In reciprocating engine mechanism, our major headache is to balance primary unbalance force along the line of stroke and this force also produces swaying couple. In reciprocating engine mechanism having two cylinders, unbalance force present along the line of stroke and makes a couple about center line YY between cylinders. The ability of this couple is to produce swaying effect in vertical axis and tends to bend engine either in clockwise or in anticlockwise direction.
For that consider a be the distance between two cylinders.
Swaying couple = [ (1 – c)mω2.r. cos θ x a/2 ] – [ (1 – c)mω2.r. cos (90° + θ) x a/2 ]
Swaying couple = (1 – c)mω2.r. a/2. (cos θ + sin θ)
By taking its derivative we know that swaying couple is maximum at 45° or 225°. After putting θ value in the above expression
Swaying couple =
The effect of swaying couple is more harmful than oscillating couple so we take the value of c from 2/3 to ¾ for two cylinder locomotives.