Kinetic scissor dome by Lucas Klerk

KINECTIC SCISSOR DOME

Authors

Yve e Eskander | 0819315 Lucas Klerk | 0784995 Luuk de Kluiver | 0660922 Peter Koelewijn | 0791992

Mastertrack Course Tutors

Building Technology 7TS25 Masterproject 2 Ir. Arno Pronk Ir. Maurice Dominicus Ing. Jeroen da Conceicao van Nieuwenhuizen

KINECTIC SCISSOR DOME

Authors

Yve e Eskander | 0819315 Lucas Klerk | 0784995 Luuk de Kluiver | 0660922 Peter Koelewijn | 0791992

Mastertrack Course Tutors

Building Technology 7TS25 Masterproject 2 Ir. Arno Pronk Ir. Maurice Dominicus Ing. Jeroen da Conceicao van Nieuwenhuizen

0 4

Foreword

5 This report is wri en for the second masterproject during mastertrack Building Technology at Eindhoven University of Technology which was tutored by Ir. Arno Pronk, Ing. Jeroen da Conceicao van Nieuwenhuizen and Ir. Maurice Dominicus. All three tutors are experts when it comes to free form design and kine c structures as they’ve devoted a lot of their own work to these topics. We would like to thank our tutors Arno Pronk, Jeroen da Conceicao van Nieuwenhuizen and Maurice Dominicus for their advice, sharing their experience and encouragement throughout the project. The goal of this project is to design a transformable kine c dome which has to follow the track of the sun during the day and during different seasons in order to efficiently catch solar energy with PV-panels/foil. The dome is designed based on research on kine c structures and should be a new innova ve type of dome, rather than trying to improve an exis ng dome. In the end the design was built with simplfied materials in order to prove the dome’s concept and movement for the final presenta on. This masterproject consists out of 5 conseque ve phases. In phase one every student or couple of students were assigned a different research and presen on topic regarding kine c structures in order to gather as much informa on as possible as a group. A er phase one, in phase two each student developed an individual concept based on a researched kine c structure topic. The four best concepts were chosen by the tutors and four groups were made to further research, design and elaborate the concepts. Phase three, four and five were all about the chosen concepts. In phase three the concept had to be elaborated into a be er researched and op mized concept regarding movement and efficiency of structure and skin. Phase four was about simplifying the dome into an affordable, lightweight and easy buildable design. Instead of thinking in expensive building materials, the (re)search was about finding suitable affordable materials to subs tude regular building materials. The design was built on a large scale 1:4, to test the materials before building an actual 1:1 model for phase five. In this report phases three to five are extensivly discussed. A er a research on the sun and a brief descrip on of the requirements for the design in chapter one, a research and explana on for the type of structure the design is based on is elaborated in chapter two. The third chapter is about the design’s concept. Then in chapter four the research proces and op miza on of the design is described before presen ng the final design in chapter five. Simplifying the design into an affordable buildable design and the actual building process of the models is discussed in chapter six. Eindhoven, June 2013

Contents

7 1 | Introduc on

1.1 | Design challenge 1.2 | Solar path 1.3 | Solar eďŹ&#x192;ciency

9 9 10

2 | Scissor structures

13 13 16 17 19

3 | Concept

3.1 | Scissor arcs 3.2 | Kine c arc type 3.3 | Scissor dome structural concept

21 22 23

4 | Design op miza on

4.1 | Introduc on 4.2 | Matrix 4.3 | Results

25 25 32

5 | Final design

5.1 | The design 5.2 | Details 5.3 | Solar-room study

34 38 41

6 | Simplifica on and building process

43 46 48 52 62

Bibliography

Appendix Concept poster phase 1 by Yve e Eskander Concept poster phase 1 by Lucas Klerk and Peter Koelewijn Concept poster phase 1 by Luuk de Kluiver

1 8

Introduc on

1.1 | Design challenge For this design assignment, the challenge is to design a kine c lightweight dome shaped structure. It’s main func on is to capture and generate solar energy, therefore the outer shell of the dome has to contain solar panels or solar foil. The structure has to be kine c as it’s required to follow the movement of the sun during the day and during all seasons, such as a suntracker with solar panels.

be oriented op mally towards the sun to achieve the maximum possible eﬃciency of the solar panels or foil.

1.2 | Solar path In order to understand the required movement of the dome towards the sun, the sun path is researched. Figure 1.2 displays the sun angles throughout the year during the day from the South. As the graph displays, the

sun angle naturally changes angle throughout the day. As the sun rises in the morning the angle increases, it decreases as it sets in the evening. Looking at the angle throughout the year, mid winter contains the lowest sun angles of the year as mid summer contains the highest angles. Besides the angle of the sun changing, also the number of sun hours decreases towards midwinter and increases towards mid-summer.

What’s important in this design process is that exis ng domes are not neccesarily something to improve and translate into a kine c dynamic structure. The challenge is rather to develope a new structure for a kine c dome with a skin based on research on domes and deployable or movable structures. The structure must be easily transportable as it’s a temporary structure. Because of the dome’s temporality, it’s also required to be easy to erect and take down. Demountability is an important characteris c for the design. A lightweight structure is therefore needed in order to be easily transportable and erected. The dome’s func on besides suntracking is to create an outside space which could serve as an ou sde sea ng area. Therefore the skin is required to be waterproof. As men oned above the skin should contain some solar panels or foil. The solar parts of the skin should at all mes Figure 1.5 | Sun angles from South (Source: Weersta on Uithoorn)

Figure 1.1 | Requirement 1: kine c suntracker

Figure 1.2 | Requirement 2: easy deployment

Figure 1.3 | Requirement 3: easily transportable

Figure 1.4 | Requirement 4: lightweight

Introduc on

Figure 1.6 shows a dome shape, it’s sun lit surface during different seasons and the sun elip cal course during the day. As in winter the sun angle is very low with an average of 16°, the maximum coverage span, determined by the suns eclip c course, is also at it’s smallest with 118°. From winter to summer the angle of the sun increases to 62° and the coverage span increases to 248° at it’s largest, which is more than double the span in winter me. In order to achieve maximum efficiency with solar panels, the dome kine c structure needs to be able to orient the solar panels into an op mal angle towards the sun. As men oned above there’s a difference in the angle of the sun in the sky during different seasons, also known as the azimuth angle. Also the movement of the dome needs to be elip cal in order to be able to follow the elip cal course of the sun, it’s al tude during the day and to be able to adapt to the difference of the sun’s course span.

1.3 | Solar efficiency Solar panels have a 100% efficiency when oriented perpendicular towards the angle of the sun. With increasing devia on in angle the efficiency also decreases. This is shown in figure 1.7 and 1.8.

