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Designing to Design Interdisciplinary Engineering Knowledge Genome: perspective and new results

Designing to Design Interdisciplinary Engineering Knowledge Genome: perspective and new results . Offer Shai and Yoram Reich Faculty of Engineering Tel Aviv University. 4 th Design Theory SIG Workshop Mines ParisTech 31 January-2 February 2011. Historical observation.

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Designing to Design Interdisciplinary Engineering Knowledge Genome: perspective and new results

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  1. Designing to DesignInterdisciplinary Engineering Knowledge Genome: perspective and new results Offer Shai and Yoram Reich Faculty of Engineering Tel Aviv University 4th Design Theory SIG Workshop Mines ParisTech 31 January-2 February 2011

  2. Historical observation • When people wish to designsomething, they end up designing some of the concepts (language), methods, tools, in order to designit • In this design, people select (design) their social infrastructure that will help them designit including: collaboration, funding agencies, students, etc. • We present one such example: the design of deployable tensegrity structures and in doing so, tells you some more about the IEKG project

  3. Types of systems UnderConstrained Systems Part of the system is under- and part well-constrained Well ConstrainedSystems Over Constrained Systems

  4. Types of systems Obtaining all types of systems from the well constrained systems UnderConstrained Systems Deletingelements Addingelements Well ConstrainedSystems Over Constrained Systems Addingelements Deletingelements

  5. Types of systems Obtaining all types of systems from the well constrained systems UnderConstrained Systems Deletingelements Addingelements Therefore, from now on, in this presentation, we discuss only well-constrained systems Well ConstrainedSystems Over Constrained Systems Addingelements Deletingelements

  6. 1864 Maxwell James Clerk Maxwell

  7. In 1864, James Clerk Maxwell found a connection between geometry and statics. Theorem (1864): The projection of any polyhedron (3D) is a 2D static framework with inner forces satisfying the equilibrium of forces in any joint. (It is unclear whether he proved the inverse theorem, but, in 1982, Prof. Whiteley from Canada proved it.)

  8. C A B D Static Framework with inner forces: satisfying the equilibrium of forces in any joint. Replacing any rod with two equal and opposite external forces results in a static framework satisfying force equilibrium in all joints

  9. No self-equilibrium of forces. There are many examples of static frameworks These are NOT static frameworks

  10. 1914 Assur 1864 Maxwell Leonid Assur

  11. Not an Assur Group Assur Group In 1914, Leonid Assur, a professor at the Saint-Petersburg Polytechnical Institute, established a new concept: Assur Groups. Every mechanism can be decomposed into Assur Groups (structures). Assur Group is a well constrained structure that does not contain an inner well constrained structure. Assur Group is a structure with zero degrees of freedom (DOF) and does not contain an inner structure with zero DOF.

  12. 1914 Assur 1864 Maxwell 1930 Artobolevski I.I. Artobolevsky

  13. From 1914 till 1930 this work has not receive attention. ONLY in 1930, the known kinematician – I.I. Artobolevsky, wrote about Assur Group in his books, and from that time on it has been widely used in the east.

  14. Mathematics Architecture Structural Topology Journal. In 1979, in the University of Montreal, Canada, a research group of architects and mathematicians was established. They established the Structural Topology Journal written both in English and in French. Concepts from Mathematics and Architecture yielded knowledge in Rigidity Theory Group.

  15. 1914 Assur 1864 Maxwell 1982 1930 Whiteley Artobolevski Walter Whiteley

  16. In 1982, Walter Whiteley proved the inverse theorem of Maxwell theorem (1864). Whiteley showed that by using Maxwell's idea it is possible to construct a corresponding polyhedron for every static framework.

  17. 1914 Assur 1864 Maxwell 1982 1930 Whiteley Artobolevski 1990 Connelly Robert Connelly

  18. In 1990, Robert Connelly from Cornell University (New York, USA) Connelly's conjecture (1990): All static Frameworks can be derived from a projection of the Tetrahedron

  19. 1914 Assur 1864 Maxwell 1982 1930 Whiteley Artobolevski 1990 2001 Jordan Connelly Tibor Jordan

  20. In 2001, Tibor Jordan, Budapest, Hungary Jordan proved Connelly’s conjecture (1990), that all the static frameworks can be derived from a projection of a Tetrahedron by applying only two operations.

  21. 1930 Artobolevski 1864 Maxwell 2001 Jordan 1914 Assur 1990 Connelly 1982 Whiteley Mobility, Georges Amar Is there a hope or benefit to the synthesis of these views? Can we make knowledge mobility work?

