Utopian Structures - Containers and Cells.

UTOPIAN INFRASTRUCTURES CONTAINERS AND CELLS

KRISHNA N. PATEL UPCT, CARTAGENA, SPAIN

TUTOR : MARTINO PEÑA FERNANDEZ-SERRANO

!2

CONTENT Introduction : Deployable Systems

03

- Emilio Perez Pínero and his work

03

- ZIPIZIP : Case study

06

- Felix Escrig and his work

06

Evolution of The Structure

09

- Stage I

09

- Stage II

13

Final Structure

16

!3

Introduction : Deployable Systems What are ‘Deployable Structures’?

Illustrations : Examples of Deployable Structures

Deployable Structures are structures that can change their shape so that they have a compact form for transportation or storage, but can then be expanded for their final use.

Simple examples include umbrellas or tents. Can be unfolded when needed, folded and kept away in storage when not.

How they work?

To better understand how it works we have to understand the pioneers who have worked on deployable structures. The first name that comes to mind is

Emilio Perez Pinero.

Born in Calasparra, España (1935).

In 1961, the students of the Architecture Schools of 54 countries were invited to the International Competition of the International Union of Architects, with the theme "AMBULANTE THEATER".

Felix Candela, Buckminster Fuller and Ove Arup were part of the jury that considered Emilio Perez Pinero’s work revolutionary.

This is when the first systems of Deployable structures started to develop.

!4

Emilio Perez Pínero, holding unfolding his model for the “Ambulante theatre”

The working of these structures is best explained by Emilio Perez Pinero in his Patents : “THREE DIMENSIONAL RETICULAR STRUCTURE” 1961 USA patent 3.185.164

“The folding three dimensional reticular structure of the invention comprises a system of rods pivotally connected to each other by couplings which can be distributed by unfolding over a three dimensional space and be folded until the rods and their coupling connections form a compact bundle which is easily manageable in general and for its transportation in particular”

“The rod are articulated at each of the associated couplings and the number of the associated couplings connected to each rod is always three, two of them at the ends and a third one at an intermediate point the spacing of which from the other two seatings depends on the curvature which the structure has when unfolded”

!5 “There are two parameters which influence the geometrical characteristics of the structure once it is unfolded: (i) The number of rods which meet in a coupling.

This influences the unfolded geometrical form of the contour or peripheral boundary in a plane perpendicular to the folded rods: if there concur three rods per coupling the unfolded contour is hexagonal, if four concur, the unfolded contour is quadrangular . (ii) Equality or inequality of distances between each intermediate coupling and the two other extreme couplings of each rod.

If the intermediate coupling is equidistant from the two others extremes ones, the extended structures does not have any curvature - It is one plane.

If the intermediate coupling is not equidistant from the others two , then the extended structure adopts the form of a curve”

“Three dimensional reticular structure” USA patent 3.185.164 by Emilio Perez Pinero

His other famous works regarding the deployable structures include : i. Transportable Pavilion for exhibitions (Madrid , Barcelona) ii. Removable cupular structure for CINERAMA iii. Designing and building the first phase of the cover of the Paleochristian Museum of Tarragona.

!6 CASE STUDY, ZIPIZIP Understanding the Basic workings of the deployable structures from Emilio Perez pinero’s work, we go on to look at some of the work done by the Team of ZIPIZIP.

Image showing ZIPIZIP model in its various stages of unfold.

Their base geometry, consisting of 6 scissors to form a horizontal ring was taken up for study. ( further discussed in next section )

Interesting to note was, the methodology and working of this model was inspired from the system devised by Felix Escrig, who considered a follower of Emilio Perez Pinero.

His contributions can be seen through his patents as well, as seen in Fig. 1

!7

“Sistema Modular” ESPAÑA patent by Felix Escrig

Where Emilio Perez Piñero’s System used a rod bundle system to form the volume of an enclosing polygon ( above) , Felix Escrig used Scissor system to form the surfaces of the enclosing polygon ( below ).

