WO2001039853A1

WO2001039853A1 - Polyhedral mechanism and method for producing the same

Info

Publication number: WO2001039853A1
Application number: PCT/DE2000/004157
Authority: WO
Inventors: Felix Pfister
Original assignee: Felix Pfister
Priority date: 1999-12-04
Filing date: 2000-11-23
Publication date: 2001-06-07
Also published as: AU2350701A; DE19958467C1

Abstract

The invention relates to a polyhedral mechanism, comprising substantially rigid bodies which are linked in an articulated manner and nodes which are fixed to said bodies; and to a method for producing the same. When the polyhedral mechanism moves, said nodes move in such a way as to form planes of movement which are each formed by polyhedral surfaces that are delimited by edges of a polyhedral. Sub-structures which are allocated to adjacent planes of movement respectively and which contain the bodies, are connected to hinges that form the nodes in such a way as to form closed kinematic loops and in such a way that a rotation of the adjacent sub-structures about their common edges of the polyhedral, respectively, is blocked and the spatial angular position of the planes of movement in relation to each other remains essentially the same while the polyhedral surfaces experience a geometrically similar or self-similar change of dimension, preferably a central extension.

Description

POLYEDERMECHANISM AND METHOD FOR THE PRODUCTION THEREOF

The invention relates to a polyhedron mechanism with articulated coupled essentially rigid bodies and body-fixed knots and a method for producing such polyhedron mechanisms.

Such polyhedron mechanisms, also known as polyhedron gears, form a system of articulated and genuinely spatially coupled rigid bodies. Such a multi-body system is used to transfer movements and / or forces from one or more bodies into movements and / or forces from other bodies. The polyhedron mechanisms are systems with one or more degrees of freedom in the sense of classic mechanics and are based on movable structures that include polyhedron surfaces.

When parts of the polyhedron mechanism move, the respective polyhedron surfaces experience a geometrical or self-similar size change, for example a central stretching. In this context, therefore, we also speak of "breathing" polyhedron structures.

These polyhedron mechanisms can be combined, for example, to form honeycomb-like, that is to say gapless polyhedron mechanisms or to sponge-like, that is to say provided with gaps, polyhedron mechanisms. On the one hand, the breathing polymer mechanisms combine the beauty of rigid poly on the other hand, enable the implementation of a variety of technical functions. An example of such polyhedron mechanisms are kinematic mobiles, such as the movable octahedron of the Heureka exhibition in 1991 in Zurich.

Breathing polyhedron mechanisms have so far been put together purely empirically. A systematic method for generating the breathing polyhedron mechanisms is not known. Furthermore, a superordinate functional and active structure on which the previously known breathing polyhedron mechanisms were based and their general principle of order and construction were not recognized. As a result, it has not previously been possible, based on specific wishes and / or specifications from users or clients, to synthesize polyhedron mechanisms based on specified boundary conditions simply and quickly, but instead one had to hope to find design solutions empirically. This method is not goal-oriented and time, cost and resource consuming and can therefore not be considered for an industrial application.

Accordingly, it is an object of the invention to define breathing polyhedron mechanisms and a method for their production, which enable a design corresponding to the user needs and a simple and inexpensive synthesis or production.

This object is achieved according to the invention by the features of patent claim 1, in particular in that the nodes move when the polyhedron mechanism moves, forming movement planes which are each formed with polyhedron surfaces delimited by edges of a polyhedron, adjacent movement planes being assigned in each case, the substructures containing the bodies are connected to the hinges forming the nodes with the formation of closed kinematic loops such that rotation of the adjacent substructures around their respective common edges of the polyhedron is blocked, so that the spatial angular position of the movements planes remains essentially the same to one another, while the polyhedron surfaces undergo a geometrically or self-similar size change, preferably a central stretching.

This is the first time that a class that is technically easily feasible is breathing

Polyhedron mechanisms defined and synthesizable, which is based on a general order and construction principle as well as a systematic function and effect structure. Now, for the first time, polyhedron mechanisms such as height-adjustable support elements, foldable solar panels, easily foldable and unfoldable structural elements for exhibition stands and / or advertising space supports, modular systems, in particular entertainment toys such as polyhedron puzzles or large-scale showpieces of the "art cinematique" can be produced in a targeted and inexpensive manner.

The hinges expediently have at least two axes of rotation, each of which has a constant axis angle with respect to one another and are formed skewed to one another or intersect at an intersection and which are normally on one of the adjacent planes of movement.

Advantageously, the polyhedron mechanism is designed such that when the polyhedron mechanism moves, at least some of the knots in certain directions along the edges of the polyhedron formed with the polyhedron surfaces and / or while maintaining a constant division ratio of edges determined by the positions of the knots on the edges - Sections moved. In the first of the two combinable cases, rotation of the adjacent substructures, which is preferably orthogonal to the blocked rotation about the respective common edges, is possible. As a result of these favorable possibilities of moving the nodes, an advantageous rotation of the bodies forming the substructures can be achieved. If the nodes assigned to a specific polyhedron surface move only while maintaining a constant division ratio of edge sections determined by the positions of the nodes on the edges of this polyhedron surface, So do not move along the edges, their geometric or self-similar size change in the form of a central stretching or compression, ie their "breathing", is particularly well visible.

The polyhedron mechanism is expediently designed with at least four polyhedron surfaces and / or at least six nodes. This allows a particularly simple, inexpensive to manufacture and because of its kinematic over-determination and due to the multiple closed kinematic loops stiff or stable polyhedron mechanism.

The edges of the polyhedron surfaces are expediently designed as preferably straight virtual rods, the adjacent rods intersecting at an intersection. This enables a particularly simple and easy-to-operate polyhedron mechanism, in which the structure and beauty of the underlying polyhedron surfaces and the polyhedron built thereon are particularly effective when the or parts of the polyhedron mechanism are moving.

It is particularly advantageous if the nodes assigned to a common polyhedron surface are always arranged in such a way that they

Subdivide straight lines delimiting the polyhedron surface into a division ratio that is preferably the same for all intersection points and is dependent on the size change of the polyhedron surfaces or on the state of motion of the polyhedron mechanism. This enables a uniformly translating movement of the nodes on the straight lines delimiting the edges of the polyhedron surface, so that the breathing polyhedron structures can be defined and formed in a particularly simple and effective manner.

A particularly simple and inexpensive construction and a polyhedron mechanism which is particularly suitable for technical support or fastening applications and at the same time has outstanding beauty can be achieved in that the substructures have flat substructure surfaces which are parallel to one another. All are arranged in relation to the movement planes, the substructures preferably being flat. By using such planar substructures, the self-similar size change can be represented particularly well when the or parts of the polyhedron mechanism move. Furthermore, due to the flat substructure surfaces, favorable contact and support conditions for objects to be supported or for the contact and attachment of objects can be achieved, wherein a flat support or support of the polyhedron mechanism itself can also be achieved in a simple manner. As a result, a stable, functional and optically advantageous construction with a sophisticated design can be achieved.

A particularly simple and inexpensive design of a polyhedron mechanism can be achieved in that the nodes are arranged in the planes of movement, i.e. that the respective movement level and the substructure level assigned to it coincide. As a result, when the or parts of the polyhedron mechanism move, the breathing size change or movement is even more clearly visible and the polyhedron mechanism can be synthesized or produced in a particularly simple and cost-effective manner.

