Development of a Tensegrity Joint a Research Into an Adjustable Joint for Tensegrity Structures with Cable-Strut Connections

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Development of a tensegrity joint a research into an adjustable joint for tensegrity structures with cable-strut connections

Bernaards, X.M.

Award date: 2014

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Development of a tensegrity joint

A research into an adjustable joint for tensegrity structures with cable-strut connections

Xander Bernaards 0597372 25-09-2014

Graduation Supervision Committee prof.Dr.-Ing. P.M. (Patrick) Teuffel Ir. A.D.C. (Arno) Pronk Ir. H.M. (Hans) Lamers

Eindhoven University of Technology Structural Innovation and Design Building Technology

A-2014.71 Development of a tensegrity joint X.M. Bernaards

Development of a tensegrity joint X.M. Bernaards

Development of a tensegrity joint

A research into an adjustable joint for tensegrity structures with cable- strut connection

Xander Bernaards

“If one starts reviewing existing technologies and is able to generate new ideas, then he is a master in that area.” Confucius

Development of a tensegrity joint X.M. Bernaards

Colofon

Author Ing. X.M. (Xander) Bernaards Studentnr 0597372 Contact [email protected]

Graduation commission

Chairman: prof.Dr.-Ing. P.M. (Patrick) Teuffel Members: Ir. A.D.C. (Arno) Pronk Ir. H.M. (Hans) Lamers

Development of a tensegrity joint X.M. Bernaards

ABSTRACT

Objective: To research the developing of a joint for a tensegrity structure on the basis of a sketched idea, where single cables can be tensioned in the joint itself and can be produced on a large scale with low costs, including the state of the art regarding tensegrity joints, design possibilities, appropriate material and production methods. The “in the joint” connection is a new connection type that makes it possible to adjust the cable during construction and makes it easier to re-tension the cable after construction caused by slack. The new connection must be proven to work properly by testing. Method: This thesis is based on literature and experimental research. Literature is researched on the history of tensegrity structures and there joints whereupon a morphological matrix of the different joint solutions is made. The morphological matrix supports the criteria given by idea sketched. The joint is developed in an iterative process, which consists of design, producing prototype, testing, evaluation and re-design. The design is made in SolidWorks to test the ability to produce a prototype. First, a 3D printed prototype is made to function as a research object to improve the design. The improved design in made in aluminium to testing the new connection between set screw, thread and steel cable. Testing is done to prove that the new connection function properly and can be used to build a tensegrity structure. To ensure the large production scale a research is done to different production methods: Injection moulding and extrusion. The injection moulding is researched by using the moulding option in SolidWorks to see if it is possible the produce the joint in one piece. After investigating production methods for aluminium and plastic a proposal for producing is written. Results: A joint is designed which shows the possibility of having a connection in the joint itself and tensioning the cables separately which makes pre-cut cables unnecessary as the cable length can be adjusted even after construction. The testing proved that the new connection method is sufficient to use the joint in a tensegrity structure with a maximum working load of 87 kilograms. The best way to produce the joint is to separate the top from the body, as the whole joint isn’t possible to produce in piece. Just like the tested prototype, the material for the production method is aluminium. The production of the body is done by extrusion and the top part is produced by injection moulding. A proposal for production is made. Conclusions: This research of separate cable connections in the joint itself. The chosen production methods will be able to produce the joint on a large scale with low costs, but will first have to be proven to work. Further research is needed to optimize the production methods.

Keywords: Tensegrity structure, cable strut joints, injection moulding, extrusion

Development of a tensegrity joint X.M. Bernaards

Contents list 1. Introduction ...... 12 1.1 Problem description and relevance ...... 12 1.2 The research questions ...... 14 1.3 Approach ...... 14 2. Tensegrity structures ...... 18 2.1 History ...... 18 2.2 What is a tensegrity structure ...... 22 2.2.1 Definitions of tensegrity ...... 22 2.2.2 How does a tensegrity work ...... 23 2.3 Use of tensegrity structures in the building environment ...... 25 2.3.1 Structures ...... 25 2.3.2 Towers ...... 25 2.3.3 Tensegrity domes ...... 26 2.3.4 Geiger dome ...... 26 2.3.5 Bridge ...... 28 2.3.6 Furniture...... 28 2.4 Overlook ...... 29 3. Joints ...... 32 3.1 Introduction ...... 32 3.2 Pioneers ...... 32 3.2.1 Kenneth Snelson ...... 33 3.2.2 Richard Buckminster Fuller ...... 37 3.2.3 Katherine A. Liapi ...... 39 3.3 Joint solutions ...... 40 3.3.1 Morphological matrix ...... 41 3.3.2 Connection types ...... 43 3.3.3 In the joint ...... 44 3.3.4 On the joint ...... 44 3.3.5 Additions ...... 45 3.4 Conclusion ...... 46 4. Development ...... 48 4.1 Introduction ...... 48 4.2 Design ...... 49 4.2.1 Similarities ...... 50 4.2.2 Values for dimensions ...... 52 4.3 Producing prototype ...... 55 4.3.1 Wooden prototype ...... 55 4.3.2 Rapid prototyping ...... 55

Development of a tensegrity joint X.M. Bernaards

4.4 Re-design ...... 57 4.4.1 Aluminium prototype ...... 58 4.5 Prototype for testing ...... 59 4.6 Conclusion ...... 60 5. Testing ...... 62 5.1 Introduction ...... 62 5.2 Maximum torque of set screws ...... 62 5.3 Maximum strength of connection (test 1) ...... 65 5.5 Strength of re-design connection (test 2) ...... 71 5.6 Final test strength (test 3) ...... 76 5.7 Conclusion testing ...... 80 6. Design ...... 82 6.1 Aluminium product ...... 82 6.1.1 New joint ...... 82 6.1.2 A ‘3-strut T-prism’ tensegrity ...... 82 6.1.3 Cable routing ...... 83 6.1.4 Angles of cables ...... 84 6.1.5 Tensioning ...... 84 6.1.6. Fixing cables ...... 84 7. Production method ...... 86 7.1 Introduction ...... 86 7.2 Aluminium casting ...... 87 7.3 Injection moulding ...... 88 7.4 Design rules for moulding ...... 89 7.4.1 Draft ...... 90 7.4.2 Undercuts ...... 90 7.5 Design mould ...... 91 7.6 Costs ...... 93 7.6.1 Material cost ...... 93 7.6.2 Production cost ...... 93 7.6.3 Tooling cost ...... 93 7.7 Conclusion ...... 94 7.8 Proposal for production ...... 95 8. Conclusion ...... 102 8.1 Conclusion ...... 102 8.2 Recommendations ...... 105 Literature ...... 106 9. Appendix ...... 110 Appendix A. Dimensions ...... 110

Development of a tensegrity joint X.M. Bernaards

Appendix B. Morphologic matrix ...... 115 Appendix C. Cable routing ...... 116

Development of a tensegrity joint X.M. Bernaards

Preface

This report is my master thesis for the completion of the master program Architecture, Building and Planning, specialization Building Technology, at Eindhoven University of Technology, the Netherlands.

The aim of this thesis is the investigation and manufacturing of an adjustable joint for a tensegrity structure with strut-cable connection. This experimental research combines existing solutions of joints to realize a new joint design. The new joint design is a first step in designing joints where the cables can be adjusted after construction. The design, engineer, testing and realizing of the adjustable joint is described in this thesis.

This would not have been possible without contribution of other people. At first I would like to thank the people of the laboratory in Eindhoven, H. Lamers and T. van de Loo, for their help for making it possible to realize and be able to test the joint. Special thanks to Ir. A.D.C. Pronk for his supervision and for providing me with the idea and the first drawing of the joint.

Finally, I like to thank my girlfriend Charlotte and my friends who supported me in the process with their ideas and patience.

Xander Bernaards Augustus, 2014

Development of a tensegrity joint X.M. Bernaards

Introduction

This chapter gives the introduction with the topic, the problem 1. definition and the objective of the thesis.

Development of a tensegrity joint X.M. Bernaards

1. Introduction

1.1 Problem description and relevance

Building lightweight and more aesthetic are currently popular topics in engineering. Building lightweight is better for the environment, because the less use of raw materials. As material costs increase and some threatened to depleted, it is reasonable that methods that make efficient use of material will become more acceptable. Building lightweight structures is one of those methods. The focus in this thesis lies on tensegrity structures, they use materials in a very economical way.

Some seventy years ago, in 1962, the American architect Richard Buckminster Fuller (1895-1983) patented a new technology based on the use of isolated components in compression inside a net of continuous tension. He called it ‘tensegrity’, a contraction of the phrase ‘tensional integrity’1. Tensegrity structures are three-dimensional structures built of struts and cables attached to the ends of the struts which balance compression with tension and yield forces without breaking.

After having worked out the principles of tensegrity, Fuller started looking for methods to put this new technology into practice. Other people who were influenced by Fuller did the same, looking for any application for architecture or engineering. From the 1960s onwards, several structures were built in which the principles of tensegrity were applied. The technology, however, remained relatively unknown to architects and engineers until the end of the previous century, when it became increasingly clear that tensegrity structures have specific advantages that merit their consideration for use as engineering structures and mechanisms. Since then, more and more people are working on the subject and new tensegrity structures or structures based on the principles of tensegrity are being built in a tempo higher than ever before. Arguably the best known example of a recent structure in which the principles of tensegrity are applied, is the Kurilpa Bridge in Brisbane, built in 2009. With a total length of 470 meters, it is the largest hybrid tensegrity structure in the world (fig. 1.1).

Figure 1.1 Kurilpa Bridge, Brisbane, Queensland, Australia

1 The origins of tensegrity are highly controversial. Although Fuller coined the term, he would not have discovered the principle of tensegrity without the experiments of his student, the American artist Kenneth Snelson (1927). For the controversy on the origins of the term, see Jáuregui 2004, pp. 6-10.

Development of a tensegrity joint X.M. Bernaards

Even though tensegrity is applicable to architecture as an established structural system nowadays, the structures in which the principles of tensegrity are applied, are all custom built. If we wish tensegrity structures to be used on a larger scale, they should be made standardized to at least some degree, otherwise they can only be used in big budget projects such as the Kurilpa Bridge. In practice the standardization of tensegrity structures comes down to the standardization of the joints, like Snelson does for his sculptures. The joint is the technically most challenging part of the structure and one of the few parts of which the form depends only to a minor degree on the structure’s intended function. A quick look at the different kinds of joints used for tensegrity structures has revealed that up till now no joint has been developed which could be easily applied to more than one project (sculpture and building). They all have one great disadvantage, which is that they leave little to no room to adjust the length of the cables after the joints have been set into place. This because they make the cables to length with leaving no space for adjustments and if there is room for adjusting than that’s mostly done to absorb slack.

The first topic will be to research the joints used in tensegrity structures. With all the joints found a morphological matrix is made.

To fill the gap – adjusting and tensioning cables after construction – Ir. A.D.C. Pronk came up with an idea and made a sketch of a new type of joint.

“.. an idea is nothing more nor less than a new combination of old elements.” (Young, 1939)

Demands given by the new joint:  Cables have to be connected in the joint.  A slim joint, esthetical, with no additions on it.  Cables should be able to be adjusted before and after construction for tensioning.  Adjusting is done by the use of set screws  No use of external tensioning additions on cables. Figure 1.2 Idea sketch, A. Pronk, 2013  The struts diameter smaller than ten

centimetre

Development of a tensegrity joint X.M. Bernaards

This sketch is a strut with an integrated joint, where the cables run through channels that are cut in the top and sides of the strut. The cables are fastened to the strut by screws or bolts loosening the screw or bolt makes it possible to easily adjust the cable length. The second topic of this research is to develop the idea into a working product (fig 1.2). In order to make this product innovative and useful, research has to be done to see if the product can be applied in different tensegrity structures. The new joint design can use the already existing joint solutions found in the first topic. The product design will go till the production method where the production is explained to realize a low cost, ready to mass produce, product.

1.2 The research questions

Working out the sketch to a useful product that has the innovation to tension a single cable and can be produced in a large scale formulates into the following research question:

“In what way can a joint in a tensegrity structures be designed, where single cables can be tensioned in the joint itself (for esthetical purpose) and can be produced on a large scale with low costs?´

The research is divided in different sub-questions with topics; products on the market, design and production. These lead to the following sub-questions:

 What is the state of the art regarding tensegrity joints?  What are the design possibilities and how is the new joint realized?  What can be an appropriate material and production method for the joint?

1.3 Approach

To find the answer of the research question and its sub-questions, a research design is made and explained in this paragraph. The focus of this study will be on the design, engineering, testing and full scale realizing of an adjustable joint. A structured design methodology is used to make choices for designing the new joint. A research model (fig 1.4) based on the approach of A.D. de Groot (Groot, de, 1994) combined with the use of the cyclical iterative design process based on S. Thomke (Thomke, 2003) model, is made to bring structure to the research

The first step of this thesis is defining the problem by a pre-study of joints and former master projects. This step has been altered by the input of the sketch (fig 1.2), which made it the leading subject in this research.

The second step to be taken is to list the criteria given by the new joint design. These criteria have to be compared with the state of the art of joints. This is done with a literature study in chapters 2 and 3.

Development of a tensegrity joint X.M. Bernaards

Where chapter 2 is the general literature study on tensegrity structures, chapter 3 takes a closer look at joints in the tensegrity structures. The literature study leads to a morphological matrix to see if the new joint design has any similarities with existing solutions. The cyclical process start after designing the joint based on the given criteria. In chapter 4 the development of the prototype for experimenting is explained. Chapter 5 will describe the experiments done with the joint. The analysis of experiments will give problems that have to be resolved. The solutions of the problems will change the joint that is seen in chapter 6 and will lead to the final joint design. A way to produce the joint is covered in chapter 7, were production methods will be discussed. All previous chapters will result in chapter 8 where the conclusion and recommendations is written.

Figure 1.3 Research design

Development of a tensegrity joint X.M. Bernaards

Tensegrity

2. structures

History and explanation of the tensegrity structures.

Development of a tensegrity joint X.M. Bernaards

2. Tensegrity structures

The new joint design is for the connection between cable and strut in tensegrity structures. To get a better understanding of the tensegrity structures this chapter will discuss the history and its founder, definitions, working and some examples.