!8 Types of scissors experimented with :

a.

b.

c.

Keeping in mind the works of Felix Escrig., the ZIPIZIP module was taken as the base module to experiment and evolve a form from.

!9

Evolution of the structure Stage I : Exploring with the Geometries using Felix Escrig’s system.

Attempt I : Studying ZIPIZIP model : - Has 6 similar scissors.

Strut Length : 27 cm

27 cm

For horizontal scissors : Length a - 09 cm Length b - 18 cm

27 cm

For Vertical scissors : Length a = Length b = 13.5 cm

LEGEND

End Joints Pin Joints

Trying to form a Geometry with more scissors : Seeing the System starts to make a curve when the joint in the scissor starts moving away from the centre of the struts, different positions of joints were tried to see what results they reap.

Pin Joint

Joint 2

CENTER

End Joint

End Joint Joint 1

Joint 3

Strut : Labelled.

CASE I : Experimentation with same joint distance, different angles between the struts. The inscribing circle radius is kept equal for all plans.

Angle : 60

Angle : 45

Angle : 30

!10

CASE II : Experimentation with Joint 1, Joint 2 & Joint 3. The Strut angle is kept constant in all plans; 60 degrees. The inscribing circle radius is derived from the geometry formed by the scissors at their respective angles.

Joint 2

GMENTS SEGMENTS S10 SEGMENTS 8 SEGMENTS 10 SEGMENTS 8 SEGMENTS 2010 SEGMENT SEGMEN 2010 S Joint 3

Joint 1

OF 10000 THEmm RADIUS CIRLE : 10000 OF THE mm RADIUS CIRLE : OF 10000 THEmm CIRLE : 10000 mm RADIUS OF THERADIUS CIRLE : OF 10000 THEmm CIRLE RADIUS : 10000OF mm RADIUS THE CIRLE OF THE : 10000 CIRLE mm: 10000 mm ENGTH 081 mm:STRUT 8660.254 LENGTH mm STRUT : 6434.1106 LENGTH mm: 7320.5081 mm STRUT LENGTHSTRUT : 6434.1106 LENGTH mm: 7320.5081 STRUT LENGTH mmSTRUT: 4158.2338 LENGTH : 6434.1106 mm mm mm 'a' : 2886.75 LENGTH mm 'a' : 2275.8768 LENGTHmm 'a' : 2496.889 mm LENGTH 'a' : 2275.8768 LENGTH mm 'a' : 2496.889 LENGTH mm 'a'LENGTH : 1672.4656 'a' : 2275.8768 mm mm mm 'b' : 5773.5027 LENGTHmm 'b' : 4158.2338 LENGTH mm 'b' : 4823.6191 mm LENGTH 'b' : 4158.2338 LENGTH mm 'b' : 4823.6191 LENGTH mm 'b'LENGTH : 2485.7683 'b' : 4158.2338 mm mm

RADIUS OFRA T STRUT LENG ST LENGTH 'a'LE: LENGTH 'b'LE:

° 60

° 60

60

°

Attempt I Results : The experimentation did not provide any fruitful solutions as the geometries had errors ( circled in red ).

• In CASE II, we see that the radius of the circle increases as the joint moves more towards the centre, proving that the geometry gets a more defined curve when the joint moves away from the centre.

•

Attempt II : Experimenting with the number of scissors to find a stable geometry. The angle between the struts at max. Unfold position is 60 degrees (constant).

