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Published byNathalie Medcalf Modified over 2 years ago

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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 structures we shall make a detour to … the works of Maxwell

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

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

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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

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Duality In 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 II VI III V I IV O

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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

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

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

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

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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.

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A two-dimensional vector v is determined by two points in the plane: an initial point P (also called the “tail” or basepoint) and a terminal point Q (also.

A two-dimensional vector v is determined by two points in the plane: an initial point P (also called the “tail” or basepoint) and a terminal point Q (also.

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