HUT71823A - Spatial elements for forming butterfly shapes and spatial mechanisms comprising interlocked chains of butterfly shapes which are open or closed by themselves - Google Patents

Abstract

A set of elements is disclosed for building open, repetitive three-dimensional structures made of butterfly-shaped pieces and of interlinked fitting butterfly-shaped pieces. The elements are provided along their demarcation lines with connecting means. The individual elements (1 to K) are designed as polygons with n sides, n being an integer >/= 5. The polygons further have at least one axis of symmetry and at least three, but maximum n-1 equal adjacent angles ( alpha ) that satisfy the mathematical equation (1) alpha = arc cos {-cos[n1-2).90/n1].cos[(n2-2).90/n2]}, in which the integers n1 and n2 >/= 3 and are freely selectable. The individual elements (1 to K) further have pairs of congruent sides.

Description

The present invention relates to a set of elements whose odd numbered and congruent elements form a common vertex and a rotating plane - so-called butterfly shapes whose convex edges are convex when viewed from the same side of the element.

and concave / thus less than 18 ° or respectively. larger / angles are locked together.

This particular rotating spatial element is interconnected by repeated / sequential / unidirectional or multidirectional structures of extremely varied, self-locking spatial structures, e.g. spheres / can be built.

An important area of application of the set of elements of the present invention is their use as a toy for developing logical, combination and spatial vision; but their ability to model macro and micro worlds is also of paramount importance; and they are also excellent for walls, partitions and other architectural works with good sound and heat insulation properties, while also having a high load capacity.

Nowadays, a number of construction toys are known and commercially available which consist of interlocking or interlocking building blocks. In the vast majority of these, the game creator defines the specific structures / eg. vehicle, building, man, man. animals / that can be made up of elements. Thus, with the help of the templates and illustrations provided in these games, they will create the desired shape.

Although these games also develop dexterity, some members of the set of items - which are designed according to the purpose of the task - extremely limit the number and types of shapes that can be created. These games include the well-known LEGO, ···· «« · «4« *

* The high quality of each element highlights the similarity of the toys.

Also known are solutions that are primarily developed for modeling and demonstration purposes. Of these, we would mention the educational aid consisting of perforated spheres and chopsticks, which, with the help of it, have different crystal forms and / or crystals. molecular structures can be formed, respectively. can be presented. With this solution, construction does not provide an aesthetic experience and does not motivate you to create.

Also known as a teaching aid is a set of planar elements (polygons), which use paper elements with tabs fastened to each other with rubber bands. By connecting elements of a set of elements / triangles, quadrilaterals, etc., various shapes, e.g. goulashes, octahedra, and other crystal shapes can be constructed, but only closed space structures bounded by daggers can be obtained at all times, with edges converging to one vertex and convex when viewed from one side of the body.

Novotion Design Ltd has also developed a game of elements, some of which have been developed by 4,874,341; 4,886,477; 4,731,041 ill. U.S. Patent Nos. 4,902,259. Some of the building blocks of this known solution are planar polygons / triangles, rectangles, pentagons, etc. of thin plastic sheets, which are provided with coupling elements / eyelets along their bounding sides; the kit also contains some special items - which are used for vehicle wheels, drives, etc. can be developed. A special feature of this known solution is that it is possible to form objects delimited by curved surfaces, which is ensured by the fact that some of its building elements are provided with a drive / not-cross-cut notch along its axis (or axes).

Hungarian Patent Application No. 195,020 discloses a three-dimensional model for the presentation of molecular structures consisting of atoms imitating / approximately tetrahedral and hemispherical / modules. These modules are formed as multi-dimensional spatial blocks and contact one another along at least one face with a common vertex.

The structure is a spatial structure where the sum of the angles enclosed by the contact sheets is greater than 360, which can be used for modeling aplanaric, cyclic compounds for scientific research and education purposes, but due to its special design, its application is severely limited.

Summarizing the range of known solutions, it can be said that although many other special building blocks 1 are known for assembling or assembling. by connecting various shapes, such as geometric shapes and models on the one hand, there is still a need for new construction kits, toys, for example, which can become a tool for research, education, demonstration / tools.

In the context of the present invention, we aim to develop a new set of elements, which further develops 4 sets of planar elements / planar polygons1 / · · · · * * * ·············································································· it allows the development of new spatial structures that are not feasible with known solutions.

