Potential application of the swivel diaphragm mechanism within a kinetic canopy

6/10/2014

Ponencia14

POTENTIAL APPLICATION OF THE SWIVEL DIAPHRAGM MECHANISM WITHIN A KINETIC CANOPY Cubierta cinética usando el mecanismo de eslabones giratorios

autor

título

tema

código

Carolina Rodriguez 1 John Chilton 2 Robin Wilson 3 1

PhD Student, The School of the Built Environment, The University of Nottingham Professor of Architectural Structures, Lincoln School of Architecture, The University of Lincoln Senior Lecturer, The School of the Built Environment, The University of Nottingham laxcmr@nottingham.ac.uk, jchilton@lincoln.ac.uk, Robin.Wilson@nottingham.ac.uk 2 3

The Swivel Diaphragm is a deployable ring mechanism developed by the authors in past research. This paper describes the basic characteristics of this mechanism and illustrates a possible application within kinetic canopies. Compared with existing canopy designs that have two stages of deployment: open and closed, the proposed canopy offers the additional advantage of various intermediate stages of deployment and coverage as well as alternative aesthetic qualities.

Key words: Deployable structures, transformable canopies, kinetic mechanisms, retractable covers, foldable umbrellas, convertible parasols.

INTRODUCTION Kinetic devices have been used for centuries in architecture for a wide range of purposes.

Over recent decades there has been a large demand for these devised within 'flexible buildings' that can efficiently serve different purposes and adapt to changing conditions. Prime examples of this are retractable covers for venues where a variety of outdoor and indoor activities can be performed. A wide range of buildings has been designed to date for this purpose, from large-scale retractable roofs for sports stadiums to various types of open-air canopies. Kinetic canopies have been particularly popular, due to their versatility of use and aesthetic possibilities. Recognized architects such as Frei Otto, Bodo Rasch (Otto F. and Rasch B., 1995) and Santiago Calatrava (Tzonis, A., 1999) have developed their own distinctive proposals, habitually inspired by the traditional umbrella. A notable example of this is the project utilizing 18 metre span convertible umbrellas, designed by SL Rasch for the courtyards of the Prophet's Holy Mosque in Medinah. In summer these umbrellas are deployed during the day to shade the courtyards, whilst they are folded at night to promote cooling by radiation to the clear night sky. Conversely, in winter, the umbrellas are folded during the day to allow the sun's rays to warm the courtyard whilst at night they are deployed to trap warm air and limit radiation to the cold night sky. Usually, umbrella based designs offer two possible useful states of deployment: fully deployed or fully folded. This limits, to a certain extent, the potential of these structures as large-scale environmental control devices. The process of deployment is time-consuming limiting its ability to respond promptly to unexpected changes in the weather. This restriction could be overcome with a canopy design that involves alternative mechanisms to those used by the umbrella, such as, for example, a retractable ring structure. Retractable ring mechanisms are relatively well studied. Primarily, they involve concentric movement and may be deployed to any intermediate stage between fully open and fully closed conditions. This could be advantageous were accurate deployment forms part of a scheme's environmental control strategy. This paper focuses on the Swivel Diaphragm, a retractable ring structure developed by the 1 st and 2 nd authors (Rodriguez , C. and Chilton, J. 2003), and its potential use within kinetic canopies.

THE SWIVEL DIAPHRAGM The Swivel Diaphragm is a novel type of retractable ring structure compromising series of angulated elements and straight elements, linked in a closed circuit by pivoted joints (fig. 1a).

