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ES2321052A1 - Union of four obstacle rectangular prisms and square section. (Machine-translation by Google Translate, not legally binding) - Google Patents

Union of four obstacle rectangular prisms and square section. (Machine-translation by Google Translate, not legally binding) Download PDF

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Publication number
ES2321052A1
ES2321052A1 ES200800890A ES200800890A ES2321052A1 ES 2321052 A1 ES2321052 A1 ES 2321052A1 ES 200800890 A ES200800890 A ES 200800890A ES 200800890 A ES200800890 A ES 200800890A ES 2321052 A1 ES2321052 A1 ES 2321052A1
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prism
equal
square
section
notches
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ES200800890A
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ES2321052B1 (en
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Jesus Molina Martinez
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Priority to ES200800890A priority Critical patent/ES2321052B1/en
Priority to ES200802625A priority patent/ES2324510B1/en
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    • A—HUMAN NECESSITIES
    • A63—SPORTS; GAMES; AMUSEMENTS
    • A63H—TOYS, e.g. TOPS, DOLLS, HOOPS OR BUILDING BLOCKS
    • A63H33/00—Other toys
    • A63H33/04—Building blocks, strips, or similar building parts
    • A63H33/06—Building blocks, strips, or similar building parts to be assembled without the use of additional elements
    • A63H33/08—Building blocks, strips, or similar building parts to be assembled without the use of additional elements provided with complementary holes, grooves, or protuberances, e.g. dovetails
    • A63H33/084—Building blocks, strips, or similar building parts to be assembled without the use of additional elements provided with complementary holes, grooves, or protuberances, e.g. dovetails with grooves
    • E—FIXED CONSTRUCTIONS
    • E04—BUILDING
    • E04B—GENERAL BUILDING CONSTRUCTIONS; WALLS, e.g. PARTITIONS; ROOFS; FLOORS; CEILINGS; INSULATION OR OTHER PROTECTION OF BUILDINGS
    • E04B1/00—Constructions in general; Structures which are not restricted either to walls, e.g. partitions, or floors or ceilings or roofs
    • E04B1/18—Structures comprising elongated load-supporting parts, e.g. columns, girders, skeletons
    • E04B1/19—Three-dimensional framework structures
    • E04B1/1903—Connecting nodes specially adapted therefor

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  • Engineering & Computer Science (AREA)
  • Architecture (AREA)
  • Physics & Mathematics (AREA)
  • Electromagnetism (AREA)
  • Civil Engineering (AREA)
  • Structural Engineering (AREA)
  • Toys (AREA)

Abstract

The present invention relates to the unión of four rectangular prisms oblique, square section. This connection is made possible by practicing a notch in each of the upper and lower faces of the prism, so that the two cutting planes are located in the same horizontal plane. Each of these notches is formed by a right dihedral angle. In this way once the four pieces are assembled, their four contact surfaces will be in the same horizontal plane. The angle of inclination of the prism is determined by a right triangle inscribed in a circle whose hypotenuse coincides with its diameter, which is equal to the square of the section of the prism. By practicing several pairs of notches along a prism, a three-dimensional network is formed. A singular case is, a construction, equal to a dodecahedron rhomb that tesela the space. (Machine-translation by Google Translate, not legally binding)

Description

Unión de cuatro prismas rectangulares oblicuos y de sección cuadrada.Union of four oblique rectangular prisms and of square section.

Sector de la técnicaTechnical sector

La invención se encuentra en el sector técnico de la arquitectura y la ingeniería, así como inédito en el campo de la geometría espacial.The invention is in the technical sector of architecture and engineering, as well as unpublished in the field of spatial geometry