In this case, the inscribing circle was divided into different numbers of segments, as shown below :

SEGMENTS 6 SEGMENTS 10 SEGMENTS 8 SEGMENTS

RADIUS OF THE CIRLE : 5000 RADIUS mm OF THE CIRLE : 5000 RADIUS mm OF THE CIRLE : 5000 RADIUS mm OF THE CIRLE : 5000 mm

10 SEGMENTS 8 SEGMENTS 20 SEGMENTS 10 SEGMENTS RADIUS OF THE CIRLE : 5000 RADIUS mm OF THE CIRLE : 5000 RADIUS mm OF THE CIRLE : 5000 RADIUS mm OF THE CIRLE : 5000 mm

STRUT LENGTH : 3660.254STRUT mm LENGTH : 4330.127mm STRUT LENGTH : 3217.0553mm STRUT LENGTH : 3660.254 mm

STRUT LENGTH : 3217.0553mm STRUT LENGTH : 3660.254 mm STRUT LENGTH : 2079.1169 STRUT mm LENGTH : 3217.0553mm

LENGTH 'a' : 1248.4445 mm LENGTH 'a' : 1443.3757 mmLENGTH 'a' : 1137.9384 mm LENGTH 'a' : 1248.4445 mm

LENGTH 'a' : 1137.9384 mm LENGTH 'a' : 1248.4445 mmLENGTH 'a' : 836.2328 mmLENGTH 'a' : 1137.9384 mm

LENGTH 'b' : 2411.8095 mm LENGTH 'b' : 2886.7513 mmLENGTH 'b' : 2079.1169 mm LENGTH 'b' : 2411.8095 mm

LENGTH 'b' : 2079.1169 mm LENGTH 'b' : 2411.8095 mmLENGTH 'b' : 1242.8839 mm LENGTH 'b' : 2079.1169 mm