2.1 History

There is much written about the founders or inventors of tensegrity’s. There are three men who claim to be the inventor of the Tensegrity: Richard Buckminster Fuller, David Georges Emmerich and Kenneth D. Snelson. They could all be inspired by the work of Karl Ioganson a Russian constructivist artist. At a constructivism exhibition in 1928 in Russia work of Ioganson was displayed, no models were left from that exhibition because of a fire. The only thing left where photographs (fig 2.1). On the pictures where structures with a resemblance to the tensegrity’s patented by Fuller, Snelson and Emmerich. Ioganson’s structures, however, can’t be classified as tensegrity as tension - one of the key elements of a tensegrity - is missing in his designs. In figure 2.2 one can see that on the left, the cable has no tension.

Figure 2.1 OBMOKhU Exhibition, Moscow Figure 2.2 Karl Ioganson "tensegrity"

Buckminster Fuller invented the name Tensegrity, by combining tension and integrity, to the structures. From an early design he made, the dymaxion house, an early tensegrity is seen (fig 2.3 and fig 2.4). The first time tensegrity was mentioned was in the patent of Richard Buckminster Fuller where he called it a tensional integrity, which transformed to tensegrity (Fuller, 1962). Fuller, who is best known for his geodesic domes, translate the tensegrity principle to the building concept The Fuller Dome and invented the “six-islanded-strut icosahedron Tensegrity”. But it never really work out for Buckminster Fuller to design a good working Tensegrity dome.

Development of a tensegrity joint X.M. Bernaards

Figure 2.4 Form of tensegrity of dymaxion house, Skelton

Figure 2.3 Dymaxion house, Buckminster Fuller

Due all the different persons who claimed to be the inventor of tensegrity, Renee Motro, an important tensegrity researcher and innovator, wrote a report about it and for clarification he sent a letter (Motro, 1990) to the self-claimed inventor Kenneth Snelson. In response he writes a letter about his first meeting with Buckminster Fuller and how he invented tensegrity sculptures.

Kenneth Snelson, an art student at University of Oregon, followed a summer course in North Carolina at Black Mountain College in 1948. Snelson went to the course because of his interested in Bauhaus, as the course was given by painter Josef Alberts who was a Bauhaus master. Buckminster Fuller came in to the picture when he substitute a guest lecture and gave a lecture in this course about his geodesic domes. After the course Snelson began working with wire sculpture that consisted of stacked elements and moved on swivel points. One of them was a small three where the elements where balanced by clay at the ends like Calder mobiles.

Figure 2.5 Snelson's Tree Figure 2.6 Calder mobile

Development of a tensegrity joint X.M. Bernaards

The next step was to remove the clay at the ends and replacing them with tension lines from one to another to stabilize it. Out of this came the idea to make the “X” module where the solid elements fixed in space by connecting them with tension members (cables).

Figure 2.7 Double X-piece (Snelson, 1948)

When shown to Buckminster Fuller, he told Snelson to use the shape of tetrahedrons. Snelson went on with experimenting with different materials, forms and structures. Snelson applied for a patent for his discoveries: “Continuous Tension, Discontinuous Compression Structures”. (Snelson, 1965)

Snelson uses, flexible and rigid components, that are arranged according to the tensegrity principle, as an art form. So Snelson is primarily interested in the artistic exploration of structure using the medium of tensegrity and is famous of his artworks like the Needle Tower 2.

Figure 2.8 Needle Tower (Snelson, 1969)

At the same time, in France, David Georges Emmerich was exploring tensegrity prisms and combinations of prisms into more complex tensegrity structures, all of which he labelled as "structures tendues et autotendantes" translated prestressed tensile structures. (Emmerich, 1963)

2 The Needle Tower II (1969) was purchased by the Kröller-Müller Museum in Otterlo, the Netherlands.

Development of a tensegrity joint X.M. Bernaards

As written above all three filed their own patent, the resemblance is very alike. (fig. 2.9)

Figure 2.9 Emmerich, Fuller and Snelson's patents

All the patents and different “inventors” didn’t lead to a building concept for some time. In Poland, however, the Spodek (1964 – 1972), by architects Maciej Gintowt and Maciej Krasiński, was build. It has one of the earliest known roofs that uses a cable structure, based on the tensegrity principle, in which compression members are connected only to cables, and not to each other. A number of wire models (fig 2.10) of this structure were made to assess feasibility.

Figure 2.10 Spodek inner hoop and wire model3

3 http://structurae.net/structures/spodek ID:54812

Development of a tensegrity joint X.M. Bernaards

2.2 What is a tensegrity structure

2.2.1 Definitions of tensegrity

To get a better understanding of the tensegrity structures and its meaning, many researchers have made their own definition to clarify it. Some are understandable, others leave it to imagination. The definitions are quoted and put under each other in chorological order.

"Structures tendues et autotendants.", (tensile and self-stressed structures). (Emmerich, 1963)

" (…) islands of compression in a sea of tension elements." ( Fuller, 1965)

“Floating compression.” (Snelson, 1965)

“A tensegrity system is established when a set of discontinuous compressive components interacts with a set of continuous tensile components to define a stable volume in space.” (Pugh, 1976)

“Internally prestressed, free-standing pin-jointed networks, in which the cables or tendons are tensioned against a system of bars or struts.” (Hanaor, 1993)

“A tensegrity is any structure realized from cables and struts, to which a state of prestress is imposed that imparts tension to all cables.” (Pellegrino, 2003)

"A tensegrity system is a system in a stable self-equilibrated state comprising a discontinuous set of compressed components inside a continuum of tensioned components inside a continuum of tensioned components." (Motro, 2003)

“Tensegrity describes a closed structural system composed of a set of three or more elongate compression struts within a network of tension tendons, the combined parts mutually supportive in such a way that the struts do not touch one another, but press outwardly against nodal points in the tension network to form a firm, triangulated, prestressed, tension and compression unit.” (Snelson, 2004)

“Tensegrity is a structural principle based on the use of isolated components in compression inside a net of continuous tension, in such a way that the compressed members (usually bars or struts) do not touch each other and the prestressed tensioned members (usually cables or tendons) delineate the system spatially.” (Jáuregui, 2004)

“A tensegrity system is composed of any given set of strings connected to a tensegrity configuration of rigid bodies.” (Skelton, 2009)

Development of a tensegrity joint X.M. Bernaards

An easiest definition found and quite understandable for people is in Dutch: "De touwtjes houden het hele bouwsel bijeen en de houtjes uit elkaar." (Heunen and Leijenhorst, 2004) Meaning something like; Strings are keeping the structure together and the wooden struts apart.

2.2.2 How does a tensegrity work

A tensegrity consists out of two components (fig 2.11). The first component is a bar or strut, for absorbing the compression force. The second component is a cable or string for absorbing the tensile force. These two components are connected in a joint on top of the strut in such way that the compression elements will never touch each other, that’s why it’s called a discontinuous compression. The tension components are continuous, because the strings or cables can converge at the ends of the compression parts, but never along the length of the strut.

Figure 2.11 Tension and compression

The compression components can be made out of various materials like steel, aluminium or wood. Compression components are structural elements that are subjected to axial compression forces only. The compression elements don’t have to bear a lot of force in a tensegrity, because there is no real axial load on them.

The tension components can be made out of different materials such as steel or even rope depending on the load and the size of the tensegrity structure they are used in. These tension members are mostly prestressed to ensure the stability of the tensegrity. This pre-stressing can be done in different ways. When one of the tension members fails, the tensegrity will collapse, because of the tension members which are in an equilibrium. As all the tension elements work together all will fail if one will fail, causing to loss the tension.

The designing of the tensegrity is an imported issue. It can only consist out of triangles otherwise it will not have enough strength and the tensegrity will not be stable enough. After a tensegrity is build it’s hard to reconfigured it as to all the elements work together, if for example one tension element is made longer on one strut it has influence on all the struts and cables and the tensegrity will not function any more. In the joints there has to be a stable equilibrium state.

Development of a tensegrity joint X.M. Bernaards

Stable equilibrium state ”The expression “Stable self-equilibrated state” expresses the initial mechanical state of the system, before any loading, even gravitation one. The system has to be a self-equilibrium stat, which could be equivalent to self-stress state, with any self-stress level. Furthermore this equilibrium is stable.” (Motro, p.99, 2002)

A simple rule is applied to find the number of strings required to make sure the structure is stable: The minimal number of strings = 3 x the number of bars (n) as shown in fig. 2.12.

Figure 2.12 Tensegrity 3 strut prism and 4 strut tensegrity (Wikipedia, 2014)

The 3 strut tensegrity prism in figure 2.12 is considered the simplest tensegrity structure. The 3 strut prims consist of three bars and nine strings, is stable according the formula above. The bars have the same length. The bars are connected at the top and bottom in a triangle by same length strings, the next step is to rotated them in one direction. When rotated the top of a bar is then connect with a string to following bottom of the next bar. The same principle is used to create the 4 strut tensegrity, where the top and bottom are connected in a square. (Burkhardt, 2008)

Development of a tensegrity joint X.M. Bernaards

2.3 Use of tensegrity structures in the building environment

Tensegrity’s are used in many different ways. To show what can be done with tensegrity a selection of how tensegrity could be used is shown in this paragraph.

2.3.1 Structures

The simples tensegrity is the three prims (fig. 2.12); three struts and nine strings are used to build this structure. The more struts are used the harder it gets to get the right stable form. This structures are mostly used for art, in Snelson’s designs, and some like the Tensegrity Icosahedron are used in dome principles of Buckminster Fuller.

Basic tensegrity structures

1 2 3 4

1. A structure with four compression members. 2. Tensegrity Icosahedron, Buckminster Fuller, 1949 3. Tensegrity Tetrahedron, Francesco della Salla, 1952 4. Tensegrity X-Module Tetrahedron, Kenneth Snelson, 1959

2.3.2 Towers The best-known application of tensegrity in a tower is in Snelson’s Needle Tower (fig. 2.8). They’re configured as assemblies of the T-prisms that were explained on pp. 22.

Figure 2.12 Snelson patent tower, Penta Tower, Warnow Tower (MERO Structures)and Zig-Zag tower

In figure 2.12 different types of tensegrity towers are shown.

Development of a tensegrity joint X.M. Bernaards

2.3.3 Tensegrity domes

Architectural building include domes or roof structures, like canopy’s . The lightweight character of the tensegrity is used to its maximum in the dome structures. A large span can be achieved by the tensegrity. Which results in a smaller amount of material use and less mass. After the Spodek, different domes were built with construction of Fuller and Geiger.

“The name “tensegrity structure” was extended to include any class of pin-connected frameworks in which some of the frame members are cables , or, complementarily, compression-only struts.” (Williams, p.2, 2007) This is the case in the “Cable-Domes” or “Wire Wheel Domes“, invented by David Geiger in 1986.

Snelson doesn’t see these domes as a tensegrity though: “The (…) domes you cite cannot be considered tensegrity, regardless what people wish to call them. They are, essentially, bicycle wheels. Did the world need a different name for that kind of solid rim, exoskeleton structure? I think not; same with a spider web.” (Jáuregui, p.140, 2004)

Figure 2.13 Fuller and Geiger dome

2.3.4 Geiger dome

The most know dome with tensegrity is the Geiger Dome by David H. Geiger. (fig 2.13 right) From the top it looks like a spider web or like a bicycle wheel with struts between the spokes. In his patens Geiger calls the roof structure a cable truss dome (Geiger, 1988). In the top layer the dome consists of an outer compression ring where cables are span to the inner tension ring. In the lower layer, cables are connect to the struts in pattern of a hoop. Here are diagonal cables form the top of the strut that go to the bottom of the next strut, like triangles (fig 2.14).

Figure 2.14 Side view cable dome (Geiger, 1988)

Development of a tensegrity joint X.M. Bernaards

Four of these type of domes have been build. In Korea there are two domes in Seoul build for the Olympic Games 1988, the Gymnastic Arena with a diameter of 119.8m and the Fencing Arena with a diameter of 89.9m. The other two are in America, the Redbird Arena with an elliptical plan, diameters 91.4m and 76.8m and the Sun Coast Dome in St Petersburg, Florida with a diameter of 210m. (Pellegrino, 1992)

Figure 2.15 Sun Coast Dome (Pellegrino, 1992)

Fuller Dome A Fuller is known for his geodesic domes that are spherical or partial-spherical shell structures made out of triangles from a icosahedron. Fuller also design a dome that consisting of struts and strings. That principle is used in the Georgia dome. It’s a non-circular oval shape, designed by Matthys Levy based on Fuller’s roof system with triangulation.

Figure 2.16 Georgia dome

Development of a tensegrity joint X.M. Bernaards

2.3.5 Bridge

The only example of a bridge made with tensegrity is the Kurilpa bridge. The bridge was opened in 2009 and designed by Cox Rayner Architects it’s 425m long with a mid-span of 128m. It consists out of prism tensegrity, where the tubes are the compression elements and the cables the tension elements. It also incorporate solar panels to provide the energy for the LED lights.

Figure 2.17 Kurilpa bridge, Cox Rayner Architects and Arup Engineers, Brisbane, Australia

2.3.6 Furniture

There are also some tables, lamps, chairs and other furniture made with tensegrity.

Figure 2.18 Tensegrity tables , Theodore Waddell

Figure 2.19 Tensegrity chair and light sculptures, right Cubic Zirconia, James Clar.

Development of a tensegrity joint X.M. Bernaards

2.4 Overlook

There is still an ongoing struggle about who was the inventor of tensegrity. The most important is that all who claimed to be the inventor, delivered a piece of the tensegrity as known now. From the different definitions is becomes clear that in a tensegrity the struts never touch and there is no need of side constructions to keep it stable, because a tensegrity should be in a stable equilibrium state. There are some interesting tensegrity structures that are worth to reproduce with the new joint. Like the 3-prism strut, Needle Tower and the Geiger cable dome. In the design of the new joint, it has to be taken in account that it could be used in these structures, so the routing of the cables should be able to handle the different configurations.

Development of a tensegrity joint X.M. Bernaards

Joints 3. The state of the art of tensegrity joints is analysed

Development of a tensegrity joint X.M. Bernaards

3. Joints

3.1 Introduction

After the literature review on tensegrity much information about the form, structures and uses of the principle is found. Less information is found about the way to connect the cables to the struts. The joint connections in tensegrity are found in the patents4 of Fuller, Snelson, Emmerich, Geiger, Berger and Liapi.5 The other joints will be explored in this chapter to get a better understanding about how they function. Functions like tension, adjustability, possibility to change cable length will be covered in this chapter. Ways to connect the tension elements (cables) to the compression elements (struts) up to now will be explored as well. Some connections are the same, but have a different material or scale. The scale of the new joint has to fit in the structures described in the conclusion of chapter 2. All these findings will result in a morphological matrix to get a clear view of the possible solutions. As written before the definition joint is preferred and used. Other terms like hub, connection, node, junction and intersection will all be named as joint.