The hinges are expediently designed with at least two rotary and / or rotary push and / or screw joints. The double swivel joints are characterized by a rigid coupling within the hinge itself, each swivel joint comprising at least one of the at least two axes of the hinges, which preferably have a constant axis angle to one another. This provides a clearly defined possibility of movement. The special arrangement of the rotary and / or rotary push and / or screw joints in the overall assembly of the polyhedron mechanism prevents the adjacent planes of movement from rotating relative to one another. Using rotary thrust joints, for example, a translatory displacement movement of the substructures can be permitted in the direction of the respective axis. By using screw joints a similar function can be realized, the ratio of rotary and thrust movement being arbitrary.

The substructures are expediently formed with at least one real body, preferably with at least one real, in particular flat, mechanism. In this way, technically favorably designed polyhedron mechanisms can be created in a variety of ways. It is expedient if the real body or the real mechanism is designed with at least one flat body. This creates particularly simple and inexpensive to manufacture and clearly defined functional and functional structures. The technical and optical functionality can be further improved if the flat body is designed as a polygon.

It is particularly advantageous if the real mechanism is designed with at least two rod-shaped bodies which are coupled to or by at least one swivel joint. Alternatively or in combination with these measures, it is particularly advantageous if the real mechanism is designed with at least one flat body and at least one rod-shaped body, which are coupled to or by at least one swivel joint. Star-shaped substructures are advantageously formed, for example from real bodies such as triangular cylinders, which are coupled to at least one swivel joint.

These measures enable a particularly simple and inexpensive modular design and construction principle of such polyhedron mechanisms and, in particular, enable easy and flexible adaptation to the respective user wishes, depending on their specifications for the movement patterns of the individual nodes along the edges of the self-similarly breathing polyhedron surfaces, each for this purpose suitable mechanisms or substructures are selected and the polyhedron mechanism is synthesized by coupling with the hinges formed in the area of the nodes. The substructures are advantageously designed with at least one virtual mechanism, which is preferably coupled to the bars containing the edges via sliding joints or to the real mechanism assigned to the substructures via rotating sliding joints in such a way that the virtual and real mechanisms form at least one closed kinematic loop. By coupling several such pairs of real and virtual mechanisms, a polyhedron mechanism can be created in a particularly advantageous manner, which is simple and easy to synthesize or manufacture, has a defined design corresponding to the needs of the user, and which provides the viewer with the optical beauty of breathing polyhedron structures, particularly when moving of the polyhedron mechanism.

Expediently, when a substructure assigned to a particular movement plane is moved, preferably fixed to the movement plane, the nodes assigned to it move along the edges of the polyhedron surface, which experiences a geometrically or self-similar size change, preferably concentrically extending, as if they were the pivot points of a virtual rotary thrust joint, the Each has an axis of rotation perpendicular to the plane of movement and a thrust axis along the relevant edge, the rotary-thrust joint connecting the substructure to a virtual mechanism which is fixed in terms of the movement and which connects the edges of the polyhedron surface as bodies and the corner points of the polyhedron surface as adjacent edges Includes thrust joints. As a result, in a further improved embodiment, a polyhedral mechanism corresponding to the user needs can be produced particularly cheaply.

The polyhedron is expediently designed as a platonic, Archimedean, uniform and / or regular polyhedron. Furthermore, the polyhedron can be designed as a polar and / or stellar structure of the Archimedean bodies or as a polymer which is synthesized from the space-forming surfaces and / or spatial diagonals of the Platonic and / or Archimedean bodies. Due to this particularly simple structural design of the polyhedra create technically, optically and aesthetically sophisticated polyhedron mechanisms.

Depending on the user requirements and in order to be able to create particularly large or extensive kinematic structures or polyhedron mechanisms, the polyhedron mechanism can also be designed with a plurality of polyhedra or a plurality of polyhedron mechanisms can be designed to form a composite of polyhedron mechanisms or a polyhedron composite.

A particularly simple and inexpensive method for producing the above-described breathing polyhedron mechanism with articulated coupled essentially rigid bodies and body-fixed knots, which enables a defined design corresponding to the user needs, can be achieved if the knots move while the polyhedron mechanism is being formed Moving planes of movement in a predeterminable direction of movement, the planes of movement being formed in each case with predeterminable polyhedron surfaces delimited by edges of at least one polyhedron, wherein respectively associated planes of motion associated with the body-containing, predeterminable substructures with predeterminable hinges forming the nodes are connected in this way, with the formation of closed kinematic loops that a rotation of the neighboring substructures around their respective common edges of the polyhedron is blocked, so that the spatial win Cellularity of the planes of movement remains essentially the same to one another, while the polyhedron surfaces undergo a geometric or self-similar size change, preferably a central extension, with the shape and spatial position of the polyhedron surfaces of the polyhedron being selected in a first step, followed by the direction of movement of the nodes and the suitable substructures and the hinges are selected and the polyhedron mechanism is then assembled from the substructures and the hinges. Depending on the technical or optical needs of the user, the basic shape of the polyhedron and its respective polyhedron surfaces must first be defined. The direction of movement of the nodes assigned to the hinges or the substructures can subsequently be defined, so that the desired movement pattern is achieved. In this way, additional technical and optical functionalities can be created and exploited, which can meet the diverse needs of the users in a special way.

The hinges expediently have at least two axes of rotation, which each take a constant axis angle to one another and are skewed to one another or intersect at an intersection, each hinge being selected such that its axis angle corresponds to the angle between the normals of the respectively adjacent planes of movement.

Depending on the polyhedra formed by the same or different polyhedron surfaces and consequently depending on the respective position and shape of the polyhedron surfaces, there is a certain structure which is easily accessible to a mathematical analysis of the angles between the adjacent polyhedron surfaces. As a result, the respective unchangeable axis angle of the individual hinges can be determined easily, so that after a selection of the desired hinge types, which can also be based on the technical and or optical needs of the user, the polyhedron gear mechanism or the polyhedron mechanism can be assembled or synthesized.

The above measures, both individually and in combination with one another, contribute to a defined design corresponding to the user needs and a simple and inexpensive synthesis or production of breathing polyhedron mechanisms. Further features, points of view and advantages of the invention can be found in the following description part dealt with on the basis of the figures.

A preferred embodiment of the invention is described below with reference to the figures. Show it:

1 shows the virtual mechanism consisting of three rods and three sliding joints;

FIG. 2 shows the planar substructure GD1, which consists of the virtual mechanism according to FIG. 1 shown here in simplified form and the real body designed as an equilateral triangle;

3 shows the equivalent graphs of the planar substructure GD1 with a positive or negative sense of rotation;

4 shows the planar substructure GD2. This consists of the simplified virtual mechanism shown in FIG. 1 and a real mechanism. As a real body, it contains an equilateral triangle and a rod, which are coupled via a swivel joint;

5 shows the virtual mechanism consisting of four rods and four thrust joints;

FIG. 6 shows the planar substructure RH1 (see FIG. 11), which consists of the simplified virtual mechanism according to FIG. 5 and a real mechanism. As a real body, this contains two equilateral triangles, which are coupled via a swivel joint;

7 shows the graph of the substructure RH1 according to FIG. 6; 8 shows a tabular representation of substructures of the GD type with associated graphs;

9 shows a tabular representation of substructures of the type RD with associated graphs;

10 shows a tabular representation of substructures of type Q with associated graphs;