Estado de la técnicaState of the art

En la actualidad existen diferentes formas de unir o superponer varios perfiles lineales que se cruzan en un mismo punto. En las primeras construcciones con piezas que debían encontrarse o cruzarse se usó el roblón para unir las diferentes piezas de arriostramiento. Mas tarde, estas piezas son abrazadas por dos placas que "moldean" su superficie al relieve del nudo generado por las secciones de los perfiles. Estas dos placas se atornillan entre sí, o se fijan a las piezas constructivas; generalmente componentes de una estructura metálica. Hoy existen sofisticados sistemas de arriostrar mediante un anclaje, un cable y un tensor del cable, que hace posible la transparencia de la arquitectura de acero y vidrio, restando importancia a los puntos de unión estructurales, pues parte de los esfuerzos los asumen estos cables tensores.There are currently different ways of join or overlap several linear profiles that intersect in a same point. In the first constructions with parts that were due meet or cross the roblón was used to join the different bracing pieces. Later, these pieces are embraced by two plates that "mold" its surface to the relief of the knot generated by sections of profiles. These two plates are screwed together, or fixed to the construction pieces; generally components of a metal structure. Today they exist sophisticated bracing systems using an anchor, a cable and a cable tensioner, which makes the transparency of the steel and glass architecture, downplaying the points of structural union, as part of the efforts assume them these tension cables.

La presente invención soluciona el encuentro y ensamblaje de cuatro prismas oblicuos (vigas o componentes de una estructura arquitectónica) que se cruzan sin necesitar de elementos complementarios para su sujeción y regida por leyes geométricas que determinan una combinatoria muy variada y diferenciada en posibilidades compositivas del espacio tridimensional.The present invention solves the encounter and assembly of four oblique prisms (beams or components of one architectural structure) that intersect without needing elements complementary for its subjection and governed by geometric laws that they determine a very varied and differentiated combinatorial in compositional possibilities of three-dimensional space.

Descripción detallada de la invenciónDetailed description of the invention

La presente invención se refiere a la unión de cuatro prismas rectangulares oblicuos, de sección cuadrada, y perpendiculares entre sí.The present invention relates to the union of four oblique rectangular prisms, of square section, and perpendicular to each other.

Todas las condiciones geométricas que se dan para la unión de estos cuatro prismas tienen que ver con el lado del cuadrado que forma la sección del prisma; para no repetirlo constantemente lo llamaré L.All geometric conditions that occur for the union of these four prisms they have to do with the side of the square that forms the prism section; not to repeat it I will constantly call it L.

Cada uno de estos prismas tiene dos entalladuras, una en la cara superior y otra en la inferior. Cada una de estas entalladuras está formada por dos planos perpendiculares entre sí: un cuadrado horizontal (6) de igual magnitud que la sección del prisma, y un rectángulo vertical (8) cuyo lado mayor es igual al del cuadrado, coincidiendo con este y formando así un ángulo diedro recto. De esta manera una vez ensambladas las cuatro piezas, sus cuatro superficies de apoyo serán cuatro cuadrados situados en el mismo plano horizontal, separados entre si una distancia igual al lado del cuadrado de la sección del prisma.Each of these prisms has two notches, one on the upper face and one on the lower. Every one of these notches is formed by two planes perpendicular to each other: a horizontal square (6) of equal magnitude than the prism section, and a vertical rectangle (8) whose major side is equal to that of the square, coinciding with this and thus forming a right dihedral angle. This way once assembled the four pieces, their four support surfaces they will be four squares located in the same horizontal plane, separated from each other a distance equal to the square of the prism section

El ángulo de inclinación del prisma Fig. 1a es igual al formado por la hipotenusa y el cateto mayor de un triángulo rectángulo que se genera mediante la intersección de dos circunferencias; una mayor de diámetro igual a 3/2 de L, y otra menor de diámetro igual a L, y con centro en un extremo del diámetro de la circunferencia mayor. Dicho triángulo es rectángulo, siendo el ángulo que forma el cateto mayor con la hipotenusa igual al ángulo de inclinación de los cuatro prismas de esta invención. Esta primera condición implica una segunda: vista la pieza en alzado Fig. 1b las dos líneas de corte en sus caras superior e inferior, dibujan en su cara frontal una sola línea que contiene a los dos segmentos de ambas entalladuras y cuya dimensión es tres veces mayor que uno de los segmentos.The angle of inclination of the prism Fig. 1a is equal to that formed by the hypotenuse and the greater leg of a right triangle that is generated by the intersection of two circumferences; a larger diameter equal to 3/2 of L, and another smaller in diameter equal to L, and centered at one end of the diameter of the major circumference. Said triangle is rectangle, being the angle formed by the greater leg with the hypotenuse equal to tilt angle of the four prisms of this invention. This first condition implies a second: view the elevation Fig. 1b the two cut lines on their upper and lower faces, they draw on their front face a single line that contains the two segments of both notches and whose dimension is three times greater than one of the segments.

