Design: a Brief Introduction

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Design a Brief Introduction Infused Dr. Offer
Shai and Prof. Yoram Reich Department of
Mechanics, Materials and Systems Faculty of
Engineering Tel-Aviv University
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Infused design - is an approach for establishing
effective collaboration between designers from
different engineering fields. In this talk we
will introduce the mathematical foundation
underlying the approach, which mainly consists of
discrete general mathematical models called graph
representations. The representations are
currently based on linear graph theory, but are
being also expanded to other fields, such as
matroid theory, bond graphs, discrete linear
programming and others.
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• The outline of the lecture
• Representing an engineering system through a
  graph containing both structural and
  geometrical properties of the system and capable
  of reflecting systems behavior.
• Transforming engineering knowledge between
  different engineering domains through graph
  relations and its application to design.
• Demonstrating the idea from a general
  perspective.

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Let us consider a simple gear system
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Building the graph representation of the system
C
A
B
2
C
rC
B
1
rB
A
rA
6
The equations underlying the system behavior
C
A
B
2
C
w1/0
rC
B
rA x w1/0
1
rB
A
rA
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The equations underlying the system behavior
C
A
B
2
C
w1/0w2/1
rC
B
rA x w1/0rB x w2/1
1
rB
A
rA
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The equations underlying the system behavior
C
A
B
2
C
w1/0w2/1w2/00
rC
B
rA x w1/0rB x w2/1rC x w2/00
1
rB
A
rA
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The equations underlying the system behavior
C
A
B
2
C
w1/0w2/1w2/00
rC
B
rA x w1/0rB x w2/1rC x w2/00
1
rB
A
rA
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These equations can now be derived directly from
the graph
C
A
B
2
C
w1/0w2/1w2/00
rC
B
rA x w1/0rB x w2/1rC x w2/00
1
rB
A
rA
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These equations can now be derived directly from
the graph
C
A
B
2
C
D1/0w2/1w2/00
rC
B
rA x D1/0rB x w2/1rC x w2/00
1
rB
A
rA
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These equations can now be derived directly from
the graph
C
A
B
2
C
D1/0D2/1w2/00
rC
B
rA x D1/0rB x D2/1rC x w2/00
1
rB
A
rA
13
These equations can now be derived directly from
the graph
C
A
B
2
C
D1/0D2/1D2/00
rC
B
rA x D1/0rB x D2/1rC x D2/00
1
rB
A
rA
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Building the dual graph
C
A
C
A
B
B
2
C
D1/0D2/1D2/00
rC
B
rA x D1/0rB x D2/1rC x D2/00
1
rB
A
rA
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Building the dual graph
C
C
A
A
C
A
B
B
B
2
C
D1/0D2/1D2/00
rC
B
rA x D1/0rB x D2/1rC x D2/00
1
rB
A
rA
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Same behavioral equations can be derived from the
dual graph
C
A
C
A
B
B
2
C
F1/0D2/1D2/00
rC
B
rA x F1/0rB x D2/1rC x D2/00
1
rB
A
rA
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Same behavioral equations can be derived from the
dual graph
C
A
C
A
B
B
2
C
F1/0F2/1D2/00
rC
B
rA x F1/0rB x F2/1rC x D2/00
1
rB
A
rA
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Same behavioral equations can be derived from the
dual graph
C
A
C
A
B
B
2
C
F1/0F2/1F2/00
rC
B
rA x F1/0rB x F2/1rC x F2/00
1
rB
A
rA
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Same behavioral equations can be derived from the
dual graph
C
A
C
A
B
B
2
C
F1/0F2/1F2/00
rC
B
rA x F1/0rB x F2/1rC x F2/00
1
rB
A
rA
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From the dual graph we construct the dual
engineering system
C
A
C
A
B
B
2
C
C
F1/0F2/1F2/00
rC
B
B
rA x F1/0rB x F2/1rC x F2/00
1
rB
A
A
rA
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Behavioral isomorphism between the two dual
engineering systems
C
A
C
A
B
B
2
C
C
PAF2/1F2/00
rC
B
B
rA x PArB x F2/1rC x F2/00
1
rB
A
A
rA
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Behavioral isomorphism between the two dual
engineering systems
C
A
C
A
B
B
2
C
C
PARBF2/00
rC
B
B
rA x PArB x RBrC x F2/00
1
rB
A
A
rA
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Behavioral isomorphism between the two dual
engineering systems
C
A
C
A
B
B
2
C
C
PARBRC0
rC
B
B
rA x PArB x RBrC x RC0
1
rB
A
A
rA
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Behavioral isomorphism between the two dual
engineering systems
C
A
C
A
B
B
2
C
C
PARBRC0
rC
B
B
rA x PArB x RBrC x RC0
1
rB
A
A
rA
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Employing this relation for design. Example case
- design of a force amplifier
C
A
C
A
B
B
2
C
C
B
B
1
A
A
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Employing this relation for design. Example case
- design of a force amplifier
C
A
C
A
B
B
2
C
C
B
1
A
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Transforming the design problem to the dual
engineering domain
C
A
B
2
C
B
1
A
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Transforming the design problem to the dual
engineering domain
2
C
B
1
A
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Transforming the design problem to the dual
engineering domain
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Searching for existent engineering designs in
the dual domain (gear systems)
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Transforming the solution back to the original
design problem
4
2
5
1
3
0
wout
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Transforming the solution back to the original
design problem
4
3
2
5
1
0
wout
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Transforming the solution back to the original
design problem
wout
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Transforming the solution back to the original
design problem
G
A
B
B
A
G
C
G
C
wout
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Constructing the solution to the original design
problem
0
G
A
B
B
A
G
C
G
C
I
II
IV
III
C
B
A
G
wout
I
III
IV
II
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Formalizing the approach
Dual
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Formalizing the approach
Dual
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Same representations used to represent other
engineering domains
Dual
Serial robots
Plane kinematical linkage
Stewart platform
Pillar system
Planetary gear systems
Determinate beams
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Same representations used to represent other
engineering domains
Dual
Serial robots
Plane kinematical linkage
Stewart platform
Pillar system
Planetary gear systems
Determinate beams
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Additional graph representations have been
developed and associated with additional
engineering domains
Dual
Serial robots
Plane kinematical linkage
Stewart platform
Pillar system
Planetary gear systems
Determinate beams
Click here to continue
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This methodology can now be applied for design in
wide variety of engineering domains
Dual
Serial robots
Plane kinematical linkage
Stewart platform
Pillar system
Planetary gear systems
Determinate beams
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Another design case this time the knowledge is
transformed from electronics
Electronic circuits
Planetary gear systems
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Another design case this time the knowledge is
transformed from electronics
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Another design case this time the knowledge is
transformed from electronics
Potential graph representation to be
found ?out?in
Dout
Din
Domain of electrical concepts
Domain of gear train concepts
Vin
Vout
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