Thingiverse

# Archimedean Pavilion by Robuses

by Thingiverse

Last crawled date: 1 year, 7 months ago

This a printable STL file of the Archimedean Pavilion.

The Archimedean is a ten-point-five-meter-long, six-meter-wide and three-point-five-meter high pavilion, which was installed on the wooden platform between the schools of Architecture and Building Engineering in the University of Seville (Spain). As in the Caterpillar project, the origin of this work lies on the combination of geometric research and teaching innovation, with the intention to carry out a generative model to be used as an Architectural Geometry exercise for both schools' students.

The starting point for this project is the projective interpretation, already made by professor Gentil-Baldrich (Gentil Baldrich, 1997), about the proposition 12 stated by Archimedes of Syracuse (287-212 B.C.) in his work “On Conoids and Spheroids” (Archimedes, 1897). That came to say that the planar section of a paraboloid of revolution, produced by a plane neither parallel nor perpendicular to the axis, is an ellipse. And that the minor axis of the ellipse is equal to the perpendicular distance between the two lines, parallel to the axis of the paraboloid, which pass through the extremes of the major axis. This is just a particular case of a generalised theorem affecting all quadrics of revolutions generated around the axis containing the foci (Martin-Pastor, Narvaez-Rodriguez, & Hernandez-Macias, 2016).

From a projective point of view, the Archimedean statement could be formulated; by using the parallel projection defined by the direction of the axis of the paraboloid, any circle on a plane perpendicular to the axis of the paraboloid is projected onto the paraboloid’s surface as an ellipse, which is a planar curve. This property means, among other interpretations, that any circle-packing arrangement can be projected onto the paraboloid to obtain a discretisation of the surface based on planar elliptical faces or rings tangent to each other at various points of the boundary.

Working on that concept to discretise rotational parabolic surfaces, the Archimedean Pavilion was originally conceived as an exploration of the different spaces generated by four rotational paraboloids under certain conditions with variable position, orientation and parameter. Therefore the result is a single space enclosed by 4 fractions of rotational paraboloids, which can be discretised by using the aforementioned projective interpretation.

The main problem laid on how to materialise the elliptical rings with enough stiffness to generate a kind of porous rigid shell for every paraboloid. The solution chosen, among the infinite possibilities, was based on lightweight conical components (Narvaez-Rodriguez & Barrera-Vera, 2016), which resulted in an very efficient method compare to alternative solutions based on rigidifying the rings by thickening the boundary, since the amount of needed material is about twenty times lower to provide the same rigidity.

Every component is made up of three fractions of conical surface, therefore developable, generating a triangular cross section. It is a system that can be fabricated with the use of laminar materials, thus it is simple to execute and normally fabricated from standard sheets or panels cut with a laser cutter or CNC milling machines. The success of the constructive system, to achieve consistency between the model for the structural analysis and the real execution of the components, relies on the appropriate execution of the three types of joints produced in the structure: (1) the surface seam of the surfaces, which must not coincide with the generators of the cones. (2) The joints between the three conical fractions of every component, which must be executed to ensure continuity. (3) The connection between different components, which should coincide with the tangency line, although the tests carried out revealed the successful use of two points of the line solved with bolts.

Although the system is thought to be carried out with metal sheets or thin wooden panels, the budget limitations took the prototype to be fabricated with one-millimetre-thick sheets of polyethylene (HDPE), whose laminar behaviour is similar in terms of fabrication and assembly, but easier and safer to be manipulated by students. Nevertheless, this material holds some properties which render it as non-appropriate for installations intended to last; non-linear deformation, variable behaviour according the temperature and, mainly, creep or cold flow, which makes it keep deforming when exposed to high levels of stress for long-term periods. In this case the sponsorship of Dow Chemical to fill the components with polyurethane foam allowed the prototype to be exposed for a longer period.

The Archimedean is a ten-point-five-meter-long, six-meter-wide and three-point-five-meter high pavilion, which was installed on the wooden platform between the schools of Architecture and Building Engineering in the University of Seville (Spain). As in the Caterpillar project, the origin of this work lies on the combination of geometric research and teaching innovation, with the intention to carry out a generative model to be used as an Architectural Geometry exercise for both schools' students.

The starting point for this project is the projective interpretation, already made by professor Gentil-Baldrich (Gentil Baldrich, 1997), about the proposition 12 stated by Archimedes of Syracuse (287-212 B.C.) in his work “On Conoids and Spheroids” (Archimedes, 1897). That came to say that the planar section of a paraboloid of revolution, produced by a plane neither parallel nor perpendicular to the axis, is an ellipse. And that the minor axis of the ellipse is equal to the perpendicular distance between the two lines, parallel to the axis of the paraboloid, which pass through the extremes of the major axis. This is just a particular case of a generalised theorem affecting all quadrics of revolutions generated around the axis containing the foci (Martin-Pastor, Narvaez-Rodriguez, & Hernandez-Macias, 2016).

