1. Face force – a multidimensional generalization of mesh currents

2. It was proved that face forces manifest some properties of electric potentials.

3. A New View on Engineering Systems through the Engineering Knowledge Genome: Structural Genes of Systems Topologies

4. General View on Systems Topologies
Over Constrained
Systems
Under Constrained
Systems
Well constrained Systems
Compositions of s-genes
Gene 1
Gene 2
Gene 3

5. Definition of s-genes
G is an s-gene IFF it is a well constrained graph
and removing any set of vertices does not result
in an s-gene.
Examples s-genes in the following disciplines:
Trusses
Linkages
Sketches
These entities are genes because they are the building blocks
of these and many other systems in different disciplines

6. Definition of s-genes in trusses
A truss is an –gene IFF it is rigid determinate truss but does not contain any substructure that is a determinate truss A B D C P1 P2 P3 1 3 4 5 6 7 8 2 A B D P1 P2 P3 3 4 6 7 8 A B D C P1 P2 P3 1 3 4 5 6 8 2
s-gene
mechanism
mechanism

7. Removing vertex C result in
Example of a system that is not an s-gene: A B D C P1 P2 P3 A B D P1 P2 P3 C
Removing vertex C result in
an s-gene
Sub system that is an s-gene
The first was not an s-gene

8. S-genes in well-constrained sketchesB 1 2 3  L1 C A B C L1 1 3 2  L3
The sketch (geometric constraint) problem.
The corresponding graph is a floating s-gene. L3 A B 1 2 3  L1 C
The s-gene after grounding edge (2,C).

9. The process of constructing all the s-gene (in 2D, for now).
(The process is complete and sound)

10. Ground edge is replaced by a triangle and two new ground edges.
Basic s-gene – the dyad. A A1 A2
Ground edge is replaced by a triangle and two new ground edges.
Fundamental Extension x y z t
Dividing edge (x,y) to two by adding an inner vertex z and connecting z to an arbitrary vertex z, can be the ground.
Regular extension

11. Example of creation s-genesB C E D O1 O2 O3 O4 F O5
(a)
(b)
(c)
(b1)
(b2)
(c1)
(c2)
(A,O2)
(B,O3)
(A,B)
(A,D)
(A,E)
The dyad.

12. The Map of all the genes in 2D

13. The Decomposition of Well-Constrained Systems into S-GenesB C D A
A,B,C,D G E F
E,F,G I H J O3
H,I,J K K O1 O2
The Decomposition Graph
(obtained computationally by pebble game)
Well Constrained Truss

14. Employing the Decomposition into S-Genes for Analysis
2* number of inner vertices = number of edges in the s-gene. I E F G H J K O3 O1 O2 1 2 3 4 7 5 6 8
2*4=8 J I K A B E C O1 O3 D F G H O2
The Determinate Truss I P6 H J K O3 O1 O2 PG P3 1 2 3 4 5 6 P8 P1
2*3=6 J K O3 O1 O2 1 2 3 4 5 6
2*3=6 P1 P6 P5 1 2 P6
2*1=2

15. Employing the s-genes for constructing well constrained sketchesB 1 2 3  L1 C A B C L1 1 3 2  L3
The sketch problem
The corresponding floating s-gene L3 A B 1 2 3  L1 C
Grounding edge (2,C) L3 A B 1 2 3  L1 C
Grounding edge (A,3)
A,1,3,B 1 B C 2
The composition graph
The composition graph

16. The process of constructing the geometric object by composing its s-genes1 A 3
(b)
(A,3)  L3 A B 1 2 3  L1 C A 3
(a)
(A,3) A B 3 L3  C L1 1
(d)
(A,3) 1 A
(A,3) B 3 L3 
(c) A B 3 L3  C L1 1 2
(e) 1
(A,3) B C 2

17. S-genes in mechanisms
Strangely!
S-genes in mechanisms are exactly the same as s-genes in trusses with the addition of a driving link

18. Deriving mechanisms’ S-genes from trusses’ s-genesB D C P1 P2 P3 1 3 4 5 6 7 8 2
(a) A
Truss s-gene A B D C P1 P2 1 3 4 5 6 7 8 2 A B D C P2 P3 1 3 4 5 6 7 8 2 A B D C P1 P3 1 3 4 5 6 7 8 2 P3 P1 P2

19. A schematic graph of the mechanism
A mechanism
A schematic graph of the mechanism 1 2 3 4 5 6 7 8 9 10 11 A B C D E F J G H I A B C D E J G F H I 2 3 4 5 10 9 8 6 7 11

20. The decomposition of the schematic graph into s-genesB C D J 2 3 4 5 G H I 8 6 7 11 10 F 9
Tetrad
Triad
Diad

21. Decomposition of the mechanism
Tetrad
Triad
Diad
Velocities of inner joints are known A C 3 B A B C D J 2 3 4 5 E 4 1 E G H I 8 6 7 11 2 F 10 9 E 5 J D 10 F 6 G 9 7 8 H I 11

22. Employing s-genes for synthesis