7 
mass of weight w at A if w,r,\(b+c)=wre, 
and w,r,(d +c) = wrb. 
_ to the crank pins 
_ the crank pin A. Reciprocating masses, such 
as D and E£, introduced to balance other re- 
 eylinders would take the place of the bob- 
ry 
- 
BALANCING 427 
in A and the axis of the shaft, and if B and C are on the opposite 
the axis to A, revolving masses of weights w, and w, placed at 
B and C respectively will balance a revolving 
_ Hence if reciprocating masses D and E 
of weights «, and w, respectively be connected 
B and ©, as shown, the 
reciprocating masses D and E will completely 
balance the reciprocating masses connected to 
ciprocating masses are called bob-weights, and 
they serve no other purpose than that of 
balancing. Instead of the masses D and E, 
which are useless except for balancing purposes, 
two additional cylinders might be introduced, —b + > 
and the reciprocating parts belonging to these Fig. 697 
weights, and the reciprocating parts of this three-cylinder engine would 
then completely balance one another. 
' Tf the stroke of the bob-weights is small, they may be driven by 
eccentrics instead of ordinary cranks. The weights w, and w, of the 
bob-weights must of course include the weights of the reciprocating 
parts connected to them. 
As a second illustration, consider a three-cylinder engine with three 
cranks at definite angles apart, say, 120° each. A, B, and C (Fig. 698) 
are the three crank pins, and it is required to balance the reciprocating 
by bob-weights driven by cranks or eccentrics on the crank shaft in 
the planes 1 and 2. 
Imagine masses equal to the reciprocating masses to be concentrated 
at their respective crank pins. The centrifugal force of the mass at A is 
l 
Bd 
R 
$a 
Fria. 698. 
balanced by forces A, and A, in the planes 1 and 2 respectively, and 
these forces are determined as in Art. 348, p. 416. In like manner 
forces B, and B,, C, and C,, which will balance the centrifugal forces of 
the masses at B and C, are determined. R,, the resultant of A,, B,, and 
C,, also R,, the resultant of A,, B,, and C,, are determined by the 
polygons of forces shown. A crank pin d at radius 7, in plane 1, and a 
crank pin e at radius 7, in plane 2, will be the drivers for the required 