  22. 1914 Assur 1864 Maxwell 1982 1930 Whiteley Artobolevski 2004 Shai & Reich 1990 2001 Connelly Jordan Offer Shai/Yoram Reich

  23. In 2004, Offer Shai and Yoram Reich from Tel Aviv University, Israel, presented Infused Design and developed the IEKG • Types of combinatorial representations: • MR – matroid representation • RGR - resistance graph representation • PGR – potential graph representation • FGR – flow graph representation • LGR – line graph representation • PLGR – potential line graph representation • FLGR – flow line graph representation

  24. IEKG IEKG 1930 Artobolevski 1864 Maxwell 2001 Jordan 1914 Assur 2004 Shai & Reich 1990 Connelly 1982 Whiteley Created the Knowledge Mobility infrastructure

  25. 1914 Assur 1864 Maxwell 1982 1930 Whiteley Artobolevski 1990 2001 Connelly Jordan Addressing some Knowledge Mobility issues

  26. Contracted Assur Graphs = all the pinned joints become one vertex. Theorem (2010): Contracted Assur Graphs ⇔ static frameworks Assur Graph

  27. Contracted Assur Graphs = all the pinned joints become one vertex. Theorem (2010): Contracted Assur Graphs ⇔ static frameworks

  28. Contracted Assur Graphs = all the pinned joints become one vertex. Theorem (2010): Contracted Assur Graphs ⇔ static frameworks

  29. Contracted Assur Graphs = all the pinned joints become one vertex. Theorem (2010): Contracted Assur Graphs ⇔ static frameworks

  30. Contracted Assur Graphs = all the pinned joints become one vertex. Theorem (2010): Contracted Assur Graphs ⇔ static frameworks

  31. Contracted Assur Graphs = all the pinned joints become one vertex. Theorem (2010): Contracted Assur Graphs ⇔ static frameworks

  32. Contracted Assur Graphs = all the pinned joints become one vertex. Theorem (2010): Contracted Assur Graphs ⇔ static frameworks Assur Graph static framework

  33. Creating a map of 2D building blocks (s-genes)

  34. Now we have the map of all 2d Building blocks

  35. IEKG: First part of the Algorithm Decomposition into Minimal inseparable components (Assur Graphs): A. Initiate the decomposition– choose the ground. B. Applythe decomposition algorithm – the Pebble Game (top down). C. Construct the inseparable components – Each directed cut-set defines a component (AG). D. Construct, simultaneously, the decomposition graph

  36. C A 1 3 A C α β LCB C B B D 2 Decomposition – separate the system (mechanism, geometric constraint) into minimal inseparable components (Assur Graphs- AGs). A 3 1 4 C A β α 6 B 5 1 3 2 D B 7 2 LCB 4 The mechanism The geometric constrains 6 5 1 3 2 7 The geometric constrains graph The structural scheme

  37. A 1 3 A D 3 1 A C B B B C C B 2 A 2 A 4 C 6 1 3 5 1 D 7 C C A D. Construct, simultaneously, the decomposition graph 4 3 3 1 1 D 6 B 5 1 3 β β α α B B C C 7 2 2 2 LCB LCB decomposition graph decomposition graph β α B. Applythe decomposition algorithm – the Pebble Game (top down). C. Construct the inseparable components – Each directed cut-set defines a component (AG). A. Initiate the decomposition– choose the ground. A 3 B α β 2 LCB B 2

  38. IEKG: Second part of the Algorithm COMPOSITION (Analysis): A. Initiate the composition – set the ground. B. Add, successively, the components - (according to the decomposition graph) and analyze/solve them. • C. Continue tillyou have completed the task • Constructing the geometric object • Analyzing the mechanism.

  39. A A A 1 1 3 3 C B B C C B A 2 2 LCB B C A 4 3 1 D 6 B 5 1 D 3 β α composition graph composition graph B C 7 2 2 LCB B. Add, successively, the components (according to the decomposition graph) and analyze/solve them. C. Continue till you have completed the task Constructing the geometric object. • Initiate the composition – • set the ground. β α LCB 3 C C 4 A 1 6 A 5 1 3 D 7 B β 2 α 2

  40. A D C A A B A 1 1 3 3 C B B C C B A 2 2 LCB B C A 4 3 1 D 6 B 5 1 D 3 β α composition graph composition graph B C 7 2 2 LCB C. Continue till you have completed the task. Analyzing the mechanism. B. Add, successively, the components (according to the decomposition graph) and analyze/solve them. • Initiate the composition- • set the ground. β α LCB C C 4 A 1 6 A 5 1 3 D 7 B β 2 α 2

  41. What has been designed? • New concepts • Face force • Equimomential line • New methods - stability of tensegrity • New theorems Telllegen’s theorem in mechanics • New design methods -Infused design • New products Adjustable deployable structure Artificial caterpillar robot Mechanical transistor

  42. Thanks you for your attention

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