The present invention is based on the discovery that if the elements of a set of elements are matched to one another in common vertices / quadrants, respectively. the sum of the angles of the even vertex to the plural / convergent angles is greater than 36O °, then the resulting spatial shapes create a special shape called a butterfly shape, which is connected by a single or multidimensional further chains can be formed.

Accordingly, the present invention relates to a set of planar shapes, more particularly polygonal contours, where the term ρο1igon contour refers to shapes bounded by straight lines whose individual vertices lie in a single common plane. Thus, in addition to planar polygons, in the practical implementation the members of the set of elements can be all building blocks which are not made of solid glides, but merely of their boundary / contour / rods, pipes, etc. available; or equivalent elements are provided where these contours are not covered with smooth surfaces or have truncations or inserts along the contour lines.

We have also discovered that the butterfly shapes can, by sequential repetition, form self-locking spatial structures that can be extended in multiple directions / so-called two-legged spines / amenj5 · ·

-t * · * · ··· <<·. . ♦ · * ♦ i. · _ '. ·· ··· Each building block is not a regular polyhedron but has a misaligned symmetry.

Based on this discovery, the present invention is directed to defining the characteristics of each element in a set of butterfly shapes or a set of butterfly shapes, that is, the set of necessary and sufficient features that each member of the item set must satisfy to form closed butterfly shapes.

Thus, some elements of the set of elements of the invention are contiguous n-side contours with n-5 sides and adjacent to their bounding lines, where n-5 / and integer / and these polygon contours have at least one axis of symmetry and at least three but not more than / n -1 satisfies the following mathematical conditions:

c / - face cos /-cos/nl-2/.90/nl/.cos //n2-2.9O/n2//, where ni and n2 - 3 are integers and arbitrary values; and the sides of each element are matched in pairs.

Preferably, the element set consists of 5 * ~ n —8-sided ρο 1 igon contours 1 / body elements1 /.

In a preferred embodiment of the present invention, the ρο1igon contours are plastic planar moldings provided with freely pivotable coupling portions along their boundary lines / contours.

· «• · · • * ♦

In a further preferred embodiment, there are coupling portions that are locked in shape by the ρο1igon contour.

It is also desirable that the polygon contour consists of rods fixed to each other and that each element is connected by an insoluble bond.

In another embodiment, magnetic coupling portions are formed along the boundary of the ρο1igon contours.

Optionally, the set of elements consists of concurrent n-sided contours of ng and n is preferably five.

It is also preferred that the set of elements have additional so-called peripheral members, which are n-sided polygons, where n - 3 and at least one angle cK satisfy the given equation; respectively. the contours enclosing the angle <~ X coincide with the contours of the members / so-called body members of the element set.

In the following, examples and figures illustrate the use of the battery set according to the present invention. we prove the correctness of the given construction formula and the so-called. formation of the pi11orphoid form, and the formation of a ternary tuft formed by sequential repetition of the pi11orphic forms, which are hereinafter referred to as self-closing or self-closing. repetitive basic elements of optionally open-space structures.

f * ·· <999 »99 4» ♦ * - · <· · ·

In our examples, we use the n = 5-sided overlapping elements of the element set to illustrate the typical spatial structure where

In FIG. two pivot shafts, a

Figure 2 shows a further phase of this, a

In Fig. 3, the so-called pi1 1 formed from ango forms. ke11östö1 csér-, a

Fig. 4 shows two mutually perpendicular gutter structures.

The diagrams contain only conceptual solutions and do not indicate the practical implementation (ie the connecting parts). / For the latter there are many known solutions - eg. staples - known./

Thus, in our examples, we construct spatial structures made of pentagons that are congruent with each other, consisting of a chain of so-called butterfly shapes.

As shown in Fig. 1, the piercing shape consists of four pentagonal elements 1 to 4 joined at their apex 01 and their adjacent sides. These pentagonal elements 1 to 4 are, according to the invention, so-called pentagons of spurious symmetry, i.e. their angles are not of equal size.

• · * ♦♦ <«·· ··« · · · · 4 · * · · · ♦ ♦ ···· <·· 4 »· ·· *

By definition, a spatial building block is just that

1 ... 4 elements (in the present case, may be pentagonal) with at least three consecutive angles of equal size.

