1. New entity in statics – “Face Force” Developing new engineering concept through graph representations

2. Kinematical Linkage Consider a kinematical linkage and its graph representation

3. Kinematical Linkage Static Structure Now, consider a static structure and its graph representation

4. Kinematical Linkage Static Structure There exist a mathematical relation between the representations of the two systems

5. Kinematical Linkage Static Structure Therefore there is the duality relation between the represented engineering systems

6. Kinematical Linkage Static Structure The relative velocity of each link of the linkage is equal to the internal force in the corresponding rod of the structure

7. Kinematical Linkage Static Structure The equilibrium of forces in the structure is thus equivalent to compatibility of relative velocities in the linkage

8. Kinematical Linkage Static Structure In classical machine theory there is no known variable corresponding to the absolute velocity of a joint in the linkage ?

9. Kinematical Linkage Static Structure ? In search for this variable in statical structures we shall make a detour to … the works of Maxwell

10. Maxwell Diagram points in the diagram are associated with the faces of the structure II VI III V I IV O

11. Maxwell Diagram lines in the diagram are associated with the rods of the structure II VI III V I IV O

12. Duality In our approach we proved that the diagram can be considered as velocity diagram of a linkage II III IV O V I VI O1O1 O2O2 O3O3 O4O4

13. Duality In our approach we proved that the diagram can be considered as velocity diagram of a linkage

15. Therefore Maxwell diagram describes both the forces in the structure and the velocities in the mechanism II VI III V I IV O

16. The length of the segment in the diagram corresponds to the force in the rod of the structure II VI III V I IV O

17. Or to the relative linear velocity of the link in the dual mechanism II VI III V I IV O

18. The coordinates of the points in the diagram correspond to the absolute velocities of mechanism joints II VI III V I IV O

19. But there is no known variable to which it corresponds in the structure. II VI III V I IV O

20. Face force – a multidimensional generalization of mesh currents

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