Winter

Spring/fall

Summer

Figure 1.6 | Sun lit dome surface during spring/fall, summer and winter

Figure 1.7 | Solar panels eﬃciency

11 Horizontal distortion

Result

##### 99,6% 98,5% 96,6% 94,0% 90,6% 86,6% 81,9% 76,6% 70,7% 64,3% 57,4% 50,0% 42,3% 34,2% 25,9% 17,4% 8,7% 0,0% 0

Vertical distortion

100,0% 100% 100%

98%

97%

94%

91%

87%

82%

77%

71%

64%

57%

50%

42%

34%

26%

17%

99,6% 100%

99%

98%

96%

94%

90%

86%

82%

76%

70%

64%

57%

50%

42%

34%

26%

17%

98,5%

98%

97%

95%

93%

89%

85%

81%

75%

70%

63%

56%

49%

42%

34%

25%

17%

96,6%

97%

96%

95%

93%

91%

88%

84%

79%

74%

68%

62%

55%

48%

41%

33%

25%

17%

94,0%

94%

93%

91%

88%

85%

81%

77%

72%

66%

60%

54%

47%

40%

32%

24%

16%

90,6%

91%

90%

89%

88%

85%

82%

78%

74%

69%

64%

58%

52%

45%

38%

31%

23%

16%

86,6%

87%

86%

85%

84%

81%

78%

75%

71%

66%

61%

56%

50%

43%

37%

30%

22%

15%

81,9%

82%

81%

79%

77%

74%

71%

67%

63%

58%

53%

47%

41%

35%

28%

21%

14%

76,6%

77%

76%

75%

74%

72%

69%

66%

63%

59%

54%

49%

44%

38%

32%

26%

20%

13%

70,7%

71%

70%

68%

66%

64%

61%

58%

54%

50%

45%

41%

35%

30%

24%

18%

12%

64,3%

64%

63%

62%

60%

58%

56%

53%

49%

45%

41%

37%

32%

27%

22%

17%

11%

57,4%

57%

56%

55%

54%

52%

50%

47%

44%

41%

37%

33%

29%

24%

20%

15%

10%

50,0%

50%

49%

48%

47%

45%

43%

41%

38%

35%

32%

29%

25%

21%

17%

13%

42,3%

42%

41%

40%

38%

37%

35%

32%

30%

27%

24%

21%

18%

14%

11%

34,2%

34%

33%

32%

31%

30%

28%

26%

24%

22%

20%

17%

14%

12%

25,9%

26%

25%

24%

23%

22%

21%

20%

18%

17%

15%

13%

11%

17,4%

17%

16%

15%

14%

13%

12%

11%

10%

8,7%

0,0%

Figure 1.8 | Solar panels eďŹ&#x192;ciency

2 12

Scissor structures

2.1 | Introduc on In this chapter the basics of scissor structures are introduced in order to understand the design process and final design of the dome. One of the diﬀerent types of deployable structures are scissor structures. Scissor structures consist of bars linked by scissor hinges. This type of structures are therefore expandable and allow folding them into a small bundle which makes the structure mobile and relocatable because of it’s easy transporta on when folded together. Compared to tradi onal buildings, deployable structures also have the advantage of easy and fast erec on. These characteris cs are of great use for temporary buildings.

Figure 2.1 | Plane unit

Figure 2.2 | Curved unit

Scissor bar units, called Scissor Like Elements (SLE’s) are two bars of the scissor structure, connected by an intermediate hinge. The intermediate hinge allows for the bars to rotate around the hinge axis. When connec ng more SLE’s with hinged joints on their end nodes, a transformable scissor structure is formed. SLE’s can also be modified (M-SLE) to increase transformability of the structure (Temmerman, 2007). Figure 2.3 | Deployment plane unit

2.2 | Types of scissor structures By changing the loca on of the intermediate hinge or the measurements of the SLE’s three basic diﬀerent scissor unit types can be named: transla onal, polar and angulated units. These basic scissor units types have the same basic similarity, the end nodes of the SLE’s are connected by unit lines. (Temmerman, 2007) Transla onal scissor units The transla onal scissor strucure has all iden cal bars. For a basic transla onal unit, the unit lines are parallel and stay the same deploying the structure. For a curved transla onal unit the bar lengths are diﬀerent which causes a curved linkage of SLE’s (Temmerman, 2007).

Figure 2.4 | Deployment curved unit

Scissor structures

Polar scissor units With polar scissor units, the intermediate hinge is moved away from the centre of the scissor bars. The scissor semi-bars (a + b) have unequal lengths on both sides of the intermediate hinge. Moving the intermediate hinge from the centre causes a natural curvature of the scissor with deployment of the structure. The unit lines are no longer parallel as with the transla onal scissor unit but intersect at angle Îł. As the intermediate hinge moves further away from the centre, the curvature of the structure increases. Angle Îł varies with deployment of the structure (Temmerman, 2007).

Figure 2.5 | Polar unit

In order for the scissor structure linkage to be foldable, a deployability constraint formula for the linkage is wri en by Escrig (1985). The formula states that semibars lengths of a + b have to be equal to the adjoining unit bar lengths c + d (Temmerman, 2007). The deployability constraint formula: a+b=c+d Structures which are not designed with the deployability constraint formula can s ll be par ally foldable but not compact.

Figure 2.7 | Deployment polar unit

Figure 2.8 | Deployability constraint deployment in three stages

Figure 2.6 | Deployability constraint formula a+b=c+d

15 Angulated scissor units The angulated units, invented by Hoberman, consists of two seperate rigidly connected semi-bars of length a instead of the previous described unit types which consist of straight bars. This connec on kinks the structure in it’s centre with angle β. The angulated units keep a constant angle γ during deployment in constrast to the previously described polar units. In order to maintain this ability a design formula states α= γ/2. Therefore these type of scissor structures are suitable for a circular linkage for radial deployable structures (Temmerman, 2007). The structure shown in figure 2.12 displays a radially angulated structure which consist of two layers of angulated structural units which one layer is arranged clockwise (grey) and the other layer is arranged counterclockwise (red). Which deployment of the structure the structural unit layers rotate the opposite way but in equal rota on (Akgun, 2010) Mul -angulated scissor units By muta ng the angulated scissor elements into elements with more than one kink angle, mul angulated elements are formed. You & Pellegrino designed this structural concept based on the regular angulated scissor units by Hoberman. With mul angulated structures, two angulated units which are hinged and interconnected at the end nodes in diﬀerent layers turn in the same direc on. These structures are rigidly connected due to the constant angle (Akgun, 2010).

Figure 2.9 | Angulated unit

Figure 2.10 | Design formula angulated unit

Figure 2.12 | Deployment radially angulated unit by Hoberman

Figure 2.13 | Deployment radially mul -angulated unit by You & Pellegrino

Figure 2.11| Mul - angulated unit

Scissor structures

2.3 | Design of 2D scissor linkage For designing a 2D scissor to form the arcs a few basic design principles for scissor linkage are necessary. For the concept and design of stucture of this dome only transla onal and polar structures are discussed as angulated scissors are not foldable into a small package, as explained in chapter 2.2, therefore this type of structure is also not easily transportable.

