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 D a in some other engineering domain D b related to D a through graph representations. T’(…(T(problem(D a ))) = problem(D b ) DESIGN=solution(problem(D a ))= =T’ -1 (…T -1 (solution(problem(g k ))) GlGl solution(problem(g k )) DjDj T -1 problem(s i ) solution(problem(s i )) problem(g k ) T …

3. Design methods We distinguish two design methods for performing design through transformations: one employing common graph representation and other employing the dual representations. GlGl kgkg DaDa kaka T -1 kbkb DbDb T’ G1G1 gigi G2G2 gjgj DaDa sisi T sjsj DbDb D

4. Common Representation Design Technique GlGl kgkg DaDa kaka T -1 kbkb DbDb T’ 2 3 6 5 4 1 C DB A

5. Common Representation Design Technique 2 3 6 5 4 1 C DB A

6. Dual Representation Design Technique G1G1 gigi G2G2 gjgj DaDa sisi T sjsj DbDb T’ D

7. Dual Representation Design Technique

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

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. 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. 2 3 6 5 4 1 B A C D Building the graph representation of the solution B A CD

15. 2 3 6 5 4 1 C DB A B A CD Building the mechanical system with the same graph representation The mechanical system will be constructed gradually by augmenting one element at a time in accordance to the edges of the graph

16. 2 3 6 5 4 1 B A CD C DB A Potential difference source edge AB – edge where the potential difference is given

17. 1 A B 2 3 6 5 4 1 B A CD A B C DB A Externally rotated shaft AB – shaft whose relative velocity is determined

18. 1 A B 2 3 6 5 4 1 B A CD A B C DB A Sign Convention Negative potentialNegative velocity – out of the plane Positive potentialPositive velocity – into the plane

19. 1 A B 2 3 6 5 4 1 B A CD A B C DB A Unidirectional edge 2 – edge forcing the potential of A be higher or equal to the potential of C C  AC  A VCVAVCVA

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

21. 1 2 A B C A B C 2 3 6 5 4 1 B A CD C DB A C VCVC Unidirectional edge 3 – edge forcing the potential of D be higher or equal to the potential of B

22. 1 2 3 A B C D A B C D 2 3 6 5 4 1 B A CD C DB A C D D B VBVDVBVD VCVC VDVD VBVB VDVD Overrunning clutch 3 – kinematical pair forcing the velocity of D be higher or equal to the velocity of B

23. 1 2 3 A B C D A B 2 3 6 5 4 1 B A CD C DB A C D VCVC VDVD Edge 4 – edge measuring the potential difference between C and D

24. 4 1 2 3 A B C D A B Output C D 2 3 6 5 4 1 B A CD C DB A Shaft 4 – shaft whose velocity is equal the relative velocity between joints C and D

25. 4 1 2 3 A B 2 3 6 5 4 1 B A CD C D A B C D C DB A A VCVC VAVA C Unidirectional edge 5 – edge forcing the potential of D be higher or equal to the potential of A

26. 4 1 2 3 A B D= - C 2 3 6 5 4 1 B A CD C D A B B A C D D 5 C DB A A VCVC VAVA C VDVD D Overrunning clutch 5 – kinematical pair forcing the velocity of D be higher or equal to the velocity of A

27. 4 1 2 3 A B D 2 3 6 5 4 1 B A CD 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

28. 4 6 1 2 3 A B D C 2 3 6 5 4 1 B A CD 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

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

30. 1 A B C D 4 A B A C D A B C D B A D C 3 6 5 2 Input Output 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

31. 1 A B C D 4 A B A C D A B C D B A D C 3 6 5 2 Input Output 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 - positive potential/velocity - negative potential/velocity

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

33. Common Representation Design Technique 2 3 6 5 4 1 C DB A

34. Developing a new design of a Steering Wheel Mechanism

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

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. Beam system to be found P in P out>> P in Simple design case – beam force amplifier

39. Meta-level Engineering Domain I Engineering Domain II Graph Representation I Graph Representation II Gear system to be found  in  out >>  in Beam system to be found P in P out>> P in Simple design case – beam force amplifier Transforming the original problem (beam) to the secondary domain (gear trains)