3.2 Pioneers

The pioneers of tensegrity structures found in previous chapter are Buckminster Fuller, George Emmerich and Kenneth Snelson have their own joint solutions for connection the cables and struts. Some of the first joint solutions have the same principle and are further developed. Two of the three patents are explained by making use of figures in the patents, supported by 3D models made by the author. In George Emmerich patent there is no clear joint design so this patent is not explained instead the joint of Liapi is explored. This joint is designed for a collapsible tensegrity.

4 The patents can be entirely found online. Addresses are listed in chapter 9 literature. 5 In the patents of Geiger and Berger the joints are for large domes and don’t meet the set criteria, they are shown in paragraph 3.3.

Development of a tensegrity joint X.M. Bernaards

3.2.1 Kenneth Snelson

Kenneth Snelson patent “Continuous tension, discontinuous compression structures”6, shows two joints that are used in the tensegrity configurations drawn in the patent. The first joint consisted out of the section FIG.27 and the top view FIG.28 in fig 3.1. In the patent a full description of the working of the joint can be found. Snelson’s joint in FIG.27 is a joint which may be used to interconnect compression members to form a lattice.

Figure 3.1 Patent Snelson, (Snelson, 1965)

To explain the two joints, the numbers given to the parts in the patent will be followed in made models, as shown in fig 3.1. This explanation will be supported by a 3D model made by the author fig 3.2.

6 Snelson, K. (1965). Continuous tension, discontinuous compression structures, U.S. Patent No. 3,169,611, February 16, 1965.

Development of a tensegrity joint X.M. Bernaards

The 3D model is made in SolidWorks and makes is possible to take a closer look at the joint. The joint (100) is a separate part that slides into a compression member (103), there is no need to fix it, as the tension members (111) will push the joint into the compression member. At the top cables (111) are inserted with a round swage sleeve at the ending (112). The bolt (110) can be screwed into the tapped hole (108). The cables are tensioned by tightening the bolt (110). A sliding insert (106) takes the cables down the hole (104) by pressing the cable endings down and also keeps them separated. The head of the bolt (113) has a recessed head where a wrench can fit into so the bolt can be turned. The use of flexible cables is advised, because they make a sharp bend over the lip (101). 113

106

111 100 101 112

110 103

104

108

Figure 3.2 Solidworks model of joint (100)

The second joint in this patent, is a modified joint according to the invention for interconnecting the ends of compression members in a compression-tension lattice. The connection of the tension members is done different as is the way how there are tensioned. This joint is made for situations where tension members would don’t have to bend at a radius in the construction, which makes it possible to use stronger stiff cables in this joint.

Development of a tensegrity joint X.M. Bernaards

Figure 3.3 Modified joint (Snelson, 1965)

The joint (fig 3.3) can be connected to a compression member. The joint (plug) has a bore (121) up to the base (122). Fitted within the bore (121) is a slidable insert member (124). This member has a rim (127) with drilled holes (128) in it. The cable ends (129) go through the holes (128) and are fastened at the inside by nuts (130). The bolt (126) can be tightened into the tapped hole (131) in the insert. The lower end of the bolt (126) abuts against the base (122), so when tightening the bolt, the insert will be pushed out of the bore. This will increase tension to all the connected cables. The difference between this joint and joint (100) is that in joint (fig. 3.2) the bolt pushes an insert down to tension the cables and in the joint in figure 3.3 the bolt make an insert slide out to tension the cables.

Modern joint In an interview with Snelson questions are asked about the modern joints and the way of tensioning (Snelson, 2004): Q: How do you adjust the tension on your sculptures?

A: “It's analogous to tuning a stringed instrument. In assembling the sculpture for the first time, I invariably need to change some of the tension members, remaking them either longer or shorter to achieve the right amount of pre stressing. Every part depends on every other part, compression and tension members alike, so that knowing which wire to alter is a matter of experience. After the final adjustment, further changes over time are seldom necessary.”

Q: Do the wires thread through the tubes?

A: “Each wire is separate and connects only specific points from one tube end to another, performing a particular task. The wires are never threaded through the structure like a string of beads as appearances might suggest.”

The first answer shows that there is little room for adjustments in the nodes after completing the tensegrity.

Development of a tensegrity joint X.M. Bernaards

In the modern sculptures of Snelson a joint like the modified joint (fig 3.3) is used. This joint has evaluated to the joint Snelson uses now a days, there is no bolt in it anymore. In his book “Kenneth Snelson; Art and Ideas” the modern joint is shown(fig. 3.4).

Figure 3.4 Joints and cables inserted and sculpture new dimension (Heartney, 2013)

In fig 3.4 the joint used in Snelson’s work “new dimension” is shown. The connection between cables and joint is realized first, which makes one big net where the struts can be placed in later. This means measuring and cutting the cables is done first. The cables all have sleeves at the end for the connection to the joint. By placing some of the last cables between joints, the joints are brought closer together by using a steel cable lever hoist for fixing the cables. Inside the joints the holes are threaded to fix the steel cables with the sleeves on them.

Figure 3.5 Solidworks model Snelson detail

Development of a tensegrity joint X.M. Bernaards

3.2.2 Richard Buckminster Fuller

Buckminster Fuller was the first to patent his tensegrity7 . The way the cable is connected to the strut in the patent is shown in figure 3.6. This joint, or boom as Fuller calls it, is used in a geodesic dome.

Figure 3.6 Fuller's joint and use in geodesic dome (Fuller, 1962)

In the patent the following description is given to the figures shown in figure 3.6 “FIG. 4 is a side elevation view of the strut and tension sling component of the discontinuous compression structural complex of FIG. 3, called a “boom.” FIG. 5 is a plan view of the boom of FIG. 4. FIG. 6 is a sectional view taken on line 6—6 of FIG. 4.”(Fuller, 1962) The tensioning happens by turning the bolt (5) into the strut or outward the strut (fig. 3.7). The cables are connected to rings with a loop (washers nr.4), so struts can be connected later by sliding the bolt through the rings into the strut. If there is any tolerance another ring can be added.

Figure 3.7 Top of joint (Fuller, 1962)

7 Fuller, R.B. (1962). Tensile-Integrity Structures, U.S. Patent No. 3,063,521, November 13, 1962.

Development of a tensegrity joint X.M. Bernaards

Buckminster Fuller and Shoji Sadao designed a joint (fig. 3.8 & 3.9) that almost works the same as Snelson’s joint (fig. 3.2). These details are from “The geodesic revolution, Part 2”

Figure 3.8 Joint Fuller 1 (Ward, 1984)

Figure 3.9 Joint Fuller 2 (Ward, 1984)

The cables are tensioned all at once, the same way as in Snelson’s joint. The only difference is that in figure 3.8 the joint is a solid piece that goes in the strut and the joint in figure 3.9 is made of several pieces. Tension is done by tightening the bolt at the top, the cables are pressed down. Different to Snelson idea is that on top of the joint the cables are laid in slots, that places the cables right in the direction they have to go so they can’t slide in a wrong direction.

Development of a tensegrity joint X.M. Bernaards

3.2.3 Katherine A. Liapi

In the patent8 of Katherine A. Liapi, a solution is described for how to make a collapsible and/or deployable tensegrity structure. By collapsing the tensegrity it can be minimized for storage, transport, etc. Cables with a fixed length are connected to steel plates (60) by coupling devices (50), here the cables also are given direction by the drilled holes in plates. To adjust tension the nuts (53, 54, 55) have to be moved on a threaded sleeve (51) so the steel plate (60) can be moved up. This threaded sleeve (51) is on top of the struts (46). The tensioning space and adjustment space is just as long as the nuts can move over the threaded sleeve.

Figure 3.10 Detail of joint (Liapi, 2003)

To collapse the tensegrity, tension should be taken off first by unscrewing the nuts (53,54) closer to the strut, so the plate (60) with the cables realises the tension. A stop (62) on the tensioned line (45) can pass through the large opening in the bracket (60) and sufficient tension is released from the tensegrity now, to allow the tensegrity to collapse. To attach another tensegrity (FIG.5), a cable from the other tensegrity can be connected to the coupling device (70), where the cable is placed in a body (72) and fixed by a retainer (76).

8 Liapi, K.A. (2003). Tensegrity Unit, Structure and Method for construction, U.S. Patent No. 2003/0009974 A1, January 13, 2003

Development of a tensegrity joint X.M. Bernaards

3.3 Joint solutions

For the development of a new joint, a research of current solutions for the cable- strut connection is necessary. There are a lot of connection between cables and struts from very simple solutions to very hard ones. For this research, the scale of the construction where the new joint is used in matters for the configuration and the strength it has to handle. Joints in tensegrity domes like the Georgia dome figure 3.11 are big and heavy steel joints. These solutions have to handle all the forces and the weight of the construction, therefore they are very large. In the domes there is always an addition to the strut for the cable to connect to. The bigger the construction the bigger the joint and it’s additions, therefore boundaries are established for the search to existing joints. The joints in this research have: - Maximal strut length of 1.5 meter. - Maximal diameter of 80mm. - Joints used in a dome with a maximal of 15 meters. - Steel cables or wires have to be between 0.1mm and 5mm. - A maximal of 6 cables to connect to the joint. - Joints that are used to build small canopies, sculptures or furniture. (Size like seen in the patents.) In big cable constructions It doesn’t really matter how the joint looks or how big it is, they just have to function. In smaller joints there is a necessities to keep the detailing fine, because its more notable when big add-ons are placed on the struts.

Figure 3.11 Georgia Dome joints, Architect Heery International; Rosser FABRAP International; and Thompson, Ventulett, 1992

There is a wide range of solutions. Most of these solutions are only useable for the project they are used in, but there are some standard solutions that can function in more projects. To have a better understanding of all these solutions a morphological matrix is made to see the different ways a joint can be made. The matrix consists of the solutions found in the literature and internet. For designing a new joint, it is easy to look in the matrix for existing solutions that can be used, whether or not in a different way.

Development of a tensegrity joint X.M. Bernaards

3.3.1 Morphological matrix

During the research on joints it is useful to put the solutions in a morphological matrix. The matrix makes it possible to quickly combine different solutions to create alternative designs for a joint. The matrix consists of a set of rows and columns, representing possible solutions and para meters for generating a new idea. By using images it becomes even clearer what the different solutions are. The morphological matrix can be used to create an array of different concept proposals for the final solution. By using this kind of matrix, documentation of solution proposals is automatically generated and structured. (Weber & Condoor, 1998) In the morphological matrix all the found joint solutions are analysed and taken apart to see its solutions. It could be used as a decision sheet for designing new joints in the future The matrix excised out of eleven main categories which are divided in different solution types of that category. The list below shows all the findings.

1. The start is what kind of strut; - Set screw - Solid - Bolt - Tube/pipe - Socket - Bored 9. How to tension; 2. What kind of top on the strut; - Turnbuckle - Round - Turning a bolt upwards - Straight - Pulling or hoist - Threaded - Cable net - Chamfer - Downwards with a bolt and insert 3. How many cables does the joint have - Telescope strut to handle. 10. Cable endings; 4. Are the cables cut joint to joint or do - None they go through. - Thimble 5. Are the cables tensioned all at once or - Threaded separate. - Clamps/clips 6. Is the cable length fixed or adjustable. - Sleeve 7. Is the connection possibility between - Socket joint and cable, in the joint, on the joint 11. Cable management; or is there an addition. - None 8. How are the cables fastened; - Slit - Insert - Additions - Loop - Holes - Nut - Modified insert

Development of a tensegrity joint X.M. Bernaards

Figure 3.12 Morphological matrix

Development of a tensegrity joint X.M. Bernaards

Every decision made in the matrix brings limitations for the next step, so some options will be eliminated, because they can’t be applied to the former steps made. There is almost a standard path from top to bottom, but making some other decisions will result in some interesting new ideas for a joint. Some options only have influence on the appearance of the joint. In order to show how the matrix works some examples will be given in the appendix.

3.3.2 Connection types

The challenge to design a new joint lies in the connection phase. The connection between the strut and the cables is the most important element of a tensegrity joint. The connection type gives the way of connecting naturally, but also the way to tensioning the cable, how many cables it can handle, sets the boundaries of were the cables can go and can make a joint look aesthetical. In the morphological matrix there is chosen to make three categories of joint connections. The first one is to design a connection solution in joint, what means the joint is part of the strut and the top of the strut is edited for receiving cables. Second is the on joint connection, these are where the receiving of the cables is outside the joint, mostly small additions are placed on the joint. The third category is additions, this category existed out of connections that can be placed in the first and second category. The additions are well designed options for connection of cables, like Snelson’s modern joint in figure 3.5, they can place in and on a joint without having to edit the joint. Most of this joints in category can be separated from the joint.

Figure 3.13 Connection types solutions

In the next paragraphs some examples of the three categories of connections are given by using existing connections in tensegrity structures.

Development of a tensegrity joint X.M. Bernaards

3.3.3 In the joint

The “in the joint connections” are connections where the strut top is edited. The easiest in the joint connection is to drill holes in the top of the strut were the cables go through or are fixed like in figure 3.14. A costomization can also be sawing into the strut like in figure 3.15, it’s a Fuller joint where slots are formed to receve tension elements or where cables can go through. A threaded end to a strut as been shown in figure 3.16 or making the inside threaded as in figure 3.17, all count as a “in the joint connection”.

Figure 3.14 Holes in joint Figure 3.15 Slots (Fuller, 1973)

Figure 3.16 bolt in threaded end (Liapi, 2004) Figure 3.17 Thread in ends

3.3.4 On the joint

A typical “on the joint connection” is a steel eye that’s attached to the top of a chamfered strut top (fig. 3.18 a). The top is chamfered so the cables won’t touch the strut when it’s placed almost horizontal. Another “on the joint connection” is a steel coupling plates welded to the site of the strut (fig. 3.18 b). Also placing plates on top is an on the joint solution, these plates be round or triangular (fig. 3.18 c) as long if the plates don’t interfere with the cables. In figure 3.18d the joint has a ring attached to the top of the strut where the cables can be connected.

