Design of engineering systems by transforming knowledge between fields

Design of engineering systems by transforming

knowledge between fields.

Solving Engineering Design Problems

Transformations make possible to seek for solution for design problem in engineering domain Da in some other engineering domain Db related to Da through graph representations.

T’(…(T(problem(Da))) = problem(Db) DESIGN=solution(problem(Da))=

=T’-1(…T-1 (solution(problem(gk)))

Gl

solution(problem(gk))

Dj

T-1problem(si)solution(problem(si))

problem(gk)T

…

Design methods We distinguish two design methods for performing

design through transformations: one employing common graph representation and other employing the dual representations.

Gl

kg

Da

kaT-1 kb

D

bT’

G1

gi

G2

gj

Da

si Tsj

D

bT’D

Common Representation Design Technique

Gl

kg

Da

ka

T-1 kb

Db

T’2

3

6

5

41

C

DB

A


2

3

6

5

41

C

DB

A

Dual Representation Design Technique

G1

gi

G2

gj

Da

si Tsj

Db

T’D


Examples

Common Design Technique:

Mechanical Rectifier

Clipping Mechanism

Alternative Rectifier

Dual Design Technique:

Beam Rectifier

Steering Wheel


Mechanical Rectifier

The given problem: design a mechanical rectifier

Input angularvelocity in

Output angular velocity out

Requirement: out=|in|

Mechanical system

to be found

Transforming the problem to the terminology of the graph representation

Input potential difference

source in

Potential Graph

to be found

Requirement: out=|in|

Output potential difference

out

Transforming the problem to the other engineering domain - electronics

The solution existing in electronics – Bridge rectifier circuit

2

3

6

5

41

B

A C

D

Building the graph representation of the solution

B

A

C D

2

3

6

5

41

C

DB

A

B

A

C D

Building the mechanical system with the same graph representation

The mechanical system will be constructed graduallyby augmenting one element at a time in accordance tothe edges of the graph

2

3

6

5

41

B

A

C D

C

DB

A

Potential difference source edge AB – edge where the potential difference is given

1A

B

2

3

6

5

41

B

A

C D

A

B

C

DB

A

Externally rotated shaft AB – shaft whose relative velocity is determined

1A

B

2

3

6

5

41

B

A

C D

A

B

C

DB

A

Sign ConventionNegative potential Negative velocity – out of the plane

Positive potential Positive velocity – into the plane

1A

B

2

3

6

5

41

B

A

C D

A

B

C

DB

A

Unidirectional edge 2 – edge forcing the potential of A be higher or equal to the potential of C

C AVCVA

1

2 A

B

2

3

6

5

41

B

A

C D

C

A

B

C

C

DB

A

C

CA

C

VC

VA

VC

Overrunning clutch 2 – kinematical pair forcing the velocity of A be higher or equal to the

velocity of C

VC<0VA=VC

VC 0VA=0 VCVA

A

C

1

2 A

B

C

A

B

C

2

3

6

5

41

B

A

C D

C

DB

A

C

VC

Unidirectional edge 3 – edge forcing the potential of D be higher or equal to the potential of B

1

2

3

A

B

C

D

A

B

C

D

2

3

6

5

41

B

A

C D

C

DB

A

C

D

DB

VBVD

VC

VD

VB

VD

Overrunning clutch 3 – kinematical pair forcing the velocity of D be higher or equal to the

velocity of B

1

2

3

A

B

C

D

A

B

2

3

6

5

41

B

A

C D

C

DB

A

C

D

VC

VD

Edge 4 – edge measuring the potential difference between C and D

4 1

2

3

A

B

C

D

A

B

Output

C

D

2

3

6

5

41

B

A

C D

C

DB

A

Shaft 4 – shaft whose velocity is equal the relative velocity between joints C and D

4 1

2

3

A

B

2

3

6

5

41

B

A

C D

C

D

A

B

C

D

C

DB

A

AVC

VAC

Unidirectional edge 5 – edge forcing the potential of D be higher or equal to the potential of A

4 1

2

3

A

B

D= - C

2

3

6

5

41

B

A

C D

C

D

A

B B

A

C

D

D

5

C

DB

A

AVC

VAC

VDD

Overrunning clutch 5 – kinematical pair forcing the velocity of D be higher or equal to the

velocity of A

4 1

2

3

A

B

D

2

3

6

5

41

B

A

C D

C

D

A

B B

A

C

D

D

5

C

DB

A

Unidirectional edge 6 – edge forcing the potential of B be higher or equal to the potential of C

4

6

1

2

3

A

B

D

C

2

3

6

5

41

B

A

C D

C

D

A

B B

A

Output

C

D

D

C

5

C

DB

A

Overrunning clutch 6 – kinematical pair forcing the velocity of B be higher or equal to the

velocity of C

2

3

6

5

41

C

DB

A

The prototype of mechanical rectifier was built at the laboratory of kinematical systems in Tel-Aviv university

and successfully tested.

1

A

B

C

D

4

A

B

A

C

D

A

B

CD

B

A

D

C

3 6

52

InputOutput

Input

Output

6

5

3

4

2

1

C

D

0

Comparing the behavior of the original electronic circuit and the mechanical rectifier: forward operation mode

- positive potential/velocity - negative potential/velocity

1

A

B

C

D

4

A

B

A

C

D

A

B

CD

B

A

D

C

3 6

52

InputOutput

Input

Output

6

5

3

4

2

1

C

D

0

Comparing the behavior of the original electronic circuit and the mechanical rectifier: inverse operation mode


Comparing the behavior of the original electronic circuit and the mechanical rectifier: illegal operation mode


1

A

B

C

D

4

B

A

C

D

A

B

CD

B

A

D

C

3 6

52

Input

Output

6

5

3

4

2

C

D


2

3

6

5

41

C

DB

A

Developing a new design of a Steering Wheel Mechanism

Electronic circuits

Frames

This general framework opens wider possibilities for employing the approach of transforming knowledge for design. Here we will show an example of developing a

new steering wheel mechanism

FGRFlow Graph

Representation

Dynamicalsystem

Electroniccircuit

RGR Resistance Graph

Representation

Electronic transistor

New concept of a power steering

mechanism

The model of the new concept for the steering wheel mechanism was built and successfully tested in the mechanical lab

of Tel-Aviv University. The properties exhibited by the device do not exist in any

of the known devices of such type.