11 shows a tabular representation of substructures of the type RH with associated graphs;

12 shows a tabular representation of a substructure of the HX type with associated graph;

13 shows a tabular representation of substructures of the type PT with associated graphs;

14 shows a three-dimensional oblique view of a substructure of the GD type, which is formed with six isosceles triangular cylinders, each overlapping in pairs, in a position in which the associated plane of movement of the nodes, which is designed as a symmetrical hexagon, takes up a minimum area;

15 shows a three-dimensional oblique view of the substructure according to FIG. 14, in an intermediate position in which a self-similar enlargement of the polyhedral surface forming the plane of movement is achieved by rotating the triangular cylinders relative to one another about their respective common rotary joints;

16 shows a three-dimensional oblique view of the substructure according to the image

15, in which the assigned plane of movement of the nodes by a central rotation of all triangular cylinders about the central axis, which is normal to the plane of movement, occupies an even larger polyhedron surface;

17 shows a three-dimensional oblique view of a substructure of the type PT, which is formed with twelve isosceles cylinder triangles overlapping each other in pairs, in a position in which the assigned plane of movement of the nodes, which represents a polyhedral surface designed as a symmetrical hexagon, is one occupies minimal area;

18 shows a three-dimensional oblique view of the substructure according to the image

17, in an intermediate position, the self-similar enlargement of the polyhedron surface designed as a hexagon initially being achieved only by a central rotation of all cylinder triangles about the central axis formed normal to the plane of movement;

19 shows a three-dimensional oblique view of the substructure according to the image

18, in which the polyhedron surface, which is designed as a symmetrical hexagon, occupies a maximum surface, this being achieved by rotating the triangular cylinders relative to one another about their respective common pivot joints;

20 shows a schematic representation of the double hinge which is formed with the two axes of rotation intersecting in the node;

21 shows a schematic three-dimensional representation of the polymer mechanism formed from the substructures GD1 and GD2 as a tetrahedroid with the enveloping virtual tetrahedron of the virtual mechanism formed with the edges of the polyhedron surfaces; FIG. 22 shows the tetrahedroid according to FIG. 21, in a representation rotated with respect to FIG. 21;

23 the tetrahedroid, shown without the enveloping tetrahedron;

24 shows a three-dimensional oblique image of a polyhedron mechanism designed as a truncated icosahedron stump (soccer ball). This assumes a position in which the assigned polyhedron surfaces, which are designed as regular pentagons or hexagons, occupy a minimal area, so that the bodies forming the polyhedron mechanism enclose a minimal volume;

25 shows a three-dimensional oblique image of the polyhedron mechanism according to FIG. 24, in an intermediate position in which a self-similar one

Enlargement of the polyhedron surfaces forming the planes of movement is achieved by rotating one or the pentagonal cylinders about a central axis of rotation arranged normal to the plane of movement. In order to better illustrate the "breathing" of the polyhedron mechanism, the boundaries of the polyhedron are

Edges shown as solid black lines;

FIG. 26 shows a three-dimensional oblique image of the polyhedron mechanism according to FIG. 24, in which the planes of movement take up a maximum area, so that those forming the polyhedron mechanism

Enclose body maximum volume;

27 shows a three-dimensional oblique image of a further exemplary embodiment of a polyhedron mechanism which is also embodied as an icosahedral stump (soccer ball). The latter occupies a position in which the assigned polyhedron surfaces, which are designed as pentagons or hexagons, occupy a minimal area, so that the poly- enclose the mechanism-forming body arranged in a star shape a minimal volume;

28 in an intermediate position in which a self-similar enlargement of the polyhedron surfaces forming the planes of motion occurs

Rotation of one or the star-shaped bodies assigned to the pentagons about a central axis of rotation arranged normal to the plane of movement is achieved. To better illustrate the "breathing" of the polyhedron mechanism, the edges delimiting the polyhedron surfaces are shown as solid black lines;

29 shows a three-dimensional oblique image of the polyhedron mechanism according to FIG. 27, in which the planes of movement take up a maximum area, so that the bodies forming the polyhedron mechanism enclose a maximum volume;

21 to 23 show the polyhedron mechanism 310 of a tetrahedroid based on a polyhedron 350 designed as a tetrahedron 311. This consists of preferably planar substructures 342, 343, 344, 345, which are coupled to form a closed kinematic loop. The substructures 342, 343, 344, 345 consist of at least one real body (triangles 346, 347) and a real mechanism (triangles 351, 352, which are coupled to the rods 355, 356 via the pivot joints 353, 354) and a virtual mechanism 371, 372, 373, 374.

The real bodies touch with some or all of their ends, which form the nodes 322, 323, 324, 325, 326, 327, the virtual mechanism 371, 372, 373, 374 on which the straight edges 316, 317, 318, 319, 320, 321 of the rods forming polyhedron surfaces 312, 313, 314, 315. The nodes 316, 317, 318, 319, 320, 321 assigned to a common polyhedron surface 312, 313, 314, 315 are always arranged in such a way that they Subdivide straight edges 316, 317, 318, 319, 320, 321 delimiting polyhedron surfaces 312, 313, 314, 315 in a ratio that is the same for all intersection points 376, 377, 378, 379. The nodes 322, 323, 324, 325, 326, 327 of the substructures 342, 343, 344, 345 consequently move along the straight lines 316, 317, 318, 319, 320, 321 of the polyhedron surfaces 312, 313, 314, 315 or along the connecting lines of the articulation points of the virtual mechanisms 371, 372, 373, 374 evenly translating to form a typical movement or speed pattern. For reasons of economics of thought, this can be characterized by a graph 338, 339, 340, 341 oriented with arrows 334, 335, 336, 337, 348, 349.

Depending on the geometric design of the respective polyhedron surfaces, there are a variety of possible movement or speed patterns. When synthesizing the polyhedron mechanism, these can be selected as desired within the framework of the boundary conditions specified by the polyhedron surfaces and are advantageously specified by the user.

The interaction of the real bodies or the real mechanisms with the edges of the polyhedron surfaces forming a virtual mechanism is described in more detail below.

1 shows the virtual mechanism 30 consisting of three bars 26, 27, 28 and three sliding joints 31, 32, 33, which here forms a polyhedron surface 25 in the shape of the equilateral triangle 35. The intersection points 36, 37, 38 of the rods 26, 27, 28 or the straight lines 51, 52, 53 of the polyhedron surface 25 form articulation points. When the sliding joints 31, 32, 33 move inwards or outwards, a self-similar movement of the virtual mechanism 30 or the edges 51, 52, 53 of the polyhedron surface 25 is induced in the form of a central extension. Self-similar in this context means that the size change of the respective polyhedron surfaces induced by a movement of parts of the polyhedron mechanism takes place in such a way that the respective polyhedron surface is geometrically trisch similarly reduced or enlarged and thereby experiences a central insertion.

FIG. 2 shows the planar substructure 20 of the GD1 type (see also FIG. 8). This is formed by coupling a real body 55, formed as an equilateral triangle 49, of the substructure 20 with the edges 51, 52, 53, formed as a straight line, of the polyhedron surface 25 forming the virtual mechanism 30. This also has the shape of an equilateral triangle 35. The coupling between the real body 55 and the edges of the virtual polyhedron surface 25 takes place via the nodes 21, 22 23, which form the corners or ends 56, 57, 58 of the real body 55. For reasons of simplification, only the polygon forming the virtual mechanism 30 without the sliding joints 31, 32, 33 is shown in FIG. 2.