!11

SEGMENTS 30 SEGMENTS 50 SEGMENTS 40 SEGMENTS 50 SEGMENTS 40 SEGMENTS 60 SEGMENTS 50 SEGMEN

IUS OF THE CIRLE : 5000 mm RADIUS OF THE CIRLE RADIUS : 5000 OFmm THE CIRLE : 5000 mm RADIUS OF THE CIRLE : 5000 mm

RADIUS OF THE CIRLE : 5000 mm RADIUS OF THE CIRLE RADIUS : 5000 OFmm THE CIRLE : 5000 mm RADIUS OF THE CIRLE : 5000 m

UT LENGTH : 1242.8834 mm STRUT LENGTH : 1553.5957 STRUT LENGTH mm : 1036.4987 mm STRUT LENGTH : 1242.8834 mm

STRUT LENGTH : 1036.4987 mm STRUT LENGTH : 1242.8834 STRUT LENGTH mm : 889.1722 mm

STRUT LENGTH : 1036.4987 mm

GTH 'a' : 550.2794 mm

LENGTH 'a' : 664.4235 LENGTH mm 'a' : 469.1741 mm

LENGTH 'a' : 550.2794 mm

LENGTH 'a' : 469.1741 mm

LENGTH 'a' : 550.2794 LENGTH mm 'a' : 408.7076 mm

LENGTH 'a' : 469.1741 mm

GTH 'b' : 692.604 mm

LENGTH 'b' : 889.1722 LENGTH mm 'b' : 567.3245 mm

LENGTH 'b' : 692.604 mm

LENGTH 'b' : 567.3245 mm

LENGTH 'b' : 692.604 LENGTH mm 'b' : 480.4646 mm

LENGTH 'b' : 567.3245 mm

SEGMENTS 70 SEGMENTS 90 SEGMENTS 80 SEGMENTS 90 SEGMENTS 80 SEGMENTS 100 SEGMENTS 90 SEGMENT

IUS OF THE CIRLE : 5000 mm RADIUS OF THE CIRLE RADIUS : 5000 OFmm THE CIRLE : 5000 mm RADIUS OF THE CIRLE : 5000 mm

RADIUS OF THE CIRLE : 5000 mm RADIUS OF THE CIRLE RADIUS : 5000 OFmm THE CIRLE : 5000 mm RADIUS OF THE CIRLE : 5000 mm

UT LENGTH : 692.6044 mm

STRUT LENGTH : 778.6367 STRUT LENGTH mm : 623.7246 mm

STRUT LENGTH : 692.6044 mm

STRUT LENGTH : 623.7246 mm

STRUT LENGTH : 692.6044 STRUT LENGTH mm : 567.3245 mm

STRUT LENGTH : 623.7246 mm

GTH 'a' : 324.7376 mm

LENGTH 'a' : 361.9488 LENGTH mm 'a' : 294.4339 mm

LENGTH 'a' : 324.7376 mm

LENGTH 'a' : 294.4339 mm

LENGTH 'a' : 324.7376 LENGTH mm 'a' : 269.2847 mm

LENGTH 'a' : 294.4339 mm

GTH 'b' : 367.8668 mm

LENGTH 'b' : 416.6878 LENGTH mm 'b' : 329.2907 mm

LENGTH 'b' : 367.8668 mm

LENGTH 'b' : 329.2907 mm

LENGTH 'b' : 367.8668 LENGTH mm 'b' : 298.0398 mm

LENGTH 'b' : 329.2907 mm

SEGMENTS

RADIUS : 5 M STRUT LENGTH

A

B

6

4330.127

1443.3757

2886.7513

8

3660.254

1248.4445

2411.8095

10

3217.0553

1137.9384

2079.1169

20

2079.1169

836.2328

1242.884

30

1553.5957

664.4235

889.1722

40

1242.8834

550.2794

692.604

50

1036.4987

469.1741

567.3245

60

889.1722

408.7076

480.4646

70

778.6367

361.9488

416.6878

80

692.6044

324.7376

367.8668

90

623.7246

294.4339

329.2907

100

567.3245

269.2847

298.0398

Table : Data showcasing the strut lengths, ‘a’, ‘b’ according to the number of segments the circle is divided in.

S

20 SEGMENTS

!12

Attempt II Results :

RADIUS OF THE CIRLE : 10000 mm STRUT LENGTH : 4158.2338 mm all 'a' cases, we discover as the numbers of segments increase • Considering LENGTH : 1672.4656 mm LENGTH 'b' : 2485.7683 mm of ’t’ decreases, where; (with a constant angle) ,the value

t = shortest distance between the end of both the struts on the same side of a scissor.

6 SEGMENTS RADIUS OF THE CIRLE : 5000 mm

100 SEGMENTS RADIUS OF THE CIRLE : 5000 mm

30

RAD STR LEN LEN

8 SEGM

RADIUS OF TH

STRUT LENGTH : 4330.127mm

STRUT LENGTH : 567.3245 mm

STRUT LENGT

LENGTH 'a' : 1443.3757 mm

LENGTH 'a' : 269.2847 mm

LENGTH 'a' : 1

LENGTH 'b' : 2886.7513 mm

LENGTH 'b' : 298.0398 mm

LENGTH 'b' : 2

=t

Comparing extreme cases (Above) • We come to the conclusion that 6 or 8 is not enough and more than 30 - 40 is too many segments, so we go forward with one case, 20 segments.

• Note, Each segment is formed by one scissor.

20 SEGMENTS RADIUS OF THE CIRLE : 5000 mm

STRUT LENGTH : 2079.1169 mm LENGTH 'a' : 836.2328 mm LENGTH 'b' : 1242.8839 mm

!13

Stage II : Finalising the Geometry.

Experiment I :To make the geometry more stable for practical use, the horizontal layer needed some strengthening on the inner part of the deploying system. Another layer of scissors in the same plane was to be added.

Two methods were tried for this: Method I : ( below, left ) Similar strut length for outer and inner scissors, Outer scissors angle fixed : 60 degrees, Inner scissors angle : Variable.

