CONTINUOUS CALCULATING MACHINES. 
397 
Investigation of work lost in friction. 
The work lost in friction in the sphere ancl roller mechanism occurs partly in rolling 
contact and partly upon the axles, which will be here investigated, is that upon the 
axles of the movable frame. There are two kinds of effect and two only upon these, 
viz., direct pressure upon the bearings and twisting of the plane of rotation. The 
combined effect of these results in 
(1.) A direct pressure on the bearings, 
(2.) End pressure resulting, according to the construction, in either pivot or collar 
friction. 
Let 
L= work lost in one revolution of the sphere 
N= number of revolutions of rollers for one revolution of sphere 
Wj = pressure on bearings (direct) 
W 2 = pressure on pivot or collar (end) 
<jf>= coefficient of friction 
R= radius of sphere 
r— radius of rollers 
p= radius of axles of rollers 
n= number of rollers in movable frame. 
Then 
L=Lj+L 3 
where 
L x = work lost in direct friction by direct pressure on bearing 
= 27rpNW 1 sin (f> 
Lo= work lost in pivot friction 
= f 7rpNW 2 tan <£ 
L=27TpN sin 
Then it is required to find an expression from which N is eliminated and W x , W 2 
expressed in terms of the force to be transmitted. 
Let figs. 30 and 31 be respectively a plan and elevation showing diagrammatic 
views of sphere G with rollers A A / B B /5 in contact respectively at points a a b b'. 
Let 
P = force to be transmitted acting on periphery of driving 
roller (generally taken as A in the figures). 
Q = reaction of the driver wheel (B). 
a = angle of vertical diametral plane to plane of rollers B. 
kJc being axis of rotation of the sphere (fig. 30). 
MDCCCLXXXV. 3 F 
