Development of a tensegrity joint · the principles of tensegrity are applied, is the Kurilpa...

Eindhoven University of Technology

MASTER

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

Bernaards, X.M.

Award date:2014

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TECHNISCHE UNIVERSITEIT EINDHOVEN

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

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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


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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


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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


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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


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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


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Appendix B. Morphologic matrix ..................................................................................... 115

Appendix C. Cable routing .............................................................................................. 116


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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


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1. Introduction

This chapter gives the introduction with the topic, the problem

definition and the objective of the thesis.


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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.


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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)

Figure 1.2 Idea sketch, A. Pronk, 2013

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.

The struts diameter smaller than ten

centimetre


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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.


15

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


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2. Tensegrity

structures

History and explanation of the tensegrity structures.


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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.


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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

Figure 2.4 Form of tensegrity of dymaxion house, Skelton


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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.


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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

http://structurae.net/structures/spodek


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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)


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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.


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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)


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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.

http://en.wikipedia.org/wiki/Buckminster_Fuller

http://en.wikipedia.org/wiki/Kenneth_Snelson

http://en.wikipedia.org/wiki/File:4-tensegrity.svg

http://en.wikipedia.org/wiki/File:Tensegrity_Icosahedron.png

http://en.wikipedia.org/wiki/File:Tensegrity_Tetrahedron.png

http://en.wikipedia.org/wiki/File:Tensegrity_X-Module_Tetrahedron.png


26

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)


27

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


28

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.

http://www.spacefurniture.com.sg/designers/105-theodore-waddell.html


29

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.


30


31

3. Joints

The state of the art of tensegrity joints is analysed


32

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.


33

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.


34

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).

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.

108

110

112

104

106

113

111 100

103

101


35

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.


36

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


37

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.


38

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.


39

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


40

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.


41

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;

- Solid

- Tube/pipe

- Bored

2. What kind of top on the strut;

- Round

- Straight

- Threaded

- Chamfer

3. How many cables does the joint have

to handle.

4. Are the cables cut joint to joint or do

they go through.

5. Are the cables tensioned all at once or

separate.

6. Is the cable length fixed or adjustable.

7. Is the connection possibility between

joint and cable, in the joint, on the joint

or is there an addition.

8. How are the cables fastened;

- Insert

- Loop

- Nut

- Set screw

- Bolt

- Socket

9. How to tension;

- Turnbuckle

- Turning a bolt upwards

- Pulling or hoist

- Cable net

- Downwards with a bolt and insert

- Telescope strut

10. Cable endings;

- None

- Thimble

- Threaded

- Clamps/clips

- Sleeve

- Socket

11. Cable management;

- None

- Slit

- Additions

- Holes

- Modified insert


42

Figure 3.12 Morphological matrix


43

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.


44

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


45

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


46

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


47

4.

Development

To see the design a prototype for testing is made.


48

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.


49

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


50

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

10

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

Similarities:

Use of set screws to fasten cables

Solid strut

Round top

Differences:

Possibility to separate joint from strut

Cable received at the top

Only good for receiving one cable

No usable for a tensegrity


51

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/)

Figure 4.8 Section orange fig. 4.7

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

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.

http://www.medamind.de/wp-content/uploads/2009/06/tensegrity.jpg


52

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 4.8kN

11, 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


53

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


54

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.


55

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)

http://en.wikipedia.org/wiki/Computer_aided_design

http://en.wikipedia.org/wiki/CAD


56

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

Figure 4.17 Larger diameter

Changes made after 3D model:

Strut diameter from 35mm to 40mm

Bigger set screws M8x8 to give them

more body (fig 4.17)


57

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.


58

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)


59

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


60

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


61

5.

Testing

The tests of the new connection in the prototype joint are

described in this chapter.


62

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 M8

16 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


63

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.


64

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


65

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


66

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).

Test 1ste value

2de 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

Test Angle Torque Steel cable diameter

Max. Tensile 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.


67

Figure 5.10 Test with 90 degree angle

Figure 5.11 Test with 45 degree angle

0

500

1.000

1.500

2.000

2.500

3.000

3.500

4.000

4.500

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

Forc

e [

N]

Displacement [mm]

Test results 1 to 4

Test 1 Test 2 Test 3 Test 4

0

500

1.000

1.500

2.000

2.500

3.000

3.500

4.000

4.500

0 2 4 6 8 10 12 14

Forc

e [

N]

Displacement [mm]

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

Test 5A Test 5B Test 5C Test 6A Test 6B


68

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


69

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.