The nodes 21, 22, 23 can always move along the edges 51, 52, 53 of the polyhedron surface 25 of the polygon formed by straight lines due to a kinematic coupling, for example via virtual rotary thrust joints. The nodes 21, 22, 23 are arranged in such a way that the edges 51, 52, 53 delimiting the polyhedral surface 25 are always in the same ratio 3621/2137, 3722/2238, 3823/2336 in the edge sections 3621, 2137, 3722, 2238, 3823, 2336 and consequently a uniformly translating movement is achieved. This relationship can be expressed in the following equation:

3621/2137 = 3722/2238 = 3823/2335

3 shows the possible movement patterns of the nodes 21, 22, 23 along the edges 51, 52, 53 of the self-similarly breathing polyhedron surface 25 in the form of the virtual mechanism 30 comprising the equilateral triangle 35 which are shown in the graphs 44 and 48 summarized arrows 41, 42, 43 and 45, 46, 47 applied. As shown in FIG. 3, the hen the directions of all arrows 40, 41, 42, the resulting graph 48 is equivalent to the original graph 44.

In the example chosen here, because of the coupling with a single real body 55, here the equilateral triangle 49, all nodes 21, 22, 23 have the same direction of rotation about the polyhedron surface 25 enclosed by the virtual mechanism 30. Therefore, here is a single sign " + "or" - "sufficient to determine the respective movement pattern (Fig. 3). So if all nodes assigned to a certain polyhedron surface have the same direction of rotation, there is usually only one sign

Characterization of the movement or speed pattern sufficient. This sign or the oriented graph characterize the direction of movement of the nodes of the substructures along the connecting line of the articulation points or along the straight lines of the self-similarly breathing polyhedron surfaces, but not the amount of speed or the exact position of the nodes themselves. The designer or To rid a designer of such marginal problems in the sense of an economy of thought is one of the advantages of the described invention.

FIG. 4 shows the planar substructure 60 of the type GD2 (see also FIG. 8) including the associated graphs 84. This differs from the graphs 44, 48 according to FIG. 3 in that the movement orientation of the node 62 (arrow 81) against the movement orientation of the nodes 61 and 63 (arrows 80 and 82) is formed. In contrast to the planar substructure 20 of type GD1 shown in FIG. 2, which comprises the real body 55 formed as an equilateral triangle 35, the substructure 60 of type GD2 in FIG. 4 is formed with the real mechanism 95. This consists of the isosceles triangle 89 and the rod 99, which are articulated via the swivel joint in 100. This planar substructure 60 has two degrees of freedom of movement. However, if you think of the swivel 99 always in

Center of gravity of the virtual mechanism 30, that is to say the virtual polyhedral surface formed with the straight edges 51, 52, 53 by the intersection points 36, 37, 38 Before 25 is blocked, the planar substructure 60 only has one degree of freedom. In this case, a movement of the nodes 61, 62, 63 again applies a uniformly translating movement, so that the nodes 61, 62, 63 respectively assigned to the polyhedron surface 25 are always arranged in such a way that they edge 51, 52 delimiting this polyhedron surface 25 , 53 in an equal ratio into the edge sections 3661, 6137, 6238, 3762, 3863, 6335 and the following applies:

3661/6137 = 6238/3762 = 3863/6335

While the exemplary embodiments shown in FIGS. 1 to 4 are based on polyhedron surfaces 25 or virtual mechanisms 30 formed with equilateral triangles 35, in the exemplary embodiment described below and shown in FIGS. 5 to 7, one is formed as a symmetrical diamond 116 Starting from polyhedron surface 135, which is enclosed by the virtual mechanism 130.

FIG. 5 shows the virtual mechanism 130 consisting of four rods 126, 127, 128, 129 and four articulation points or thrust joints 131, 132, 133, 134 and the polyhedron surface 125 encompassed by this, designed as a diamond 135. This is by a characterized by diamond 135 formed from two equilateral triangles. This virtual mechanism 130 has two degrees of freedom of movement. The polygon formed by the four bars 126, 127, 128, 129 or the polyhedron surface 125 formed thereby can remain self-similar when the virtual mechanism 130 moves or remains due to the constraints imposed on the virtual mechanism 130 by adding the real mechanism 155 self-similar.

For reasons of a simplified representation and the economics of thought, the virtual mechanism 130 is illustrated in FIGS. 6 and 7 only by the polygon or the polyhedron surface 125 of the symmetrical diamond 135 assigned to it. 6 shows the planar substructure RH1 (see also FIG. 11). In addition to the virtual mechanism 130 described above, this consists of the real mechanism 155. The real mechanism 155 consists of the real bodies 168, 169, which are coupled via the swivel joint 165 and are each formed as an equilateral triangle 166, 167. The nodes 121, 122, 123, 124 of the real mechanism 155, which each form two of the planes or corners 171, 172, 173 and 174, 175, 176 of the triangles 166 and 167, always move along the rods 126, 127, for example due to a kinematic coupling via virtual rotary thrust joints , 128, 129 or along the edges 151, 152, 153, 154 of the polyhedron surface 125 which run through the intersection points 136, 137, 138, 139. Again, the nodes 121, 122, 123, 124 are always arranged such that the edges 151, 152, 153, 154 delimiting the polyhedral surface 125 in an equal ratio into the edge sections 136122, 122137, 123138, 137123, 124139, 138124, 139121, 1211 Subdivide 36 and accordingly move again, evenly translating, so that the following equation applies:

136122/122137 = 123138/137123 = 124139/138124 = 139121/121136

FIG. 7 shows the graph 144 of the planar substructure 120 of the type RH1 formed with the arrows 140, 141, 142, 143 (see also FIG. 11). It identifies the direction of movement of the nodes 121, 122, 123, 124 along the edges 151, 152, 153, 154 of the self-similarly breathing polyhedron surface 125 designed as a diamond 135 (FIG. 6). A sign alone is not sufficient to identify this movement pattern, because not all nodes 121, 122, 123, 124 run around the diamond 135 in the same direction.

8 to 19 show some typical examples of flat or planar substructures which are formed by coupling typical real bodies or mechanisms with typical virtual mechanisms. As shown by way of example in FIGS. 8 to 19, the real bodies can consist of equilateral triangles, isosceles triangles, right-angled triangles, one or more rods, squares, rhombuses, symmetrical polygons and the like, and the real mechanisms can be achieved by coupling the real body mentioned above can be formed with real rotary and / or sliding joints.

Virtual mechanisms comprising typical polyhedral surfaces are formed, for example, with equilateral triangles, right-angled triangles, squares, a rhombus, a symmetrical hexagon, a regular polygon or the like. Depending on the shape of these polyhedron surfaces, the different types of typical substructures 201 to 215 as well as 231 and 233 with their respective short designations are GD = equilateral triangle, RD = right-angled triangle, Q = square, RH = symmetrical rhombus (rhombus), HX = symmetrical hexagon (Hexagon), PT = symmetrical pentagon (pentagon).

The parts of the figures arranged on the right in FIGS. 8 to 13 each show one of the two possible equivalent graphs 216 to 230 and 232 and 234, which can be realized with the real bodies or mechanisms shown on the left.

