PALMER: THE DESIGNING OF CONE PULLEYS. 73 
Now construct the diagram for open or crossed belts, as the case 
may be. For illustration, take the diagram for open belts, Fig. 8. 
Lay off AJ = the number of revolutions n, and GJ=N, using any 
convenient scale. Then choose point K so that KH and AH will 
be of suitable size for the radii, r, and R,, respectively. 
1 
Then ATR. =I; 
5 re NO 
so two pairs of steps can be drawn. Through K draw KS a 
45°-line, and through S draw SA’ parallel to KA, thus locating A’. 
Produce a horizontal through A’ to the belt line, and 1, the half 
length of belt required, is shown at once in the same scale. 
Now from A’ lay off A) W=n, and WR=N, using any scale. 
jom: Reto. AVand point Tf gives T1L=1, and A’ L—k,. 
Then ier —al sone 
AV Rio also: ri. 
So now all the radii are determined and the steps may be drawn. 
If there were more steps the proceeding would be just the same. 
If there should be an odd number of steps one pair of steps would 
be equal, and their radii would be found given by point F. If the 
belt be crossed the operations are just the same, using the diagram 
of Fig. 9, where a straight line replaces the arc BE. 
The only difference is in reading off the length of belt. In Fig. 
g, for the position A’ the half length of belt is 6U, the position of 
a horizontal through A’, which is included between the arc and 
the straight belt line WD. 
CASE II—Special Conditions. 
SPECIAL RULES FOR SMALL THREE STEP CONES. 
OPEN BELTS. 
When the cones for an open belt are to have three steps each, 
with speeds in geometrical progression, and the distance between 
centers is to be great in proportion to the size of the cones then 
the steps may be figured by arithmetic, and this is the only case of 
cones for an open belt which can be. In general it 1s impossible 
to deal with cones for an open belt correctly in any way, except by 
the regular use of the diagram. 
This one exception is due. to the fact that when the distance be- 
tween centers in Fig. 8 is great and the radii for the first pair of 
steps are small, we have a very large circle, BE, of which but a 
