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

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’

Common Representation Design Technique 2 3 6 5 4 1 C D B A Db Gl Da T’ T-1 kb kg ka

Common Representation Design Technique 2 3 6 5 4 1 C D B A

Dual Representation Design Technique Db Da D T’ gj gi sj T si

Dual Representation Design Technique

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

Common Representation Design Technique Mechanical Rectifier

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

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

Transforming the problem to the other engineering domain - electronics

The solution existing in electronics – Bridge rectifier circuit

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

Building the mechanical system with the same graph representation 5 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

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

Externally rotated shaft AB – shaft whose relative velocity is determined 5 2 A C 1 4 1 A B B 3 D 6 A A B C D B

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

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

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

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

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

Edge 4 – edge measuring the potential difference between C and D 5 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

Shaft 4 – shaft whose velocity is equal the relative velocity between joints C and D 5 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

Unidirectional edge 5 – edge forcing the potential of D be higher or equal to the potential of A 2 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

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

Unidirectional edge 6 – edge forcing the potential of B be higher or equal to the potential of C 5 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

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

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

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

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

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

Common Representation Design Technique 2 3 6 5 4 1 C D B A

Developing a new design of a Steering Wheel Mechanism

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

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.

Dual Representation Design Technique Case Study

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

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 ? ?

? ? ! 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 ? ? !

Transforming solution to original domain II 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 ? !

Transforming solution to original domain B 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 ! ? !

DESIGN A BEAM FORCE AMPLIFIER ? !

Additional Design Examples Design of clipping mechanism

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

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

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

The solution existing in electronics V A B C

Systematic design of clipping mechanism V A B C A B V C

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

Systematic design of clipping mechanism B A A A C V B B

Systematic design of clipping mechanism B A A A C V B B C C

Systematic design of clipping mechanism B A A A C V B B C C

Systematic design of clipping mechanism B A A A C V B V B C C

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

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

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

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

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

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

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

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

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

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.

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.

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.

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.

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.

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.

Additional Design Examples Additional design of mechanical rectifier

A B A A 1 A A 1 1 3 1 2 C 4 B 3 A 3 B B 3 B B

A A A A 2 A 2 2 C C 1 3 1 C 3 B B B B

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

B A 1 3 C 2 4 A B A 2 C 4 C B

A B A A 2 B C C 4 4 C C B A 2 B