Design: a Brief IntroductionInfused
Dr. Offer Shai
and
Prof. Yoram Reich
Department of Mechanics, Materials and SystemsFaculty of Engineering
Tel-Aviv University
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, whichmainly consists of discrete general mathematicalmodels called graph representations.
The representations are currently based on linear graph theory, but are being also
expanded to other fields, such as matroidtheory, bond graphs, discrete linear programming and others.
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.
rA
rC
rB A
C
B
1
21
0
2
A C
B
1/0+2/1
rA x 1/0+rB x 2/1
The equations underlying the system behavior
rA
rC
rB A
C
B
1
21
0
2
A C
B
1/0+2/1+2/0=0
rA x 1/0+rB x 2/1+rC x 2/0=0
The equations underlying the system behavior
rA
rC
rB A
C
B
1
21
0
2
A C
B
1/0+2/1+2/0=0
rA x 1/0+rB x 2/1+rC x 2/0=0
The equations underlying the system behavior
rA
rC
rB A
C
B
1
21
0
2
A C
B
1/0+2/1+2/0=0
rA x 1/0+rB x 2/1+rC x 2/0=0
These equations can now be derived directly from the graph
rA
rC
rB A
C
B
1
21
0
2
A C
B
1/0+2/1+2/0=0
rA x 1/0+rB x 2/1+rC x 2/0=0
These equations can now be derived directly from the graph
rA
rC
rB A
C
B
1
21
0
2
A C
B
1/0+2/1+2/0=0
rA x 1/0+rB x 2/1+rC x 2/0=0
These equations can now be derived directly from the graph
rA
rC
rB A
C
B
1
21
0
2
A C
B
1/0+2/1+2/0=0
rA x 1/0+rB x 2/1+rC x 2/0=0
These equations can now be derived directly from the graph
rA
rC
rB A
C
B
1
21
0
2
A C
B
I
0 A
C
B
1/0+2/1+2/0=0
rA x 1/0+rB x 2/1+rC x 2/0=0
Building the dual graph
rA
rC
rB A
C
B
1
21
0
2
A C
B
I
0 A
C
B
A
C
B
1/0+2/1+2/0=0
rA x 1/0+rB x 2/1+rC x 2/0=0
Building the dual graph
rA
rC
rB A
C
B
1
21
0
2
A C
B
I
0 A
C
B
F1/0+2/1+2/0=0
rA x F1/0+rB x 2/1+rC x 2/0=0
Same behavioral equations can be derived from the dual graph
rA
rC
rB A
C
B
1
21
0
2
A C
B
I
0 A
C
B
F1/0+F2/1+2/0=0
rA x F1/0+rB x F2/1+rC x 2/0=0
Same behavioral equations can be derived from the dual graph
rA
rC
rB A
C
B
1
21
0
2
A C
B
I
0 A
C
B
F1/0+F2/1+F2/0=0
rA x F1/0+rB x F2/1+rC x F2/0=0
Same behavioral equations can be derived from the dual graph
F1/0+F2/1+F2/0=0
rA x F1/0+rB x F2/1+rC x F2/0=0
1
0
2
A C
B
I
0 A
C
B
rA
rC
rB A
C
B
1
2
Same behavioral equations can be derived from the dual graph
rA
rC
rB A
C
B
1
21
0
2
A C
B
I
0 A
C
B
rA
rC
rBA
C
BF1/0+F2/1+F2/0=0
rA x F1/0+rB x F2/1+rC x F2/0=0
From the dual graph we construct the dual engineering system
rA
rC
rB A
C
B
1
21
0
2
A C
B
I
0 A
C
B
rA
rC
rBA
C
BPA+F2/1+F2/0=0
rA x PA+rB x F2/1+rC x F2/0=0
Behavioral isomorphism between the two dual engineering systems
rA
rC
rB A
C
B
1
21
0
2
A C
B
I
0 A
C
B
rA
rC
rBA
C
BPA+RB+F2/0=0
rA x PA+rB x RB+rC x F2/0=0
Behavioral isomorphism between the two dual engineering systems
rA
rC
rB A
C
B
1
21
0
2
A C
B
I
0 A
C
B
rA
rC
rBA
C
BPA+RB+RC=0
rA x PA+rB x RB+rC x RC=0
Behavioral isomorphism between the two dual engineering systems
rA
rC
rB A
C
B
1
21
0
2
A C
B
I
0 A
C
B
rA
rC
rBA
C
BPA+RB+RC=0
rA x PA+rB x RB+rC x RC=0
Behavioral isomorphism between the two dual engineering systems
A
C
B
1
21
0
2
A C
B
I
0 A
C
B
A
C
B
Employing this relation for design.
Example case - design of a force amplifier
A
C
B
1
21
0
2
A C
B
I
0 A
C
B
C
Employing this relation for design.