WITH SIMILAR STRUT LENGTH INSIDE

RADIUS OF THE CIRCLE : 10000 mm STRUT LENGTH : 4158.2338 mm LENGTH 'a' : 1672.4656 mm LENGTH 'b' : 2485.7683 mm RADIUS OF THE CIRCLE : 6728. 1636 mm STRUT LENGTH : 4158.2338 mm LENGTH 'a' : 1221.2617 mm LENGTH 'b' : 2936.9721 mm

60* ANGLE STRUTS

RADIUS OF THE CIRCLE : 10000 mm STRUT LENGTH : 4158.2338 mm LENGTH 'a' : 1672.4656 mm LENGTH 'b' : 2485.7683 mm

RADIUS OF THE CIRCLE : 4526.8177 mm STRUT LENGTH : 1882.3566 mm LENGTH 'a' : 757.0947 mm LENGTH 'b' : 1125.262 mm

RADIUS OF THE CIRCLE : 6728. 1636 mm STRUT LENGTH : 2797.7284 mm LENGTH 'a' : 1125.2623 mm LENGTH 'b' : 1672.4661 mm

RADIUS OF THE CIRCLE : 3045.717 mm STRUT LENGTH : 1266.4803 mm LENGTH 'a' : 509.3857 mm LENGTH 'b' : 757.0947 mm

RADIUS OF THE CIRCLE : 2797.7278 mm STRUT LENGTH : 2797.7278 mm

Method II : ( above, right ) Different Strut length for all different rings of scissors, Angle for all scissors : 60 degrees.

Experiment I Results : Method II was discarded and it was decided to go further with Method I as it has less variation in members.

!14 Experiment II : Going Vertical. Here, experimentation was done in the regard as to the placement of vertical scissors.

Case I : In the Outer Ring.

PLAN : Showing the vertical scissors in the outer ring ( red line )

PERSPECTIVE VIEW : Showing the structure ( 2 horizontal rings, one set of vertical scissors.)

Vertical scissors in outer ring.

!15

ELEVATION : Showing vertical scissors in the outer ring.

Case II : In the Inner Ring.

PLAN : Showing the vertical scissors in the Inner ring ( red line )

PERSPECTIVE VIEW : Showing the structure ( 2 horizontal rings, one set of vertical scissors .)

Vertical scissors in Inner ring.

!16

ELEVATION : Showing vertical scissors in the Inner ring.

CASE III : A third Case was tried, a vertical scissor connected from the pin joints of inner and outer scissors.

PLAN : Showing the vertical scissors in springing from the pin joints of the Outer and Inner ring in the horizontal plane.( red line )

In this Geometry we could see, different kinds of interesting spaces being formed.

Semi Covered Spaces.

Enclosed Spaces.

Semi Covered Spaces.

Open to Sky Spaces.

Figure showing PLAN and its dierent spatial zones.

!17

PERSPECTIVE VIEW : Showing the structure ( 2 horizontal rings, one set of vertical scissors .)

Vertical scissors springing from the pin joints of the inner and outer ring of scissors in the horizontal plane.

ELEVATION : Showing vertical scissors springing from the pin joints of the inner and outer ring of scissors in the horizontal plane.

This is the final Geometry constructed.

MODEL : Full elevation

!18

MODEL : Showing inner geometry.

MODEL : Full model with Human Scale.

MODEL : Full model with Human Scale and how different spaces can be used.

!19

MODEL : Human eye perspective, hypothetical case. Showing usage of semi covered space on the outer edge.

MODEL : Human eye perspective, hypothetical case.

MODEL : Human eye perspective, hypothetical case. Close up.

!20

MODEL : Human eye perspective, hypothetical case. Showing usage of semi covered space on the inner edge.

MODEL : Human eye perspective, hypothetical case. Showing cross section of the structure.

MODEL : Human eye perspective, hypothetical case. Showing all three layers - inner edge.

!21

MODEL : part elevation showing interesting spaces created on the outer edge.

MODEL : bird eye view showing inner dynamic space created.

You can also check out the Time Lapse video of the model construction on Youtube. : https://www.youtube.com/watch?v=lc9cefxMwcM&t=16s THANK YOU