New entity in statics – “Face Force”
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Transcript of New entity in statics – “Face Force”
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New entity in statics – “Face Force”
Developing new engineering concept through graph
representations
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Kinematical Linkage
Consider a kinematical linkage and its graph representation
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Kinematical Linkage Static Structure
Now, consider a static structure and its graph representation
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Kinematical Linkage Static Structure
There exist a mathematical relation between the representations of the two systems
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Kinematical Linkage Static Structure
Therefore there is the duality relation between the represented engineering systems
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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
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Kinematical Linkage Static Structure
The equilibrium of forces in the structure is thus equivalent to compatibility of relative velocities
in the linkage
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Kinematical Linkage Static Structure
In classical machine theory there is no known variable corresponding to the absolute velocity
of a joint in the linkage
?
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Kinematical Linkage Static Structure
?
In search for this variable in statical structureswe shall make a detour to …
the works of Maxwell
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Maxwell Diagrampoints in the diagram are associated with the
faces of the structure
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Maxwell Diagramlines in the diagram are associated with the
rods of the structure
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DualityIn our approach we proved that the diagram can be
considered as velocity diagram of a linkage
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IIIIV
O
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O1O2O3O4
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DualityIn our approach we proved that the diagram can be
considered as velocity diagram of a linkage
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DualityIn our approach we proved that the diagram can be
considered as velocity diagram of a linkage
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Therefore Maxwell diagram describes both the forces in the structure and the velocities
in the mechanism
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The length of the segment in the diagram corresponds to the force in the rod of the
structure
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Or to the relative linear velocity of the link in the dual mechanism
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The coordinates of the points in the diagram correspond to the absolute velocities of
mechanism joints
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I
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O
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But there is no known variable to which it corresponds in the structure.
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Face force – a multidimensional generalization of mesh currents
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It was proved that face forces manifest some properties of electric potentials.
pathrodFF ii
rodface i