Designing to DesignDesigning to DesignInterdisciplinary Engineering Knowledge Genome: Interdisciplinary Engineering Knowledge Genome:

perspective and new results perspective and new results

4th Design Theory SIG Workshop Mines ParisTech

31 January-2 February 2011

Offer Shai and Yoram ReichOffer Shai and Yoram ReichFaculty of EngineeringFaculty of Engineering

Tel Aviv UniversityTel Aviv University

Historical observation

• When people wish to design something, they end up designing some of the concepts (language), methods, tools, in order to design it

• In this design, people select (design) their social infrastructure that will help them design it including: collaboration, funding agencies, students, etc.

• We present one such example: the design of deployable tensegrity structures and in doing so, tells you some more about the IEKG project

Part of the system is under- and part well-constrained

UnderConstrained Systems

Over Constrained Systems

Well Constrained Systems

Types of systems

UnderConstrained Systems

Over Constrained Systems

Well Constrained Systems

Deletingelements

Deletingelements

Addingelements

Addingelements

Types of systemsObtaining all

types of systems from

the well constrained

systems

UnderConstrained Systems

Over Constrained Systems

Well Constrained Systems

Deletingelements

Deletingelements

Addingelements

Addingelements

Types of systemsObtaining all

types of systems from

the well constrained

systemsTherefore, from now on, in this presentation, we discuss only

well-constrained systems

1864Maxwell

1850 1900 1950 20001864 1914 1930 1979200119901982

2010

James Clerk Maxwell

In 1864, James Clerk Maxwell found a connection between geometry and statics.

Theorem (1864): The projection of any polyhedron (3D) is a 2D static framework with inner forces satisfying the equilibrium of forces in any joint.

(It is unclear whether he proved the inverse theorem, but, in 1982, Prof. Whiteley from Canada proved it.)

1850 1900 1950 20001864 1914 1930 1979200119901982

2010

Static Framework with inner forces:satisfying the equilibrium of forces in any joint.

A B

D

C

Replacing any rod with two equal and opposite external forces results in a static framework satisfying force equilibrium in all joints

1850 1900 1950 20001864 1914 1930 1979200119901982

2010

There are many examples of static frameworks

No self-equilibrium of forces.

These are NOT static frameworks

1850 1900 1950 20001864 1914 1930 1979200119901982

2010

18641914

Maxwell

Assur

1850 1900 1950 20001864 1914 1930 1979200119901982

2010

Leonid Assur

In 1914, Leonid Assur, a professor at the Saint-Petersburg Polytechnical Institute, established a new concept: Assur GroupsAssur Groups.

Every mechanism can be decomposed into Assur Groups (structures).

Assur Group is a well constrained structure that does not contain an inner well constrained structure.

Assur Group is a structure with zero degrees of freedom (DOF) and does not contain an inner structure with zero DOF.

Assur Group Not an Assur Group

1850 1900 1950 20001864 1914 1930 1979200119901982

2010

1850 1900 1950 20001864 19301914 1979200119901982

2010

1864Maxwell

1914 Assur

1930Artobolevski

I.I. Artobolevsky

From 1914 till 1930 this work has not receive attention.

1850 1900 1950 20001864 1914 1930 1979200119901982

2010

ONLY in 1930, the known kinematician – I.I. Artobolevsky, wrote about Assur Group in his books, and from that time on it has been widely used in the east.

In 1979, in the University of Montreal, Canada, a research group of architects and mathematicians was established.

Architecture Mathematics

Structural Topology Journal.

They established the Structural Topology Journal written both in English and in French.

Concepts from Mathematics and Architecture yielded knowledge in Rigidity Theory Group.

1850 1900 1950 20001864 1914 1930 1979200119901982

2010

1864

1914

1982Whiteley

Assur

Maxwell

1930Artobolevski

1850 1900 1950 20001864 1914 1930 1979200119901982

2010

Walter Whiteley

In 1982, Walter Whiteley proved the inverse theorem of Maxwell theorem (1864).