Figure 2.14 | Display transla onal scissor deployability constraint

Figure 2.15 | Display polar scissor deployability constraint

Figure 2.16 | Movement transla onal by deployability constraint

Figure 2.17 | Movement polar by deployability constraint

There are two design methods for scissor linkage, a pure geometric construc on or a geometric design method using using equa ons in order to provide the complete deployed geometry (Temmerman, 2007). Both design methods are based on the deployability constraint formula [a + b = c + d], as men oned in chapter 2.2, in order to be foldable. This constraint is a minimum design requirement according to Temmerman (2007). When scissor units are linked to eachother, the loca on of the intermediate hinge has to be determined and s ll keep the deployability constraint for semi-bar units c + d in tact. The locus M of the intermediate hinges, due to the deployability constraint, is displayed graphically as an ellipse for transla onal units in figure 2.14 and as a circle for polar units in in figure 2.15. In this report only the geometric construc on method for designing 2D scissor linkage is discussed as the structural design for this project was based on this method. In addi on, the second method, geometric design using equa ons, goes beyond the structural design and concept for this project.

2.4 | Design method: geometric construc on As a base curve for designing scissor linkage, a circular curved arc is the most common basic structure to start with. The base curve is determined by the span (S) and rise (Hr) as displayed in figure 2.20 (Temmerman, 2007). Polar linkage Temmerman (2007) states that linking polar units can be done with two methods. The first method is to divide the base curve into equal length segments by polar units lines. The division points are used as intersec on points for intermediate hinges of the scissors. The thickness of the units (t), can be constant or variable and is described as the distance between the internal and external nodes as shown in figure 2.18. For a constant unit thickness all intermediate points are on the base curve in point C, as well as the intersec on of the circle for the deployability constraint. M represents the centre of the constraints circle. The unit lines intersect in the centre. MC is tangent to the base curve and perpendicular to OC which also determines the unit thickness t as its the bisector of unit angle 2Î´. The circles intersec on with the base curve determines the intermediate point of the next scissor unit. An irregular unit thickness introduces unit thickness t1 and t2 instead of a constant t, results in diďŹ&#x20AC;erent scissor unit semi-lengths and creates an irregular scissor unit linkage. The other design parameters remain the same as with the constant scissor linkage and all intermediate points and the deployability constraint circle intersec on are s ll on the base curve in point C. The diďŹ&#x20AC;erence is the placing of M which represents the centre of the circle determined by the changed radius of the subsequent deployability constraint circle.

Figure 2.18 | Polar unit

Figure 2.21 | Base curve

Figure 2.19 | Parameters design method 1 constant polar unit

Figure 2.22 | Linked constant polar units with method 1

Figure 2.20 | Parameters design method 1 irregular polar unit

Figure 2.23 | Linked irregular polar units with method 1

Scissor structures

The second method for polar linkage is with an inner and outer curve with a distance t, unit thickness, which determines the inner and outer end nodes of the scissors. By connec ng these nodes a constant polar unit linkage is made. This method can also be used for a pluricentred arc as Temmerman (2007) widely describes in his thesis, instead of the discussed base arc with a single centre. Using such an arc can increase the headroom compared to a single centered arc with the same span and rise. Further details of the diďŹ&#x20AC;erence in design of a pluricentered arc will not be discussed in this report.

Figure 2.24 | Parameters design method 2 constant polar unit

Figure 2.25 | Linked irregular polar units with method 1

Transla onal linkage As polar linkages are mostly based on circular cuves, transla onal linkages can be based on any arbitrary curve according to Temmerman (2007). Both constant or variable unit thickness linkages can be made. The most common method, for a constant unit linkage, is to start with a base curve with midpoints M and Mâ&#x20AC;&#x2122; of PQ and ST with represent the unit thickness t. The ellipse for the deployability constraint contains points P, S, Q and T. A double ellipse which is twice the size of the original ellipse determines points M and Mâ&#x20AC;&#x2122;. A scissor unit is made by connec ng P, G and S, T, which are the points of the end nodes.

Figure 2.26| Parameters design constant transla onal unit

Figure 2.27 | Deployability constraint ellipses for constant transla onal unit

Figure 2.28 | Linkage constant transla onal units

19 With a variable unit thickness t, the transla onal scissor bars have variable semi-lengths. The intersec on points with the base curve of the original ellipses for the deployability constraint determine the loca on of the intermediate hinges. The double ellipse method can’t be used due to the variable unit thickness as explained by Temmerman (2007). Each conseque ve unit’s intermediate hinge has to be determined by drawing the next ellipse seperately for the deployability constraint. The M variables which determine the unit thickness t1 and t2 (etc.) are drawn as the centre of each consequen ve ellipse which intersects on the base curve. A er drawing the ellipse, points P, Q, S and T are determined which are the end nodes of the transla onal scissor units as with the constant units. Points PQ and ST are connected through point K which is the intersec on point of two conseque ve ellipses.

Figure 2.29| Parameters design irregular transla onal unit

2.5 | Modified-SLE (M-SLE) SLE’s can be modified in such a way that it’s freedom of movement can be increased. M-SLE’s differ from regular SLE’s because of addi on of extra revolute joints. Not only is the SLE modified, the whole transforma on capacity of the scissor structure is affected (Akgun, 2010). The scissors before and a er the posi on of M-SLE behave as a constant sub-structure and have the ability to move without affec ng the other part of the structure. M-SLE’s therefore divide the scissor structure into seperatly transforming sub-structures. The movment and transforma on of a structure is related to the number of M-SLE’s (Akgun, 2010). Furthermore the type of top and bo om scissor elements of an arc can be described as half an M-SLE. The type of hinge on the top or bo om connec on has a great influence of the transforma on proper es of the whole structure.

Figure 2.31| Examples of M-SLE’s

Figure 2.30| Linkage irregular transla onal unit

3 16

Concept

3.1 | Scissor arcs For designing a kine c dome based on 2D scissor structures, designing a 2D dimensional kine c scissor arc is the start. By connec ng two mirrored curved arcs, a dome shaped scissor arc is formed. By modifying the scissor by moving the structures units, their unit lines are changed and therefore the focus of the arcs. This dome shaped connected arc can take up many shapes. This gives the oppertunity to change the surface angle towards the sun, with eye on the purpose of the design of the dome to follow the sun track.

Figure 3.3 | Scissor arc shape possibili es

Figure 3.1 | Kine c scissor arc

A dome consis ng out of scissor structured arcs can have many diﬀerent configura ons. The amount of axes are variable, the axes direc on is changable and diﬀerent types of scissor structural units are op onal.