Estas tres condiciones: Ángulo de inclinación del prisma. Entalladuras situadas en un mismo plano horizontal. Y una separación entre dos prismas igual a la longitud del lado del cuadrado de la sección del prisma, hacen posible el ensamblaje de estas cuatro piezas. Manteniéndose fija su posición estática siempre que sus extremos inferiores apoyen en el plano horizontal del suelo.These three conditions: Tilt angle of the prism Notches located in the same horizontal plane. Y a separation between two prisms equal to the length of the side of the square of the prism section, make the assembly of These four pieces. Keeping his static position fixed provided that its lower ends rest on the horizontal plane ground.

Todo esto se cumple independientemente de la escala y de los materiales.All this is accomplished regardless of the Scale and materials.

Si se prolongan los extremos superiores de las cuatro piezas que forman el nudo y se realizan varias entalladuras a lo largo de sus caras superior e inferior y a una distancia igual en las cuatro piezas; se puede construir una red tridimensional en el espacio.If the upper ends of the four pieces that form the knot and several notches are made along their upper and lower faces and at an equal distance in the four pieces; you can build a three-dimensional network in the space.

Un caso singular de este nudo es la construcción de un rombo dodecaedro, donde ocho de sus rombos iguales tienen ángulos de 84º y 96º. Siendo los ángulos de los otros cuatro rombos de 141º y 39º. Materializando las aristas de este poliedro por piezas lineales de sección cuadrada; y sus vértices por el nudo que reúne a cuatro de estas piezas, queda construido un armazón cuyas características geométricas coinciden con las de un rombo dodecaedro.A unique case of this knot is the construction of a dodecahedron rhombus, where eight of its equal rhombuses have 84º and 96º angles. Being the angles of the other four rhombuses of 141º and 39º. Materializing the edges of this polyhedron by linear pieces of square section; and its vertices by the knot that it brings together four of these pieces, a frame is built whose geometric features match those of a rhombus dodecahedron.

Esta composición tesela el espacio tridimensional; para ello hay que sustituir las piezas de un solo par de entalladuras por otras de mayor longitud y varias entalladuras a lo largo de las caras superior e inferior.This composition tiles the space three-dimensional; to do this you have to replace the pieces of a single pair of notches for others of greater length and several notches along the upper and lower faces.

Descripción de las figurasDescription of the figures

La Fig. 1a representa el trazado del ángulo del prisma. La Fig. 1b, el alzado del prisma con el trazado de las entalladuras. Y una perspectiva del prisma con las dos entalladuras Fig. 1c.Fig. 1a represents the plot of the angle of the prism. Fig. 1b, the elevation of the prism with the layout of the notches And a perspective of the prism with the two notches Fig. 1c.