Whiteley showed that by using Maxwell's idea it is possible to construct a corresponding polyhedron for every static framework.

1850 1900 1950 20001864 1914 1930 1979200119901982

2010

1864

1914

1982Whiteley

Assur

Maxwell

1930Artobolevski

1850 1900 1950 20001864 1914 1930 1979200119901982

2010

1990Connelly

Robert Connelly

In 1990, Robert Connelly from Cornell University (New York, USA)

Connelly's conjecture (1990): All static Frameworks can be derived from a projection of the Tetrahedron

1850 1900 1950 20001864 1914 1930 1979200119901982

2010

1864

1914

1982Whiteley

Assur

Maxwell

1930Artobolevski

1990Connelly

1850 1900 1950 20001864 1914 1930 1979200119901982

2010

2001Jordan

Tibor Jordan

In 2001, Tibor Jordan, Budapest, Hungary

Jordan proved Connelly’s conjecture (1990), that all the static frameworks can be derived from a projection of a Tetrahedron by applying only two operations.

1850 1900 1950 20001864 1914 1930 1979200119901982

2010

1864Maxwell

1914Assur

1982Whiteley

1930Artobolevski

1990Connelly

2001Jordan

1850 1900 1950 20001864 1914 1930 1979200119901982

20102004

Mobility, Georges Amar

Is there a hope or benefit to the synthesis of these views?

Can we make knowledge mobility work?

1864

1914

1982Whiteley

Assur

Maxwell

1930Artobolevski

1990Connelly

2001Jordan

Offer Shai/Yoram Reich

2004Shai & Reich

1850 1900 1950 20001864 1914 1930 1979200119901982

20102004

1850 1900 1950 20001864 1914 1930 1979200119901982

20102004

Types of combinatorial representations:•MR – matroid representation•RGR - resistance graph representation•PGR – potential graph representation•FGR – flow graph representation•LGR – line graph representation •PLGR – potential line graph representation •FLGR – flow line graph representation

In 2004, Offer Shai and Yoram Reich from Tel Aviv University, Israel, presented Infused Design and developed the IEKG

1864Maxwell

1914Assur

1982Whiteley

1930Artobolevski

1990Connelly

2001Jordan

2004Shai & Reich

1850 1900 1950 20001864 1914 1930 1979200119901982

20102004

Created the Knowledge Mobility infrastructure

IEKGIIEEKK GG

1864

1914

1982Whiteley

Assur

Maxwell

1930Artobolevski

1990Connelly

2001Jordan

1850 1900 1950 20001864 1914 1930 1979200119901982

2010

Addressing some Knowledge Mobility issues

Contracted Assur Graphs = all the pinned joints become one vertex.

Contracted Assur Graphs ⇔ static frameworksTheorem (2010) :

Assur Graph

1850 1900 1950 20001864 1914 1930 1979200119901982

2010

Contracted Assur Graphs = all the pinned joints become one vertex.

Contracted Assur Graphs ⇔ static frameworksTheorem (2010) :

1850 1900 1950 20001864 1914 1930 1979200119901982

2010

Contracted Assur Graphs = all the pinned joints become one vertex.

Contracted Assur Graphs ⇔ static frameworksTheorem (2010) :

1850 1900 1950 20001864 1914 1930 1979200119901982

2010

Contracted Assur Graphs = all the pinned joints become one vertex.

Contracted Assur Graphs ⇔ static frameworksTheorem (2010) :

1850 1900 1950 20001864 1914 1930 1979200119901982

2010

Contracted Assur Graphs = all the pinned joints become one vertex.

Contracted Assur Graphs ⇔ static frameworksTheorem (2010) :

1850 1900 1950 20001864 1914 1930 1979200119901982

2010

Contracted Assur Graphs = all the pinned joints become one vertex.

Contracted Assur Graphs ⇔ static frameworksTheorem (2010) :

1850 1900 1950 20001864 1914 1930 1979200119901982

2010

Contracted Assur Graphs = all the pinned joints become one vertex.