Figure 3.2 | Diﬀerent configura ons for a dome with scissor arcs

Figure 3.4 | Diﬀerent configura ons for a dome with scissor arcs with a fla end surface

Concept

3.2 | Kine c arc type The movement of a kine c arc depends on the type of scissor units used for the arcs structure. Figure 3.5 and 3.6 show a transla onal arc and a polar arc and their movement. A movement in the transla onal arc directly affects the folding or stretching of the other scissor units in the arc. As by the example shown in figure 3.5 the right half of the arc stretches, the le part of the arc folds together. In other words, the movement of one unit line affects the posi on and therefore moves the other unit lines. Both halfs of the arc are not seperatly changable in length or posi on. For the polar arc, movement of half of the arc by pivot of the intermediate hinges, does not necessarily immediately fold in or stretch out the other half of the arc as both sides of the arc have their own focus points. This makes it possible for half of the arc to stretch in or out by changing its focus point while maintaining the focus point of the other half of the arc. This half of the arc only gets pushed or pulled out of it’s original posi on as shown in the top drawings of figure 3.6. It’s therefore also possible to change the configura on of only one half of the arc. Because of the advantage of changing both halfs of the arc seperately, the decision is made to design a dome with polar arcs. With this advantage, movement of the dome is be er to control into the right posi ons for the best angles towards the sun to maximize the solar efficiency of the solar panels. The base curve is kept as a star ng point for the design.

Figure 3.5 | Kine c movement transla onal arc

original

intermediate hinge & multiple end nodes

Figure 3.6 | Kine c movement polar arc

intermediate hinge

intermediate hinge & 2 end nodes

intermediate hinge

2 outer end nodes

3.3 | Scissor dome structural concept As described in the foreword of this report, this project consists out of mul ple phases. A er phase two, which is the design of an individual concept described in this paragraph in order to sketch a clear context for the following chapters, is the concept design which was chosen to improve and elaborate star ng from phase three. The structural concept is based on polar scissor units as men oned in sec on 3.2. This first structural design was a configura on of three arcs consis ng out of six halfs or six legs connected in the top node of the dome with a rigid connec on of the bo om nodes. Each part consists out of three SLEâ&#x20AC;&#x2122;s, one M-SLE and the top and bo om scissor elements. Figure 3.7 to 3.10 show the steps for assemblage and erec on of the structure.

Figure 3.7 | Step 1: assemblage of the scissor arcs and connec ng the top node

Figure 3.8 | Step 2: folding out the scissor arcs and connec ng the bo om founda on nodes

Figure 3.9 | Step 3: connec ng the linear actuators

Figure 3.10 | Step 4: using the linear actuators to rise the structure

The movement and transformability of the structure is controlled by linear actuators. Linear actuators are components which control the structural movement by expanding or retrac ng the scissor components. This conceptual design contains a total of six linear actuators. Although the structure is kine c, it doesnâ&#x20AC;&#x2122;t meet the required transformability/movability in order to follow the sun track during day and the seasons in the most eďŹ&#x192;cient and op mal way. Also there are opportuni es to improve and op mize the configura on or amount of structure. Beside these required improvements, a suitable skin design and moun ng on the structure has to be elaborated. The proces of op miza on and improvements leading to the final design is presented in chapter 4.

4 24

Design op miza on

25 design to keep 6 legs could be to keep the structure more dome shaped, however a well designed skin would also maintain a dome shape. The set-up of the matrix includes three parts containing the design, tes ng and grading of the varia ons of structures.

4.1 | Introduc on The (re)search for the most efficient and op mized design started with figuring out improvement opportuni es and variables for the concept described in sec on 3.3. As men oned in the previous chapter, the transformability of the structure isn’t op mal as the whole structure wasn’t designed to en rely move in a spherical way to follow the spherical path of the sun in the most efficient way. Improving the movement of the structure is the most important requirement. The scissor arcs could also be op mized in terms of quan ty, the number of SLE’s/M-SLE’s and the number of arcs. A larger number of linear actuators equals a rela vely higher cost, besides the increasing difficulty of control of movement. Different types of hinges is also a variable for the movement and difficulty of the structure. In order to op mize and improve the design, a matrix was made which contains a variety of different scissor structures which were designed, tested, compared and graded on several aspects concerning the quan ty and quality of structure and it’s movement and difficulty. The matrix starts with the first concept design with four legs instead of six and ends with the designed structure which was a first improvement of the first structural concept, figure 4.1 to 4.3, as described in sec on 3.3. These first improvements include changing the bo om node rigid connec on to a two way hinge for increasement of transformability and mo on and reloca on of M-SLE’s and their linear actuators.

Part one is the design of a variety of diﬀerent 2D scissor arcs. The variability lies in the number of SLE’s and M-SLE’s as wel as the type of hinge used for the top and bo om node and M-SLE hinge. Five diﬀerent arcs were designed. Figure 4.1 | First improvements study model sleep posi on

The second step involves tes ng the designed varia on of scissor structures. The arcs were tested as a 2D arc instead of a whole dome, this way the movement of the arcs were tested as well as the ability to track the sun during the day and diﬀerent seasons in the most eﬃcient and op mal way. In other words, the transformability and adabtability of the structures was tested.

Figure 4.2 | First improvements study model mid-day posi on

4.2 | Matrix Before se ng up the matrix, the decision was made to con nue the process of op miza on with two arcs consis ng out of four legs instead of the ini al three arcs and six legs, as this many legs aren’t needed for the movement of the structure. The only reason for this

Figure 4.3 | 2D arc first improvements

The third and final step is concerned with comparing and grading the structure varia ons on several aspects regarding the quan ty and quality of the structures. The varia ons were judged on whether the movement with the sun is spherical as required, the structural quan ty which is the number of scissors and legs and the number of actuators. These quan ty parameters are also reflected in the costs of the dome with a difference in costs per type of component. Actuators are more expensive than scissor units. The difficulty of the structure implies the complexity of the movement which is linked to the number of actuators and also judges the type of hinges. The sun lit surface takes into account the surface size and the effec vity of the solar panels is judged by the possible angles towards the sun and therefore the op mal angles for the highest effec vity of the solar panels.