/ Because we have chosen pentagons, the criteria set for the pages are automatically met. /

As can be seen in the figure, the resulting shape rotates out of plane because the quadrilateral angle at point 01 is greater than 360 °. In our figure we denote by cT or / the two angles which the four bounding elements 1 ... 4 close in pairs, of which, as can be seen, on the same side / eg. from above / when viewing the structure, one angle P is less than 180 °, while the other angle d is greater than 180. In the figure, we have seen with arrows that the structure thus formed is not rigid; by approaching or removing the A-C vertices, the B-D vertices move in the opposite sense, respectively. approach each other. / This is the name of this saddle-shaped spatial structure, because the movement thus created is reminiscent of butterfly wing strikes. /

In Fig. 2, the spatial structure was further extended with elements 5 and 6 in the direction of vertex C, so that vertex C became a more common vertex, vertex 02, again denoted by the angles Γ and γ respectively. On the one hand, the arrows were used to indicate that the vertices A and E can be combined to form a closed space structure that is A-E, 01, and 1, respectively. It encloses a virtual triangle with 02 vertices, forming a double funnel.

w ··· ···········································································································································

By the virtual term, it is meant and will continue to be used consistently that the spatial structural elements of the present invention enclose portions of space (in this case, a triangular space). / The resulting shapes are called virtual po1igons.

In Figure 2, the element 7 indicates a further possible direction of further construction, and it will also be appreciated that combining the vertices A-E would eliminate the possibility of further construction.

THE 3 . Figure 4 further illustrates the unique t and year 1 of the butterfly orms 1 which form a double polygon VI which represents a virtual polygon VI forming a regular pentagon, and in Figure 4 also delimit a virtual polygon V2 forming a regular hexagon in another direction. 1 to 18 elements in the form of a funnel.

1-4. In Figures 1 to 4, it is intended to illustrate by numerically mirroring the digits 1 that the outer or inner half of each of the elements 1 to 18 may be seen. The spatial structure of Figure 3, and in particular of Figure 4, clearly shows that the interlocking butterfly shapes are part of several spatial structures at the same time. so e.g. the elements 3, 4, 9 and 10 of FIG. 4 are simultaneously constituting the double funnel forming the regular pentagonal virtual polygon VI and the double funnel forming the virtual polygon V2 having the regular effect.

t «·· * ·· * ·« »• · · · ·· ·

9

The exemplary spatial structures illustrate only the basics of the constructability (or regularity) that can be realized using the set of elements of the present invention.

···· ···· · ·

9 9

99

Figures 3 and 4 help to clarify that it is clear that closed / thus virtual polygons / spatial structures cannot be regularized by gonok1 only by satisfying / mathematical / conditions elements of the present invention.

As an example, let us guide you through the realization of the three-dimensional pentagonal 1 ... K elements shown in the figures:

If the elements 1 ... K were regular pentagons, all 3 angles would be 108 °. If our goal is to create a nI = 5-sided VI virtual polygon tern, then the

Looking at the markings in Figure 3:

I = 108 ° is required. / That is, one side of the butterfly shape is bounded / In this way, by creating additional common vertices at A and E, we can create a binary polygon that forms a regular pentagonal VI polygon VI in the plane defined by A-01-02-E ....

However, in this case (for I = 108 °), the value of angle J is 116 ° 33 '54.1, and there is no regular polygon whose angles assume this value, respectively.

Thus, in the case of regular pentagonal elements 1 ... K, it is not possible to extend the spatial structure in another direction, i.e. by continuing the element 7 shown in Figure 3.

However, if elements 1 to B have the features of the present invention, choosing n = n2 = 5 / that is, for double-edged terns that form five-sided virtual polygons VI and V2, / r-A <= 108 ° substituted in their equation = 110 ° 12 '42.4.

From the known formula for the internal angles of n-sided polygons, one can also calculate:

remaining angles of p = /n-2/.18O°

It will be appreciated that for each vertex where we wish to further expand the shape into a butterfly shape, the value of the CP angle should be calculated, so in the example selection, the four angles of the pentagon / or / n-1 / angle / equals / P = 110 ° 12 '42.4 /, while the fifth angle is p = 99 ° 9' 10.05

As an appendix to our description, we have shown in a table, by way of example, what kind of pentagonal shapes that make up various V1-V2 virtual polygons can be used to construct pentagons with corrupted symmetry.

The planes of VI and V2 virtual polygons are approximately perpendicular to each other; and is a function of what complex spatial structure we ultimately implement.

If the values of ni and n2 are odd numbers / virtual polygons VI and V2 are odd polygons, then the created spatial structures cannot completely close by themselves. If both n1 and n2 are even numbers, we can implement wavy, lace-like shapes between the pGld4ul X planes.