El ángulo de inclinación del prisma (1) es igual al formado por la hipotenusa y el cateto mayor de un triángulo rectángulo que se genera mediante la intersección de dos circunferencias; una mayor de diámetro igual a 3/2 de L, y otra menor de diámetro igual a L y con centro en un extremo del diámetro de la circunferencia mayor. Siendo la hipotenusa (2) igual al diámetro de la circunferencia mayor; y el cateto mayor (3) la línea que une el otro extremo de dicho diámetro con el punto de intersección de las dos circunferencias. Por tanto la línea que forma el cateto mayor, determina la arista (4) del prisma. Trazando una línea paralela (5) a la primera arista obtenida y a una distancia igual a L, obtenemos la vista en alzado del prisma. Prolongando la línea horizontal de la que forma parte la hipotenusa (2) hasta cortar a la línea (5) obtengo la línea del plano horizontal de corte, que ejecuta uno de los dos planos, el cuadrado horizontal (6), de que consta la entalladura. Esta línea horizontal es tres veces mayor que L, y si trazamos cuatro líneas perpendiculares a esta y a una distancia una de otra igual a L; las dos líneas paralelas y verticales centrales (7) son las proyecciones de los dos pianos verticales de corte que forman la entalladura (8).The angle of inclination of the prism (1) is equal to the one formed by the hypotenuse and the greater leg of a triangle rectangle that is generated by the intersection of two circumferences; a larger diameter equal to 3/2 of L, and another smaller in diameter equal to L and centered at one end of the diameter of the major circumference. Being the hypotenuse (2) equal to diameter of the largest circumference; and the major leg (3) the line which joins the other end of said diameter with the point of intersection of the two circumferences. Therefore the line that form the major leg, determine the edge (4) of the prism. Tracing a line parallel (5) to the first edge obtained and to a distance equal to L, we get the elevation view of the prism. Extending the horizontal line of which the hypotenuse is part (2) until I cut to the line (5) I get the line of the plane horizontal cut, which runs one of the two planes, the square horizontal (6), which consists of the notch. This horizontal line it is three times greater than L, and if we draw four lines perpendicular to this and at a distance from each other equal to L; the two central parallel and vertical lines (7) are the projections of the two vertical cutting pianos that form the notch (8).

La Figura 2 es una perspectiva de la unión de las cuatro piezas en posición estática sobre el espacio horizontal.Figure 2 is a perspective of the union of the four pieces in static position on space horizontal.

La Figura 3 representa las cuatro piezas de este nudo con dos pares de entalladuras (10), tres pares de entalladuras (11) y cuatro pares de entalladuras para dar una idea de su aplicación constructiva como elemento estructural (12) y (13).Figure 3 represents the four pieces of this knot with two pairs of notches (10), three pairs of notches (11) and four pairs of notches to give an idea of your constructive application as a structural element (12) and (13).

En la Figura 4 se representa una construcción realizada con este nudo (14) cuyas características geométricas son idénticas a la de un ROMBO DODECAEDRO (15) con idénticos ángulos en sus caras; característica esta del nudo que permite teselar el espacio tridimensional combinando piezas de varias entalladuras a lo largo de la pieza (16).A construction is represented in Figure 4 made with this knot (14) whose geometric characteristics are identical to that of a ROMBO DODECAEDRO (15) with identical angles in their faces; feature is the knot that allows tessellation three-dimensional space combining pieces of several notches to throughout the piece (16).

Claims (4)

