New entity in statics – “Face Force”

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

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

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

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

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

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

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

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

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

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

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

12. DualityIn our approach we proved that the diagram can be considered as velocity diagram of a linkage I VI IV V III O3 O2 O1 O4 II O

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

14. DualityIn 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 I VI IV V III II O

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

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

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

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

20. Face force – a multidimensional generalization of mesh currents

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