In the case / and only if n is odd or respectively. n2 is an even value, the resulting spatial structure may be spherically self-closing (where n1-n2 /).

/ In the latter case, the virtual polygons VI and V2 only come into close perpendicular plane if a sphere of sufficient radius is created. /

In our example, one of the simplest applications of the set of spatial elements of the present invention is shown, the use of overlapping elements 1 ... K / pentagons.

Theoretically, there is no obstacle for the elements 1 ... K to have any number of pages, but it can be seen that by increasing the number of pages, the possibility of further building the spatial construct is reduced / there is a lack of space; since it is not permissible for each element to intersect /, so n = 8 is a practical ceiling.

we can create, move that or that here too 1. . . K elements

Further, our example was limited to the design of four butterfly shapes of four to four elements. However, a butterfly shape can be created from any number of elements, such as three, four, or even. multi-axis articulated / spatially obtained spatial structures. Again, it is pointless and meaningless to increase the number at the common vertex, which again limits the freedom of movement of the created form.

The richest variety of variations is provided by four butterfly shapes of 1 to 4 elements, which bend out of the plane along two perpendicular / near / perpendicular axes, thus exhausting every possible portion of the three-dimensional space.

According to the present invention, non-compact glides, tie rods, tubes may be formed. they also work at their peaks. authority. /. . .K but / because of that. .

spatial structures are also equivalently applied by using elements that are only contoured by their contour lines ρο 1 igoncontact.K elements can also be provided with elements or, if necessary, truncated

Practical implementation of the individual decorative / A switch parts: we did not go into diversity due to their recognition

In addition to construction toys, the application of the present invention opens up unpredictable perspectives. The spatial structures that can be implemented with some elements of the element set faithfully model reality - molecular structures, crystal shapes, etc ... - so that they can become auxiliary tools for each specialized attack. The formed spatial structures - in all cases where the elements are self-locking - are extremely load-bearing and can be loaded in many directions; at the same time, the interiors / cavities created in the spatial structure have a specific effect on the various wave propagations (such as sound and electromagnetic waves).

In summary, the set of elements according to the invention can be used to form new spatial structures / butterfly shapes in double-funnel closed butterfly shapes - and nested double terns 1 that can / can be self-locking spherical shapes ... , which has a wide range of variations / applications and thus a wide range of applications.

The number of individual elements of the same type of congruent 1 ... K elements of the set of space elements can be arbitrarily large, while the minimum number of elements is the simplest spatial structure / piform or double1 tern / determined.

There is also an arbitrary number of types of 1 ... K elements according to the invention within a kit. It is advisable / for economic reasons / to sell 1 ... K elements that can be combined with each other / similarly to different LEGO series / in smaller sets; and gradually expand the basic stock.

However, we would like to emphasize that the set of congruent pentagons also provides (in case of a sufficiently large number) a number of exciting combinations.

Claims (6)

Claims 1. / Space set for the creation of open and self-closing spatial structures consisting of an interlocking chain of butterfly shapes and butterfly shapes, each of which has switching portions along the boundaries of each of its elements, characterized in that each element is a 1/1 ... .5, the elements /1...K/ having at least one axis of symmetry and having at least three but not more than n-1 adjacent angles // of equal size and satisfying the following condition: <d ~ circ CG ^ -Ccs / joC-Z) yifC-cpsIfy where ni and n2 É 3 and any integer optionally, and the associated sides of each element are paired. 2. / A set of space elements according to claim 1, characterized in that it is preferably 5 to n 8 side elements / 1. . .K / pseudonym 1. 3. A set of spatial elements according to claim 1 or 2, characterized in that it is formed from 1 to 1 units of pentagonal elements. 4 / 1-3. A set of spatial elements according to any one of claims 1 to 4, characterized in that each of its elements / 1. . . . K / plastic flat fittings with coupling parts pivoting along their boundaries. ···· ···································• 5. / 1-4. A set of spatial elements according to any one of claims 1 to 3, characterized in that each of its elements consists of rods fixed to one another and the coupling parts thereof form an insoluble bond. 6 / 1-5. A set of spatial elements according to any one of claims 1 to 5, characterized in it also has peripheral elements that satisfy at least one of the angles / o (/) satisfying the condition given by /1...K/ for the trunk elements, and n - 3 ο 1da1u.