designing to design interdisciplinary engineering knowledge genome: perspective and new results
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Designing to Design Interdisciplinary Engineering Knowledge Genome: perspective and new results . Offer Shai and Yoram Reich Faculty of Engineering Tel Aviv University. 4 th Design Theory SIG Workshop Mines ParisTech 31 January-2 February 2011. Historical observation. - PowerPoint PPT PresentationTRANSCRIPT
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
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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.
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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
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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