If the speed of the pistons in their path along the cylinders was constant then the laws of Harmonic Motion would apply - but the fact it, they do not. From TDC (Top Dead Centre) the piston travels more than half the length of its stroke in the first 90' of the crankshaft rotation, then it travels relatively slowly while the big end of the connecting road traverses the bottom 180' of the crank throw - then it speeds up rapidly for the return up the cylinder. The figure below illustrates this:

So far from being a  smooth harmonic motion, the speed of the piston varies: fast - slow - slow - fast for every crankshaft rotation. At the same time that two pistons are travelling fast, two others are travelling slowly and so there is a net upward force - the Secondary balance. The diagram below illustrates the four cylinder engine with the two forces:

The net effect is a vibration in the vertical plane at a frequency twice that of the speed of the crank. In a three cylinder engine with throws at 120' the Secondary forces cancel out - like this:

Although three cylinders sounds odd, in fact it has a very good Primary and Secondary balance: the one piston exerting force is balanced by the other two. Since a V6 or Straight 6 engine can be seen as a double 3 cylinder engine, this explains why it is much smoother than a four cylinder engine of the same capacity and why it is used in more expensive cars where refinement is expected.

It is to defeat the Secondary forces that vehicle designers have spent millions developing more absorbent engine mountings. These isolate the vehicle interior from the 'boom' which is felt and heard at certain higher speeds in four cylinder cars and which is conspicuously absent in those with six cylinders. However, even hydraulic engine mountings used in Fords have their limits - and the larger the engine capacity, the greater the mass of the pistons and the greater the Secondary vibration.

Even so, the Ford 2.3 litre DOHC was noted by many motoring journalists as a very quiet, refined engine. So what is going on here? The answer was provided by a certain Mr Lanchester in 1911.

Secondary Balancer