500mm, the height of the internal framework is about 700mm, the centroid of the internal framework coincides with the half-cube, a horizontal square frame is added at the middle height, and the angular point corresponds to the vertex of the half-cube.

And 7, setting 12 driving points in total by taking each vertex of the truncated cube as a driving point, and ensuring constant-speed expansion of the vertex along the vector direction of each vertex from the centroid of the truncated cube by using an auxiliary stay bar (fig. 13).

And 8, performing motion simulation by a computer, and performing round angle cutting treatment on the surface sheets at the edges of the half-square, so as to avoid collision of the adjacent surface sheets (fig. 14).

And 9, adding an over-rotation preventing rivet to prevent the triangular dough piece from over-rotating.

And 10, adding an inductor and a signal control system to realize induction control, ensuring that the maximum extension length of the driving rod is less than 156mm, and completing a device system.

The above describes a driving mechanism based on planar hinged mosaic and vertex synchronous expansion, and a systematic generation method for forming a volume-variable uniform convex polyhedron device. The invention provides a design method of a uniform convex polyhedron with a variable volume, and provides a systematic solution for innovative design of three-dimensional movable buildings, movable structures and other forms. The method can be applied to both regular polyhedrons and archimedes polyhedrons defined in the current geometry. The present invention is not limited to the above embodiments, and any modifications or variations which do not depart from the technical solution of the present invention, i.e. only modifications or variations which are known to those skilled in the art, are included in the scope of the present invention.

Other embodiments of the present application will be apparent to those skilled in the art from consideration of the specification and practice of the disclosure herein. This application is intended to cover any variations, uses, or adaptations of the application following, in general, the principles of the application and including such departures from the present disclosure as come within known or customary practice within the art to which the application pertains.

It is to be understood that the present application is not limited to the precise arrangements and instrumentalities shown in the drawings, which have been described above, and that various modifications and changes may be effected without departing from the scope thereof.

Claims

1. A method of designing a uniformly convex polyhedron device of variable volume, comprising the steps of:

determining the expansion and contraction size of the driving member according to the minimum value of the linear expansion rate of each surface, and designing the shape and the size of the internal frame to ensure that each vertex synchronously moves at constant speed along the vector direction pointing to each vertex from the centroid of the uniform convex polyhedron;

2. The method of claim 1, wherein the uniformly convex polyhedron type is one of a regular polyhedron or an archimedean polyhedron.

3. The method of claim 1, wherein selecting a suitable mosaic pattern based on each regular polygon of the polyhedron, filling each regular polygon, comprises:

4. The method according to claim 1, wherein the linear expansion coefficient P1 of the square face is calculated by:

P1＝L/l

5. The method according to claim 1, wherein the linear expansion coefficient P2 of the regular triangle face is calculated by:

P2＝L/l

6. The method according to claim 1, wherein the linear expansion coefficient P3 of the regular hexagonal surface is calculated by:

P3＝L/l

7. The method of claim 1, wherein determining the telescoping dimension of the driving member based on the minimum value of the linear expansion coefficient of each face, designing the shape and dimensions of the internal frame to ensure constant velocity expansion of each vertex in a vector direction from the centroid of the uniformly convex polyhedron toward each vertex, comprises:

8. The method of claim 1, wherein chamfering the face pieces at each face edge location comprises:

9. The method of claim 1, wherein adding means for preventing over-rotation to the triangular shaped panel if the drive point is on the triangular shaped panel comprises:

10. The method of claim 1, wherein the step of providing the sensing system to control the drive member as needed to ensure the drive point movement is synchronized to achieve the desired movement response comprises:

and a control system comprising an inductor and a signal control element is added, so that the volume of the polyhedral device is changed according to the requirements of light, temperature, movement or other kinds of interactive response, the synchronous movement of the driving rod is ensured, and the maximum extension length is not more than the distance of the movement of the top point relative to the starting point after expansion.