Design op miza on | Matrix part 1 design varia ons & 2 tes ng

Figure 4.4 | Variant V1A

Figure 4.5 | Movement

Figure 4.6 | V1A morning

Figure 4.7 | V1A winter mid-day

Figure 4.10 | Variant V1B

Figure 4.11 | Movement

Figure 4.12 | V1B morning

Figure 4.13 | V1B winter mid-day

Figure 4.18 | Variant V2A

Figure 4.19 | Movement

Figure 4.20 | V2A morning

Figure 4.21 | V2A winter mid-day

Figure 4.8 | V1A summer mid-day

Figure 4.9 | V1A evening

Figure 4.14 | V1B spring/fall mid-day

Figure 4.15 | V1B summer mid-day

Figure 4.16 | V1B evening

Figure 4.17 | V1B night/sleep

Figure 4.22 | V2A spring/fall mid-day

Figure 4.23 | V2A summer mid-day

Figure 4.24 | V2A evening

Figure 4.25 | V2A night/sleep

Design op miza on| Matrix part 1 design varia ons & 2 tes ng

Figure 4.26 | Variant V2B configura on 1

Figure 4.27 | Movement

Figure 4.28 | V2B1 morning

Figure 4.29 | V2B1 winter mid-day

Figure 4.34 | Variant V2B configura on 2

Figure 4.35 | Movement arc E/W

Figure 4.36 | V2B2 arc E/W morning

Figure 4.37 | V2B2 arc E/W winter mid-day

Figure 4.42 | Movement arc N/S

Figure 4.43 | V2B2 arc N/S morning

44 | V2B2 arc N/S winter mid-day

Figure 4.30 | V2B1 spring/fall mid-day

Figure 4.31 | V2B1 summer mid-day

Figure 4.32 | V2B1 evening

Figure 4.33 | V2B1 night/sleep

Figure 4.38 | V2B2 arc E/W spring/fall mid-day

Figure 4.39 | V2B2 arc E/W summer mid-day

Figure 4.40 | V2B2 arc E/W evening

Figure 4.41 | V2B2 arc E/W night/sleep

Figure 4.45 | V2B2 arc N/S spring/fall mid-day

Figure 4.46 | V2B2 arc N/S summer mid-day

Figure 4.47 | V2B2 arc N/S evening

Figure 4.48 | V2B2 arc N/S night/sleep

Design op miza on | Matrix part 3 comparison & grading

Figure 4.49 | Previous configura on V3

Figure 4.50 | Movement

Figure 4.51 | V3 morning

Figure 4.52 | V3 winter mid-day

Comparison and grading A er tes ng the varia ons all designs were compared to eachother and to the previous design as shown above. The evalua on grades are as follows: ++ = +2 | + = +1 | +/- = 0 | - = -1 |-- = -2. Variant V1A (figure 4.4-4.9) Legs: 4 Scissors: 8 per arch, total 16 Actuators: 2 per arch Total actuators: 4 Movement: one way, linear

Variant V1B (figure 4.10-4.17) Legs: 4 Scissors: 8 per arch, total: 16 Actuators: 2 per arch Total actuators: 4 Movement: spherical movement legs linear movement midpoint

Variant V2A (figure 4.18-4.25) Legs: 4 Scissors: 8 per arch, total 16 Actuators: 4 per arch Total actuators: 8 Movement: spherical movement legs linear movement mid-leg points

Movement (spherical) w/ sun: no Diﬃculty of structure: Structure quan ty: Actuator quan ty: Costs: Sun lit surface: Eﬀec vity solar panels:

-++ ++ ++ ++ ---

Movement (spherical) w/ sun: partly Diﬃculty structure: Structure quan ty: Actuator quan ty: Costs: Sun lit surface: Eﬀec vity solar panels:

+/+ ++ ++ ++ +/+/-

Movement (spherical) w/ sun: yes Diﬃculty structure: Structure quan ty: Actuator quan ty: Costs: Sun lit surface: Eﬀec vity solar panels:

++ + ++ + + + +

Total score:

Figure 4.53 | V3 summer mid-day

Figure 4.54 | V3 evening

Variant V2B1 (figure 4.26-4.33) Legs: 4 Scissors: 12 per arch, total 24 Actuators: 4 per arch Total actuators: 8 Movement: spherical movement leg extra linear movement mid-leg points

Figure 4.55 | V3 night/sleep

Variant V2B2 (figure 4.34-4.48) Legs: 4 Scissors: 12 per arch, total 24 Actuators: 4 per arch Total actuators: 8 Movement: spherical movement leg extra linear movement mid-leg points

Variant V3 (previous variant, figure 4.49-4.55) Legs: 6 Scissors: 8 per arch, total 24 Actuators: 5 per arch Total actuators: 15 Movement: spherical movement leg Spherical movement midpoint linear movement mid-leg points

Movement (spherical) w/ sun: yes Diﬃculty structure: Structure quan ty: Actuator quan ty: Costs: Sun lit surface: Eﬀec vity solar panels:

++ + + + + + +

Movement (spherical) w/ sun: yes Diﬃculty structure: Structure quan ty: Actuator quan ty: Costs: Sun lit surface: Eﬀec vity solar panels:

++ + + + + ++ ++

Movement (spherical) w/ sun: yes Diﬃculty structure: Structure quan ty: Actuator quan ty: Costs: Sun lit surface: Eﬀec vity solar panels:

++ + ++ ++

Total score:

Design op miza on | Matrix part 4 decision

4.3 | Results The evalua on process as shown on the previous pages shows that variant V2B2 scored best. Therefore variant V2B2 is chosen as the most op mal structure to elaborate. A er this decision was made, a comparison study was done with two diďŹ&#x20AC;erent configura ons of variant V2B2. Also two diďŹ&#x20AC;erent types of solar panels were used to compare and test for further elabora on as well. As the first configura on requires two more actuators for movement, it requires two less scissors. The second structure is therefore easier to control the movement of than the first because of the fewer actuators, this also means that the controlled mo on direc on is limited. The second structure has a larger movement range but is also a bit unstable because of the great number of scissors. The choice of configura on 1 was because of a more stable structure with a few less scissors. The advantage of a few less actuators for the second does not weigh greater against greater stability and less scissors. In chapter 5 the final design is presented.

Configura on 1 Legs: 4 Scissors: 12 per arch, total 24 Actuators: 4 per arch Total actuators: 8 Movement: spherical movement leg extra linear movement mid-leg points

Figure 4.56 | Config. 1 morning

Configura on 2 Legs: 4 Scissors: arch EW 14 arch NS 12 Total scissors: 26 Actuators: arch EW 2 arch NS 4 Total actuators: 6 Movement: spherical movement leg extra linear movement mid-leg points Figure 4.61 | Config. 2 morning

Figure 4.57 | Config. 1 winter mid-day

Figure 4.58 | Config. 1 spring/fall mid-day

Figure 4.59 | Config. 1 summer mid-day

Figure 4.60 | Config. 1 evening

Figure 4.62 | Config. 2 winter mid-day

Figure 4.63 | Config. 2 spring/fall mid-day

Figure 4.64 | Config. 2 summer mid-day

Figure 4.65 | Config. 2 evening

5 34

Final design

5.1 | The design In this chapter the final design of the dome is presented. This design presented in this chapter, is elaborated in a way such that it could be build by the building industry with regular building materials in order to understand and properly simplify the structure and it’s materials a er with other simple more aﬀordable materials in chapter 6. A er the op miza on process the final configura on of the scissor arcs is defined. The structure consists out of two diﬀerent arcs. A North-South arc which is shorter, as it’s consists out of less scissor units and requires one less linear actuator than the East-West arc. The N/S arc is used to control the angles towards the sun during the seasons. The E/W arc controls the sun tracking movement during the day. Each arc is connected to two linear actuators at the endings, which control the folding and stretching of the structure. The other linear actuators control the bending. Together the linear actuators control the angle of the structure towards the sun.