Figure 3.18 a) Ring on top, b) Steel coupling pates, c) Plate on the joint, d) On the website of Dave Strasiuk

Development of a tensegrity joint X.M. Bernaards

3.3.5 Additions

Two examples of “additions” are the joints from the patents of Fuller and Snelson in figures 3.2 and 3.8. Figure 3.19 is an “additions” which is described in “Free-standing Tension Structures” (Bin Bing, p.147 2004) as a spherical joint. The sphere is the addition and functions as connection centre for incoming cables. The cables are connected by the use of threaded ends which are connected inside the sphere by nuts or turnbuckles. The sphere can be bolted or welded to a strut, if bolted it’s possible to separate the joint from the strut. A sphere joint is also used in the master thesis of Marielle Rutten as shown in figure 3.20, where the sphere joint is it’s placed on a pneumatic strut. (Rutten, 2008)

Figure 3.19 Welded ball type joint (Bin Bing, 2004)

Figure 3.20 Marielle Rutten joint design Figure 3.21 Hub design 9

The additions in figure 3.21 show solutions where there is freedom of placing the cables. The cables in this joint are bicycle spokes that are connected to the hub exactly as the would be connected to the rim of a bicycle wheel.

9 http://bobwb.tripod.com/synergetics/photos/spoke.html

Development of a tensegrity joint X.M. Bernaards

3.4 Conclusion

In the matrix, made in this paragraph, it can be seen that there have been many changes in the design of joints from the first patents to the current designs. The joint design very much depends on the size of the tensegrity structure. Among the joints there are almost no joints where the cables are tensioned separately and in the joint. If they can be tensioned separately the set space is very limited, because the cables are cut to fit almost exactly in a structure or the set space is only for absorbing slack. Every decisions made in the matrix will lead to a different joint. The matrix might not be complete, because some of the designed joints are not included in the matrix. The matrix can be a start for a good inventory of existing joints to show the different solutions. In the matrix can be seen that an opportunity for designing a new joint is at the manner cables are tensioned, especially tensioning one cable and not all at once. Also a solution for not having to cut cables to size in advance has some design opportunity for a new joint. The solution with additions it’s easier to change the strut length and the addition can be reused in an another tensegrity configuration, this can be an opportunity for creating a standard joint.

It seem like the idea, figure 1.2, for the new joint can fill the gap in the matrix where cables can be tensioned separately in the joint and where cables are not cut to length, so they can be adjusted after construction. It also seen that the devised solution for connection between steel cable and set screw is used in other solutions.

Figure 3.22 Design opportunities

Development of a tensegrity joint X.M. Bernaards

Development 4. To see the design a prototype for testing is made.

Development of a tensegrity joint X.M. Bernaards

4. Development

4.1 Introduction

In this chapter the start of the development of the joint after the research. A detailed explanation of the design of the joint is described. It will contain the process steps taken from the drawing of Ir. A.D.C. Pronk up to the prototype for testing. This is done with an iterative process (Fig. 4.1), in chapter 5 testing is done and chapter 6 will give the re designed joint after testing.

Figure 4.1 Iterative process

Following a different path on the matrix leads to a different design, this is done to design the new joint. By making use of exciting methods, but in a different configuration. With the new joint design there is tried to find a solution for adjusting the cable length in a joint and finding a way for tensioning the cable before and after construction of a tensegrity.

Development of a tensegrity joint X.M. Bernaards

4.2 Design

The design started with an idea for a new joint in tensegrity structure. The idea started with a simple pen drawing of a section of the strut with the joint in it. The connection of the cable and the tension occur in the joint. So adjusting the cable can be done before and after construction of a tensegrity.

Figure 4.2 Drawn joint

Criteria given by this drawing;  Cables must be attached separately to the joint.  A slim joint, esthetical, with no additions on it.  Cables should be able to be adjusted before and after construction for tensioning.  Fixing the cable is done by the use of set screws.  Adjusting cable length is done by unscrewing set screws.  No use of external tensioning additions on cables.  The connection is made in the joint.

Following the path in the morphological matrix by the given criteria gives the chart in figure 3.12.

Figure 4.3 Path in morphological matrix

Development of a tensegrity joint X.M. Bernaards

4.2.1 Similarities

A research is done to see if the new joint design shows any similarities with already produced products. The search is based on the solutions found in the morphological matrix and are shown in figure 4.4. These are the solutions that are leading in the new joint.

Figure 4.4 Solutions to search for from the matrix

The found products that show similarities are; A cable tensioner for making fences in the garden or for railings for stairs. The back end of the tensioner is connected to the wall or banisters, and between two cable tensioners a cable is tensioned. The cable is received in the top of the tensioner and fastened by two set screws. To absorb slack it’s possible to rotated the head in or outward.

Figure 4.5 Cable tension adjuster10

Figure 4.6 Drawings of cable tension adjuster Differences: Similarities:  Possibility to separate joint from strut  Use of set screws to fasten cables  Cable received at the top  Solid strut  Only good for receiving one cable  Round top  No usable for a tensegrity

10 http://www.mbs-standoffs.com/Cable-Tension-Adjuster_p_2258.html

Development of a tensegrity joint X.M. Bernaards

In search for a similar product for a tensegrity, Project 52/26: Mathe um dich herum, is found. Figure 4.7 shows the designed joint with a solution for connecting cables in holes. It can be seen as a “in the joint” connection, but also as an “addition”, because the joint can be taken of the strut. The cables go through the joint and are fixed with a set screw (fig 4.8). Some cables got through more than two joints in a triangle and are connected double in a top. Tensioning is probably done by pulling.

Figure 4.7 Projekt 52/26: Mathe um dich herum (http://www.medamind.de/projekt-52/2009/projekt-5226- mathe-um-dich-herum/)

Similarities:  Use of set screws to fasten cables  Round top  Solid strut  Cables go out to the sides  Used for tensegrity

Differences:

 Possibility to separate joint from strut Figure 4.8 Section orange fig. 4.7  Cables go through joint  Only good for receiving two cable  Height between cable connections

With these similar product there can be said that there is potential in the new joint design. The next step of designing is to determination of a variety of materials.

Development of a tensegrity joint X.M. Bernaards

4.2.2 Values for dimensions

For making decisions for the dimensions, materials have to be chosen in advanced to get dimensions to work with to produce a prototype.

Strut The first values to set are the dimensions of the strut. The strut is a solid piece where the joint is preserved. The measurements of the strut are, a diameter of 35mm and a length of 400mm. Its presumed that the joint is to be used in a tensegrity structure not bigger than a dome with a diameter of 10m or a structure with a greater height than 10m. This makes the dimension of the chosen strut sufficient.

Steel cable For this first design the steel cable has a diameter of 2,5mm, with a carrying load of 4.8kN11, which is enough for a small tensegrity structure. The cable must be able to bend around the top of the joint, so a fibre core steel cable is desired. To have a little tolerance there is chosen to have a maximum cable thickness of 3mm going through the slits. If the cable is 3mm the slits have to be 3,4mm wide to receive the cable. Than changing of the cables for a lager configuration isn’t a problem. The 6x7 fibre core galvanised steel cable meets the requirements needed. (DIN 3055)

Figure 4.9 Steel wire rope section and properties 12 (Red box is imported for test 3)

Set screw In the joint the steel cable connection is done by set screws that are screwed in the slits. The set screws are there for fixation of cable and to be able to adjust the cable before and after construction. The connection with the set screw in the slit will function like the connection of steel cable fences (fig 4.10) where cables cross a clamp and are fixed with a set screw. The decision to use set screw is that they are flat and can be screwed into the joint so they won’t stick out this way the joint will be smooth and slim all the time. There are different type of set screws:  Cup Point Set Screws  Cone Point Set Screw  Flat Point Set Screw  Half Dog Point Set Screw  Knurled Cup Point Set Screws  Oval Point Set Screws

11 Description of cable: 6x7+TW with working load of 80Kg with safety factor 6 gives 4800N (for testing) 12 http://www.tocolifting.co.za/Categorys.asp?Category=6x7+FIBRE+CORE+GALVANISED+STEEL+WIRE+ROPE&ID=164

Development of a tensegrity joint X.M. Bernaards

The flat set screw is chosen, because it’s presumed that it will do less damage to the cable if it’s screw into the slits and presses on the cable. There is a wide range of dimensions for set screws. The dimension that fits best in the joint is the M6x6 that means the set screw is 6mm tick and long.  The fastening of the steel cable is done by flat set screws M6x6 that are placed in the centre of the slit where threaded holes are made.  DIN 913 Flat point

Figure 4.10 Set screw connection in fence construction

Slits/Slots The connection is made in the joint by making slits/slots in the joint. For the dimension of the depth of the slits the following decisions are made:  The slits are made 3,4mm wide to keep a tolerance of 0,4mm if cable of 3mm is used.  The slits are evenly distributed round the diameter of the joint.  The joint is designed for four cables, so four incoming slots and four outgoing slots are made, so there will be a total of eight slits on the side and on top.  The slits assure that the cable neatly disappears in the joint. This way the joint stays slim.  These slits have inwards curves. This is because when the cable gets fixed by the set screws the pressure on the cable will make it curve a little around the pressure point of the set screw.  The depth of the slits variant from at the curve of 9.4mm where the steel cable and the set screw (6mm) meet, to 3,4mm where just the cable runs through (fig. 4.11).  The depth of the cut on top where the slits come together is 128mm, by the assumption that four steel cables could overlap in the top.

Figure 4.11 Section of the joint

Development of a tensegrity joint X.M. Bernaards

The joint With the determination of the materials and their dimensions the idea of the new joint can be made digital.

Figure 4.12 Side view, section and top view of the first digital drawing made

To see how the dimension relations are, a 3D model is made in SketchUp.

Figure 4.13 First 3D model SketchUp

The rounding in the top has not yet been fully dimensioned. Is very hard to get a feeling of the dimension of the rounding by just looking at the drawings, therefore it is necessary to make prototypes. From the drawings it’s clear the chosen dimensions are working well on the 35mm diameter strut.

Development of a tensegrity joint X.M. Bernaards

4.3 Producing prototype

4.3.1 Wooden prototype

To get a better look and feeling of the joint a prototype is made. This is a wooden prototype. The joint is made in a round wooden pole with a diameter of 35mm. The dimensions of the drawing are adopted. The main purpose of the wooden model is to see if the design of the joint functions and is worth to research further. The wooden prototype is placed in a Geiger dome configuration (fig. 4.14 middle picture) to see if it is possible. Also the first impressions of the cable routing are found in figure 4.14 on the right picture.

c Figure 4.14 Wooden model

After the wooden prototype is finished it’s clear that it isn’t detailed enough, as making the slots curved and placing set screws in the joint is more difficult than expected. After the wooden model is studied a decision is made to make a separate joint that will fit in a tube. This is done to save material, making the joint easier to produce and to be able to change the tube length. Changes made after wooden prototype:  Separate joint from strut  Use of a tube as strut

4.3.2 Rapid prototyping

In order to get more detailed joint to make more decisions, the joint is drawn in a 3D program to produce a 3D model. By making use of rapid prototyping13 it’s possible to create a 3D prototype early in the development process. It’s detailed and just one piece can be made. To create the joint it’s modelled in Solidworks (fig. 4.15) and transferring it to a .STL file, this is makes it possible to print a 3D model of the drawing. The 3D printed model is made from a very soft material so tests can’t be done with it.

13 Rapid prototyping is a group of techniques used to quickly fabricate a scale model of a physical part or assembly using three- dimensional computer aided design (CAD) data.(Wikipedia 24-8-2014)

Development of a tensegrity joint X.M. Bernaards

Figure 4.15 First Solidworks drawing

The 3D printed model (fig. 4.16) showed that the dimension of the joints diameter are very small, for the constructions the joint will be used in. In order to make those construction possibilities the diameter of the joint and strut have to increase. The size of the chosen set screws M6x6 looks very fragile in the joint. There is a small amount of body at the sites (fig. 4.17) of the set screw to hold on to. With the larger diameter of the joint a bigger set screws will be applied. The set screws will properly go up one size to M8x8.

Figure 4.16 3D printed model

Changes made after 3D model:  Strut diameter from 35mm to 40mm  Bigger set screws M8x8 to give them more body (fig 4.17)

Figure 4.17 Larger diameter

Development of a tensegrity joint X.M. Bernaards

4.4 Re-design

After the wooden prototype and the 3D model these changes are made to the joint:  Diameter changed to 40mm  Set screws to M8x8 to give it more body on the sites  Separate joint from strut

By these change the whole joint design changed and new drawings are necessary to show the new dimensions (fig.4.18). These dimensions14 are approved to be used for production of prototype for testing. For the prototype to be made, there is chosen to make the joint out of aluminium. Aluminium is easy to processed and the production of an aluminium joint is possible in the Pieter van Musschenbroek laboratory on the University of Eindhoven.

Figure 4.18 Re-design of joint

14 In the appendix the dimensions of all the joint can be found.

Development of a tensegrity joint X.M. Bernaards

4.4.1 Aluminium prototype

The final drawings (figure 4.18) where given to the workshop at Pieter van Musschenbroek laboratory on the University of Eindhoven. One joint is produced at first to see the new design. The joint is made by the production method of milling.

Figure 4.19 Milling process

Milling The production of the joint starts with a solid aluminium round rod that is placed in the milling machine. The dimension are set in the computer and the production is closely watched to avoid errors. The slits are made with a circular sawblade, side milling cutter, for the curves in the slit (fig 4.19 bottom left). The bottom of the joint is 2mm narrower to make it able to fit in a tube, with a depth of 150mm, to give an good steady surface for fixing the joint in the tube (fig 4.20 a), this is also used to make the top of the joint round. The final step is tapping M8 threaded holes in the centre of the slits (fig 4.20 b).

Figure 4.20 a) Bottom and b) tapping (custompartnet.com, 2014)

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4.5 Prototype for testing

The finished alumiunium milled joint is a perfect outcome of the drawings and meets the requirements of the first drawn idea. The joint is ready for testing the new connection for fastening the steel cable with a set screw in the joint.

Figure 4.21 3D print next to aluminium joint

Figure 4.22 Prototype for testing

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4.6 Conclusion

The aluminium prototype is made and ready for testing and all dimensions are fixed. The new joint gives a solution for the missing possibilities of a joint, where cables can be tensioned separately and the length can be adjusted. The new connection has to proof itself in the tests that follow. By putting these option in the morphological matrix and mixing them with existing solutions, the path15 to follow on the matrix for the new joint is:  Solid joint  Top of strut round  Strut top solid  Connection  Tensioning by pulling  Fastening cables by set screws  Cable length not pre set  Cable ending, open  Cable management by guidance slit

Figure 4.26 Following the orange line delivers the new joint design, see appendix B

15 The path on the matrix is shown in the appendix B with some other examples

Development of a tensegrity joint X.M. Bernaards

Testing

The tests of the new connection in the prototype joint are 5. described in this chapter.