The angulated elements are formed by three joints placed to create a triangle, where one of the joints is fixed to a support allowing the element to swivel. The straight elements link neighbouring angulated elements by the non-fixed joints, forming a closed ring where forces are transmitted from one element to the next. As a consequence the overall diaphragm moves from and towards its centre, when opening and closing respectively (fig. 1b).

file:///E:/DOCUMENTS/Documents/Caro2/General%20bibliografy%20reference/Conference%20proceddings/Tenso%20Estructuras%20Venezuela%2…

1/7

6/10/2014

Ponencia14

Fig. 1a: Hexagonal Swivel Diaphragm with identical angulated elements

Fig. 1b: Deployment process of a Hexagonal Swivel Diaphragm

In many retractable ring mechanisms the disposition of the pivoting joints and bars forms rhomboidal shapes that are, inherently, deformable when the joints have at least one degree of freedom . This is the case for retractable rings that use pantographic elements (also called scissor-like-elements). They are capable of expanding and contracting towards their own perimeter, however, during this process they change in size. Consequently, they present difficulties when attached to an external support, since it is necessary to use relatively complex fixed supports additional to the structure such as rails or extra pivoting members.

Structures of this kind have been studied by numerous researchers such as C. Hoberman (Hoberman, C. , 1996), P. Kassabian Z.You and S. Pellegrino (Kassabian, P. You, Z. and Pellegrino , S. 1997) , and F. Jensen (Jensen, F. V. 2001), amongst others.

In a similar way to retractable pantographic rings, in the swivel diaphragm (fig 1a) the joints AA1B2B form a rhomboid where A and B are fixed to an external support. This type of assembly is commonly known as four-bar linkage and is widely used in engineering to transmit forces and motion. The link between the fixed points A and B is usually called the frame , the link A1B2 opposite to the frame is called the coupler link , and the links AA1 and BB2 are called the side links. Four-bar linkages have been used before in the design of retractable ring structures by Z. You ( You, Z., 2000) who proposed a general method to create closed loops named -the base structure . The swivel diaphragm advances on this topic by involving series of four-bar linkages interconnected by angulated elements set to a specific angle (fig 1a).

The angulated elements operate on a different layer to the straight elements in order to avoid collisions during the retraction. For the swivel diaphragm to be kinetic every four-bar linkage has to fulfil the following basic conditions: AB = A1B2 (1) and, AA1 = BB2

(2)

As stated in equation 1, the dimension between the two joints of a straight element (or couple link) is restricted by the adopted dimension between the corresponding fixed joints (or frame).

However, the dimensions between the joints of the angulated element (or side links) can vary as long as they stay equivalent according to equation 2. Notice that during the deployment process, the straight element (or coupler link) A1B2 runs parallel to the fixed joints AB (or the frame) and equally, AA1 (side link) runs parallel to BB2 (side link).

Various designs are achievable by changing the following main variables of the system: • The polygonal shape described by the fixed joints, • The dimension of the side links, the internal angle in the angulated element, • The angle of deployment .

Certain rules apply to each design in order to avoid collision between the elements and dead points, where some joints lock between each other preventing the diaphragm from deploying further. This paper describes the basic parameters of the swivel diaphragm; in so doing it uses the following nomenclature to refer to the various components of the systems:

file:///E:/DOCUMENTS/Documents/Caro2/General%20bibliografy%20reference/Conference%20proceddings/Tenso%20Estructuras%20Venezuela%2…

2/7

6/10/2014

Ponencia14

Polygonal shape The swivel diaphragm offers more flexibility in terms of geometry as compared with similar retractable systems such as retractable rings. It can adopt almost any polygonal shape, regular or irregular. Regular shapes provide a more homogeneous process of deployment and are relatively easier to calculate and study. Figure 2 illustrates examples of regular polygonal configurations possible with the swivel diaphragm. The following formula can be used to obtain the angle in a diaphragm with a regular polygonal shape:

Fig. 2: Examples of regular polygonal configurations with the Swivel Diaphragm

Deployment angle The deployment angle is used to describe the different stages of movement of the angulated elements, relative to the perimeter of the polygonal shape. Within the same diaphragm, this angle can vary from one angulated element to the next. Depending on the desired requirements for the overall arrangement, this angle can be manipulated in different ways. For example, the rig can be configured to maintain an equivalent deployment angle throughout the movement for every angulated element (fig. 1b). Such design allows the ring to have a open stage of deployment where all the angulated elements are aligned with the sides of the base polygon. Likewise, they meet simultaneously at the centre of the polygon at a closed stage. The minimum angle needed for the diaphragm to go from an open to a closed stage is inversely proportional to the number of sides of the polygonal shape of the diaphragm. In a diaphragm based on a regular polygon this angle can be calculated using the following equation:

With an appropriate design, any angulated element in a swivel diaphragm can achieve a deployment angle of 360 ° . This allows the diaphragm to swivel uninterruptedly in one direction (clockwise and/or anti-clockwise) without collision between the angulated elements.

