1919.] Jenkinson.—Engine-balancing : The Connecting-rod. 
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ENGINE-BALANCING : THE CONNECTING-ROD. 
By S. H. Jenkinson, Railway Department. 
The theory of engine-balancing has hitherto been incomplete from the 
lack of an exact method of treating the connecting-rod. This is of less 
importance in the case of multi-cyclinder balanced engines where the 
various rods are in opposed phase and their various disturbing forces 
have a zero resultant; but for the case of one- or two-cyclinaer and 
other unbalanced engines it is satisfactory to be able to bring forward a 
simple exact method of evaluating all the inertia forces of the connecting- 
rod. 
The difficulty lies in the fact that one point in the rod reciprocates 
with the crosshead and another revolves in a circle with the crank-pin, 
while all other points have a motion compounded of these two. The 
most obvious method of attack is to attempt to divide the whole weight of 
the rod into two parts, one concentrated at the crosshead-pin and one at 
the crank-pin, which would together generate the same inertia forces as 
the whole rod. This leads, however, to an indeterminate result, since 
that division of the parts which gives correct values for the horizontal 
components gives incorrect values for the vertical components, and vice 
versa. The deadlock was only surmounted by the individual designer 
choosing that compromise which best suited his personal intuition on the 
subject. The difficulty, however, disappears if the rod is treated as a 
whole, and the horizontal and vertical components separately evaluated 
for the engine. 
Let AB in fig. 1 represent the centre-line of the rod, and BN a 
perpendicular drawn from the crank-pin B on to the line of stroke AO. 
Denoting the crank-angle BOA by 0, the crank-radius OB by r, the 
linear velocity of the crank-pin by v, and the length of the connecting- 
rod by l, we have 
Horizontal component of velocity of B 
d d dO . A 
= ~1t 0N = - Tt r eos 6 = r sin e di~ ° sm 0 ' 