FIG. 8 shows typical substructures 201, 202, 215, 231 of the GD type, the virtual mechanism of which comprises polyhedron surfaces formed with at least one equilateral triangle. The numerical data following the type designations describe certain typical designs of the real bodies or mechanisms. Accordingly, the substructure 201 of the GD1 type has the real body formed with an equilateral triangle, while the substructure 202 of the GD2 type comprises a real mechanism which is formed with an isosceles triangle and a rod which are coupled via a swivel joint. Substructure 215 of type GD3 is also shown. This has a real mechanism, which is formed with six equilateral triangles, each of which is horizontally overlapping and can be moved in pairs, the triangles being coupled via six rotary joints (cf. also FIGS. 14 to 16). In contrast to the substructures 201 to 214, the substructure 215 has the special feature of the graph 230, which is also characterized by arrows pointing outwards in the center. This means that when the triangular cylinders forming substructure 215 rotate about their common swivel joints, the knots are maintained while maintaining a constant division ratio of the positions of the knots on the edges (51, 52, 53; 151, 152, 153, 154; 256, 257; 316, 317, 318, 319, 320, 321) move certain edge sections, here perpendicular to the edges of the polyhedron surface forming the plane of movement (here an equilateral triangle; see Figs. 14 and 15 and Figs. 18 and 19 ).

Finally, substructure 231 of type GD 4 is shown in FIG. This includes a real mechanism that is formed with two isosceles triangles. These are coupled via a swivel joint arranged at the corner points of the largest angle. As a further special feature, two nodes are now arranged on one edge. As a result, when the nodes move, a non-uniformly translating movement in connection with non-uniform division ratios is achieved. The corresponding graph 232 is characterized in accordance with the movement pattern on one side with two arrows pointing in opposite directions.

If the polyhedron surface or the virtual mechanism according to FIG. 9 is designed as a right-angled triangle and the real body is designed with a right-angled triangle (substructure 203 of the RD1 type), it moves on the hypotenuse of the right-angled triangle or the virtual mechanism nodes are not, but remain in the middle of the hyphotenuse. This is marked with a dot in graph 218 shown on the right in FIG. 9. Furthermore, the substructure 233 of the type RD 2 is shown in FIG. 9, which is designed similarly to the substructure 231 of the type GD 4. This also includes a real mechanism. However, this is formed with two right-angled triangles, which are also coupled via a swivel joint. In this case, two nodes are arranged on an edge, which here corresponds to the hypotenuse of the polyhedron surface formed as a right-angled triangle. Again, when the knots move, a non-uniformly translating movement in connection with non-uniform division ratios is achieved. The associated graph 234 is also characterized by two arrows pointing in opposite directions.

FIG. 10 shows typical substructures 204, 205, 206, 207 of type Q, the virtual mechanism of which comprises square polyhedron surfaces which are coupled to different real structures. The graphs 219, 220, 221, 222 that can be achieved with it are each shown on the right. In the case of the substructure 204 of the type Q1, a square is also provided as the real body. In the case of substructure 205 of type Q2, a real mechanism is provided, two right-angled triangles being coupled to one another via a swivel joint. The Q3 substructure 206 is characterized by a real mechanism consisting of two bars coupled by a swivel. The Q4 substructure has a real mechanism that is formed with four right-angled triangles. In this case, two of the triangles are coupled at the corner points of their cathets via a swivel joint to form a pair of triangles. These pairs of triangles are coupled to each other at one of their corner points of their hypotenuses, forming a closed kinematic loop via two further swivel joints.

FIG. 11 shows typical substructures 208, 209, 210, 211 of the RH type, the virtual mechanism of which comprises polyhedron surfaces formed with a rhombus. The movement patterns assigned to the individual substructures 208, 209, 210, 211 of the types RH1, RH2, RH3, RH4 are based on the graphs 223, 224, 225, 226 each illustrated on the right. The substructure 208 of the type HR1 has the real mechanism formed by two equilateral triangles, the two equilateral triangles being coupled to one another by a swivel joint. In the case of substructure 209 of type RH2, this also has the real mechanism formed with equilateral triangles. However, the triangles are coupled by two rods, each with swivel joints attached to their ends. These swivel joints are arranged on the one hand at the corners or ends of the equilateral triangles which do not form nodes, and on the other hand in the center of gravity of the adjacent equilateral triangle. The substructure 210 of the RH 3 type is configured similarly to the substructure Q 4 (FIG. 10). The substructure RH 3 also has a real mechanism which is formed with four right-angled triangles. Two of the triangles are coupled to a triangle pair at the corner points of their cathets via a swivel joint. These triangular pairs are forming a closed kinematic

Loop coupled to each other at one of your corner points of your hypotenuses via two further swivel joints. The substructure 211 of the RH4 type has a real mechanism which is formed with two crossing bars which are coupled to one another with a swivel joint arranged in the region of the intersection of the bars.

The typical HX1 type substructure 212 shown in FIG. 12 is a hexagon derived substructure. This is formed by coupling a real body designed as a symmetrical hexagon with the straight lines of the edges of the polyhedral surface of the symmetrical hexagon forming the virtual mechanism. One of the graphs 227 that can be achieved in this way is illustrated on the right in FIG. 12.

Further examples of typical substructures 213, 214 of the PT type with virtual mechanisms which comprise polyhedral surfaces designed as any symmetrical pentagons or pentagons are shown in FIG. 13. According to the real structures that can be selected or selected there, the associated gene graphs 228, 229 each shown on the right. Similar to the substructure HX1, the substructure 213 of the type PT1 is formed by coupling a real body with the straight edges of the polyhedron surface forming the virtual mechanism. However, the real body is now a symmetrical pentagon and the polyhedron surface is designed as a symmetrical pentagon. One of the graphs 228 that can be achieved in this way is illustrated in FIG. 13 at the top right. Finally, the particularly advantageous star-shaped substructure PT2 is shown in FIG. 13 below. This is formed by coupling a real mechanism formed with 10 isosceles triangles with the straight edges of the polyhedron surface forming the virtual mechanism in the form of a symmetrical pentagon. The triangles are coupled in groups of two triangles each via the swivel joints attached to one of their corner points of their greatest angle. The respective other corner points of their largest angle are each coupled via a swivel joint formed with a knot. One of the graphs 229 that can be achieved in this way is illustrated in FIG. 12 at the bottom right. It follows that the substructure PT2 has two degrees of freedom. First of all, the real mechanism formed with the isosceles triangles can be rotated about a central axis of rotation 236 perpendicular to the plane of movement or the polyhedron surface, so that the nodes move along the edges of the polyhedron surface. In addition, when the triangles forming substructure 214 rotate about their common swivel joints, the nodes can move while maintaining a constant division ratio of edge sections determined by the positions of the nodes on the edges, that is to say here perpendicular to the edges as a symmetrical pentagon designed polyhedron surface. This possibility of movement is illustrated by the centrally pointing arrows of graph 229.