This paper will refer to this type of diaphragm as reversible (fig. 3).

Angulated elements The design of the angulated element is the key point of the swivel diaphragm system. The dimensions and angles between the joints and the shape of the angulated element can be used to determine the degree of deployment of the ring and its aesthetic features during every stage of movement. The three main characteristics of the angulated element are: the internal angle

, the dimension between the joints (side links) and the overall shape of the element.

The internal angle

is described between the three joints of the angulated element A, A1

and A2 (fig. 1a). The value of this angle depends on the number of four-bar linkages in the diaphragm and the desirable action for the overall structure. In a swivel diaphragm the angulated elements can have identical or different internal angles Îą as long as the sum of all the angles fulfils the following condition:

If all the angulated elements have identical internal angle

, this angle can be calculated

file:///E:/DOCUMENTS/Documents/Caro2/General%20bibliografy%20reference/Conference%20proceddings/Tenso%20Estructuras%20Venezuela%2‌

3/7

6/10/2014

Ponencia14 as follows:

The angulated elements can adopt various shapes as long as the internal angle

is

preserved. Since the joints describe a triangle, there are three possible bar configurations of the angulated elements (fig. 4), where, angles

and

are relative to

as follows:

Fig. 4: Three possible configurations of the angulated element in an irregular octagonal Swivel Diaphragm

In addition to the internal angle

, the dimensions between the joints or side links S also

play a very important role in the operation of the diaphragm (fig 1a). By varying these dimensions it is possible to stop the deployment at a determined angle or conversely, to allow the ring to be reversible. In the case of reversible rings, there is a maximum dimension possible for the side link in order to avoid interference between neighbouring angulated elements during the deployment. These maximum dimensions Smax can be calculated as follows: For reversible diaphragms based on regular polygon that use angulated elements with identical internal angle:.

For reversible diaphragms based on irregular polygon with identical angulated elements:

In reversible diaphragms based on irregular polygons that use angulated elements with different internal angles, each four-bar linkage has to be studied separately, taking into consideration their neighbouring elements. For example, in order to obtain Smax for AA1 in fig. 5, it is necessary to use the following two equations, taking into account

1,

2 and

7, and adopt the shortest Smax between both of them:

Fig. 5: Irregular swivel diaphragm (seven sides)

file:///E:/DOCUMENTS/Documents/Caro2/General%20bibliografy%20reference/Conference%20proceddings/Tenso%20Estructuras%20Venezuela%2‌

4/7

6/10/2014

Ponencia14 The shape of the angulated element can vary to cover large areas or restrict the degree of deployment as long as the maximum dimensions Smax for the side link and the internal angle are preserved. Figures 6, 7 and 8 show three different options of coverage with diverse aesthetic qualities.

Fig. 6: Cover design for a heptagonal reversible swivel diaphragm

Fig. 7: Cover design for a hexagonal swivel diaphragm

Fig. 8: Cover design for a nonagonal swivel diaphragm

KINETIC CANOPY DESIGNS A kinetic canopy was the type of structure chosen to illustrate the potential of the swivel diaphragm mechanism since there is a current and increasing demand for these structures within architectural projects. Covers of this kind have a wide variety of applications such openair theatres, indoor-outdoor swimming pools, exposition pavilions, catwalks, amongst others.

