APPLICATION OF GRAPHIC METHODS 293 



portant in the given question. 1 The relation between the 

 longitudinal stresses in the elements e, /, 6, is given by the 

 dynamic frame, Fig. 11 a, which takes the friction into account at 

 all the joints. The friction circles are drawn for joints ae, ab, of, 

 be, and bf; the circle for the joint bf is, for clearness in the 

 diagram, supposed to be a little larger than that for be. Arrows 

 are placed at each friction circle to denote the motion of one 

 part relatively to the other at the joints ; each arrow is marked 

 with the letter of the element, the motion of which it denotes ; 

 thus, at the joint ae the arrow marked a shows that, when the 

 driving element e moves the lever, the rotation of a is left-handed 

 relatively to e. Similarly, the arrow marked b at the joints be 

 and bf denotes that, relatively to e and /, the rotation of b is 

 right-handed. The letter b also denotes that the pin is fixed in 

 b ; (it is not a matter of indifference in which element this pin 

 is fixed). Links 1, 3, and 4 can now be drawn, each tangent to 

 their two friction circles. We choose the side on which to draw 

 them as follows : The forces acting on A balance one another, 

 and therefore meet in one point marked A (Fig. Ha) ; the 

 directions of the forces acting on a are marked by three arrow- 

 heads near A, and the equal opposite forces by opposite arrow- 

 heads near B. The links 1 and 4 appear as compression links 

 in the dynamic frame, whereas they are tension links in the 

 machine. The direction of the stress is also reversed in link 3. 

 In explanation it must be remembered that the point A repre- 

 sents the lever, while the bar BjBBjj, which may be drawn 

 anywhere between the links, represents the element b. The 

 links must be placed on that side of the circles where the arrow- 

 heads of the forces acting on a (shown near A) oppose the 

 motion of the arrows a, while the arrow-heads of the forces 

 acting on b (shown near B) oppose the motion of the 

 arrow b. The manner of drawing the figure for this ex- 

 ample has been described in fuller detail than will in future 

 be thought necessary. The relation between the driving 

 effort in link 1 and the resistance in link 4 can be found from 

 Fig. Ha by the ordinary graphical or trigonometrical methods, 



1 When the method of reciprocal figures is used to find the stresses in the 

 links, it will be necessary in all cases to substitute a stiff frame of 3 links for 

 the bars shown in the diagrams. 



