1. Design of engineering systems by transforming knowledge between fields.

2. 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))) … Dj Gl T
T-1
solution(problem(gk))
problem(gk)
solution(problem(si))
problem(si)

3. Design methods D T’ T T’ T-1
We distinguish two design methods for performing design through transformations: one employing common graph representation and other employing the dual representations. G1 gi G2 gj Da si T sj Db T’ D Gl kg Da ka
T-1 kb Db T’

4. Common Representation Design Technique2 3 6 5 4 1 C D B A Db Gl Da T’
T-1 kb kg ka

5. Common Representation Design Technique2 3 6 5 4 1 C D B A

6. Dual Representation Design TechniqueDb Da D T’ gj gi sj T si

7. Dual Representation Design Technique

8. Alternative Rectifier
Examples
Common Design Technique:
Mechanical Rectifier
Steering Wheel
Clipping Mechanism
Alternative Rectifier
Dual Design Technique:
Beam Rectifier

9. Common Representation Design Technique
Mechanical Rectifier

10. The given problem: design a mechanical rectifier
Input angular
velocity in
Output angular velocity out
Requirement: out=|in|
Mechanical
system
to be found

11. Requirement: out=|in|
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

12. Transforming the problem to the other engineering domain - electronics

13. The solution existing in electronics – Bridge rectifier circuit

14. Building the graph representation of the solution5 2 A C B A C D 1 4 B 3 D 6

15. Building the mechanical system with the same graph representation5 2
The mechanical system will
be constructed gradually
by augmenting one element
at a time in accordance to
the edges of the graph A C 1 4 B 3 D 6 B A C D

16. Potential difference source edge AB – edge where the potential difference is given5 2 A C 1 4 B 3 D 6 A C D B

17. Externally rotated shaft AB – shaft whose relative velocity is determined5 2 A C 1 4 1 A B B 3 D 6 A A B C D B

18. Sign Convention Negative potential
Negative velocity – out of the plane
Positive potential
Positive velocity – into the plane 5 2 A C 1 4 1 A B B 3 D 6 A A B C D B

19. Unidirectional edge 2 – edge forcing the potential of A be higher or equal to the potential of C5 2 A C 1 4 1 A B B 3 D 6 A A B C D B
C  A
VC VA

20. Overrunning clutch 2 – kinematical pair forcing the velocity of A be higher or equal to the velocity of C 5 2 A C 1 4 C 1 A 2 B B 3 D 6 VC C C A VC C C A B VA A C D C A B
VC<0VA=VC
VC VA
VC  0VA=0

21. Unidirectional edge 3 – edge forcing the potential of D be higher or equal to the potential of B5 2 A C 1 4 C 1 A 2 B B 3 D 6 VC C C A A B C D B

22. Overrunning clutch 3 – kinematical pair forcing the velocity of D be higher or equal to the velocity of B 5 2 A C 1 4 C 1 A 2 3 D B B 3 D 6 VC C C A
VB VD A B D D VD B VB C D D VD B

23. Edge 4 – edge measuring the potential difference between C and D5 2 A C 1 4 C 1 A 2 3 D B B 3 D 6 VC C A A B D VD C D B

24. Shaft 4 – shaft whose velocity is equal the relative velocity between joints C and D5 2 A C 1 4 4 C 1 A 2 3 D B B 3 D 6 C A
Output A B D C D B

25. Unidirectional edge 5 – edge forcing the potential of D be higher or equal to the potential of A2 A C 1 4 4 C 1 A 2 3 D B B 3 D 6 C A A B VA VC C D A C D B

26. Overrunning clutch 5 – kinematical pair forcing the velocity of D be higher or equal to the velocity of A 5 2 A C 1 4 4 C 1 A
D= - C 2 5 3 D B B 3 D 6 C A D D VD A A B VA C B D VC A C D B

27. Unidirectional edge 6 – edge forcing the potential of B be higher or equal to the potential of C5 2 A C 1 4 4 C D 1 A 2 5 3 D B B 3 D 6 C A D A A B D B C D B