Development of a tensegrity joint X.M. Bernaards

5. Testing

5.1 Introduction

The aluminium prototype joint has to have several tests to understand how it will function. The test done are to see what forces the new connection in the joint can handle. The connection between set screw, thread, steel cable and joint.

5.2 Maximum torque of set screws

5.2.1 Goal Testing at what torque the thread will strip out. To determine with what torque the set screws will be set for further testing, without damaging the thread and the cable.

5.2.2. Material  Torque wrench FACOM  Set screw M8x8 flat  Steel cable ∅ 2.5 mm  Aluminium rod of 5.5 cm, ∅ 40mm with 6 threaded holes

Figure 5.1 a) torque wrench, b) set screw, c) steel cable and d) rod

5.2.3 Hypotheses The torque will come near the given torque for screw M816 with a strength class 8.8 according to (ISO898 / 1 NF E 25100 NF EN 20898-1) of 23Nm.

5.2.4 Test design An aluminium rod, with the diameter of joint 40 mm, containing six threaded holes for set screws M8x8. A slit, such as in the design, is made to lay the cables in. The slit is 9.4mm deep in which the steel cable of 2.5mm can be placed, leaving 6.9mm over for the set screw. The set screw is 8mm so the cable will be pressed, and damaged. The torque wrench must be set manually back to zero after a test is done.

16 http://facom.nl/notices/K.200DB-K.202DB-M.200DB.pdf

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5.2.5 Executing the test To be able to fasten the set screws, the aluminium rod is clamped in a bench clamp. The torque wrench is turned to zero and is placed in the set screw. The set screw is screwed into the thread until it the thread strips out. On the display of the torque wrench is shown how much Nm maximum is used to break the thread. This test is repeated six times in order to increase reliability.

Figure 5.2 Using the torque wrench

5.2.6 Results After repeating the test six the following values are found: Test Value 1 24 Nm 2 22 Nm 3 25 Nm 4 21 Nm 5 22 Nm 6 23 Nm Figure 5.3 Values

The strength class of the screw was not given prior to the test, but seems to come close to strength class of 8.8 with a value of 23Nm.

5.2.7 Conclusion The maximal torque is not used in the following test. This to prevent the stripping out of the thread and damaging the cable by pressing too hard on it. When the thread is broken one of the key features of the joint is lost, adjusting the cable length after constructing and void the possibility of reuse. That is not the intention. It is opted to go for a torque of 20 Nm for the following tests17.

5.2.8 Discussion The accuracy of reading the analogue torque wrench may have a small deviation. A digital torque wrench will be much more accurate. The values of the torque will decrease after using the same threaded hole in the aluminium over and over again. This must be avoided in order to ensure reuse.

17 This was decided after the first test of test 1, which had a torque of 15Nm and cable slipped out too quickly from under the set screw.

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5.2.9 Further testing To get a better idea if the torque decreases after using a threaded hole several times test have to be done to confirm this. To prevent the threaded holes in the aluminium to lose their power after all the inserting a possible solution found; the use of stainless steel inserts (fig. 5.4), which can be glued into the holes, make sure there are no problems with repeated use of the threaded holes. The inserts also holds the cable in place when tensioned. Without the insert the cable is only pressed down by the set screw, when pulling and tensioning, the cable presses upwards against the set screw, this makes that there is some tension lost when the set screw is tightened. This application will be further studied.

Figure 5.4 Self tapping threaded inserts

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5.3 Maximum strength of connection (test 1)

5.3.1 Goal Determination of the maximum tensile force in the new connection in the joint. There is going to be examined at which maximum pulling force the connection starts to slip or at which point the steel cable breaks. This is done to determine how much force the connection is able to handle before placing the joint in a tensegrity.

5.3.2. Material  Universal testing machine. Set up to test tension.  Set screw M8x8 flat  Steel cable ∅ 2.5 mm (found in the laboratory so no specifications known)  Aluminium joint

Figure 5.5 testing machine Figure 5.6 Angles of the cable

5.3.3 Hypotheses The connection between the set screw, thread and steel cable will reach such a force that makes it possible to realize the desired construction. There should be a difference in force between the different the angles the cable is placed in. The cable in 90° degrees should be stronger than the cable in 45°degrees upwards (fig. 5.6).

5.3.4 Test design The joint has six working threaded holes that will be used. Some holes will be used several times. The joint is clamped at the bottom and at the top the cable is clamped and secured with additional plates to prevent slipping (fig. 5.7). The tensile force is increased by 1.5mm/min, and is pulled until the connection fails, slips or if the cable breaks. The test is done with an angle of 90° and 45° up (fig. 5.6), since these are the angle that the cable will make it in the construction. The results of the test are given in Newton.

Figure 5.7 Clams at the bottom and top

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5.3.5 Executing the test First, the set screw tightened to the specified torque from test 1; this was 20N/m. If the joint is clamped the tension is build up slowly. After breaking or slipping of the cable, the test stops. The found values of the test can be seen in figure 5.9. The test is repeated four times for both angles in order to obtain reliable results. After testing the 90° degree there is tested how much the maximum torque still is, this turned out to be less better than the first time. This is because the thread holes a little worn out by tightening the first time and by deformation of the thread through the tensile test (fig. 5.8). 1ste 2de Test value value 1 20 Nm 15 Nm 2 20 Nm 18 Nm 3 20 Nm 16 Nm 4 20 Nm 16 Nm Figure 5.8 Difference torque before and after test

With testing the 45° angle the joint was on a piece of steel with a cut-out V-angle of 45°. The joint cannot be clamped, such as at the angle of 90° degrees, but it is pressed between two points. For this the sides of the joint were flattened for a better grip. Because the use of a different testing machine the connection at the top for the steel cable was different, the cable are sandwiched between two points in this machine. The pressure force between these points was too large for the cable, which made that the cables almost immediately broke. For this purpose, there are placed two aluminium plates between the pressure points. This is done so that the cable could settle in these plates in order to prevent them from being crushed. This had the effect that testing is possible, but in the end still some the steel cables broke in the upper connection between the clamps of the machine (fig.5.12d).

5.3.6 Results

Steel cable Max. Tensile Test Angle Torque diameter strength 1 90° 20 Nm ∅2,5mm 3932 N 2 90° 20 Nm ∅2,5mm 3898 N 3 90° 20 Nm ∅2,5mm 3914 N 4 90° 16 Nm ∅2,5mm 4334 N 5A 45° 20 Nm ∅2,5mm 3247 N 5B 45° 20 Nm ∅2,5mm 4042 N 6A 45° 16 Nm ∅3,0mm 3355 N 6B 45° 16 Nm ∅3,0mm 3301 N 5C 45° 18 Nm ∅2,5mm 3823 N Figure 5.9 Sheet with all data

The letter indicates how many times a threaded hole is used, so 5B is threaded hole 5, used for the second time.

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4.500 Test results 1 to 4

4.000

3.500

3.000

2.500

2.000 Force[N]

1.500

1.000

500

0 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 Displacement [mm] Test 1 Test 2 Test 3 Test 4

Figure 5.10 Test with 90 degree angle

4.500 Test results 5A, 5B, 5C, 6A and 6B

4.000

3.500

3.000

2.500

2.000 Force[N]

1.500

1.000

500

0 0 2 4 6 8 10 12 14 Displacement [mm] Test 5A Test 5B Test 5C Test 6A Test 6B

Figure 5.11 Test with 45 degree angle

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Figure 5.12 a)Test 3, b)Test 4, c)Test 5B, d)breaking of cables in aluminium plates Observations test;  In test 1, the wire rope slipped loose at a force of 3932N. It can be seen that the wire rope has been slipping, because there is made a groove in the slit. The steel cable is also flattened over a greater area than the surface of the set screw which also indicates that the cable is slipped.

 Test 2. Same slipping as in Test 1 the values are 34N apart.

 The 3rd tensile test the steel cable shifted (slipping). The steel cable slipped over a longer length than in the first two tests, but remains on the same tensile force and makes a small peak at the end (fig 5.12a).

 At the 4th test a thread is used that isn’t located right in the middle of the slit (eccentric). The set screw is threaded with a torque of 16Nm and the thread is stripped than. This test achieved the highest value of all the tests. The steel cable break at the of the set screw connection for the first time. The high value probably, because there is more body now on the left side for the set screw to hold on to. This makes it harder for the set screw to move forward in the slit by the pulling force this counteracts skidding (fig.5.12b).

 In test 5, the first dip in the chart is when one strand of the steel cable breaks. This occurs in the middle of the cable. Then tension in build up again till the cable slips loose.

 Test 5B the second test in hole 5. In the graph can be seen that the stands of the steel cable break strand after stand (fig. 5.12c). The break of the strands occurs at the aluminium plates where the cables are clamped at the top. This is a different place then in test 5A.

 In test 6 is the first time with thicker aluminium plates to clamp the steel cable at the top. This to try to embed the steel cable even more. In this test a steel cable of 3mm is used this results in a lower torque namely 16Nm. The aluminium plates do not have the desired result, the steel cable breaks again on the clamping point. The thickness of the steel cable has no effect on

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tensile strength, it seems like a slacker cable than the 2.5mm cable used in all other tests. The value is hardly higher than tests 5 A and B.

 Hole 6 test second time. Same as 6A values are 54N apart.

 Test 5C five hole 5 used for 3rd time. Now the aluminium plates that clamp the steel cable are even thicker than previous tests. In this test the tensile force is the highest of the tests with an angle of 45°. This is because the steel wire does not break at the clamping above, but breaks at the set screw connection as in test 4, it will therefore be assumed that this value is the closest to the actual tensile force at an angle of 45°. The thicker aluminium plates do their job fine for embedding the steel cable.

5.3.7 Conclusion Testing has shown that the in the joint connection is sufficiently strong enough to allow building a small scale tensegrity. The minimum value out of the test is 3301N which corresponds to 330kg that can be handled by the connection. The connection can have that force before slipping or breaking. Some safety factor have to be taken into account before using the joint in a tensegrity structure. What is also clear is that the threaded holes lose strength (torque) after each test (fig. 5.8), which is not conducive to the re-tensioning of the steel cables. The possibly of using inserts could prevent this from happening (as indicated in the tests of maximum torque). The steel cable is crushed by the set screw at the connection (fig. 5.13). This is not conducive for making the cable longer in a construction, but it is unavoidable.

Figure 5.13 Crushing of steel cable

5.3.8 Discussion In the clamping point of the steel cable in the test of the 45 ° angle, the cable kept slipping ever time, so these values are likely to be lower than that the actually joint can handle. The values are also lower than in the test of the angle of 90 °, which also was expected. To eliminate the problem in the clamping point, two joints could be tested opposite to each other (fig. 5.14). Given the difference in quality of the steel cables used, this is found in the results of the tests, in the next test one steel cable has to be used to get uniform results. Also the properties of the steel cable have to be known given by the manufacturer. An option to prevent slipping is to use two set screws, this could also increase the strength of the connection.

Development of a tensegrity joint X.M. Bernaards

Figure 5.14 Next test set up proposal Figure 5.15 Clamping plates for cable

5.3.9 Further testing The clamping problem has to be solved for the next test. In this test the aluminium clamping plates (fig.5.15) were soft enough to embed the steel cable. To prevent the aluminium threads to wear out the use of inserts is advised. Also one quality of steel cable with known specifications is helpful to have to see if the connection is stronger than the cable and to get more reliable test results.

Development of a tensegrity joint X.M. Bernaards

5.5 Strength of re-design connection (test 2)

5.5.1 Goal In this test the determination of the maximum tensile force in the connection of in the joint connection with the use of inserts and smaller set screws.

5.5.2. Material  Universal testing machine. Set up to test tension.  Insert M8x9 adjusted to M8x6  Set screw M6x6 flat  Steel cable ∅ 2.5 mm (Working load of 80Kg)  Aluminium joint

Figure 5.15 Test set up, inserts and inserts glued in joint

5.5.3 Hypotheses The connection between the set screw, thread and steel cable will be lower, because of the use of smaller set screws.

5.5.4 Test design In the threaded holes in the joint insert are placed (fig. 5.15). The inserts are screwed 6mm into the threaded 9.4mm deep holes and are extra fixed with a dual component adhesives. The insert are M8x10, but there is only 6mm needed, so 3mm is grinded after application. The joint is protected by aluminium plates in order to prevent dents (fig. 5.16). The tensile force is increased by 1.5mm/min, and is pulled until the connection fails or the cable breaks or slips. The test is done with an angle of 90° degrees

Figure 5.16 Clams at the bottom and top

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5.5.5 Executing the test The maximum torque of set screws can’t be determined, because there is no bit holder for a M6 hexagon bit in the Pieter van Musschenbroek laboratory. There is tried to make a homemade torque wrench with a long steel bar fixed to a hexagon bit and by placing weights at the end of this arm (fig 5.16). The making failed and there is chosen to tighten the set screws by hand for the first four tests. In the last three test there is made use of a socket head screw instead of a set screw. The socket head screw is tightened with a torque of 20N/m. The tests are done in an angle of 90° degrees. The tensile force is increased by 1.5mm/min, and is pulled until the connection fails or the cable breaks or slips. The displacement of the steel cable isn’t measured anymore, only the force by time is measured.

Figure 5.16 Homemade torque wrench

To discover whether the insert is secure, there is tested to try to pull the insert out. The test is done by leading a cable under insert and then clamp the two ends in the top. The cable is tensioned and stops when the cable breaks or when the insert is pulled out. The first option happens, the cable breaks under the insert. Conclusion the insert is well secured.

Figure 5.17 Checking insert

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Observations test; Test Torque Breaking point Clamp What happens 1 Hand Upper clamp No plate Slips 2 Hand Upper clamp Alu. Plate 2mm Slips 3 Hand Upper clamp Alu. Plate 2mm Slips/breaks 4 Hand Upper clamp No plate Slips 5 Socket head screw Under bolt No plate Breaks 6 Socket head screw No plate Breaks 7 Socket head screw Piece Breaks

5.3.6 Results

4000

3500

3000

Test 1

2500

Test 3

2000 Force(N) Test 5 1500

Test 6 1000

Test 7 500

0 0 100 200 300 400 500 Seconds (Sec)

Figure 5.18 Graph with tests 1,3,5,6 and 7

Graphs 2 and 4 are left out figure 5.18, because something went wrong with those tests.