Figure 5.1 | East-West arc

The material used for the scissor units is wood which are connected by steel hinges with bearrings and bolts. The decision for wood is made based on the material proper es. Steel and aluminum are besides being more expensive, much heavier to work with which is a great disadvantage as the structure is ought to be lightweight in order to be easily foldable and transportable. Possible scissor materials Steel: Aluminum: Wood (depends on the type): (Source: ekbouwadvies.nl)

Weight 7800 kg/m3 2700 kg/m3 350-1000 kg/m3 Figure 5.2 | North-South arc

Final design

For the skin a secondary flexible piping structure is designed to fit on and between the scissor structure. The PVC skin is connected to the piping railings. The solar foil used to capture sun energy is shaped as a

Figure 5.3 | Interior impression

kippah and is placed as the top part of the skin. This top part of the dome is the part which is constantly focused to the sun by transforming and moving the structure during the day and seasons. The structure arcs are each

divided into three sub-arcs by M-SLEâ&#x20AC;&#x2122;s. The middle subarc is the kippah shaped suntracking part of the dome.

Figure 5.4 | Top impression

Figure 5.6 | Impression

Figure 5.5 | Eye level impression

Final design

5.2 | Details

Figure 5.7 | Structure impression

Figure 5.8 | Detail scissor unit

Figure 5.10 | Detail M-SLE

Figure 5.9 | Detail scissor unit exploded

Figure 5.11 | Detail M-SLE exploded

Final design

Figure 5.12 | Detail top node

Figure 5.13 | Detail skin structure

5.3 | Solar-room study As a final check for the adabtability of the structure towards the sun and the eďŹ&#x20AC;ec vity of the solar panels, a study was done in the solar-room. In this solar room the sun and itâ&#x20AC;&#x2122;s track are simulated. The results are presented in this chapter.

Figure 5.14 | Winter me 08:30

Figure 5.15 | Winter me 13:00

Figure 5.16 | Winter me 15:30

Figure 5.17 | Spring/fall me 08:30

Figure 5.18 | Spring/fall 13:00

Figure 5.19 | Spring/fall me 15:30

Figure 5.20 | Spring/fall me 17:30

Figure 5.21 | Summer me 08:30

Figure 5.22 | Summer me 13:00

Figure 5.23 | Summer me 15:30

Figure 5.24 | Summer me 19:00

6 42

Simplifica on and building process

6.1 | Subs tu on of building materials In order to build the dome in a 1:1 full scale model, the building materials needed to be subsituted into aﬀordable and simple materials which don’t neccessary have to be materials used in regular buildings. A few experiments were done using PVC pipes and MDF wood as shown in figure 6.1. These materials were unfortunately not suitable to build a 1:1 model with. These materials were good for small scale models, as the scale increases the proper es of the materials to serve as building materials failed as they started to bend and eventually break or tear. The bolted hinge connec ons made to connect the PVC pipe scissors lead to increasing sizes of the openings made for the connec on as PVC is a rela vely weak material. The MDF scissors started to tear at the connec ons eventually leading to breakage of the scissor unit.

Figure 6.3 | Measurements scissor units full scale model Figure 6.1 | Material experiments with PVC and MDF

At first using metals wasn’t an op on as these materials are expensive and usually have to be ordered far in advance. During the material experiments done with PVC and MDF, contact was made with a few metal scrap collec ng companies in Eindhoven. An idea for subsitu ng scissor units for example is to use old climber or scaﬀolding pipes used in building construc on. Fortunately these companies reacted posi vely and agreed to sponsor this project by lending metal materials which are aluminum climber pipes and steel screwthread to make linear actuators and bolts. The (lock)nuts were sponsored. Beside scrap collec ng companies, also contact was made with a sail company which also agreed to sponsor the project with PVC sail material for the skin. To test the materials and func oning of the design, a model was made scale 1:4 before building a full scale model.

Figure 6.4 | Scissor unit of aluminum pipes

Figure 6.5 | M-SLE unit of aluminum pipes Figure 6.2 | Shopping at the metal scrap company

Simplifica on and building process

Connec on details With using diďŹ&#x20AC;erent materials for the models, diďŹ&#x20AC;erent connec ons needed to be designed. The connec ons also had to be simplified and converted into the available materials. The hinges are simplified into simple bolt and nut connec ons. The top and ground node are also simplified into easier and be er buildable connec ons using the available materials.

Figure 6.7 | Detail scissor units

Figure 6.6 | Detail top node

Figure 6.8 | Detail scissor units exploded view

The ground node was ini ally designed to consist out of a L-shaped angle steel profile which is connected to a short round profile made out of the same scaďŹ&#x20AC;older pipes as the scissor units as shown in figure 6.9 and 6.10. Together this ground node func ons as a two way hinge. The 1:4 model was built

Figure 6.9 | Detail ground node and skin

using this designed connec on but for the full scale model another founda on was needed. This will be discussed in sec on 6.3 The connec on of the PVC membrane for the skin is done with PVC piping. PVC pipes are flexible to bend in a circular way into the dome shape and is connected to the scissor structure

by sliding and fixing it onto the screwthread which is used for the hinge connec ons. The membrane itself consists of one dome shaped sail.

Figure 6.10 | Detail ground node and skin exploded view

Simplifica on and building process

6.2 | Inventory For the next step an inventorylist was generated to list and collect the needed materials to build the models.

Sponsored by: Pro-Seal Zeilmakerij B.V. Hoppelkuil 17 5626 DD Eindhoven Van de Mortel B.V. Kanaaldijk-Noord 105-107 5642 JA Eindhoven Van der Winkel Hurksestraat 20B 5652 AK Eindhoven

For the full scale model aluminum scaďŹ&#x20AC;olding pipes are used for the scissor structure. The structure consists of aluminum pipes with a length of 1 m for the basic scissors. The pipes for the M-SLEâ&#x20AC;&#x2122;s are 0,58 and 0,48 meters long. The pipes are a ached to eachother by screw thread and fixed with locknuts and rings. The aluminum pipes are sponsored by A.M. van de Mortel B.V. in Eindhoven. The locknuts and rings are sponsored by Van der Winkel in Eindhoven as well as the PVC piping used for the secondary structure for the skin. The top node of the structure is a middlepoint which consists of a short piece of pipe with both arcs crossed and fixed with a hinge on this mid-point. The mid-point itself moves with the mo on of the structure as well as the structure moving around the mid-point. The arcs are fixed on the ground with steel pipe corner pieces with a double hinge in order to be able to move the arcs in two direc ons. The linear actuators consist of screw-thread through two small L-shaped corner pieces connected to the scissor structure. The screw-thread is screwed in or out with motors to move the structure. The motors used to control the linear actuators are washing machine motors and are loaned from Van der Mortel. For the skin PVC pipes are used as a railing for the membrane. The skin membrane consists of PVC. This PVC membrane is also sponsored by ProSeal Zeilmakerij B.V. in Eindhoven. The membrane is a ached to the rails with rings.

Simplifica on and building process

6.3 | Building process 1:4 model As men oned before, first a prototype tes ng model scale 1:4 was built to test the design and materials. This model is shown in figure 6.11 - 6.17. The results of the tes ng of this 1:4 model were great. The model worked and moved properly as shown in figure 6.18 - 6.25.