For the sake of clarity, two preferred typical substructures 215, 216 are shown in three-dimensional oblique view in different movement positions in FIGS. 14 to 19. FIGS. 14 to 16 show the substructure 215 of the GD type. This is designed with a real mechanism, which has the six triangular cylinders 264, 265, 266, 267, 268, 269, which overlap each other horizontally in pairs and are formed with equilateral triangles. Each triangular cylinder is coupled to three further triangular cylinders via swivel joints. The structural change associated with a movement of the triangular cylinders 264, 265, 266, 267, 268, 269 forming the substructure 215 and the “breathing” of the associated movement plane 270, which is designed here as an equilateral triangle, can be clearly seen as a sequence of FIGS. 14 to 16. FIG. 14 shows the minimal spatial extent of the plane of motion 270 that can be achieved with the selected triangular cylinders 264, 265, 266, 267, 268, 269. An intermediate position is shown in FIG. 15 in which a self-similar enlargement of the polyhedron surface forming the plane of movement is achieved solely by rotating the triangular cylinders relative to one another about their respective common rotary joints. In this case, the nodes do not move along the

Edges of the polyhedron surface. FIG. 16 shows a further intermediate position of the substructure, in which, starting from FIG. 15, the assigned movement plane takes up an even larger area through a central rotation of all triangular cylinders about the central axis 287 which is normal to the movement plane. The nodes move along the edges of the polyhedron surface. It goes without saying that the aforementioned possibilities of movement can also be combined as desired. As a result, the "breathing" of the mechanism, that is to say the self- or geometrically similar change in size of the polyhedron surface in connection with a specific movement pattern of the real body or of the real mechanism, can be effected in accordance with the user wishes.

FIGS. 17 to 19 show the substructure 235 of the HX type. This is designed with a real mechanism that has the twelve triangular cylinders 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, which overlap each other in pairs horizontally and are formed with isosceles triangles. There are two triangular cylinders at a corner points above each Swivel joint coupled. The structural change associated with a movement of the triangular cylinders 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286 forming the substructure 235 and the "breathing" of the associated movement plane 290, which is designed here as a symmetrical hexagon is clearly recognizable as a sequence of FIGS. 17 to 19. FIG. 19 shows the minimum spatial extent that can be achieved with the selected triangular cylinders 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286 and FIG. 19 shows the maximum possible extent of the movement plane 290. 18 shows a three-dimensional oblique view of the substructure 235 according to FIG. 17, in an intermediate position, the self-similar enlargement of the

Hexagonal polyhedron surface is initially achieved only by a central rotation of all cylindrical triangles about the central axis 297, which is normal to the plane of movement. A further enlargement of the polyhedron surface can be achieved by rotating the triangular cylinders relative to one another about their respective common swivel joints without the nodes moving along the edges of the polyhedron surface, the maximum extent of the polyhedron surface or the plane of movement shown in FIG. 19 being achievable is.

The design and configuration of the hinges 240 is described below with reference to FIG. 20. The hinges 240 have the two axes of rotation 241 and 242. These are rigidly coupled to one another in such a way that they intersect at an intersection 244 formed with one of the nodes and have at least one degree of freedom. However, it goes without saying that the axes of rotation 241 and 242 can also be designed skew to one another. Furthermore, the axes of rotation 241 and 242 each take a constant, that is to say time-invariant, position relative to one another, so that the axis angle 246 is also constant. This axis angle 246 is typical for the adjacent polyhedron surfaces 251, 252 formed as movement planes 247, 248 for the nodes 243. These are schematized here as triangles. 20 illustrates how the hinge 240 designed as a double hinge with the two adjacent real mechanisms 253 and 254 forms a spatial mechanism 255 is coupled. The two axes of rotation 241 and 242 of the hinge 240 are always perpendicular or normal to the respective movement plane 247 or 248 of the node, which can move along the coincident edges 256, 257 of the polyhedron surfaces 251, 252. In the exemplary embodiment shown in FIG. 20, the movement planes 247, 248 and the substructure planes 258, 259 arranged parallel to them coincide. However, it goes without saying that the movement planes 247, 248 and the substructure planes 258, 259 can also each have a distance from one another, these distances also being able to be of different sizes.

The method for synthesizing the polyhedron mechanism is first explained in general below and then in more detail using an exemplary embodiment.

The starting point for producing a self-similar polyhedron mechanism is one or more rigid polyhedra which are formed with a predeterminable number of polyhedron surfaces with a predeterminable shape. If the polyhedron with its polyhedron surfaces is selected, the graphs are entered in the form of directional arrows on the straight edges of the polyhedron surfaces, whereby not all edges of the polyhedron need to be provided with directional arrows and the polyhedron also need not be completely closed with polyhedron surfaces. The direction of movement of the nodes is thus determined by defining the graphs. Subsequently, the substructures suitable for realizing these graphs can be selected with the real structures, for example using the types of substructures 201 to 215, 231 and 235 shown in FIGS. 8 to 19.

Finally, for each pair of two abutting polyhedron surfaces that form the planes of motion for the nodes, the angle enclosed by these planes is determined. This can easily be determined graphically or mathematically using conventional geometry. The ever because the associated axis angle of the double hinge corresponds to the angle enclosed between the levels. These hinge angles are determined for all adjacent or abutting polyhedron surfaces or movement planes.

In the following, the respective hinges are selected according to the wishes of the users,

Thrust, rotary push and / or screw hinges can be provided. Finally, the polyhedron mechanism is assembled or synthesized from the hinges and the real structures of the substructures in accordance with the previously defined plan.

The polyhedron mechanisms described in the exemplary embodiments are characterized in that their polyhedron surfaces do not have to be designed as real material bodies, but rather can be designed to be virtual, that is to say invisible. The edges of the polyhedron surfaces are part of a virtual mechanism. However, the virtual mechanisms or the polyhedron surfaces can remain visible when the polyhedron mechanism moves. This results when the nodes are along the invisible, i.e. Move virtual edges of the polyhedron surfaces along, so that the viewer of the polyhedron mechanism can see the edges of the polyhedron surfaces that are not visible per se and consequently the breathing, self-similar size change of the polyhedron surfaces.

The method for manufacturing a basic polyhedron mechanism 310 and the shape of this polyhedron mechanism 310 will be explained below with reference to FIGS. 21 to 23.

The polyhedron mechanism 310 is based on the polyhedron 350 designed as a tetrahedron 311, which is shown in FIGS. 21 and 22 with the aid of thin solid lines. The polyhedron 350 has the four polyhedron surfaces 312, 313, 314, 315 formed with equilateral triangles. Based on this selection the shape (equilateral triangles) and spatial position (tetrahedron) of the polyhedron surfaces 312, 313, 314, 315 are consequently fixed. Corresponding to the number of the six edges 316, 317, 318, 319, 320, 321 of the tetrahedron 311, the six nodes 322, 323, 325, 326, 327 are provided, which are also the hinges 328, 329, 330, 331, 332, 333 train (Fig. 23). Consequently, in this exemplary embodiment, the movement planes of the nodes 322, 323, 324, 325, 326, 327 and the substructure planes formed with the real bodies or mechanisms correspond to the respective polyhedron surfaces 312, 313, 314, 315. The nodes 322, 323, 324, 325, 326, 327 can move along the straight edges 316, 317, 318, 319, 320, 321 of the tetrahedron 311, the edges 316, 317, 318, 319, 320, 321 being the Bars 362, 363, 364, 365, 366, 367 of the virtual

Form mechanisms 371, 372, 373, 374 that intersect at intersections 376, 377, 378, 379.

After the shape and spatial position of the polyhedron surfaces 312, 313, 314, 315 forming the tetrahedron 311 are selected, as illustrated in FIG. 21, the

The directions of movement of the nodes are determined via the graphs 338, 339, 340, 341 provided with the arrows 334, 335, 336, 337.