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Test Torque Steel cable Max. Tensile Min B.L. Force left of diameter strength cable (%) 1 ? Nm ∅2,5mm 3165 N 4800 N 65,9% 2 ? Nm ∅2,5mm 2973 N 4800 N 61,9% 3 ? Nm ∅2,5mm 1921 N 4800 N 40,0% 4 ? Nm ∅2,5mm 1846 N 4800 N 38,4% 5 ? Nm ∅2,5mm 2817 N 4800 N 58,7% 6 ? Nm ∅2,5mm 3610 N 4800 N 75,2% 7 ? Nm ∅2,5mm 2799 N 4800 N 58,3% 2,2 ? Nm ∅2,5mm 3685 N 4800 N 76,8% 4,2 ? Nm ∅2,5mm 3673 N 4800 N 76,5% Mean 2943 N

Figure 5.19 Sheet with all data

Test 2 6000

4000

2000 Test 2 Force(N) 0 0 500 1000 -2000 Seconds (sec)

Figure 5.20 Graph test 2

Test 4 4000 3000 2000 Test 4 1000 0 0 200 400 600 800 -1000

Figure 5.21 Graph test 4

In tests 2 and 4 the testing wasn’t stopped before trying the test over again. This can be concluded by the line hitting the zero for a long time, meaning that there is no tension, and then going up again. The maximum values of the second upward line are 2.2 and 4.2 in figure 5.19 and are incorporated in the results.

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5.5.7 Conclusion To many things went wrong with the tests to get a good understanding of the forces that the joint connection can handle, if inserts are used. The failure of most tests is still in the clamping of the cables. Even when this whole test seems to fail there is a bright spot, the connection between the set screw and the cable only fail once. So the connection is still the strongest point in the test.

5.5.8 Discussion In the last test a solution has been found to prevent the cables from breaking in the upper clamp. First a piece of an aluminium strut is clamped in the top of the tension machine and the steel cable is turned around it and fastend with a cable grip. This solution didn’t work, the cable slipped off and the grip was to big. The final solution is a hole in the middle of the piece where the cable can go througth. Then the there is made a node in the cable to prevent it slipping back throught the hole. For thitghtening the cable is turned around the piece, it needs to be ensured that the cables are rolled over each other for extra grip (fig. 5.22). So the testing wasn’t done for nothin, because the is a solution found for futher testing.

Figure 5.22 Top clamping solution with aluminium round piece

5.5.9 Further testing For the next tests the round aluminium piece has to be used for connecting the cable in the upper clamp. This will rule out the breaking of the cable in the upper clamp. When that failing point is gone the test can be performed in good order to get good results. Also a good steel cable must be used, where the properties are known, a 3mm cable is preferred. For the following test is also useful to keep the cable routing in mind.

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5.6 Final test strength (test 3)

5.6.1 Goal To determine the maximum tensile force in the connection after applying the recommendations of the previous test.

5.6.2. Material  Universal testing machine. Set up to test tension.  Insert M8x9  Set screw M6x6 flat  Steel cable ∅ 3 mm  Aluminium joint

Figure 5.23 Test set up

5.6.3 Hypotheses The recommendations applied should be able to handle more force than previous tests. The connection between the set screw, thread and steel cable will reach a higher force, what makes it possible to realize larger construction.

5.6.4 Test design The joint has no glued inserts like in test 2. The joint has eight working threaded holes in the beginning of the test that will be used. The joint is clamped at the bottom and protected by to plates with a halve circle in them. The cable at the top is inserted in a round aluminium piece (fig. 5.25) and is rolled around it for extra grip. This round piece is clamped so the cables can’t be pressed and break, like in the previous tests. The test stops if the cable breaks and this test is repeated four times in different slits to obtain reliable results. The test is done with an angle of 90° degrees since this is angle that the cable will make in most construction. The results of the test are given in Newton. The test is done with the cable routing shown in figure 5.24. This routing makes it possible to connect four cables and adjust them separately.

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Figure 5.24 Cable routing for test 3

Figure 5.25 Clams with halve circle at the bottom and top with round aluminium piece

5.6.5 Executing the test The torque of the set screws have to be determined again, because the steel cable diameter is changed to 3mm, 6x7 - fibre core wire rope, with properties in figure 4.9. The found torque value is 8N/m. The inserts are tightened by hand, when the set screws are tightened with the torque wrench the insert will be tightened further. The insert will protrude approximately 3mm, because they are 10mm long and have to be 6mm (fig. 5.26). The tensile force is increased by 1.5mm/min, and is pulled until the connection fails or the cable breaks or slips. The displacement of the steel cable isn’t measured anymore, only the force by time is measured. After the first test, it became clear that not all the slit can be used again. The clamping force deformed the top of the joint shown in figure 5.27 so that some slits can’t receive the cable of 3mm anymore, therefore, six tests can be done maximal.

Figure 5.26 Insert sticking out Figure 5.27 Deformation of top

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5.6.6 Results

6000 Test 1 to 6

5000

4000 Test 1

Test 3 3000 Test 2

Force(N) Test 4 Test 5 2000 Test 6

1000

0 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 Seconds (sec) Figure 5.28 Sheet with data

Test Torque Steel cable Max. Tensile Min B.L. 1960 Force left of cable diameter strength (%) 1 8 Nm ∅3mm 5375 N 5860 N 91,7% 2 8 Nm ∅3mm 5173 N 5860 N 88,3% 3 8 Nm ∅3mm 5130 N 5860 N 87,5% 4 8 Nm ∅3mm 5405 N 5860 N 92,2% 5 8 Nm ∅3mm 5531 N 5860 N 94,4% 6 8 Nm ∅3mm 5309 N 5860 N 90,6% Mean 5320 N Figure 5.29 Table with all values

. Figure 5.30 The point where the cable breaks in all tests

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5.6.7 Conclusion In all five tests the cables break at the point where the cable has an angle and is pressed against the sharp corner of the slit, seen in figure 5.30. There no failure at the connection between cable and set screw, no sliding or breaking occurs. With the found value of maximum tensile strength, the minimum breaking load of the cable is found, when the cable is used in the joint (fig. 5.29). If the joint is used in a construction, standards and regulations require that design factors be applied to the cables minimum breaking force to determine the maximum working load. The maximum working load has to be calculated, the design factor is defined as the ratio of the minimum breaking force of a steel cable to the total load it is expected to carry, max. working load = minimum breaking load / design factor. There may be other limiting factors in an application that make the maximum load the equipment can handle less than the cables maximum working load.

Typical safety factors (5-8) 6 Minimum breaking load 5130N max. working load = 5130N / 6 = 855 N.

So a working load of 87 kilo is safe to use on the cable.

Test 6 is done with the cable going straight, so without an angle, this shows that even when there is no angle where the cable breaks, like in test 1 to 6, a value is reached around 5300N. What is almost the same as the tests with an angle. This could mean that the angle is not the failure point, but the breaking point of the cable.

5.6.8 Discussion The tests went very well and this set up can be used to find all the values of different angles of the cable. The cables break, because they are pressed against the sharp corner in the top of the joint. In the design of the joint the sharp corners should be fillet, rounded, so the corner aren’t that sharp anymore. Probably the values to be found then will even higher or the cable will break on another point.

5.6.9 Further testing All the possible cable routings have to be tested to get all the data of the joint. That has to be done to make clear what effect the angles in the joint have on the cables breaking point. Tests 6 has to be repeated 5 times to determine if the angle is the failure point in the joint or the cable itself.

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5.7 Conclusion testing

In the first two tests it became clear that the use of insert is recommended. The down side of using inserts in this design is that the set screws got smaller. If the insert is M8 the set screw is M6, the surface in order to press on the steel cable becomes smaller, but after test 3 it didn’t seem to be a problem using a smaller set screw. The maximum force went up, but this is also due to the larger steel cable. An option to prevent slipping, what is the main failure in the first test, is to use two set screws, this could also increase the strength of the connection. Test 3 shows that there is no need for an extra set screw, if the joint is used with a 3mm steel cable and M8 insert with M6 set screws.

The steel cable is crushed by the set screw at the connection every test. This is not conducive for making the cable longer in a construction, but it is unavoidable. This could be prevented by placing a small plate between set screw and cable. Leaving it this way makes it only possible to tension the cable.

Recommended is to enlarge the insert and set screw, because it’s very difficult to fasten the small set screw and they’re easily broken. In the tests the M6 set screw is over twisted very fast, so getting it out of the threaded hole becomes a problem. If it’s bigger it would be easier to fasten and loosen the set screw. After these tests it seems that the new connection, set screw, thread and steel cable works well and does the job where it was designed for, holding the steel cable in a joint for a tensegrity structure. Further testing is necessary to find all the values of the forces in the joint if the joint is placed in different angles, what is likely seen the tensegrity structures.

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Design 6. The adjustments after the tests are applied in this chapter

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6. Design

6.1 Aluminium product

After the test, the decision is made to produce eight joints to build some tensegrity structures with them. In appendix A all the dimensions can be found.

6.1.1 New joint

Figure 6.1 Solidworks render joint

The dimensions are the same as in figure 4.16 and in the appendix.

6.1.2 A ‘3-strut T-prism’ tensegrity

The prism mentioned in paragraph 2.2.2 is a 3 strut prims and is one of the tensegrity structures that has to be able to be built with the final designed joint. In figure 6.2 the made model is shown that is made with the joints.

Figure 6.2 Three strut prism tensegrity

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While making this tensegrity it became clear that the cable configuration in the joint doesn’t allow adjusting a single cables. The cables run over each other what makes setting a single cable hard, because if one cable is tensioned over another cable the cable underneath is fixed as well. Before the joint is used in a tensegrity there has to be looked at the routing of the cables. This to avoid problems with adjusting.

6.1.3 Cable routing

If it is clear in what tensegrity the joint is used. The slits at the top in the joint can be adjusted (depth of the incisions) so the cables can run over each other. For example if there are four cables with no angle up or down and an angle of 900 degrees between them the solution in figure 6.3 must be chosen. The red lines show where cuts in the top slits have to be made for this solution, with a depth of 3.4mm.

Figure 6.3 Four cables, cuts and possibilities for tree cables

For a configuration of the Geiger Dome the top and the bottom have different incoming cables. The colours are the different incoming cables.

Figure 6.4 Bottom and top connection Geiger Dome

There have to be cuts in the red and green line to let all the cables run over one and another. In the top joint the red cable goes down and the green goes up so it is possible to run through one exit slit. For more cable routings and solutions for tensegrity structures see the appendix C. If the joint is used in a tensegrity structure, first has to be made clear what the cable routing is to adjust the depth of the slits to make sure that cables run over each other.

Development of a tensegrity joint X.M. Bernaards

6.1.4 Angles of cables

The angle of the cable going outwards has a limitation. When the cable is between 900 and 520 degrees (fig. 6.5), the cable can go out of the slit. If the cable is out of the slit the stability is lost in the joint and it could occur that the joint rotates, because the other cables remains in the slit and pull the joint in another direction. This is tested in the 3 prism tensegrity of figure 6.2. When the cable is between 00 degrees at 520 degrees it remains in the slit.

Figure 6.5 Maximum angle of out- or inward cable

6.1.5 Tensioning

The cables can be tensioned by hand, but that’s very heavy and impractical. The best way if tensioned by hand is to make use of a rotating wire tensioner (fig. 6.6). There are some solutions to tension steel cables found and are included in the morphological matrix. The method found and preferred is tensioning by pulling, a solution for tensioning by pulling can be achieved by using a grip hoist (fig. 6.7).

Figure 6.6 Rotating wire tensioner Figure 6.7 Tirfor grip hoist or winch

6.1.6. Fixing cables

Fixing the cables is with the use of the new connection with set screws. In the tests 1 and 2 is seen that by fixing the cables with the set screw, the cable is damaged at that point and breaks sometimes at this connection. The set screws press too hard on the cable so it’s is squeezed and losses tensile strength. To prevent this, it is possible to make use of padding, a gasket or other material that inhibits damage of the cable by the set screw, but it seem unavoidable to damage the steel cable.

Development of a tensegrity joint X.M. Bernaards

Production

7. method

In order to achieve mass production, production methods are examined in this chapter.

Development of a tensegrity joint X.M. Bernaards

7. Production method

7.1 Introduction

As stated in the research question the joint has two demands to the production method:  Mass produced  As cheap as possible These two demands must be achieved. That’s not going to happen if the joint is produced by milling aluminium, like described in chapter 4. The milling process used to make the joint was done by one man using a milling machine. The position of the aluminium bar has to be changed every time a new joint is made. This all takes time and time is money. In search of a faster and cheaper method to produce the joint, various types of moulding will be examined. There are all sorts of different materials that can be used to create the joint. Like the milled aluminium joint there are different ways for creating the joint in aluminium. Casting aluminium will be able to realize a higher production rated than milling, there are all sorts of casting methods (fig. 7.1), but presumed is that injection moulding with plastic will only be able to realize the two set demands. Injection moulding is able to have a high production rate and plastic is a good replacement for aluminium.

Figure 7.1 Top left to bottom right; Lost wax casting, permanent mould casting, sand casting and lost foam casting18

18 Custumpart.net

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7.2 Aluminium casting

To produce the joint in aluminium it can be casted in different ways. To get a better understanding and idea about the casting methods a brief introduction is given with some advantages and disadvantages.

 Sand casting A print of the model is made in Green sand 19and this will be filled with molten aluminium. There could be added a core to make the cast hollow, but this has to be removed afterwards. The most important advantage is that both small and large castings are possible, and difficult corners can be made. The biggest disadvantage is that a sand texture stays on the product and it’s not suitable for mass production.

 Lost wax casting A wax model is made and coated with ceramic to create a shell. The next step is to heat the shell so the wax flows out. Now aluminium can be poured into the cast (ceramic shell). When the shell cooled off, the ceramic shell can be removed, leaving a perfect copy of the wax model. The advantage of this method is that the level of detail, complexity and size tolerances are very high.

 Lost foam casting A foam model is made and coated like the lost wax method to keep a barrier between the foam and the sand. A cluster of patterns can be made by attaching multiple foam models to a string. The cluster goes in to a flask which is then filled with sand. The aluminium is directly poured on the cast, burning through the foam. The two main disadvantages are that pattern costs can be high for low volume applications and the patterns are easily damaged or distorted due to their low strength (Degamo, Black and Koher, 2003). If a die is used to create the patterns there is a large initial cost (Kalpakjian and Schmid, 2006).

