PALMER: THE DESIGNING OF CONE PULLEYS. 65 
For open beits the diagram to be used is of one form and for 
crossed belts it is of another. But one is equally as simple as the 
other. And the one corresponds exactly to the other, so that if 
the use of one is understood the other may be used in just the same 
way. Both may be easily constructed with the ordinary drafting 
instruments, without the use of irregular curves or any special ap- 
pliance. Being very simple both can be remembered easily after 
using a few times, so that they may be quickly drawn for any case 
in hand. 
FORM OF DIAGRAMS. 
The form of the diagram will be given for each of these two gen- 
eral conditions, and then the various cases of the problem will be 
taken up in turn and their treatment explained in reference to both 
diagrams, the two being so nearly alike and their use so similar. 
NOTATION USED. 
For convenience certain letters will be used to denote the quan- 
tities of the problem, and to avoid explaining them repeatedly they 
will be given here: 
Let  R be the radius of one step of the cone on the driving shaft, 
and__—ir the radius of the corresponding step on the driven shaft. 
Let N_ be the number of revolutions the driving shaft makes; 
and =n the number which the driven shaft is to make when the 
belt is on this pair of steps. 
irentjce i ho. ho; &C:, 
Tigey isint Ba sks 3 OSC.’ 
3? 
and Me aoe an 
i? 2? 3? 
cessive steps, 
n,, &c., be corresponding values for the suc 
N being constant. 
Let 1 be the half length of belt required, 
and di the distance between centers, all in the same units and 
drawn to the same scale. 
OPEN BELTS. 
To design a pair of cones for an open belt draw first the rectangle 
ABCD, shown in Fig. 8, making AB=d the distance between cen- 
ters of the shafts, using any scale most convenient. Make BC=rd, 
that is 3.1416 times the distance between centers. Then draw the 
“belt line” BD. Now draw the 450-line FA, produced through C. 
Lay out the small square AC, shown, making the side of this 
square just ;!,th of AB, the distance between centers. Then set 