Subsequently, the substructures suitable for realizing the movement pattern defined with the graphs 338, 339, 340, 341 are selected. The substructures of the GD type shown in FIG. 8 and described above are available for this purpose. In the present case, two substructures 342, 343 of type GD1 and two substructures 344, 345 of type GD2 are used to implement the movement pattern defined with graphs 338, 339, 340, 341. As shown in particular in FIG. 22, the planar substructures 342, 343 of the GD1 type with the real, flat and equilateral triangles 346, 347 and the virtual ones, the edges 316, 317, 318, 319, 321 of the tetrahedral surfaces (polyhedron surfaces 312, 313) comprehensive virtual mechanisms. The panar substructures 344, 345 of the As can be seen in particular from FIG. 21, types GD 2 are each with the isosceles triangles 351, 352, which form the real mechanisms, the bars 355, 356 coupled to them via the swivel joints 353, 354 and also with the virtual ones, the edges 316 , 317, 319, 320, 321 of the tetrahedral surfaces (polyhedron surfaces 314, 315) comprising virtual mechanisms. The respective rotary joints 353, 354, which serve for the coupling between the triangles 351, 352 and the rods 355, 356 of the substructures 344, 345 of the GD2 type, are also shown in FIGS. 21 to 23.

The axis angles of the hinges are determined during or after the selection of the substructures 342, 343, 344, 345. For this purpose, the angle between the abutting polyhedron surfaces 312, 313, 314, 315 must first be determined. This can easily be done arithmetically or with the help of the graphical methods known from geometry theory. It follows from this that the angle between the tetrahedral surfaces 312, 313, 314, 315 is in each case approximately 70.5 degrees. This angle corresponds to the axis angle of the individual hinges 328, 329, 330, 331, 332, 333.

Then the hinges 328, 329, 330, 331, 332, 333 are selected, which in the present case are designed as pure rotary hinges, that is to say as hinges with one degree of freedom.

The polyhedron mechanism 310 is then assembled from the above-mentioned real bodies (triangles 346, 347) or mechanisms (triangles 351, 352, pivot joints 353, 354, rods 355, 356) to form the tetrahedroid 360 shown in FIG.

Particularly advantageous embodiments of relatively complex polyhedron mechanisms are shown in Figs. 24-29. The polyhedron mechanisms 400, 500 shown there are each based on a polyhedron in the form of a truncated icosahedron or a soccer ball. Its polyhedron surfaces are designed with pentagons and hexagons, which each form the planes of motion for the nodes.

The in Figs. 24 to 26 shown polyhedron mechanism 400 is designed with substructures of the type GD3 (see also FIG. 8), each with six equilateral triangular cylinders, and with substructures of the type PT1 (see also FIG. 13), each with a symmetrical pentagonal cylinder. The substructures of type GD3 are each designed with a real mechanism, which has six triangular cylinders, each overlapping horizontally in pairs and formed with equilateral triangles (see FIGS. 14 to 16), two of the triangular cylinders being coupled with rotary hinges.

The sequence of FIGS. 24 to 26 clearly shows the "breathing" of the polyhedron mechanism 400, which occurs when the polyhedron mechanism 400 or parts thereof are moved. The truncated icosahedron shown in FIG. 24 assumes a position in which the associated polyhedron surfaces, which are designed as regular pentagons or hexagons, occupy a minimal area, so that the bodies forming the polyhedron mechanism 400 enclose a minimal volume. FIG. 25 shows a three-dimensional oblique image of the polyhedron mechanism 400 according to FIG. 24, in an intermediate position in which a self-similar enlargement of the polyhedron surfaces forming the planes of movement is achieved by rotating at least one of the pentagonal cylinders about a central axis of rotation arranged normal to the plane of movement. To better illustrate the "breathing" of the polyhedron mechanism, the edges delimiting the polyhedron surfaces are shown as solid black lines. In Fig. 26, the planes of movement occupy a maximum area so that the bodies forming the polyhedron mechanism 400 enclose a maximum volume.

The in Figs. The polyhedron mechanism 500 shown in FIGS. 27 to 29 is likewise designed as an icosahedron stump (soccer ball) and has substructures of the type PT2 (see also FIG. 13) and substructures of the type HX. The substructure Ren of the type PT 2 are each designed with a real mechanism, which comprises ten, triangular cylinders arranged in a star shape, each overlapping in pairs horizontally, formed with isosceles triangles. The substructures of the HX type are each designed with a real mechanism, which comprises twelve triangular cylinders arranged in a star shape, each overlapping in pairs horizontally and formed with isosceles triangles (cf. FIGS. 17 to 19).

In the position shown in FIG. 27, the polyhedron mechanism 500 assumes a position in which the associated polyhedron surfaces formed as pentagons or hexagons take up a minimal area, so that the bodies arranged in a star shape forming the polyhedron mechanism 500 enclose a minimal volume. The intermediate position shown in FIG. 28 with self-similarly enlarged polyhedron surfaces is achieved by rotating at least one of the star-shaped real mechanisms about a central axis of rotation arranged normally to the associated movement plane. To better illustrate the

"Breathing" of the polyhedron mechanism, in turn, the edges delimiting the polyhedron surfaces are shown as solid black lines. 29 shows the polyhedron mechanism 500 in a position in which the movement planes or the polyhedron surfaces take up a maximum area, so that the bodies forming the polyhedron mechanism 500 enclose a maximum volume.

Claims

PATENT CLAIMS

1. polyhedron mechanism with articulated, essentially rigid bodies and body-fixed nodes, which move when the polyhedron mechanism is moved, forming movement planes (247, 248, 270, 290), each with edges (51, 52, 53; 151, 152, 153, 154; 256, 257; 316, 317, 318, 319, 320, 321) of a polyhedron (350) limited polyhedron surfaces (25; 125, 251, 252; 274; 298; 312, 313, 314,

315) are formed, with respective sub-structures (20; 60; 120; 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212) assigned to each of the adjacent movement planes (247, 248) and containing the body , 213, 214, 215, 231, 233, 235; 342, 343, 344, 345) with the nodes (21, 22, 23; 61, 62, 63; 121, 122, 123, 124; 243; 322, 324 , 325, 326, 327) forming hinges (240; 328, 329, 330, 331, 332, 333) are connected to form closed kinematic loops such that rotation of the adjacent substructures (20; 60; 120; 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 231, 233, 235; 342, 343, 344, 345) around their respective common edges (51, 52, 53; 151, 152, 153,

154; 256, 257; 316, 317, 318, 319, 320, 321) of the polyhedron (350) is blocked, so that the spatial angular position of the movement planes (247, 248, 270, 290) remains essentially the same, while the polyhedron surfaces (25; 125, 251, 252; 274; 298; 312, 313, 314, 315) undergo a geometrically fresh or self-similar size change, preferably a central extension.

2. Polyhedron mechanism according to claim 1, characterized in that the hinges (240; 328, 329, 330, 331, 332, 333) have at least two axes of rotation (241, 242), which each take a constant axis angle (246) to each other and skewed are formed to each other or intersect at an intersection (244) and are normally on one of the adjacent planes of movement (247, 248).

3. Polyhedron mechanism according to one of claims 1 or 2, characterized in that when the polyhedron mechanism (310; 400; 500) moves, at least some of the nodes (21, 22, 23; 61, 62, 63; 121,

122, 123, 124; 243; 322, 324, 325, 326, 327) in certain directions along the edges (51, 52, 53; 151, 152, 153, 154; 256, 257; 316, 317, 318, 319, 320, 321) of the with the Polyhedron surfaces (25; 125; 251, 252; 274; 298; 312, 313, 314, 315) formed polyhedron (350) and / or moved while maintaining a constant division ratio of edge sections determined by the positions of the nodes.