 Permanent mould casting A mould that consists of two halve is made, a core can be used. The mould can be filled completely for a solid piece or only filled with a little aluminium to create a thin walled piece. The main advantages are the reusable mould, good surface finish, good dimensional accuracy, and high production rates. There are three main disadvantages: high tooling cost (making of the mould), limited for low-melting- point metals, and short mould life. The high tooling costs make this process uneconomical for small production runs.

Overall, there have to be made several assessments to make a decisions which production method to pick.

19 Green sand is an aggregate of sand, bentonite clay, pulverized coal and water.

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7.3 Injection moulding

To look for other options for producing the joint research is done to see if the joint can be made with injection moulding with plastic. Injection moulding can both be done with metals as plastic, but in this paragraph only plastic injection moulding is explained. Plastic parts are mostly manufactured by injection moulding. Injection moulding is a rapid process, the choice of material and colour are flexible, the labour costs are low and most plastics are recycled, which is good for the environment. The disadvantages are a high initial tooling cost (making of the mould) and the design of the part has some restrictions or rules.

The production cycle: A mould is made from steel or aluminium, it consist of two halves so it can be opened and closed along the parting line (the line where the mould is widest) to eject the product. The moulds are placed in the clamping part of the moulding machine (fig. 7.3). The clamping ensures a tight seal between the two mould parts so no plastic is spilled.

The raw plastic (plastic resin) is fed into the hopper. The plastic is heated by heaters to make it fluent. By turning the reciprocating screw (pressure) the heated plastic pushed into the nozzle. The nozzle shots an amount of pre-set material, like ABS, nylon, PC, ect.20, in the mould.

When in the mould the plastic immediately starts to cool. The cooling also causes the plastic to shrink, this depends on the used plastic. If designing a mould for plastic there has to be taken into account to make the mould bigger to accommodate shrinkage of the part. When the part is cooled it can be ejected from the mould. This has to be done with some force, because of the shrinkage and the adheres to the mould. After the part is made the process starts over again from the start.

Figure 7.2 Mould21 Figure 7.3 Moulding machine19

20 http://www.protolabs.com/resources/molding-design-guidelines/materials 21 http://www.custompartnet.com/wu/InjectionMoldin

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7.4 Design rules for moulding

The design rules for moulding have to be taken into account, when developing a mould for the joint1,2,3. The prototype of the joint has to be adjusted to the rules for designing a mould. The design must meet the following rules.

Maximum wall thickness  Decrease the maximum wall thickness of a part to shorten the cycle time (injection time and cooling time specifically) and reduce the part volume  Uniform wall thickness will ensure uniform cooling and reduce defects

Corners  Round corners to reduce stress Figure 7.4 Wall thickness concentrations and fracture  Inner radius should be at least the thickness of the walls

Core-cavity  Make use of a cavity

Coring out  Remove unnecessary plastic Figure 7.5 Corners round

Ejector pins  Chose places for ejector pins

Ribs  Avoid deep and thin ribs

 Deep ribs require draft and clearance Figure 7.6 Core - cavity Size limitations  There are limitations of size

Draft and undercut are leading design rules for moulds and are explained separately in the next paragraph.

Figure 7.7 Ribs with draft

1) http://www.protolabs.co.uk/resources/molding-design-guidelines/ 2) http://www.makeitbig.com/2013/05/14/design-guide-top-5-rules-for-injection-molding/ 3) http://www.custompartnet.com/wu/die-casting

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7.4.1 Draft

Firstly, the mould must allow the molten plastic to flow easily into all of the cavities. Equally important is the removal of the solidified part from the mould, so a draft angle must be applied to the mould walls. If plastic parts have completely vertical walls, drag marks will occur on the plastic as it scrapes along the metal tool face. The amount of draft required (in degrees) will vary with geometry and surface texture requirements of the part. Several rules for using draft properly: Use at least between 0.5 and 1 degree of draft on all "vertical" faces  1 ½ degrees of draft is required for light texture  2 degrees of draft works very well in most situations  3 degrees of draft is a minimum for a shutoff (metal sliding on metal)  3 degrees of draft is required for medium texture

Figure 7.8 Draft 6 degree

7.4.2 Undercuts

These are recessed surface that cannot be moulded using a single pull mould. Undercuts make it impossible to remove a part from a mould and need special solutions:  Minimize the number of external undercuts  External undercuts require side-cores which add to the tooling cost  Some simple external undercuts can be moulded by relocating the parting line  Redesigning a feature can remove an external undercut  Minimize the number of internal undercuts  Internal undercuts often require internal core lifters which add to the tooling cost  Designing an opening in the side of a part can allow a side-core to form an internal undercut  Redesigning a part can remove an internal undercut  Minimize number of side-action directions  Additional side-action directions will limit the number of possible cavities in the mould

Figure 7.9 Undercuts

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7.5 Design mould

In Solidworks there is the option to make and test a mould design for the joint. Analysis are done with this option to see if the model follows the design rules for injection moulding and if it is possible to make a mould for the joint. The steps taken will be explained. The joint is first analysed split in two horizontal (fig. 7.11). This should reduce the draft, because the round shape of the joint.

Design In the joint design the design rules for injection moulding where not taken into account. So the rules have to be applied to the joint. (Fig 7.11).

Draft analysis The draft analysis start by giving the direction of pulling. Direction of how the joint is pulled out of the mould. The green is the positive side Figure 7.11 New joint and red the negative (Upper and lower mould). In the figure 7.12 there is also yellow. This means that, that surface has to be draft. It has to have draft to make it possible to remove the finished joint from the mould.

Undercut analysis The Undercut Analysis tool finds trapped areas in a model (red) that cannot be ejected from Figure 7.12 Draft analysis the mould (fig 7.13). These areas require a side core. When the main core and cavity are separated, the side core slides in a direction perpendicular to the motion of the main core and cavity, enabling the part to be ejected. So the joint with the inside curves needs eight sided cores, but this is very difficult to manufactory.

Pulling the joint horizontal isn’t possible without Figure 7.13 Undercut analysis the use of side cores. The next step is to see if the joint can be pulled vertical.

Development of a tensegrity joint X.M. Bernaards

The joint is changed following the design rules pulled out of the mould. and the changes will be (fig. 7.14): Only problem now is adding the top part and  Fillet of all the right corners fitting the cables into the slits again.  Removed inner curve slits  Removed threaded hole  Extending slit to the bottom

If the joint is tested pulling vertical the same results as horizontal remain.  Slits are too long and are not able to be pulled that far  Site faces are also too long to pull

 Draft is needed Figure 7.14 Pulling vertical

Even when pulling direction is changed back to horizontal with the design changes, fillet corners of the slits. The pulling of the slits right and left are now possible, see red arrow (fig. 7.15).

Even changing the solid joint into a thin walled Figure 7.15 Pulling horizontal joint doesn’t matter for the pulling proses of the mould. Even if the slits have inner draft (fig. 7.18) it still isn’t possible for the joint to be ejected out of the mould

Solutions are: Figure 7.18 Pulling with draft slit on the right  Draft the long vertical surfaces

 Draft the slits  Use of side cores Side cores can increase the cost of the moulded and added complexity of the moulding machine. The middle piece of the joint can be made by injection moulding, leaving the top of, by putting a 0.5 degrees of draft on the sites and the slits(fig. 7.19), but the top of the slit remains 3.4mm width and the bottom width Figure 7.19 Mould with draft only of centre changes to 2mm, but the piece is able to be

Development of a tensegrity joint X.M. Bernaards

7.6 Costs

The costs of injection moulding consists of the costs for material, production and tooling.

7.6.1 Material cost

The material costs of injection moulding is determined by: the weight of the plastic that is needed and the price of the chosen plastic. The weight can be calculated by the volume of the joint and the channels to fill the mould. The costs can be reduced by making use of less material by making the walls thinner or looking for unnecessary material.

7.6.2 Production cost

The production cost is primarily calculated from the hourly rate and the cycle time. The hourly rate is proportional to the size of the injection moulding machine being used, so it is important to understand how the part design affects machine selection. The required clamping force is determined by the projected area of the part and the pressure with which the material is injected. Also, certain materials that require high injection pressures may require higher tonnage machines. The size of the part must also comply with other machine specifications, such as clamp stroke, platen size, and shot capacity.

The cycle time can be broken down into the injection time, cooling time, and resetting time. By reducing any of these times, the production cost will be lowered. The injection time can be decreased by reducing the maximum wall thickness of the part and the part volume. The cooling time is also decreased for lower wall thicknesses, as they require less time to cool all the way through. Several thermodynamic properties of the material also affect the cooling time. Lastly, the resetting time depends on the machine size and the part size. A larger part will require larger motions from the machine to open, close, and eject the part, and a larger machine requires more time to perform these operations.

7.6.3 Tooling cost

The tooling cost consists of the mould base and the machining of the cavities. The cost of the mould depends on the size of the envelope of the part. The costs of the cavities have to do with the geometry of the part. The greater the size of the cavity the more it costs. Other additions that take time will cost money, like tapping holes afterwards. The more joints the more expensive the mould. For a large quantity of joints a higher class mould is needed, one that will not wear out quickly. The stronger mould material is used the higher the mould cost and more machining time is needed to make it. As stated before the number of side-action directions can have effect on the cost too. The additional cost for side-cores is determined by how many there are used.

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7.7 Conclusion

Advantages of injection moulding include:  Shorter production cycles than other methods (transfer moulding, compression moulding) as a result of higher clamping/injection pressure from the curing temperature  High clamping pressure on the mould means the parts have little to no flash, as compared to the other methods  Higher production rates which leads to lower unit costs  Oftentimes parts do not need additional finishing processes  Automatic processes of the machine reduce labour costs

Disadvantages of injection moulding:  In order to be practical, larger production runs are necessary  Initial tooling costs are higher than the other methods. Making mould  There are some design restrictions, so not all compounds are suitable for injection moulding

As seen, there are many advantages to injection moulding the joint, but there are also restrictions, meaning it’s not always the right choice for every application. Some of the designed parts are not possible to make with injection moulding, because of the design rules. The joint has to be completely customized to be able to make it with injection moulding. It has to be split in two parts. An invented solution is to use eight side-core to create a solid joint with the slits in it (Fig 7.20). This is very expensive and it is not for sure that it is possible to produce by the moulding machine.

Figure 7.20 Side-core

Injection moulding plastic doesn’t seem like the perfect solution to produce the joint in one piece, that‘s why the next paragraph will give a whole new proposal for production. The found separation of middle and top will be used in the next production method, because this will lead to less problems with production.

Development of a tensegrity joint X.M. Bernaards

7.8 Proposal for production

For production there are some changes made to the joint design that make it easier to produce the it. These are some changes that could be applied;  Try to make it hollow the save material,  Slits straight, so no curve anymore. Easier to produce.  Slit go through till the end, so the cable can be hidden in the strut  Use of two set screws, for more grip and to prevent the cable to curve With these new findings several adjustments are made in the joint designed. Seen is that it is hard for injection moulding to make the middle section of the joint. This is because of the draft that is needed on the surfaces to eject the joint out of the mould. Looking in to another production method it is also a smart to split the joint in different parts.  Top part  Middle part  Strut connection If the joint is split in different parts it is possible to produce these parts with different methods. The round top can be made with injection moulding now, if it is loose a part. The draft needed on the slits doesn’t have a great effect anymore on the size slits, because the distance to draft is much less. With a draft of 1p degree it is possible to eject the top out of the mould, this is tested in the moulding option in SolidWorks, seen in figure 7.21 right is the mould design for the top part. To save material normally a part is made hollow, this is not advised in the top part, because the cables run through the slits and will rub against the sides and press down on the top, if the wall is not thick enough they could break. Also when the walls are ticker then three millimetres it is not possible to use injection moulding anymore, because the walls will touch each other inside the top and ejection of the mould is not possible. The only thing needed went using different parts is a way to connect them with each other. A solution for this connection is to add a little section at the bottom of the top part like a circle with a extrusion on the side (fig. 7.21 right picture). This section will fit into a made section in the middle part so the top part won’t slip or rotate. The shape can be anything as long it prevents the top of turning. There is chosen for this method instate of a mechanical or other fastening method.

Figure 7.21 Mould design and final product

Development of a tensegrity joint X.M. Bernaards

Now that the production of the top is clear, injection mouling, the hard part is to produce the middle part, because the slits are an obstacle. When searching for a method of production without having to add draft , extrusion a good solution. If the middle part is made by extrusion it is like making a profile. Extrusion works very well with metals and plastics. There is chosen to change the material back to aluminium, because the test are all done with an aluminium joint and the values of the connection are known. If produced in plastic the results of the tests are not representative and have to be done over with a plastic made joint. Also almost the same shape of the joint is found (fig. 7.22) in a publication of the aluminum extruders council, extrusion spotlight, pp 5, 2000. So expertise of make such a form in aluminum is known.

Figure 7.22 Similar produced shapes as the middle of the joint.

With extrusion it is also possible to make a long extrusion of so that multiple parts can be cut of it. The process of aluminium is hot extrusion and works as follows; a block is placed behind a ram that presses the hot aluminium through a die, with the form to obtain, and the product is guided down a cooling table by a puller. (Kalpakjian, 2013) The investment of extrusion is the die, to keep price low some simple design rules have to be taken into account;  Avoid sharp corners, it's very expensive to extrude sharp corners. (Min radius 0.4mm)  Keep the wall thickness of the profile to be extruded as similar as possible.  When the stiffness of a hollow profile is not necessary, then try to make an open (solid) profile, this saves significant costs. (AEC, 2013)

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Figure 7.23 Solid, hollow middle, hollow straight corners and hollow round corners

Take into account material saving and with the mould design, the middle can be extruded with different solutions; it can be a solid, solid sides with hollow middle, hollow with straight corners and hollow with fillet corners. (fig. 7.23). The solid solutions can also be made with round corners to keep die pricing low. To add the set screws threaded holes have to be drilled in the slits after production. This becomes a problem in the hollow middle parts options, because the slit is 3,4mm wide and the walls variety between 1 and 3 mm and the M8 insert is 8mm wide. This make that there is almost no thread, because the surface is very small. (fig. 7.24). This is no problem with the solid and hollow middle solution.

Figure 7.24 Tapped holes in hollow middle part Figure 7.25 Ring

The thread problem can be solved with an addition on the joint, but this is not preferred. To give the set screws more thread, a ring can be placed over the holes, in this ring thread are made to give the set screws more grip. This solution is shown in figure 7.25.

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To make a decision what solution for the middle part is best the table in figure 7.26 is made.