Additional design cases have been solved by means of the approach. Some of them

have systematically yielded known devices that only recently have been patented.


Case Study

Beam system to be found

Pin Pout>> Pin

Simple design case – beam force amplifier

Meta-levelMeta-level

EngineeringDomain

I

EngineeringDomain

II

GraphRepresentation

I

GraphRepresentation

II

Gear systemto be found

in out>>in Beam system to be found

Pin Pout>> Pin

Simple design case – beam force amplifier

Transforming the original problem (beam) to the

secondary domain (gear trains)


EngineeringDomain

I

EngineeringDomain

II

GraphRepresentation

I

GraphRepresentation

II

Gear systemto be found

in out>>in Beam system to be found

Pin Pout>> Pin

Drilling machine

Other gear systems

Gearbox

Electrical screwdriver transmission

out

A

C

B

G G

A

C

B

53

1

2 4

in

Existing solutions in the domain of gear trainsChoosing one of the solutions


EngineeringDomain

I

GraphRepresentation

I

GraphRepresentation

II

System to be found

Pin Pout>> Pin

A AB B

GG CCG

0

432 51

out

A

C

B

G G

A

C

B

53

1

2 4

in

I II IV

0

IIIG CC

A BB AG

out

A

C

B

G G

A

C

B

53

1

2 4

in

Transforming solution to original domain


EngineeringDomain

I

GraphRepresentation

I

GraphRepresentation

II

System to be found

Pin Pout>> Pin

I II IV

0

IIIG CC

A BB A

G

G

I III IVII

P

C

B

A

G

A AB B

GG CCG

0

432 51

out

A

C

B

G G

A

C

B

53

1

2 4

in

Transforming solution to original domain

DESIGN A BEAM FORCE AMPLIFIER

CC CC

Additional Design ExamplesDesign of clipping mechanism

Requirement: lout= lin - lc

Output coordinate mustn’t exceed a given limit

Input is any coordinate

Systematic design of clipping mechanism

Kinematicalsystem

to be found

Requirement: out = inc


Input potential difference

source in

Potential Graph

to be found

Output potential difference

out


VVin

Electronic circuit

to be found

Requirement: Vout = Vin - Vc

V

A

0

B

C

The solution existing in electronics

A

B V

0 C


V

A

0

B

C

A

0

A

V

A

0

B

C

0

Step 1 Step 4


A

0

A

BB

V

A

0

B

C

0


A

0

A

BB

CV

A

0

B

C

0 C


A

0

A

BB

CV

A

0

B

C

0 C


A

0

A

BB

CV

V

A

0

B

C

0 C


C

0

A

B

VC

0

BA

V

Output

V

VC

t

Input

V

t

Correspondence between the behavior of mechanism and behavior of the isomorphic electronic circuit

C

0

A

B

Output

V

VC

t

Input

V

t

VC

0

BA

V

Conducting mode


C

0

A

B

Output

V

VC

t

Input

V

t

VC

0

BA

V

Non-conducting

mode

L=0

U=0


C

0

A

B

Output

V

VC

t

Input

V

t

VC

0

BA

V

Non-conducting

mode

L=0

U=0


C

0

A

B

Output

V

VC

t

Input

V

t

VC

0

BA

V

Non-conducting

mode

L=0

U=0


C

0

A

B

Output

V

VC

t

Input

V

t

VC

0

BA

V

Conducting mode


C

0

A

B

Output

V

VC

t

Input

V

t

VC

0

BA

V


C

0

A

B

Output

V

VC

t

Input

V

t

VC

0

BA

V

Conducting mode


Validity rule

• The engineering system is valid if and only if the transformed engineering system is valid.

C

0

A

B

VC

0

BA

V

Output

VVC

t

Input

V

t

Correspondence between the behavior of mechanism and behavior of the isomorphic electronic circuit in invalid configuration.

0

A

B

VC

0

BA

V

Output

V

t

Input

V

t

VC

Conducting mode

C


C

0

A

B

VC

0

BA

V

Output

V

t

Input

V

t

VC

Conducting mode

L≠0


C

0

A

B

VC

0

BA

V

Output

V

t

Input

V

t

VC

Conducting mode


C

0

A

B

VC

0

BA

V

Output

V

t

Input

V

t


C

0

A

VC

0

BA

V

Output

V

t

Input

V

t

VC

Conducting mode

B


Additional Design ExamplesAdditional design of mechanical

rectifier

3

B

1

0

A

1

0

A

B

A

0

1

3

AA

B

AB

1

2

C

4

0

B

3

A

0

A

3

BB

B

A

B

0

A

0

B

A

0

1

3

A

B

0

A

3

BB

A

B

1

2AC

C

C

A

C

2 20

C

1

0

A

0

B

A

0

1

3

A

B

0

A

3

BB

A

B

2

C

C

A

C

2 2

B

C

4

0

4

BC

4

C

C

0

0

A

B

C

A 2

B

4

C

B

A

0

1

3

C

2

C

0

4

0

0

A

B

C

A 2

B

4

C

0

A

B

C

A 2

B

4

C

Documents

Design of engineering systems by transforming knowledge between fields