10 PROFESSOR FLEEMING JENKIN’S APPLICATION OF GRAPHIC METHODS 
_ where all the joints are made by circular pins and eyes, this is readily done by 
making the directions of the links tangent to, and on the proper side of, circles 
drawn with their centres at the centres of the pins, and having each a radius 
equal to 7 sin ¢, where is 7 the radius of the pin in question, and ¢ the angle 
of which the tangent is equal to the coefficient of friction for the surfaces in 
question. 
These circles will, in what follows, be called /riction circles. The following 
mnemonic rules will be found useful in selecting the side of the circle to which 
any given link must be tangent. Case 1. When the link represents an element 
with only two joints, and therefore does not end in any geometrical joint named 
by the same letter as an element. Consider the link as terminating in an eye 
which rotates on a pin fastened to the other element. Mark by an arrow the 
direction of rotation of the pin inside the eye. Mark also by an arrow the 
direction of the force exerted by the link at the joint, then place the tangent so 
that the force indicated by the arrow in the link appears to oppose the motion 
of the pin. It must be remembered that the arrow indicating the direction of 
the force exerted by the link may, in the diagrams, frequently be found at the end 
of the link furthest from the jot. Case 2. When the link ends in a geometrical 
joint marked with the letter denoting the element in which any pin is fast, then 
the arrow on the half link, next that geometrical joint, must point as if opposing 
the motion of the pin relatively to the other element. 
Fig. 5¢ shows the dynamic frame when the friction at the jomts has been 
-taken into account, or as it may be called the dynamic frame with friction. 
Eight friction circles are first drawn, arrows are placed on the links, as in fig. 5a, 
to indicate whether these are in tension or compression ; the directions of stress 
are by hypothesis known in links 1 and 6, and we easily see what must be 
the direction of stress in the other links to keep links 1 and 6 in equili- 
brium. We next put arrows at each friction circle in fig. 5c, showing the motion 
of each pin relatively to its eye when e contracts, and / is lengthened ; before 
doing this, we must choose in which element the pin is to be fixed. The links 
of the dynamic frame are then drawn tangent to the friction circles, so as to 
make the stated angle with the surface of each joint, The point where the pin 
bears against the eye, marked by a dot on the surface of each pin, will aid in 
showing thé meaning of the diagram, as explained in§ 7. The italic letters near 
the arrows denote the element in which the pin is fast, and the arrows show the 
direction of rotation of that element relatively to the other element of the joint. 
If / were made the driver the direction of these rotations would all be reversed, 
and consequently the links would all have to cross over to the other sides of —~ 
the friction circles. This would materially alter the form of the diagram, and in 
many machines would result in an impracticable diagram, showing that the 
machine, cannot be driven backwards. 