Solid Hollow middle Hollow straight Hollow round Weight (gr.)22 189.07 135.48 43.67 42.57 Volume (cm3 ) 70.03 50.18 16.17 15.77 Tooling cost Very low +/- Very high High Complexity part Very low +/- Very high Very high Round corners Possible Possible Not present Present Wall thickness Thick +/- Thin Thin Placing inserts Simple Simple Hard Hard Connecting parts Possible Possible Easy Very easy Strength of part Strong +/- Fragile Fragile Figure 7.26 Decision sheet

The best option is the solid joint solution with round corners if necessary. The key point for choosing the solid joint is the that the placing of the inserts is simple and strength of the inserts is guaranties by the wall thickness the insert can hold on to. If a hollow joint is chosen the insert need an additions to created more body to hold on to. The only disadvantage of the solid joint is that it’s not the lightest solution, but the weight of the tensegrity structure the joint will be used in, will make this right. It is also the strongest solution, the hollow parts could deform is too much tension is on them. The hollow part could pressed or bent, because the structure of the tube is weakened by the slits (fig. 7.27)

Figure 7.27 Hollow part deforming by pressure

The deformation is an assumption based on the fact that a tube is strong, but with the slits the core of the tube is adjusted and can therefore deform like an accordion.

22 Aluminium alloy 6061

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To conclude the finale design of the joint where adjustments are made for the chosen production method. The iterative process design can go one and one, but choices are made in this thesis and supported by tests and research. This leads to the best possible solution for designing and producing the new joint according the research in the thesis. A brief summary to summarize all decision;

Design:  Strut diameter 40mm  Height of 95mm  Round top round 10  Slit are 9.4mm deep and run till the end  Use of M8x6 inserts  Use of M6 set screws  Two parts top and body

Production is;  Top part injection moulding with aluminium  Middle part made by extrusion  Thread is bored after extrusion  Bottom 150mm of the joint has a radius of 36mm made by milling

The connection methods are;  Top and middle by a connector  Middle and strut connection is made by sliding the bottom 150mm in the strut.

Finale joint design

Figure 7.28 renders of finale joint design

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Conclusion 8. The conclusion, discussion and recommendations.

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8. Conclusion

8.1 Conclusion

The goal of the research is to develop a joint for a tensegrity structure, where single cables can be tensioned in the joint itself and can be produced on a large scale with low costs.

Different topics are handled including products on the market, design and production, which has led to the following questions:

Conclusion research The literature study showed that, despite being an important part of the construction, not much has been written about the joints itself. Not many joints have the possibility to tension single cables in the joint itself and most joints aren’t able to adjust the cable length after constructing. The adjusting of the cable length can be helpful, because there is no need for pre-cut cables while constructing a tensegrity structure and faults in length are easily corrected . Over time, the ways of tensioning has changed from tensioning all the cables at once to tensioning cables separately. When tensioning the cables separately, al little room is left for adjusting, which is needed to absorb slack and can’t be used to adjust the cable length as these cables are set to the correct length and are fastened to never come loose. The outcomes shows that the sketch for a new joint is a good start to an innovation in single cable tensioning in joints.

Conclusions design After completion it can be concluded that the design goal is achieved. Elaborating on the first sketch, a new joint is developed. In this joint it is possible to either have a connection in the joint itself as to tension the cables separately and as pre-cut cables aren’t necessary anymore, cable length can be adjusted anytime. The following set criteria are achieved:  Cables have to be connected in the joint.  A slim joint, esthetical, with no additions on it.  Cables should be able to be adjusted before and after construction for tensioning.  Adjusting is done by the use of set screws  No use of external tensioning additions on cables.  The struts diameter smaller than ten centimetre

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To control the used design and for further research, this thesis also delivers a morphological matrix of the different joint solutions found till now. The matrix shows the design possibilities used by other designs of joints. For innovation a path on the matrix can made and a new design can rollout. The followed path for the designed joint is an innovation in cable-strut connections. The design possibilities seemed endless, but keeping the criteria in mind, the finale joint design depended on the testing and production method. Major changes were:  Use of two set screws, for more grip and to prevent the cable to curve  Slits straight, so no curve anymore  Slit go through till the end, so the cable can be hidden in the strut  The depth of the incisions at the top may vary for cable routing

Conclusion testing In this thesis the only joint tested is a milled, aluminium prototype of the joint. The testing done is based on trial and error so many things went wrong during testing. The tests are done to research the new connection in the joint. The set screw, thread and cable connection isn’t found in the manner used in the joint so the testing is done. Test showed that the connection is strong enough to be able to have a working load of 87 kg. This is sufficient to build a small tensegrity structure with the joint as stated in the introduction.

Conclusion production method The production method of the prototype by milling is a long and expensive process and is therefore not the preferred method if the joint has to be put in mass production.

The study of the production method was larger than expected so only a scan of the literature is accepted and the use of SolidWorks for the mould design, outcomes remain superficial. The proposed production method of injection moulding with plastic was dropped after choosing for extrusion as production method with aluminium. After testing in SolidWorks it does not seem to be capable of producing the entire joint with injection moulding in one time. Looking for different production methods the financial requirement went to the background and will therefore not be completely answered in this thesis. The finale production method existed out of two methods, namely injection moulding and extrusion. By combining the two production methods for the different parts of the joint, it is possible to produce the joint as designed in aluminium. It can be stated that an appropriate material and production method for the joint is given in this thesis.

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Conclusion costs23 In this thesis the exact costs will not be given, but the choices of material and production method are made on basic written advantages for cost given, paragraph 7.6 and by manufacturers of aluminium products. It’s hard to make an estimation about the costs, because it depends on many different factors; Size of part, Volume, Wall thickness, (depends on alloy) Complexity of part have a large impact on pricing, Weight of moulding, Types of material, Price raw materials, Tooling costs, Number of parts planned to produce.

23 For the submission of the thesis, several manufactures are emailed to get the pricing of the joint.

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8.2 Recommendations

Further research The development of a tensegrity joint, where the cables can be tensioned in the joint itself is not commonly seen in the solutions found for the morphological matrix. Even the development of joint needs further research, there are a lot of solutions and it seems that everybody who designs a tensegrity, designs his own joint, isn’t it simpler to have a standardised joint?

Testing There are no strength tests done with the joint fully operational in a tensegrity structure, so nothing can be said about the behaviour of the joint in a structure. This is a critical test before taking the joint in production. Also testing with the proposed two set screws has to be done to prove that the connection will be able to handle more load that way. When material and production method are decided, producing the joint can start. Adequate testing has to be done before there can be said something about the finale joint connection, as the real properties of the joint can be made clear after testing. For working with the joint on side it’s recommend to use larger set screws like M10 inserts and M8 set screws, because during testing tightening the small inserts is very inconvenient as the small inserts easily break.

Production The production methods can be endless and have to be researched. There are so many possibilities to produce the designed joint and so are the different materials. The production method in this thesis is pure theoretical and supported by moulding programs. The final joint has to be made and tested first to see if the injection moulding of the top and the extrusion of the middle design are really possible to make, before taking the joint in mass production. Through really producing the joint like described in the proposal for production in chapter 7, things can be said about costs and functioning of the joint instead of guessing.

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Literature

AEC (2013). Aluminum extrusion manual, 4th edition, Illinois: Alumininum extruders council. AEC (2000). Extrusion spotlight design, the shapemakers, Wouconda, USA. Bin Bing, W. (2004). Free-standing Tension Structures, London: Spon Press page147 Burkhardt, R.W. (2008). A practical guide to tensegrity design, 2nd edition, Degarmo, E.P., Black, J.T. and Kohser, R.A. (2003). Materials and Processes in Manufacturing, 11th edition, 321-322. Hoboken: John Wiley & Sons Jáuregui, V.G. (2004). Tensegrity Structures and their Application to Architecture. Thesis MSc Architecture in Queen’s University Belfast. Jáuregui, V.G. (2009). Controversial Origins of Tensegrity. Proceedings of the International Association for Shell and Spatial Structures (IASS) Symposium 2009, Valencia Groot, A.D. de (1994). Methodologie: grondslagen van onderzoek en denken in de gedragswetenschappen, 12th edition. Assen: Van Gorcum. Hanaor, A. (1993). Double-Layer Tensegrity grids as deployable structures. International Journal of Space Structures, Vol.8, 135-145. Heartney, E. (2013). Kenneth Snelson; Art and Ideas, n.b Heunen, C. and Leijenhorts, D. van, (2004). Tensegerities. NAW 5/5 nr.4 December 2004 Kalpakjian, S. and Schmid, S.R.(2013). Manufacturing Engineering & Technology, 7th edition, 297-299, New Jersey: Prentice Hall. Kostic, M.M. and Reifschneider, L.G. (2007). Design of extrusion dies, Encyclopedia of Chemical Processing, Vol. 1, 633-649, New York; Taylor & Francis Motro, R. (2003). Tensegrity: Structural Systems for the Future. London: Kogan Motro, R. (1992). Tensegrity systems: the state of the art. International Journal of Space Structures, Vol.7, 75–83. Motro, R. (2002). Tensegrity: the stat of art. International Journal of Space Structures, Vol.5, volume 1, 96-106. Pugh, A. (1976). An Introduction to Tensegrity. Berkeley: University of California Press. Pellegrino, S. and Tibert, A.G. (2003). Review of form-finding methods for tensegrity structures. International Journal of Space Structures, Vol.18, 209-223. Pellegrino, S. (1992). A class of tensegrity domes. International Journal of Space Structures, Vol.7, 127–142. Rutten, M.F.A. (2008). Pneu-Tensegrity, "Tensegrity-constructie in combinatie met pneumatisch voorgespannen elementen als onderdeel van de hoofddraagconstructie". Master Thesis,

University of Eindhoven. Snelson, K. (1990). “Letter from Kenneth Snelson” to R.Motro. Published in November 1990, International Journal of Space Structures , and in Motro (2003). Also available in http://www.grunch.net/snelson/rmoto.html. Snelson, K. (2004). Kenneth Snelson. http://www.kennethsnelson.net/faqs/faq.htm. (Accessed : 10th April 2014).

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Skelton, R. E. and Oliveira, M.C. (2009). Tensegrity Systems. Dordrecht, Heindelberg, London, New York: Springer Thomke, S.H. (2003). Experimentation matters, Unlocking the potential of New Technologies for Innovation. Boston: Harvard Business School Publishing Corporation. Young, J. W., (1939). A technique for producing ideas. USA: The McGraw hill companies. Ward, J, (1984). The Artifacts Of R. Buckminster Fuller, A Comprehensive Collection of His Designs and Drawings in Four Volumes: Volume One. The Dymaxion Experiment, 1926–1943; Volume Two. Dymaxion Deployment, 1927–1946; Volume Three. The Geodesic Revolution, Part 1, 1947–1959; Volume Four. The Geodesic Revolution, Part 2, 1960–1983. New York: Garland Publishing. Williams, W.O. (2007). A primer on the mechanics of tensegrity structures. N.b.

Weber, R., and Condoor, S. (1998). Conceptual Design Using a Synergistically Compatible Morphological Matrix. IEEE Frontiers in Education Conference, vol. 1, pp. 171-176.

Patents Emmerich, D.G. (1964). Construction de réseaux autotendants, French Patent No. 1,377,290, September 28, 1964 Fuller, R.B. (1962). Tensile-Integrity Structures, U.S. Patent No. 3,063,521, November 13, 1962. Fuller, R.B. (1973). Non-symmetrical tension-integrity structures, U.S. Patent No. 3,866,366, Augustus 1973. Geiger, D.H. (1988). Roof structure, U.S. Patent No. 4,736,553, April 12, 1988. Liapi, K.A. (2003). Tensegrity Unit, Structure and Method for construction, U.S. Patent No. 2003/0009974 A1, January 13, 2003 Snelson, K. (1965). Continuous tension, discontinuous compression structures, U.S. Patent No. 3,169,611, February 16, 1965.

Websites Proto labs, Molding design guidelines. http://www.protolabs.com/resources/molding-design-guidelines/ (Accessed: 10th August 2014). Make It Big, Design guide: Top 5 rules for injection molding. http://www.makeitbig.com/2013/05/14/design-guide-top-5-rules-for-injection-molding/ (Accessed: 10th August 2014). Custumpart.net, Die casting. http://www.custompartnet.com/wu/die-casting. (Accessed: 10th August 2014). Custumpart.net, Injection molding. http://www.custompartnet.com/wu/InjectionMolding. (Accessed: 10th August 2014). Mbs-standoffs, Cable tensioner. http://www.mbs-standoffs.com/Cable-Tension-Adjuster_p_2258.html. (Accessed: 15th August 2014).

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TOCO Lifting Equipment, http://www.tocolifting.co.za/Categorys.asp?Category=6x7+FIBRE+CORE+GALVANISED+STE EL+WIRE+ROPE&ID=164. (Accessed: 15th August 2014).

Tensegrity: http://en.wikipedia.org/wiki/Tensegrity http://tensegrity.wikispaces.com/

Extrusion: http://en.wikipedia.org/wiki/Extrusion http://www.johnrussert.com/plastic_and_aluminum_extrusions.htm

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Appendix 9.

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9. Appendix

Appendix A. Dimensions

Joint for prototype : Slit curved with one set screw

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Joint slit curved with two set screws

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Joint slit continuous with one set screw

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Joint slit continuous with two set screws

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Finale design

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Appendix B. Morphologic matrix

Joint design by P. Koelewijn When the red line is followed Snelson’s joint is found. Other and L.S. Klerk. (2014) Kinegrity examples are marked with circles in the colour that –Energy producing structure correspondents with the colour of the image border.

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Appendix C. Cable routing

Geiger dome solution cable routing. The top and bottom of the joint connection in the Geiger dome are different, because the number of incoming cables and their angle. With the joint there is possible to let the cables run over each other.

Figure C1 Geiger dome

Three cables at the top, where two run over each other, one down and one up. The cable routing has to be done like in figure 2 on the left side. At the bottom also three cables connect. One 90o and two with an angle of 67.5o these angles are not possible to connect in the designed joint. Therefore the top incisions have to be changed, instead of four there is need for only three. Seen in figure 2 on the right is the solution for the bottom joint for the Geiger Dome.

Figure C2 Cable routing Geiger Dome

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For the connection of the cable routing there are several possibilities in the way the top incisions are made.

Figure C3 Cable routing

Figure C4 Render of cable routing three cables, round incision at top.

Figure C5 Render of cable routing three cables with two incisions

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