28. Overrunning clutch 6 – kinematical pair forcing the velocity of B be higher or equal to the velocity of C 5 2 A C 1 4 4 C A D 1 2 5 3 D B 6 C B 3 D 6 C A D A
Output A B D B C C D B

29. The prototype of mechanical rectifier was built at the laboratory of kinematical systems in Tel-Aviv university and successfully tested. 5 2 A C 1 4 B 3 D 6

30. Comparing the behavior of the original electronic circuit and the mechanical rectifier: forward operation mode - positive potential/velocity negative potential/velocity A 4 1 5 2 C D 2 A 5 1 4 D C 3 B 6 D C
Input 6
Output 3 B C D A A A
Input B B D C
Output

31. Comparing the behavior of the original electronic circuit and the mechanical rectifier: inverse operation mode - positive potential/velocity negative potential/velocity A 4 1 5 2 C D 2 A 5 4 1 D C 3 B 6 D C
Input 6
Output 3 B
Input C D A A A B B D C
Output

32. Comparing the behavior of the original electronic circuit and the mechanical rectifier: illegal operation mode - positive potential/velocity negative potential/velocity
Output A 4 1 5 2 C D 2 A 5 4 D C 3 B 6 D C
Input 6 3 B C D A A B B D C

33. Common Representation Design Technique2 3 6 5 4 1 C D B A

34. Developing a new design of a Steering Wheel Mechanism

35. Flow Graph Representation Resistance Graph Representation
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
FGR
Flow Graph Representation
Dynamical
system
Electronic
circuit
RGR
Resistance Graph Representation
New concept of a power steering mechanism
Electronic circuits
Electronic transistor
Frames

36. 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.

37. Dual Representation Design Technique
Case Study

38. Simple design case – beam force amplifier
Beam system
to be found
Pin
Pout>> Pin

39. Simple design case – beam force amplifier
Graph
Representation I
Graph
Representation II ? ?
Meta-level
Transforming the original problem (beam) to the secondary domain (gear trains)
Engineering
Domain I
Engineering
Domain II
Gear system
to be found
win
wout>>win
Beam system
to be found
Pin
Pout>> Pin ? ?

40. ? ? ! Choosing one of the solutions
Existing solutions in the domain of gear trains
Graph
Representation I
Graph
Representation II
Meta-level
Drilling machine
Gearbox
Electrical screwdriver
transmission
wout A C B G 5 3 1 2 4
win
Engineering
Domain I
Engineering
Domain II
Gear system
to be found
win
wout>>win
Beam system
to be found
Pin
Pout>> Pin
Other gear systems ? ? !

41. Transforming solution to original domainII IV
III G C A B A B G C 4 3 2 5 1
Graph
Representation I
Graph
Representation II
Meta-level
wout A C B G 5 3 1 2 4
win
wout A C B G 5 3 1 2 4
win
Engineering
Domain I
System
to be found
Pin
Pout>> Pin ? !

42. Transforming solution to original domainB G C 4 3 2 5 1
Engineering
Domain I
Graph
Representation II
System
to be found
Pin
Pout>> Pin G B A B A C G C I II
III IV
Meta-level G
wout A C B G 5 3 1 2 4
win C B A P G I II
III IV ! ? !

43. DESIGN A BEAM FORCE AMPLIFIER? !

44. Additional Design Examples Design of clipping mechanism

45. Systematic design of clipping mechanism
Input is any coordinate
Output coordinate mustn’t exceed a given limit
Kinematical
system
to be found
Requirement: lout= lin - lc

46. Requirement: Dout = Din - Dc
Systematic design of clipping mechanism
Input potential difference source
in
Output potential difference
out
Potential Graph
to be found
Requirement: Dout = Din - Dc