1. Unión de cuatro prismas rectangulares oblicuos y de sección cuadrada, caracterizado porque cada uno de estos prismas tiene dos entalladuras, una en la cara superior y otra en la inferior. Cada una de estas entalladuras está formada por dos planos perpendiculares entre sí: un cuadrado horizontal (6) de igual magnitud que la sección del prisma, y un rectángulo (8) vertical cuyo lado mayor es igual al del cuadrado, coincidiendo con este y formando así un ángulo diedro recto. Ensamblados los cuatro prismas, las superficies de apoyo y contacto, son cuatro cuadrados (6) situados en el mismo plano horizontal y separados entre si una distancia igual al lado del cuadrado de la sección del prisma.1. Union of four oblique rectangular prisms and square section, characterized in that each of these prisms has two notches, one on the upper face and one on the lower. Each of these notches is formed by two planes perpendicular to each other: a horizontal square (6) of equal magnitude than the prism section, and a vertical rectangle (8) whose greater side is equal to that of the square, coinciding with this and forming thus a right dihedral angle. Assembled the four prisms, the support and contact surfaces, are four squares (6) located in the same horizontal plane and separated from each other a distance equal to the square side of the prism section. 2. Unión de cuatro prismas rectangulares oblicuos y de sección cuadrada, según reivindicación 1 caracterizada porque el ángulo de inclinación del prisma (1) es igual al formado por la hipotenusa (2) y el cateto mayor (3) de un triángulo rectángulo que se genera mediante la intersección de dos circunferencias; una mayor de diámetro igual a 3/2 del lado de la sección del prisma e igual a la hipotenusa del triángulo rectángulo, y otra menor de diámetro igual a el lado de la sección del prisma y con centro en un extremo del diámetro de la circunferencia mayor, siendo el cateto mayor (3) la línea que une el otro extremo de dicho diámetro con el punto de intersección de las dos circunferencias la que determina una arista del prisma 4, y trazando una línea paralela (5) a la primera arista obtenida y a una distancia igual a el lado de la sección del prisma, obtenemos la otra arista de la cara frontal del prisma. Prolongando la hipotenusa (2), corta a la arista inferior (5) en un punto que define la situación de la entalladura en la cara inferior del prisma. Esta línea horizontal es tres veces mayor que el lado de la sección del prisma, y es también la proyección del plano horizontal y de corte correspondiente al cuadrado horizontal (6) de las entalladuras. Los dos planos verticales del ángulo diedro que forma las entalladuras quedan definidos por las verticales (7) situadas en los extremos del diámetro de la circunferencia menor. Los puntos de intersección de estas líneas (7) con la horizontal y las aristas superior (4) e inferior (5) del prisma, son los extremos de un segmento que es el lado menor del rectángulo (8) que forma la pared vertical de la entalladura.2. Union of four oblique rectangular prisms and of square section, according to claim 1 characterized in that the angle of inclination of the prism (1) is equal to that formed by the hypotenuse (2) and the larger leg (3) of a right triangle generated by the intersection of two circles; a larger one with a diameter equal to 3/2 on the side of the prism section and equal to the hypotenuse of the right triangle, and a smaller one with a diameter equal to the side of the prism section and centered on one end of the diameter of the circumference greater, the greater leg (3) being the line that joins the other end of said diameter with the point of intersection of the two circumferences which determines an edge of prism 4, and drawing a parallel line (5) to the first edge obtained and at an equal distance to the side of the prism section, we get the other edge of the front face of the prism. Prolonging the hypotenuse (2), cut the bottom edge (5) at a point that defines the notch situation on the underside of the prism. This horizontal line is three times larger than the side of the prism section, and is also the projection of the horizontal and cutting plane corresponding to the horizontal square (6) of the notches. The two vertical planes of the dihedral angle that forms the notches are defined by the vertical ones (7) located at the ends of the diameter of the smaller circumference. The points of intersection of these lines (7) with the horizontal and the upper (4) and lower (5) edges of the prism are the ends of a segment that is the smaller side of the rectangle (8) that forms the vertical wall of the notch. 3. Unión de cuatro prismas rectangulares oblicuos y de sección cuadrada según reivindicación 1 y 2 caracterizada porque cada uno de estos prismas puede tener a lo largo de sus caras un número indeterminado de entalladuras separadas entre si la misma distancia, obteniéndose una retícula tridimensional, cuyos huecos son rombos.3. Union of four oblique rectangular prisms and square section according to claim 1 and 2 characterized in that each of these prisms can have along its faces an indeterminate number of notches separated from each other the same distance, obtaining a three-dimensional grid, whose Hollows are rhombuses. 4. Unión de cuatro prismas rectangulares oblicuos y de sección cuadrada según reivindicación 1, 2 y 3 caracterizada porque una de las construcciones tridimensionales que se forma con este ensamblaje es igual a un rombo dodecaedro, formado por ocho y cuatro rombos iguales Fig. 4 (14) y (15).4. Union of four oblique rectangular prisms and of square section according to claim 1, 2 and 3 characterized in that one of the three-dimensional constructions formed with this assembly is equal to a dodecahedron rhombus, formed by eight and four equal rhombuses Fig. 4 ( 14) and (15).
ES200800890A 2008-03-31 2008-03-31 UNION OF FOUR OBLIQUE RECTANGULAR PRISMS AND SQUARE SECTIONS. Expired - Fee Related ES2321052B1 (en)

