In the past the usual method of dealing with the articulated rod has been to treat the problem graphically. Although this method may be sufficiently accurate for a first approximation the inherent difficulties often lead to serious errors after the first few stages. A graphical method is always sufficiently accurate to determine the travel of a piston operated by an auxiliary rod ; but, the double differentiation of the displacement curve by graphical means (to obtain the acceleration curve), is not only inaccurate but a long and tedious operation.

To remedy this defect a Fourier's series has been developed which can be differentiated at sight and which gives a remarkable accuracy.

The geometrical properties of the mechanism have been analysed and thus equations are formed giving the resultant radial and tangential components at the crank pin, the bending forces and tensions on the master rod, etc.