EQUILIBRIUM PotvcoN 2j 



a force polygon and (b) is called a funicular or an equilibrium polygon. 

 It will be seen that the magnitude and direction of the resultant of a 

 system of forces is given by the closing line of the force polygon, and 

 the line of action is given by the equilibrium polygon. 



The force polygon in (a) Fig. 13 closes and the resultant, R, of 



the forces P lf P 2 , P 3f P, P 5 is parallel and equal to P Q , and is opposite 

 in direction. The system is in equilibrium for translation, but is not in 

 equilibrium for rotation. The resultant is a couple with a moment 

 = P Q h. The equilibrant of the system of forces will be a couple 

 with a moment + P Q h. From the preceding discussion it will be 

 seen that if the force polygon for any system of non-concurrent forces 

 closes the resultant will be a couple. If there is perfect equilibrium 

 the arm of the couple will be zero. 



Second Method. Where the forces do not intersect within the 

 limits of the drawing board, or where the forces are parallel, it is not 

 possible to draw the equilibrium polygon as shown in Fig. 12 and Fig. 

 13, and the following method is used. % 



The point o, (a) Fig. 14, which is called the pole of the force poly- 

 gon, is selected so that the strings a o, b o, c o } d o and e o in the equi- 

 librium polygon (b), which are drawn parallel to the corresponding 