Figure 6.11| Folded structure model 1:4

Figure 6.13 | Detail linear actuator and M-SLE model 1:4

Figure 6.14 | Building the skin secondary structure

Figure 6.12 | Folded sctructure model 1:4

Figure 6.15 | Building the skin secondary structure

Figure 6.16 | Building the skin secondary structure

Figure 6.17 | Ground node detail model 1:4

Simplifica on and building process

Figure 6.18 | Model 1:4 sleep/night mode

Figure 6.20 | Model 1:4 before noon

Figure 6.19 | Model 1:4 morning

Figure 6.21 | Model 1:4 summer a ernoon / mid-day

Figure 6.22 | Model 1:4 winter a ernoon / mid-day

Figure 6.24 | Model 1:4 late summer evening

Figure 6.23 | Model 1:4 summer evening

Figure 6.25 |Model 1:4 winter evening

Simplifica on and building process

6.4 | Building process full scale model A er the succesfully built and tested 1:4 model, the construc on of the full scale model began. At the same me of building the 1:4 model, a detail part with a linear actuator of the 1:1 model was built as a prototype for the full scale model. This model is shown in figure 6.14 in the background. The tes ng of this detail model was unfortunately not so succesful as the screwthread used for the linear actuator turned out to be too weak. Luckily thicker screwthreads were available at the sponsoring scrap companies which could be used in the full scale model. Also precision of the sawing the scissor units and drilling holes for the hinge connec ons in the pipes turned out to be very important. When drilling holes in the pipes they were likely to be crooked on the opposite side. Extreme precision with sawing and drilling posi ons had to be taken into account with producing the scissor units.

Figure 6.26 | Folded scissor arc a er assembly

A er sawing the scissor units and drilling holes precisely for the full scale model, the scissor arcs were assembled. Figure 6.26 - 6.28 show one of the scissor arcs in folded and unfolded state.

Figure 6.27 | Unfolding the scissor arc

Figure 6.29 | Founda on peg

The model was ini ally designed to be built inside the cupola at the TU terrain, then the idea was conceived to set the full scale model up outside on the green area next to Ver go, faculty of architecture. A er receiving permission to build the model outside on this green area, the founda on elements had to be redesigned in order to fix the model into the grass. A tent-like peg was made out of aluminum pipes to pin into the ground as shown in figure 6.29 and 6.30. This fixa on turned out to be more stable than the founda on elements as presented in sec on 6.1, figure 6.9 and 6.10.

Figure 6.28 | Unfolded scissor arc

Figure 6.30 | Founda on peg

53 A er producing the scissor elements, assembling the scissor arcs and fixa ng the founda on pipes into the ground a er measuring out their exact posi on, the building of the model began with se ng up the arcs and connec ng them to eachother as shown in figure 6.31 - 6.42.

Figure 6.31 | Fixated founda on pegs

Figure 6.33 | Se ng up the arcs

Figure 6.32 | Se ng up the arcs

Figure 6.34 | Connec ng the arcs

Simplifica on and building process

Figure 6.35 | Building the dome (1)

Figure 6.37 | Building the dome (3)

Figure 6.36 | Building the dome (2)

Figure 6.38 | Building the dome (4)

Figure 6.39 | Building the dome (5)

Figure 6.41 | The dome in sleep/night mode (2)

Figure 6.40 | The dome in sleep/night mode (1)

Figure 6.42 | The dome in sleep/night mode (3)

Simplifica on and building process

The first steps of se ng up and connec ng the arcs went nicely. No problems occured at this stage of the building process. A er se ng up the dome in sleep/ night mode as shown in figure 6.31 - 6.42, unfolding the top part of the structure, which is the suntracking kippah shaped part of the dome, turned out to be almost impossible because of the great forces, the height of the dome and bending of the screwthread used for the actuators (M12 instead of M10) as well as the hinges (M10 instead of M8) on the M-SLE’s. Even though the screwthread was already thicker than with the prototype scissor built of the 1:1 model before the defini ve model, it s ll wasn’t s ﬀ enough to take up the momentum on the hinges nor to bear the forces and weight of the structure. This resulted into bended M-SLE hinges as shown in figure 6.43 as these hinges are the weakest and the structure couldn’t be unfolded. The M-SLE hinges were therefore replaced by M12 instead of M10. In order to unfold the structure all the top linear actuators on the M-SLE’s were dismounted and a forkli was needed to li the structure up, a ach the structure to the founda on, then assemble and set the the linear actuators in posi on and finally removing the forkli to a ach the skin secondary PVC pipe structure and the skin membrane as shown in figure 6.44 - 6.65.

Figure 6.43 | Bended M-SLE hinge screwthread

Figure 6.44 | Replacing the M-SLE hinge screwthread

Figure 6.45 | Assembling the scissor arcs a er replacing the M-SLE hinges

Figure 6.46 | Pu ng the scissors in posi on for the forkli

Figure 6.48 | Forkli li ing the structure (1)

Figure 6.47 | Driving the forkli under the structure

Figure 6.49 | Forkli li ing the structure (2)

Simplifica on and building process

Figure 6.50 | A aching the linear actuators

Figure 6.52 | Removing the forkli (1)

Figure 6.51 | A aching the linear actuators and fixa ng the founda ons

Figure 6.53 | Removing the forkli (2)

Figure 6.54 | The dome structure completed

Figure 6.56 | Moun ng the skin secondary PVC pipe structure (2)

Figure 6.55 | Moun ng the skin secondary PVC pipe structure (1)

Figure 6.57 | Moun ng the skin secondary PVC pipe structure (3)

Simplifica on and building process

Figure 6.58 | Moun ng the skin secondary PVC pipe structure (4)

Figure 6.60 | Completed secundary PVC pipe structure (2)

Figure 6.59 | Completed secundary PVC pipe structure (1)

Figure 6.61 | Completed secundary PVC pipe structure and suntrack kippah (3)

Figure 6.62 | Completed dome model

Figure 6.64 | Transforming structure to mid-day posi on

Figure 6.63 | Transforming structure to morning posi on

Figure 6.65 | Transforming structure to evening posi on

Simplifica on and building process

6.5 | Conclusions and recommenda ons As men oned in sec on 6.4, the building process of the 1:1 model wasn’t as succesfull as it should’ve been. First of all the se ng up of the dome didn’t succeed in the way as it was meant to be set up. The structure should’ve been a ached on the founda on/ground nodes and then li ed up from folded state into unfolded state by adjus ng the linear actuators. With the 1:4 model this method worked perfectly. As decribed in the previous sec on the linear actuators of the full scale model weren’t strong enough to li the weight of the structure nor bear the forces. Therefore a forkli was needed to li the structure, a ach the ground nodes and then a ach and adjust the linear actuators. With scaling the structure from the 1:4 model to the full scale model, the dimensions of the scissor units/arcs and their span were scaled up, but the screwthread used for the hinges and linear actuators wasn’t scaled up four mes as did the rest of the structure. The angle profiles of the actuators bended as well. The hinge size went from M8 to M10 and the linear actuators went from M10 to M12. Both sizes of screwthead used should have gone up at least 3 to 4 sizes as well to M18 and M20. A more eﬀec ve, stronger and easier controllable solu on would be replacing the screwthread linear actuators with hydraulic or pneuma c pumps. Another cause for the bending of the hinge screwthread is the great momentum in the hinges. This could be solved by using rectangular or square scissor units instead of round pipes as the fric on of the scissor units would be decreased. Another solu on could be fla ening the ends of the round pipes into plates or moun ng flat plates onto the round pipes to decrease the hinge length as done on a project for a swimming pool cover in Seville, Spain. This solu on is shown in

figures 6.68 - 6.70. With this solu on the momentum decreases with the decreasing length of the hinges. Also the fric on of the structural elements is decreased.