47. Systematic design of clipping mechanism
Electronic
circuit
to be found V
Vin
Requirement: Vout = Vin - Vc

48. The solution existing in electronicsV A B C

49. Systematic design of clipping mechanismV A B C A B V C

50. Systematic design of clipping mechanismB A A A C V
Step 1
Step 4

51. Systematic design of clipping mechanismB A A A C V B B

52. Systematic design of clipping mechanismB A A A C V B B C C

53. Systematic design of clipping mechanismB A A A C V B B C C

54. Systematic design of clipping mechanismB A A A C V B V B C C

55. Correspondence between the behavior of mechanism and behavior of B
Input V t
Output V VC t V C B A
Correspondence between the behavior of mechanism and behavior of
the isomorphic electronic circuit

56. Correspondence between the behavior of mechanism and behavior of A B
Input
Output V VC t
Conducting mode V V C B A t
Correspondence between the behavior of mechanism and behavior of
the isomorphic electronic circuit

57. Correspondence between the behavior of mechanism and behavior of A B
DL=0
Input V t
Output V VC t
Non-conducting mode V C B A
DU=0
Correspondence between the behavior of mechanism and behavior of
the isomorphic electronic circuit

58. Correspondence between the behavior of mechanism and behavior of
DL=0 A C B
Input V t
Output V VC t
Non-conducting mode V C B A
DU=0
Correspondence between the behavior of mechanism and behavior of
the isomorphic electronic circuit

59. Correspondence between the behavior of mechanism and behavior of
DL=0 C B
Input V t
Output V VC t
Non-conducting mode A V C B A
DU=0
Correspondence between the behavior of mechanism and behavior of
the isomorphic electronic circuit

60. Correspondence between the behavior of mechanism and behavior of A B
Input V t
Output V VC t
Conducting mode V C B A
Correspondence between the behavior of mechanism and behavior of
the isomorphic electronic circuit

61. Correspondence between the behavior of mechanism and behavior of A B
Input V t
Output V VC t V C B A
Correspondence between the behavior of mechanism and behavior of
the isomorphic electronic circuit

62. Correspondence between the behavior of mechanism and behavior of B
Input
Output
Conducting mode V V A V C B A VC t t
Correspondence between the behavior of mechanism and behavior of
the isomorphic electronic circuit

63. Validity rule
The engineering system is valid if and only if the transformed engineering system is valid.

64. Correspondence between the behavior of mechanism and behavior of B
Input V t
Output VC V V C B A t
Correspondence between the behavior of mechanism and behavior of
the isomorphic electronic circuit in invalid configuration.

65. Correspondence between the behavior of mechanism and behavior of B
Input V t
Output
Conducting mode VC V V C B A t
Correspondence between the behavior of mechanism and behavior of
the isomorphic electronic circuit in invalid configuration.

66. Correspondence between the behavior of mechanism and behavior of
DL≠0 A C B
Input V t
Output
Conducting mode VC V V C B A t
Correspondence between the behavior of mechanism and behavior of
the isomorphic electronic circuit in invalid configuration.

67. Correspondence between the behavior of mechanism and behavior of B A
Input V t
Output
Conducting mode VC V V C B A t
Correspondence between the behavior of mechanism and behavior of
the isomorphic electronic circuit in invalid configuration.

68. Correspondence between the behavior of mechanism and behavior of B
Input V t A
Output V V C B A t
Correspondence between the behavior of mechanism and behavior of
the isomorphic electronic circuit in invalid configuration.

69. Correspondence between the behavior of mechanism and behavior of B A
Input V t
Output
Conducting mode VC V V C B A t
Correspondence between the behavior of mechanism and behavior of
the isomorphic electronic circuit in invalid configuration.

70. Additional Design Examples Additional design of mechanical rectifier

71. A B A A 1 A A 1 1 3 1 2 C 4 B 3 A 3 B B 3 B B

72. A A A A 2 A 2 2 C C 1 3 1 C 3 B B B B

73. A B A 1 A A 2 A 2 2 C C 1 3 C 4 3 B B 4 C C B 4 B

74. B A 1 3 C 2 4 A B A 2 C 4 C B

75. A B A A 2 B C C 4 4 C C B A 2 B