Example case - design of a force amplifier
AForce amplifier
Pout=1000Pin
Pin Pout
System to be found
Pin Pout
A
C
B
1
21
0
2
A C
B
Transforming the design problem to the dual engineering domain
AForce amplifier
Pout=1000Pin
Pin Pout
Fin Fout
Graph representation
to be foundFout=1000Fin
A
C
B
1
2
Transforming the design problem to the dual engineering domain
AForce amplifier
Pout=1000Pin
Pin Pout
Fin Fout
Graph representation
to be foundFout=1000Fin
inout
Dual graph representation
to be foundΔout=1000 Δin
AForce amplifier
Pout=1000Pin
Pin Pout
Fin Fout
Graph representation
to be foundFout=1000Fin
inout
Dual graph representation
to be foundΔout=1000 Δin
Transforming the design problem to the dual engineering domain
inout
Gear system to be found
ωout=1000 ωin
AForce amplifier
Pout=1000Pin
Pin Pout
Fin Fout
Graph representation
to be foundFout=1000Fin
inout
Dual graph representation
to be foundΔout=1000 Δin
Searching for existent engineering designs in the dual domain (gear systems)
inout
Gear system to be found
ωout=1000 ωin
A
CB
G GA
CB
531
2 4
in
inout
Dual graph representation
to be foundΔout=1000 Δin0
432 51
out
Transforming the solution back to the original design problem
A
C
B
G G
A
C
B
53
1
2 4
in
AForce amplifier
Pout=1000Pin
Pin Pout
Fin Fout
Graph representation
to be foundFout=1000Fin
inout
Dual graph representation
to be foundΔout=1000 Δin
A AB B
GG CCG
0
432 51
Transforming the solution back to the original design problem
AForce amplifier
Pout=1000Pin
Pin Pout
Fin Fout
Graph representation
to be foundFout=1000Fin
A
C
B
G G
A
C
B
53
1
2 4
in out
inout
Dual graph representation
to be foundΔout=1000 Δin
I II IV
0
III
Transforming the solution back to the original design problem
A
C
B
G G
A
C
B
53
1
2 4
in
AForce amplifier
Pout=1000Pin
Pin Pout
Fin Fout
Graph representation
to be foundFout=1000Fin
A AB B
GG CCG
0
432 51
out
inout
Dual graph representation
to be foundΔout=1000 Δin
Fin Fout
Graph representation
to be foundFout=1000Fin
G CC
A BB A GGI II IV
0
III
Transforming the solution back to the original design problem
AForce amplifier
Pout=1000Pin
Pin Pout
A
C
B
G G
A
C
B
53
1
2 4
in
A AB B
GG CCG
0
432 51
out
inout
Dual graph representation
to be foundΔout=1000 Δin
Fin Fout
Graph representation
to be foundFout=1000FinI II IV
0
IIIG CC
A BB A GG
I III IVII
P
C
B
A
GBeam system to be found
Pin Pout
Pout=1000Pin
Constructing the solution to the original design problem
A
C
B
G G
A
C
B
53
1
2 4
in
A AB B
GG CCG
0
432 51
out
A AB B
GG CCG
0
432 51
I II IV
0
IIIG CC
A BB A GG
I III IVII
P
Planetary gear systems
Determinate beams
PLGRPotential Line Graph
Representation
FLGRFlow Line Graph Representation
Formalizing the approach
Dual
A
C
B
G G
A
C
B
53
1
2 4
in out
FLGRFlow Line Graph Representation
PLGRPotential Line Graph
Representation
Planetary gear systems
Determinate beams
CC
A AB B
GG CCG
0
432 51
I II IV
0
IIIG CC
A BB A GG
Formalizing the approach
Dual
FLGRFlow Line Graph Representation
PLGRPotential Line Graph
Representation
Planetary gear systems
Determinate beams
Serial robotsPlane kinematical
linkageStewart platform
Pillar system
Stewart
platform
Serial robot
CC
Same representations used to represent other engineering domains
Dual
0
1
2
3
4
5
1/0
A
B D
E
F
C
2' 1' C
B A D E
F
P
FLGRFlow Line Graph Representation
PLGRPotential Line Graph
Representation
Planetary gear systems
Determinate beams
Serial robotsPlane kinematical
linkageStewart platform
Pillar system
2'
P
A B
D E
F
C 1'
1
2
3
4
5
A B
C
D
E
F
Stewart
platform
Serial robot
CC
Same representations used to represent other engineering domains
Dual
FLGRFlow Line Graph Representation
PLGRPotential Line Graph
Representation
Planetary gear systems
Determinate beams
Serial robotsPlane kinematical
linkageStewart platform
Pillar system
Additional graph representations have been developed and associated with additional engineering domains
Dual
Click here to continue
Frames
Trusses
Electronic circuits
Dynamical system
Static lever system
PGRPotential Graph Representation
LGRLine Graph
Representation
RGRResistance Graph
Representation
FGRFlow Graph
Representation
FLGRFlow Line Graph Representation
PLGRPotential Line Graph
Representation
Planetary gear systems
Determinate beams
Serial robotsPlane kinematical
linkageStewart platform
Pillar system
This methodology can now be applied for design in wide variety of engineering domains
Dual
Electronic circuits
Planetarygear systems
PGRPotential Graph Representation
Another design case: this time the knowledge is transformed from electronics
Electronic circuits
Planetarygear systems
PGRPotential Graph Representation
Design a voltageRectifierVout=|Vin|
Vin Vout
Potential graph representation
to be foundΔout=|Δin|
in out
Design a unidirectional
Gear trainωout=|ωin|
in out
Another design case: this time the knowledge is transformed from electronics
Electric circuits
Planetarygear systems
PGRPotential Graph Representation
Design a unidirectional
Gear trainωout=|ωin|
in out
Design a voltagerectifierVout=|Vin|
Vin Vout
Potential graph representation
to be foundΔout=|Δin|
in out2
3
6
5
41
B
A C
D
A
B
C
D C
D
A
B
CO
Another design case: this time the knowledge is transformed from electronics
D
A
C
6
5
3
42
B
D
A
C
6
5
3
42
B
Domain of gear train concepts
Domain of
electrical concepts