design: a brief introduction infused dr. offer shai and prof. yoram reich department of mechanics,...

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.

Let us consider a simple gear system

A

C

B

1

2

rA

rC

rB A

C

B

1

21

0

2

A C

B

Building the graph representation of the system

rA

rC

rB A

C

B

1

21

0

2

A C

B

1/0

rA x 1/0

The equations underlying the system behavior

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


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


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


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


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


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


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


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


AForce amplifier

Pout=1000Pin

Pin Pout

Fin Fout



inout

Dual graph representation

to be foundΔout=1000 Δin

AForce amplifier

Pout=1000Pin

Pin Pout

Fin Fout



inout




inout

Gear system to be found

ωout=1000 ωin

AForce amplifier

Pout=1000Pin

Pin Pout

Fin Fout



inout



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


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



inout



A AB B

GG CCG

0

432 51


AForce amplifier

Pout=1000Pin

Pin Pout

Fin Fout



A

C

B

G G

A

C

B

53

1

2 4

in out

inout



I II IV

0

III


A

C

B

G G

A

C

B

53

1

2 4

in

AForce amplifier

Pout=1000Pin

Pin Pout

Fin Fout



A AB B

GG CCG

0

432 51

out

inout



Fin Fout



G CC

A BB A GGI II IV

0

III


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



Fin Fout


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



Representation


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



Representation


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



Representation


Determinate beams



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



Representation


Determinate beams



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



Representation


Determinate beams



Pillar system

This methodology can now be applied for design in wide variety of engineering domains

Dual

Electronic circuits

Planetarygear systems


Another design case: this time the knowledge is transformed from electronics

Electronic circuits



Design a voltageRectifierVout=|Vin|

Vin Vout

Potential graph representation

to be foundΔout=|Δin|

in out

Design a unidirectional

Gear trainωout=|ωin|

in out


Electric circuits



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


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

design: a brief introduction infused dr. offer shai and prof. yoram reich department of mechanics,...

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