PALMER: THE DESIGNING OF CONE PULLEYS. 
43 
Bearing in mind these five specific conditions, and the require- 
ments as to the character of the solution desired, as already dis- 
cussed, we may proceed to analyze the problem and derive a satis- 
factory treatment. 
CENERAL ANALYSIS. 
There are two general cases of the problem: I. Open Belts; II. 
Crossed Belts. 
CASE I—OPEN BELTS. 
leikese, a 
Let l=half length of belt. 
d—distance between centers of shafts. 
R=radius of pulley on one shaft. 
r—radius of pulley on the other. 
a—‘‘angle of the belt,” as shown in Fig. 1. 
From the geometry of the figure we have 
T a MIG 
one +d cos a—_—r—ar, 
2 nae: 2 
from which 
l=d cos a+ *(R+r)+a(R—r). 
And 
1—d cos a— —(R+r) 
C= 
R—r 
From the figure 
Sim ¢— = 
and 
Vd? —(R—r)?| 
