Polygon of forces

Left: four different powers; Right: polygon of forces. denotes the resulting force ${\displaystyle {\vec {F}}_{R}}$

The polygon of forces or force polygon (more rarely force polygon or Kräfteeck / Forces Eck ) is in the graphical statics the figure that arises when several forces connects drawing together so that the starting point of the following force each match of the preceding with the endpoint. To put it clearly, the individual force vectors are linked to one another. The force polygon is used to combine different forces into one resulting force and is based on the procedure of the parallelogram of forces . It is a graphic variant of vector addition .

As a result, the connection between the starting point and the end point of the last drawn force forms the resulting force and closes the polygon. Due to the commutative law of addition, the order in which the forces are drawn does not matter for the size and direction of the resulting force. If you add an additional force, which acts exactly in the opposite direction to the resulting force (so to speak, turns this force arrow around), then all forces are kept in balance .

example

In the picture you can see four different sized forces pointing in different directions. The resulting force can also be found by drawing a force polygon by drawing in the forces one after the other starting from one point so that each force arrow connects to the previous one. If the starting point is connected to the end point of the last drawn force, this resulting force has been obtained. ${\displaystyle {\vec {F_{1}}},{\vec {F_{2}}},{\vec {F_{3}}},{\vec {F_{4}}}}$ ${\displaystyle {\vec {F}}_{R}}$

Together with the force , the force polygon would be closed, i.e. the resulting force would be zero or the forces in equilibrium. ${\displaystyle {\vec {F_{5}}}}$ ${\displaystyle {\vec {F_{1}}},{\vec {F_{2}}},\ldots ,{\vec {F_{5}}}}$

literature

• Otto Lueger: Lexicon of the entire technology . 2nd Edition. ( zeno.org - 1904-1920).