A New Analogy Between Mechanical and Electrical Systems

By considering each mass in a linear mechanical system as having two terminals, one fixed in the mass and one fixed to the frame of reference, every linear mechanical system is reduced to a multiplicity of closed mechanical circuits to which force and velocity relations similar to Kirchhoff's laws, may be applied. The conventional mechanical-electrical analogy is derived from the similarity of the equations v = f/z and I = E/Z. It is incomplete the following respects which lead to difficulty in its application. I. There is a lack of analogy in the use of the words “through” and “across” which indicates a fundamental difference in the nature of the analogous quantities, for instance, force through and e.m.f. across. II. Mechanical elements in series must be represented by electrical elements in parallel, and vice versa. III. Mechanical impedances in series must be combined as the reciprocal of the sum of the reciprocals while electrical impedances in series are additive. IV. There is an incompleteness the mechanical analogues of Kirchhoff's laws. The new analogy is derived from the similarity of the following equations: v = fz̄ and E = IZ where z̄ is the reciprocal of the mechanical impedance as usually defined. This new analogy is complete in all of the above-mentioned respects in which the old analogy failed. It leads to analogous relations of a simple sort and permits an equivalent electrical circuit to be drawn in an easy intuitive manner.