From a projective point of view, the Archimedean statement could be formulated; by using the parallel projection defined by the direction of the axis of the paraboloid, any circle on a plane perpendicular to the axis of the paraboloid is projected onto the paraboloid’s surface as an ellipse, which is a planar curve. This property means, among other interpretations, that any circle-packing arrangement can be projected onto the paraboloid to obtain a discretisation of the surface based on planar elliptical faces or rings tangent to each other at various points of the boundary.

Working on that concept to discretise rotational parabolic surfaces, the Archimedean Pavilion was originally conceived as an exploration of the different spaces generated by four rotational paraboloids under certain conditions with variable position, orientation and parameter. Therefore the result is a single space enclosed by 4 fractions of rotational paraboloids, which can be discretised by using the aforementioned projective interpretation.

The main problem laid on how to materialise the elliptical rings with enough stiffness to generate a kind of porous rigid shell for every paraboloid. The solution chosen, among the infinite possibilities, was based on lightweight conical components (Narvaez-Rodriguez & Barrera-Vera, 2016), which resulted in an very efficient method compare to alternative solutions based on rigidifying the rings by thickening the boundary, since the amount of needed material is about twenty times lower to provide the same rigidity.

Every component is made up of three fractions of conical surface, therefore developable, generating a triangular cross section. It is a system that can be fabricated with the use of laminar materials, thus it is simple to execute and normally fabricated from standard sheets or panels cut with a laser cutter or CNC milling machines. The success of the constructive system, to achieve consistency between the model for the structural analysis and the real execution of the components, relies on the appropriate execution of the three types of joints produced in the structure: (1) the surface seam of the surfaces, which must not coincide with the generators of the cones. (2) The joints between the three conical fractions of every component, which must be executed to ensure continuity. (3) The connection between different components, which should coincide with the tangency line, although the tests carried out revealed the successful use of two points of the line solved with bolts.

Although the system is thought to be carried out with metal sheets or thin wooden panels, the budget limitations took the prototype to be fabricated with one-millimetre-thick sheets of polyethylene (HDPE), whose laminar behaviour is similar in terms of fabrication and assembly, but easier and safer to be manipulated by students. Nevertheless, this material holds some properties which render it as non-appropriate for installations intended to last; non-linear deformation, variable behaviour according the temperature and, mainly, creep or cold flow, which makes it keep deforming when exposed to high levels of stress for long-term periods. In this case the sponsorship of Dow Chemical to fill the components with polyurethane foam allowed the prototype to be exposed for a longer period.

## Similar models

3dwarehouse

free

### Archimedes Trammel Model

...n. the semi-axes a and b of the ellipses have lengths equal to the distances from the point on the rod to each of the two pivots.

grabcad

free

### Trammel of Archimedes (Ellipse Generator Mechanism)

...path. the semi-axes a and b of the ellipse have lengths equal to the distances from the end of the rod to each of the two pivots.

grabcad

free

### ELLIPTICAL TRAMMEL MECHANISM.

...ich is attached to the shuttles by pivots at fixed positions along the rod. ... this circle is also a special case of an ellipse.

grabcad

free

### ELLIPTICAL TRAMMEL Mechanism & Design

...d”)
to perpendicular channels or rails, and a rod which is attached to the
shuttles by pivots at fixed positions along the rod.

thingiverse

free

### conic cone by doghound678

...three conic sections, but if you print out two, you get these three (with a full ellipse) and a hyperbola, another conic section.

grabcad

free

### Trammel of Archimedes

...trammel of archimedes
grabcad
trammel of archimedes is a mechanism that generates the shape of an ellipse.

grabcad

free

### Bevel & Spur Gear Motion

... transfer power from one shaft to another shaft.)
whereas, bevel gear is used to transmit power between two perpendicular shafts.

grabcad

free

### Elliptical Trammel

...tions along the rod. as the shuttles move back and forth, each along its channel, the end of the rod moves in an elliptical path.

grabcad

free

### Archimedes Trammel

...archimedes trammel
grabcad
used to generate the shape of an ellipse

thingiverse

free

### Conic sections by laurent_despeyroux

...39;s surface.
the last one with an angle intermediate between the central one and the one of the parabola illustrate the ellipse.

