16 PROFESSOR FLEEMING JENKIN’S APPLICATION OF GRAPHIC METHODS 
§13. Simple Machines—Lever.—Let a, fig. 11, be a lever to which a driving 
effort is applied by the spring e, and a resistance by the spring 7 Let the 
lever have a fulcrum or bearing in the element 6 to which the elements e and 
fare jointed, making a complete or self-contained machine. This system isa self- 
strained frame, with one stiff bar, namely the lever. The bar in this, as in the 
other drawings, may be regarded as the symbol of a stiff frame, the form or design 
of which is unimportant in the given question.* The relation between the 
longitudinal stresses in the elements e, f, 6, is given by the dynamic frame, 
fig. 11a, which takes the friction into account at all the joints. The friction 
circles are drawn for joints ae, ab, af, be, and 6/; the circle for the joint U/ 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 ¢ moves the lever, the rotation of a is 
left-handed relatively to e. Similarly, the arrow marked 0 at the joints de and 
bf denotes that, relatively to e and /, the rotation of } is right-handed. The 
letter 6 also denotes that the pin is fixed in 0; (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 there- 
fore meet in one point marked A (fig. 11a) ; 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 represents the lever, while the bar B,BB,, which 
may be drawn anywhere between the links, represents the element 0. 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 6 (shown near B) oppose the motion of the arrow 0. 
The manner of drawing the figure for this example 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. 11a 
by the ordinary graphical or trigonometrical methods. The conception of a 
complete machine has not been recognised by any writer on mechanics as 
necessary for the statement of problems connected with the lever. If, however, 
these problems are to be practical, and not confined to abstractions, such as 
“forces applied to points,” they do require the consideration of a complete 
* 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. 