Contracted Assur Graphs ⇔ static frameworksTheorem (2010) :

Assur Graph static framework

1850 1900 1950 20001864 1914 1930 1979200119901982

2010

Creating a map of 2D building blocks (s-genes)

A A B

C C

B A E

D

O1 O2 O1 O2 O3 O1 O2 O3 O4

A B

C

O1 O2 O3

O4 D

C

B A E

D

O1 O2 O3 O4

A B

C

O1 O2 O3

O4 D

F

C

B A E

D

O1 O2 O3

F

O4

O5

(a) (b) (c)

(b1)

(b2)

(c1)

(c2)

Fundamental extension applied on ground edge (A,O2)

Fundamental extension applied on ground edge (B,O3)

Regular extension applied on edge (A,B)

E

Regular extension applied on edge (A,D)

Regular extension applied on edge (A,E)

The dyad.

The dashed line represents an omission in the extension and the bold lines the additions.

Now we have the map of all 2d Building blocks

Decomposition into Minimal inseparable components (Assur Graphs):

B. Apply the decomposition algorithm – the Pebble Game (top down).

C. Construct the inseparable components – Each directed cut-set defines a component (AG).

A. Initiate the decomposition– choose the ground.

D. Construct, simultaneously, the decomposition graph

IEKG: First part of the Algorithm

Cβα

2

3 1

A

B

LCB

3

4

5

2

6

7

1

3

4

5

2

6

7

1

The structural scheme

The mechanism

C B

A

1

2

3

βα

LCB

The geometric constrains graph

The geometric constrains

A

B

C

D

A

B

C

D

Decomposition – separate the system (mechanism, geometric constraint) into minimal inseparable components (Assur Graphs- AGs).

C B

A

1

2

3

Cβα

2

3 1

A

B

LCB

13

2

3

4

5

2

6

71

A

B

AC

D B

13

C

2

B

D

C

B

A

3

A

1A

B

4

5

C

C B

2

decomposition graphdecomposition graph

βα

LCB

α β

Cβα

2

3 1

B

LCB

6

7

D

A. Initiate the decomposition– choose the ground. B. Apply the decomposition algorithm –

the Pebble Game (top down).C. Construct the inseparable components –

Each directed cut-set defines a component (AG).

D. Construct, simultaneously, the decomposition graph

COMPOSITION (Analysis):

A. Initiate the composition – set the ground.

B. Add, successively, the components - (according to the decomposition graph) and analyze/solve them.

C. Continue till you have completed the task1. Constructing the geometric object2. Analyzing the mechanism.

IEKG: Second part of the Algorithm

LCB

composition graphcomposition graph

C

2

B

3

A

1

β

α

LCBC

2

B

3

A

1

D

C

B

A

A

B

2

3

β

1α

A

B

Cβα

2

3 1

LCB

3

4

5

2

6

71

3

4

5

2

6

7

1

AC

D B

AC

D

B

C

A. Initiate the composition – set the ground.

B. Add, successively, the components )according to the decomposition graph (

and analyze/solve them .

C. Continue till you have completed the taskConstructing the geometric object.

C

A

B

D

LCB

composition graphcomposition graph

C

2

B

3

A

1

β

α

LCBC

2

B

3

A

1

A

B

2

β

1α

A

B

Cβα

2

3 1

LCB

3

4

5

2

6

71

3

4

5

2

6

7

1

AC

D B

AC

D

B

C

C

A

B

D

A. Initiate the composition- set the ground.

B. Add, successively, the components (according to the decomposition

graph) and analyze/solve them .

C. Continue till you have completed the task.Analyzing the mechanism.

What has been designed?• New concepts

– Face force– Equimomential line

• New methods - stability of tensegrity

• New theorems Telllegen’s theorem in mechanics

• New design methods -Infused design

• New products Adjustable deployable structure Artificial caterpillar robot Mechanical transistor

Thanks you for your attention