## Archimedean

turbosquid

free

### Water treatment plant

...filter water from the sea) are more cost-effective solutions.<br><br>1:

**archimedean**screws<br>2: coarse sieve<br>3: fine sieve<br>4: grit chamber<br>5: adding of...turbosquid

$7

### 0008 8-Grid Truncated Icosahedron #Grid 8

...truncated icosahedron #grid 8<br>width 211.607 mm<br>height 214.799 mm<br>depth 206.332 mm<br>

**archimedean**solids: truncated icosahedron has 12 regular pentagonal faces, 20...turbosquid

$7

### 0006 8-Grid Truncated Icosahedron #Grid 6

...truncated icosahedron #grid 6<br>width 161.817 mm<br>height 164.258 mm<br>depth 157.783 mm<br>

**archimedean**solids: truncated icosahedron has 12 regular pentagonal faces, 20...turbosquid

$7

### 0005 8-Grid Truncated Icosahedron #Grid 5

...truncated icosahedron #grid 5<br>width 136.922 mm<br>height 138.988 mm<br>depth 133.509 mm<br>

**archimedean**solids: truncated icosahedron has 12 regular pentagonal faces, 20...turbosquid

free

### 0009 8-Grid Truncated Icosahedron #Grid All (1-8)

...gets bigger as it goes out. there are 8 grids.<br>

**archimedean**solids: truncated icosahedron has 12 regular pentagonal faces, 20...turbosquid

free

### 0003 8-Grid Truncated Icosahedron #Grid 3

...8-grid truncated icosahedron #grid 3<br>width 87.132 mm<br>88.447 mm<br>depth 84.96 mm<br>

**archimedean**solids: truncated icosahedron has 12 regular pentagonal faces, 20...turbosquid

free

### 0001 8-Grid Truncated Icosahedron #Grid 1

...truncated icosahedron #grid 1<br>width 37.342 mm<br>height 37.906 mm<br>depth 36.412 mm<br>

**archimedean**solids: truncated icosahedron has 12 regular pentagonal faces, 20...turbosquid

free

### 0010 8-Grid Truncated Icosahedron #Grid All (1-8)

...gets bigger as it goes out. there are 8 grids.<br>

**archimedean**solids: truncated icosahedron has 12 regular pentagonal faces, 20...turbosquid

free

### 0007 8-Grid Truncated Icosahedron #Grid 7

...truncated icosahedron #grid 7<br>width 186.712 mm<br>height 189.529 mm<br>depth 182.058 mm<br>

**archimedean**solids: truncated icosahedron has 12 regular pentagonal faces, 20...turbosquid

free

### 0004 8-Grid Truncated Icosahedron #Grid 4

...truncated icosahedron #grid 4<br>width 112.027 mm<br>height 113.717 mm<br>depth 109.235 mm<br>

**archimedean**solids: truncated icosahedron has 12 regular pentagonal faces, 20...## Pavilion

3d_export

$99

### Tori Gate 02 3D Model

...monument imperial palace temple joss monastery shrine pavilions gloriette

**pavilion**china chinese culture chinatown gate entrance japan archway tori...turbosquid

$45

### Islamic Octagonal Building

...islamic octagonal building turbosquid

**pavilion**octagon 8 sided rotunda arab arabic islamic islam desert...turbosquid

$6

### pavilion_01

... available on turbo squid, the world's leading provider of digital 3d models for visualization, films, television, and games.

3d_export

$24

### Pergola 7 Freestanding 3D Model

...pergola 7 freestanding 3d model 3dexport pergola gazebo shelter

**pavilion**brick patio backyard garden structure shade ramada wood wooden...3d_ocean

$19

### Trade pavilion 13

...garden house housing marquee pavilion stall summer tabernacle tent
beautiful shopping pavilion to trade any products, and things.

3d_ocean

$17

### Trade pavilion 1

...garden house housing marquee pavilion stall summer tabernacle tent
beautiful shopping pavilion to trade any products, and things.

3d_export

$5

### Trade pavilion 1 3D Model

... tabernacle body housing cor
trade pavilion 1 3d model download .c4d .max .obj .fbx .ma .lwo .3ds .3dm .stl mahus 110523 3dexport

cg_studio

$79

### Event Tents v2.0 Customizable3d model

...grass wedding camping outdoor ceremony realistic vray reception gazebo

**pavilion**event complex circus teahouse .3ds .max .obj .fbx -...archive3d

free

### Arbor 3D Model

...arbor 3d model archive3d arbor summerhouse arbour

**pavilion**arbor china 1 n190516 - 3d model (*.gsm+*.3ds) for...archive3d

free

### Building 3D Model

...building 3d model archive3d building

**pavilion**construction building 1 marlin studio n051012 - 3d model...