Figure 6.68 | Swimming pool cover in Seville, Spain

Figure 6.66 | Detail of the full scale model scissor hinge

Figure 6.69 | Detail hinge connec on smimming pool cover

Figure 6.67 | Detail of 1:4 model scissor hinge

Figure 6.70 | Detail founda on swimming pool cover

Furthermore the placing of the linear actuators on the scissor structure eďŹ&#x20AC;ects the forces and momentum built up on these elements which causes the linear actuators to bend. The actuators on the model are placed on the side of the scissor unit as shown in figure 6.71 and 6.72. With replacing all linear actuators to the neutral midpoint in between the two scissor bars of a scissor unit instead of on the side of the scissor structure, the built up momentum decreases in the actuator preven ng the actuator from bending. Placing the PVC skin structure in between the scissor structure as described in chapter 5, turned out to be of benefit for the stability of the scissor structure. The PVC pipes for the skin were placed on the hinges of the scissor structure, this is shown in figure 6.73. The PVC skin pipes were subject to pressure of the scissor structure and therefore also func oned as pressure bars stabilizing the en re structure beside suppor ng the skin.

Figure 6.71 | Linear actuator placing on side of structure

Figure 6.73 | PVC skin pipes connec on to scissor structure

Despite of the diďŹ&#x192;cul es men oned, both the 1:4 and the full scale model were stable. Both models moved and transformed the way they should following the sun track during the day and diďŹ&#x20AC;erent seasons in op mal posi ons, with some manual help here and there, which makes the structural design of the kine c scissor dome a succes. With this design, the design goals were also succesfully met as set in chapter 1 as the structure is lightweight, foldable and therefore easy transportable.

Figure 6.72 | Bent linear actuator

Bibliography

Literature Akgun. Y. (2012) A novel transforma on model for deployable scissor-hinge structures, Stu gart: Universit채t Stu gart EK Bouwadvies (2009) Tabellen bouwmaterialen. op [h p://www.ekbouwadvies.nl/tabellen lambdamaterialen.asp], Geraadpleegd: 21 mei 2013 Temmerman, N., de (2007) Design and Analysis of Deployable Bar Structures for Mobile Architectural Applica ons, Brussel: Vrije Universiteit Brussel, Faculty of engineering

Figures Figure 1.1 Weersta on Uithoorn (2010) Zonnestand. op [h p:// www.weersta onuithoorn.nl/Weer/Zonnestand.htm], Geraadpleegd: 25 april 2013 Figure 2.1, 2.2, 2.5 - 2.15, 2.18-2.30 Temmerman, N., de (2007) Design and Analysis of Deployable Bar Structures for Mobile Architectural Applica ons, Brussel: Vrije Universiteit Brussel, Faculty of engineering Figure 2.31 Akgun. Y. (2012) A novel transforma on model for deployable scissor-hinge structures, Stu gart: Universit채t Stu gart

Appendix

| Structure moƟon

Dynamics

| ParƟally moved structure in the morning hours

| Impression West elevaƟon mid-day

| Impression North elevaƟon mid-day

| MulƟple rigid panels + < two scissors

| Impression North-West angle mid-day

| MulƟple rigid panels + two scissors

| Impression West angle mid-day

Design

| CombinaƟon rigid panel + scissor

Concept

Rigidized scissors

YveƩe Eskander | 0819315

Moving mechanism For moving the structure a centre column is installed to the centre of the structure. The column can be branched and connected to an outer part of the structure. By swinging the column back and forth in the arched moƟon in which the structure moves. It’s important that the column only moves in a linear direcƟon.

A membrane with PV panels, would be a stretchy fabric in order to move with the structure. It could be aƩached on or between the structure.

Detailing Similar to the bone hinges of a human body, the joints connecƟng the parts of this structure are hinged joints. Like a human arm or leg the moƟon of the body part is limited to one direcƟon with a maximum inŇecƟon angle. This parƟcular property is important to integrate into the joints of this design as this limits the moƟon of the whole structure to prevent the joints from rotaƟng too far causing the structure to collapse.

The dome is designed to move along a arched linear moƟon from East to West. The arched linear moƟon line follows the path of the sun, as the sun rises from the East in the morning with a low angle. At this point of day the structure is fully ‘scissored’ in the right angle towards the East for the PV-panels to catch the right angle of solar energy. Towards midday the sun moves along higher to the South-West and therefore also has a higher angle. The structure with PV-panels also moves along the arched moƟon to the centre and is on it’s highest point at midday. AŌer midday the sun starts to set providing lower angles coming from the West unƟl sunset. The structure moves along the arched moƟon towards the West with the right angles for catching the solar energy. The diīerent angles of the arch in which the structure moves also suites the diīerent angles of the sun during summer and winter.

Structural design The structural design is based on the concept of scissors combined with rigid panels with the restricƟon of a maximum of two mutually connected scissors at a Ɵme to create stability in the structure movement.

Requirements and funcƟon The design is dome (like) shaped. It has to follow the sun to capture solar energy with PV-panels as it’s main funcƟon (1). Therefore the structure needs to be kineƟc in order to be able to move towards the sun. The structure span is 10 meters (2). It can be used as outside terrass shading (3).

Trial shows that the combinaƟon of centered scissors and rigid panels on the side to them, moves the scissors on a linear path and contracƟng the rigid panels along to the center in a linear movement perpendicular to the movement of the scissors. Combining two scissors which are mutually connected at the same Ɵme with rigid panels is a way to control the movement of the scissors and hinges. When combining more than two scissors connected mutually, the scissor moƟon becomes less controlable and allows the hinges to move separately in diīerent direcƟons causing the structure to collapse.

Concept As the Ɵtel describes, this concept is a mixture between scissor systems and rigid panels. The scissor systems are oriented horizontally and supported with rigid panels to prevent the scissor panels from scissoring their own way separately. So the rigid panels have two funcƟons; supporting the scissors and controlling their (sequence of) movement.

| Moving principle

| Hinge joint

Details

| Top impression mid-day

| Structure movement E/W secƟon

| Track and angle of the sun in Holland

(Source: WeerstaƟon Uithoorn)

Sun tracking

Requirements 10 meter

M2 Building Technology | Individual concept presentaƟon Date | April 4th 2013 Tutors | A.D.C. Pronk | J.B. da Conceicao van Nieuwenhuizen

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