40. Meta-level Engineering Domain I Engineering Domain II Graph Representation I Graph Representation II Gear system to be found  in  out >>  in Beam system to be found P in P out>> P in Drilling machine Other gear systems Gearbox Electrical screwdriver transmission  out A C B GG A C B 5 3 1 24  in Existing solutions in the domain of gear trains Choosing one of the solutions

41. Meta-level Engineering Domain I Graph Representation I Graph Representation II System to be found P in P out>> P in AABB GGCC G 0 43251  out A C B GG A C B 53 1 24  in IIIIV 0 III GC C ABBA G  out A C B GG A C B 53 1 24  in Transforming solution to original domain

42. Meta-level Engineering Domain I Graph Representation I Graph Representation II System to be found P in P out>> P in IIIIV 0 III GC C ABBA G G I IVII P C B A G AABB GGCC G 0 43251  out A C B GG A C B 5 3 1 24  in Transforming solution to original domain

43. DESIGN A BEAM FORCE AMPLIFIER CCCC

44. Additional Design Examples Design of clipping mechanism

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

46. Requirement:  out =  in  c Systematic design of clipping mechanism Input potential difference source  in Potential Graph to be found Output potential difference  out

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

48. V A 0 B C The solution existing in electronics

49. A B V 0 C Systematic design of clipping mechanism V A 0 B C

50. A 0 A V A 0 B C 0 Step 1Step 4 Systematic design of clipping mechanism

51. A 0 A B B V A 0 B C 0

52. A 0 A B B C V A 0 B C 0 C

53. A 0 A B B C V A 0 B C 0 C

54. A 0 A B B C V V A 0 B C 0 C

55. C 0 A B V C 0 B A V Output V VCVC t Input V t Correspondence between the behavior of mechanism and behavior of the isomorphic electronic circuit

56. C 0 A B Output V VCVC t Input V t V C 0 B A V Conducting mode Correspondence between the behavior of mechanism and behavior of the isomorphic electronic circuit

57. C 0 A B Output V VCVC t Input V t V C 0 B A V Non- conducting mode  L=0  U=0 Correspondence between the behavior of mechanism and behavior of the isomorphic electronic circuit

58. C 0 A B Output V VCVC t Input V t V C 0 B A V Non- conducting mode  L=0  U=0 Correspondence between the behavior of mechanism and behavior of the isomorphic electronic circuit

59. C 0 A B Output V VCVC t Input V t V C 0 B A V Non- conducting mode  L=0  U=0 Correspondence between the behavior of mechanism and behavior of the isomorphic electronic circuit

60. C 0 A B Output V VCVC t Input V t V C 0 B A V Conducting mode Correspondence between the behavior of mechanism and behavior of the isomorphic electronic circuit

61. C 0 A B Output V VCVC t Input V t V C 0 B A V Correspondence between the behavior of mechanism and behavior of the isomorphic electronic circuit

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

65. 0 A B V C 0 B A V Output V t Input V t VCVC Conducting mode C Correspondence between the behavior of mechanism and behavior of the isomorphic electronic circuit in invalid configuration.

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

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

68. C 0 A B V C 0 B A V Output V t Input V t Correspondence between the behavior of mechanism and behavior of the isomorphic electronic circuit in invalid configuration.

69. C 0 A V C 0 B A V Output V t Input V t VCVC Conducting mode B 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. 3 B 1 0 A 1 0 A B A 0 1 3 1 2 C 4 0 B 3 A 0 A 3 B B A B

72. 0 A 0 B A 0 1 3 0 A 3 B B A B 1 2 C A C 2 2 0 C

73. 1 0 A 0 B A 0 1 3 0 A 3 B B A B 2 C A C 2 2 B C 4 0 4 4 C C 0

74. 0 A B C A 2 B 4 C B A 0 1 3 C 2 C 0 4 0

75. 0 A B C A 2 B 4 C 0 A B C A 2 B 4 C