Priority Applications (2)

Application Number Priority Date Filing Date Title
ES200800890A ES2321052B1 (en) 2008-03-31 2008-03-31 UNION OF FOUR OBLIQUE RECTANGULAR PRISMS AND SQUARE SECTIONS.
ES200802625A ES2324510B1 (en) 2008-03-31 2008-09-16 IMPROVEMENTS IN THE OBJECT OF THE MAIN PATENT P200800890 FOR "UNION OF FOUR OBLIQUE RECTANGULAR SQUARES OF SQUARE SECTION".

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Application Number Priority Date Filing Date Title
ES200800890A ES2321052B1 (en) 2008-03-31 2008-03-31 UNION OF FOUR OBLIQUE RECTANGULAR PRISMS AND SQUARE SECTIONS.

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ES2321052A1 true ES2321052A1 (en) 2009-06-01
ES2321052B1 ES2321052B1 (en) 2010-03-12

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ES200802625A Expired - Fee Related ES2324510B1 (en) 2008-03-31 2008-09-16 IMPROVEMENTS IN THE OBJECT OF THE MAIN PATENT P200800890 FOR "UNION OF FOUR OBLIQUE RECTANGULAR SQUARES OF SQUARE SECTION".

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Families Citing this family (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
DE102013100306A1 (en) * 2013-01-11 2014-07-17 Wilhelm Notte Frame for e.g. desk, has feet connected with one another in connection area over notches, where notches are formed by sectional planes defined by edges of corners of standing surface and edges of intersection and supporting surfaces

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NL7603046A (en) * 1976-03-23 1977-09-27 Anthonius Henrikus Johannus Ma Nodal geodetic building structure - has set of tubes each fitting in slots milled in ends of adjacent ones
US4731962A (en) * 1986-12-24 1988-03-22 Tensegrity Systems Corporation Compression-tension strut-cord units for tensile-integrity structures
WO1989008172A1 (en) * 1988-03-04 1989-09-08 Graham Brown Three-dimensional structures
EP0900890A1 (en) * 1996-05-22 1999-03-10 Taiyo Kogyo Corporation Frame structure and method for forming the same
WO2000055439A2 (en) * 1999-03-03 2000-09-21 Coventry University Module for a space structure and a space structure
US20020081936A1 (en) * 2000-12-21 2002-06-27 Snelson Kenneth D. Space frame structure made by 3-D weaving of rod members

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Publication number Priority date Publication date Assignee Title
US5074502A (en) * 1990-04-19 1991-12-24 Scott Glendinning Universal table base
GB2279867B (en) * 1993-07-12 1997-01-22 Simon Clark Improvements in or relating to support structures
DE102005021521A1 (en) * 2005-05-10 2006-11-16 Joachim Frost Table leg system comprises four bars with triangular notches in their edges, allowing them to interlock at angle so that they form spiral whose top is level

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
NL7603046A (en) * 1976-03-23 1977-09-27 Anthonius Henrikus Johannus Ma Nodal geodetic building structure - has set of tubes each fitting in slots milled in ends of adjacent ones
US4731962A (en) * 1986-12-24 1988-03-22 Tensegrity Systems Corporation Compression-tension strut-cord units for tensile-integrity structures
WO1989008172A1 (en) * 1988-03-04 1989-09-08 Graham Brown Three-dimensional structures
EP0900890A1 (en) * 1996-05-22 1999-03-10 Taiyo Kogyo Corporation Frame structure and method for forming the same
WO2000055439A2 (en) * 1999-03-03 2000-09-21 Coventry University Module for a space structure and a space structure
US20020081936A1 (en) * 2000-12-21 2002-06-27 Snelson Kenneth D. Space frame structure made by 3-D weaving of rod members

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ES2324510A1 (en) 2009-08-07
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