4. Polyhedron mechanism according to one of claims 1 to 3, characterized in that at least four polyhedron surfaces (25; 251, 252; 312,

313, 314, 315) and at least six nodes (21, 22, 23; 61, 62, 63; 243; 322, 323, 324, 325, 326, 327) are formed.

5. polyhedron mechanism according to at least one of claims 1 to 4, characterized in that the edges (51, 52, 53; 151, 152, 153, 154;

256, 257; 316, 317, 318, 319, 320, 321) of the polyhedron surfaces (25; 125; 251, 252; 274; 298; 312, 313, 314, 315) as preferably straight rods (26, 27, 28; 126, 127, 128, 129; 362, 363, 364, 365, 366, 367) are formed, the adjacent bars (26, 27, 28; 126, 127, 128, 129; 362, 363, 364, 365, 366, 367) at an intersection (36, 37, 38;

136, 137, 138, 139; 376, 377, 378, 379) cut.

6. polyhedron mechanism according to at least one of claims 1 to 5, characterized in that the respective one common polyhedron surface (25; 125) associated nodes (21, 22, 23; 61, 62, 63; 121, 122, 123, 124) such are arranged in such a way that the edges (51, 52, 53; 151, 152, 153, 154) delimiting this polyhedron surface (25, 125) in a division ratio (3621/2137, 3722 that depends on the size change of the polyhedron surfaces (25; 125) / 2238, 3823/2335; 3661/6137, 6238/3762, 3863/6336; 136122/122137, 123138/137123, 124139/138124, 139121, 121136).

7. polyhedron mechanism according to at least one of claims 1 to 6, characterized in that the substructures have flat substructure surfaces (258, 259) which are arranged parallel to the movement planes (247, 248), the substructures preferably being flat.

8. polyhedron mechanism according to one of claims 1 to 7, characterized in that the nodes (21, 22, 23; 61, 62, 63, 121, 122, 123, 124; 322, 323, 324, 325, 326, 327) are arranged in the movement planes (247, 248).

9. polyhedron mechanism according to one of claims 1 to 8, characterized in that the hinges (240; 328, 329, 330, 331, 332, 333) are formed with at least two rotary and / or rotary push and / or screw joints.

10. Polyhedron mechanism according to one of claims 1 to 9, characterized in that the substructures (20) are formed with at least one real body (55).

11. Polyhedron mechanism according to one of claims 1 to 10, characterized in that the substructures (60, 120) with at least one rea- len, preferably flat mechanism (95; 155) are formed.

12. Polyhedral mechanism according to claim 10 or 11, characterized in that the real body (55) or the real mechanism (95, 155) is formed with at least one flat body (55, 168, 169).

13. Polyhedron mechanism according to claim 12, characterized in that the flat body (55; 168, 169) is designed as a polygon.

14. Polyhedral mechanism according to at least one of claims 11 to 13, characterized in that the real mechanism is formed with at least two rod-shaped bodies which are coupled to at least one swivel joint.

15. Polyhedral mechanism according to at least one of claims 11 to 14, characterized in that the real mechanism (95) is formed with at least one flat body and at least one rod-shaped body, which are coupled to at least one swivel joint (100).

16. Polyhedral mechanism according to at least one of claims 1 to 15, characterized in that the substructures (20; 60; 120; 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213 , 214, 215, 232, 233, 235; 342, 343, 344, 345) with a virtual mechanism (30; 130; 371, 372, 373, 374).

17. Polyhedral mechanism according to claim 16, characterized in that the virtual mechanism (30; 130; 371, 372, 373, 374) with preferably the edges (51, 52, 53; 151, 152, 153, 154; 316, 317, 318, 319, 320, 321) containing rods (26, 27, 28; 126, 127, 128, 129) via sliding joints

(31, 32, 33; 131, 132, 133, 134) is coupled in such a way that a closed kinematic loop is formed.

18. The polyhedron mechanism according to at least one of claims 1 to 17, characterized in that when a substructure assigned to a specific movement plane, preferably fixed to the movement plane, moves, the nodes assigned to it along the edges of a geometrically or self-similar size change undergoing, preferably move centrically extending polyhedron surface as if they were articulation points of a virtual rotary thrust joint, each having an axis of rotation perpendicular to the plane of movement and a thrust axis along the relevant edge, the rotary thrust joint connecting the substructure to a virtual mechanism which is fixed at the plane of movement and which acts as thrust axes contains imaginary edges of the polyhedron surface as bodies and the corner points of the polyhedron surface as adjacent edges connecting thrust joints.

19. Polyhedron mechanism according to at least one of claims 1 to 18, characterized in that the polyhedron is designed as a Platonic, Archimedean, uniform and / or regular polyhedron.

20. Polyhedron mechanism according to at least one of claims 1 to 19, characterized in that the polyhedron mechanism with several

Polyhedra is formed.

21. A method for producing a polyhedron mechanism with articulated coupled substantially rigid bodies and body-fixed nodes, according to one of claims 1 to 20, wherein the nodes move when the polyhedron mechanism is moved with the formation of movement planes (247, 248) in a predeterminable direction of movement, the planes of movement (247, 248, 270, 290) each having edges (51, 52, 53; 151, 152, 153, 154; 256, 257; 316, 317, 318, 319, 320, 321) of at least one polyhedron (350) limited predeterminable polyhedron surfaces (25; 125, 251, 252; 274; 298; 312, 313, 314, 315) are formed, with adjacent planes of movement (247, 248) being assigned in each case. nete, predeterminable substructures containing the body (20; 60; 120; 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213,

214, 215, 231, 233, 235; 342, 343, 344, 345) with the predeterminable hinges (240; 23; 32; 323; 328, 329, 330, 331, 332, 333) are connected to form closed kinematic loops such that rotation of the adjacent substructures (20; 60; 120; 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214,

215, 231, 233, 235; 342, 343, 344, 345) around their respective common edges (51, 52, 53; 151, 152, 153, 154; 256, 257; 316, 317, 318, 319, 320,

321) of the polyhedron (350) is blocked, so that the spatial angular position of the movement planes (247, 248, 270, 290) remains essentially the same, while the polyhedron surfaces (25; 125, 251, 252; 274; 298;

312, 313, 314, 315) undergo a geometrically or self-similar change in size, preferably a central stretching, the shape and spatial position of the polyhedron surfaces (312,

313, 314, 315) of the polyhedron (350) are selected, subsequently the direction of movement of the nodes (322, 323, 324, 325, 326, 327) as well as the suitable substructures (342, 343, 344, 345) and the hinges ( 328, 329, 330, 331) are selected and then the polyhedron mechanism (310) is composed of the substructures (342, 343, 344, 345) and the hinges (328, 329, 330, 331).

22. A method for producing a polyhedron mechanism according to claim 21, characterized in that the hinges (240; 328, 329, 330, 331,

332, 333) have at least two axes of rotation (241, 242), which each take a constant axis angle (246) to each other and are skewed to one another or intersect at an intersection (244), each hinge being selected such that its axis angle ( 246) corresponds to the angle between the normals of the respectively adjacent movement planes (247, 248).