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Designing to Design Interdisciplinary Engineering Knowledge Genome: perspective and new results

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### Designing to DesignInterdisciplinary Engineering Knowledge Genome: perspective and new results

Offer Shai and Yoram Reich

Faculty of Engineering

Tel Aviv University

4th Design Theory SIG Workshop

Mines ParisTech

31 January-2 February 2011

Historical observation

- When people wish to designsomething, they end up designing some of the concepts (language), methods, tools, in order to designit
- In this design, people select (design) their social infrastructure that will help them designit 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

Types of systems

UnderConstrained Systems

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

Well ConstrainedSystems

Over Constrained Systems

Types of systems

Obtaining all types of systems from the well constrained systems

UnderConstrained Systems

Deletingelements

Addingelements

Well ConstrainedSystems

Over Constrained Systems

Addingelements

Deletingelements

Types of systems

Obtaining all types of systems from the well constrained systems

UnderConstrained Systems

Deletingelements

Addingelements

Therefore, from now on, in this presentation, we discuss only well-constrained systems

Well ConstrainedSystems

Over Constrained Systems

Addingelements

Deletingelements

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.)

A

B

D

Static Framework with inner forces:

satisfying the equilibrium of forces in any joint.

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

No self-equilibrium of forces.

There are many examples of static frameworks

These are NOT static frameworks

Assur Group

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

From 1914 till 1930 this work has not receive attention.

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.

Architecture

Structural Topology Journal.

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

They established the Structural Topology Journal

written both in English and in French.

Concepts from Mathematics and Architecture yielded

knowledge in Rigidity Theory Group.

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.

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

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.

Artobolevski

1864

Maxwell

2001

Jordan

1914

Assur

1990

Connelly

1982

Whiteley

Mobility, Georges Amar

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

Can we make knowledge mobility work?

Assur

1864

Maxwell

1982

1930

Whiteley

Artobolevski

2004

Shai & Reich

1990

2001

Connelly

Jordan

Offer Shai/Yoram Reich

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

- 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

IEKG

1930

Artobolevski

1864

Maxwell

2001

Jordan

1914

Assur

2004

Shai & Reich

1990

Connelly

1982

Whiteley

Created the Knowledge Mobility infrastructure

Assur

1864

Maxwell

1982

1930

Whiteley

Artobolevski

1990

2001

Connelly

Jordan

Addressing some Knowledge Mobility issues

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

Theorem (2010):

Contracted Assur Graphs ⇔ static frameworks

Assur Graph

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

Theorem (2010):

Contracted Assur Graphs ⇔ static frameworks

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

Theorem (2010):

Contracted Assur Graphs ⇔ static frameworks

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

Theorem (2010):

Contracted Assur Graphs ⇔ static frameworks

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

Theorem (2010):

Contracted Assur Graphs ⇔ static frameworks

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

Theorem (2010):

Contracted Assur Graphs ⇔ static frameworks

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

Theorem (2010):

Contracted Assur Graphs ⇔ static frameworks

Assur Graph

static framework

IEKG: First part of the Algorithm

Decomposition

into Minimal inseparable components (Assur Graphs):

A. Initiate the decomposition– choose the ground.

B. Applythe 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

A

1

3

A

C

α

β

LCB

C

B

B

D

2

Decomposition – separate the system (mechanism, geometric constraint)

into minimal inseparable components (Assur Graphs- AGs).

A

3

1

4

C

A

β

α

6

B

5

1

3

2

D

B

7

2

LCB

4

The mechanism

The geometric constrains

6

5

1

3

2

7

The geometric constrains graph

The structural scheme

1

3

A

D

3

1

A

C

B

B

B

C

C

B

2

A

2

A

4

C

6

1

3

5

1

D

7

C

C

A

D. Construct, simultaneously,

the decomposition graph

4

3

3

1

1

D

6

B

5

1

3

β

β

α

α

B

B

C

C

7

2

2

2

LCB

LCB

decomposition graph

decomposition graph

β

α

B. Applythe 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.

A

3

B

α

β

2

LCB

B

2

IEKG: Second part of the Algorithm

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 tillyou have completed the task
- Constructing the geometric object
- Analyzing the mechanism.

A

A

1

1

3

3

C

B

B

C

C

B

A

2

2

LCB

B

C

A

4

3

1

D

6

B

5

1

D

3

β

α

composition graph

composition graph

B

C

7

2

2

LCB

B. Add, successively, the components

(according to the decomposition graph) and analyze/solve them.

C. Continue till you have completed the task

Constructing the geometric object.

- Initiate the composition –
- set the ground.

β

α

LCB

3

C

C

4

A

1

6

A

5

1

3

D

7

B

β

2

α

2

D

C

A

A

B

A

1

1

3

3

C

B

B

C

C

B

A

2

2

LCB

B

C

A

4

3

1

D

6

B

5

1

D

3

β

α

composition graph

composition graph

B

C

7

2

2

LCB

C. Continue till you have completed the task.

Analyzing the mechanism.

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

- Initiate the composition-
- set the ground.

β

α

LCB

C

C

4

A

1

6

A

5

1

3

D

7

B

β

2

α

2

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

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