420 APPLIED MECHANICS 
accelerating force becomes negative. The force tending to displace th 
frame of the engine is at every instant equal and opposite to the 
accelerating force on the piston. It follows -that if the engine frame ie 
not bolted down it will oscillate backwards and forwards, making one 
complete oscillation for each revolution of the crank shaft.  Bolti a ; 
down the engine frame will not eliminate the oscillations, but wil 
reduce their amplitude to an amount depending on the rigidity of the 
connections and the mass of the foundations. 
It is important to understand that the disturbing forces on the frame, 
as determined above, are independent of the way in which the reciprocat-— 
ing masses are driven, whether by the action of fluid pressure on the 
piston, as in a steam-engine, or by a torque on the crank shaft, as ina . 
pump or air compressor. 
351. Effect of Transferring Reciprocating Mass to Crank Pin 
Suppose that the reciprocating parts which are connected to the crank 
pin by a slotted bar connecting-rod are removed, and . 
that a mass C of equal weight W is placed at the 
crank pin (Fig. 688). The centrifugal force of this 
revolving mass at the crank pin is Wwr/g. Let 
this force be represented by OA, and let OX be , 
the line of stroke of the reciprocating parts (now ’ 
removed). Draw AB perpendicular to OX. The Fic. 688. > 
force OA is equivalent to two forces OB and BA acting at O, OB- 
Ww?2r cos a aud BA woual ti Wo?r sin 0 
in the preceding Article that the effect of the acceleration of the recipro- 
cating parts was to cause a thrust on the crank shaft in the line of - 
Ww? cos 0 
being equal to It was shown 
stroke, the magnitude of this thrust being Hence a mass — 
equal to that of the reciprocating parts, but placed at the crank pin, has 
the same disturbing effect on the frame in the line of stroke as the reci-— 
procating parts themselves have. 
352. Changing the Direction of the Disturbing Force.—If two 
masses DD (Fig. 689) be placed on the crank arms produced so as to — 
balance the mass C referred to in the preceding Article, then at every — 
instant the component of the centri- 
fugal force of DD in the line of stroke 
will balance the component of the 
centrifugal force of C im that line. 
Hence if the mass C be removed from 
the crank pin, and the reciprocating 
parts be again connected to it, the 
thrust on the frame in the line of 
stroke, due to the acceleration of the z 
reciprocating parts, will be entirely balanced. But the centrifugal force 
of DD has a component at right angles to the line of stroke, the magni- 
tude of which tee. Goa chien aed baal 
g 7 
The effect of the balance weights DD is therefore to balance the 
disturbing force in the line of stroke, and to introduce another disturb 
Fia. 689. 