70

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.


71

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.


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


72

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


73

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

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.

0

500

1000

1500

2000

2500

3000

3500

4000

0 100 200 300 400 500

Forc

e (

N)

Seconds (Sec)

Test 1

Test 3

Test 5

Test 6

Test 7


74

Test Torque Steel cable diameter


Min B.L. Force left of 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

Figure 5.20 Graph test 2

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.

-2000

0

2000

4000

6000

0 500 1000

Forc

e (

N)

Seconds (sec)

Test 2

Test 2

-1000

0

1000

2000

3000

4000

0 200 400 600 800

Test 4

Test 4


75

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.


76

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.


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.


77

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


78

5.6.6 Results

Figure 5.28 Sheet with data

Test Torque Steel cable diameter


Min B.L. 1960 Force left of cable (%)

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

0

1000

2000

3000

4000

5000

6000

0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400

Forc

e (

N)

Seconds (sec)

Test 1 to 6

Test 1

Test 3

Test 2

Test 4

Test 5

Test 6


79

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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6.

Design

The adjustments after the tests are applied in this chapter


82

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.


84

6.1.4 Angles of cables

The angle of the cable going outwards has a limitation. When the cable is between 900 and 52

0

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 52

0 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.


85

7.

Production

method

In order to achieve mass production, production methods are

examined in this chapter.


86

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 casting

18

18

Custumpart.net


87

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 19

and 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.

http://en.wikipedia.org/wiki/Bentonite

http://en.wikipedia.org/wiki/Clay

http://en.wikipedia.org/wiki/Coal_dust

http://en.wikipedia.org/wiki/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

http://www.protolabs.com/resources/molding-design-guidelines/materials

http://www.custompartnet.com/wu/InjectionMoldin


89

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

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

Ejector pins Chose places for ejector pins

Ribs Avoid deep and thin ribs

Deep ribs require draft and clearance

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 7.4 Wall thickness

Figure 7.5 Corners round

Figure 7.6 Core - cavity

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

http://www.protolabs.co.uk/resources/molding-design-guidelines/

http://www.makeitbig.com/2013/05/14/design-guide-top-5-rules-for-injection-molding/

http://www.custompartnet.com/wu/die-casting


90

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

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

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

the use of side cores. The next step is to see if

the joint can be pulled vertical.

Figure 7.11 New joint

Figure 7.12 Draft analysis

Figure 7.13 Undercut analysis


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The joint is changed following the design rules

and the changes will be (fig. 7.14):

Fillet of all the right corners

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

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

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:

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

changes to 2mm, but the piece is able to be

pulled out of the mould.

Only problem now is adding the top part and

fitting the cables into the slits again.

Figure 7.14 Pulling vertical

Figure 7.15 Pulling horizontal

Figure 7.18 Pulling with draft slit on the right

Figure 7.19 Mould with draft only of centre


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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.


94

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.


95

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


96

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)


97

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.


98

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


99

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


100


101

8.

Conclusion

The conclusion, discussion and recommendations.


102

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:

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?

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.


106

Literature

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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

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edition, 321-322. Hoboken: John Wiley & Sons

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gedragswetenschappen, 12th edition. Assen: Van Gorcum.

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Space Structures, Vol.8, 135-145.

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96-106.

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127–142.

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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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http://www.kennethsnelson.net/faqs/faq.htm


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(Accessed: 10th August 2014).

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Custumpart.net, Die casting. http://www.custompartnet.com/wu/die-casting. (Accessed: 10th August

2014).

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10th August 2014).

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TOCO Lifting Equipment,

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EL+WIRE+ROPE&ID=164. (Accessed: 15th August 2014).

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9. Appendix


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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

When the red line is followed Snelson’s joint is found. Other

examples are marked with circles in the colour that

correspondents with the colour of the image border.

Joint design by P. Koelewijn

and L.S. Klerk. (2014) Kinegrity

–Energy producing structure


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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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Development of a tensegrity joint · the principles of tensegrity are applied, is the Kurilpa...

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