This paper shows only one experimental canopy project, however, the swivel diaphragm mechanism is very versatile and allows numerous configurations and designs. In the proposed canopy (fig. 9, 10), the angulated members overlap at the closed stage forming a 1.5m side hexagon. They achieve a deployment of 50° at the open stage forming a 3m side hexagon and increasing the area of coverage by almost three times. The angulated members comprise a rigid frame that supports triangular lightweight covers. It is proposed to build the frame in a high-strength but lightweight material such as fibre reinforced composite and the covers in translucent, lightweight, rigid material such as impregnated Paraglass 3-D glass fabric. The covers are tilted towards the pivoting support in order to direct the rainwater towards the centre of the canopy, where it is drained through the central column into the floor drains. The rigid frame is designed in a way that allows the angulated elements to meet at the centre of the canopy at the closed stage without interfering with each other. A hexagonal beam and six arms hold up the fixed pivoting supports. These arms transport the loads to a central steel column and help to support the central covers. Lighting is placed above the column capital reflecting the light onto the covers. At the end of the column there is a base plate that attaches the structure to the foundations. The canopy operates with two electric motors located in two opposite fixed supports, allowing the structure to gradually swivel until it riches 50°. A series of these canopies could be placed together in a grid to cover large areas (fig.11).

file:///E:/DOCUMENTS/Documents/Caro2/General%20bibliografy%20reference/Conference%20proceddings/Tenso%20Estructuras%20Venezuela%2‌

5/7

6/10/2014

Ponencia14

Fig. 9: Kinetic canopy design

Fig. 10: Deployment process of kinetic canopy

Fig. 11: Grid of six kinetic canopies

CONCLUSION The kinetic canopy concept presented in this paper uses an alternative and innovative device to achieve the deployment. Using the principle of the swivel diaphragm explained above, it is possible to design a very diverse range of kinetic canopies to suit different needs. These types of canopies offer the advantage of intermediate stages of deployment over traditional options.

Such a characteristic has great design potential since it provides an ever changing cycle with visually different stages of movement. However, further research is needed on additional structural aspects of this design such us its behaviour under wind, rain and snow loading during every stage of deployment. Moreover, a feasibility study is required to determined cost implications and constructional advantages and/ or disadvantages against traditional options of canopies.

REFERENCIAS Candela, F., Perez -Piñero. E., Calatrava, S., Escrig, F. and Perez, V.J. (1993), “Arquitectura Transformable”, Escuela Superior de Arquitectura de Sevilla, Spain.

Hoberman, C. (1996), “Temporary Unfolding Structures”, Detail: Temporary Structures, Germany.

Jensen, F. V. (2001), “Cover Elements for Retractable Roof Structures”, First Year Report, PhD University of Cambridge, UK. Kassabian, P., You, Z. and Pellegrino, S. (1997), “Retractable Structures Based On Multi Angulated Elements”, Proceedings of the International Colloquium Structural Morphology, University Of Nottingham, UK, 92-99.

Otto F. and Rasch B. (1995), “Finding Form, Towards an Architecture of the minimal”, Catalogue for the Exhibition in the Villa Stuck, Munich, Germany Rodriguez, C. (2000), “Arquitectura Metamórfica”, Eds. ICFES- National University Of Colombia, Bogotá, Colombia.

Rodriguez, C. and Chilton, J. (2003), “Swivel Diaphragm a New Alternative for Retractable Ring Structures”, Journal of the International Association for Shell and Spatial Structures (IASS), Vol. 44 (3), 181-188.

Tzonis, A. (1999), “Santiago Calatrava: The Poetics of Movement”, Ed. Thames & Hudson.

Great Britain You, Z. (2000), “A new Approach to Desing of Retractable Roofs”, IUTAM-IASS Symposium on Deployable Structures: Theory and Applications, Ed. Kluwer Academic Publishers, The Netherlands, 477-483.

file:///E:/DOCUMENTS/Documents/Caro2/General%20bibliografy%20reference/Conference%20proceddings/Tenso%20Estructuras%20Venezuela%2…

6/7

6/10/2014

Ponencia14

file:///E:/DOCUMENTS/Documents/Caro2/General%20bibliografy%20reference/Conference%20proceddings/Tenso%20Estructuras%20Venezuela%2‌

7/7