Analogies are especially useful in analysing mechanical filters. A mechanical system by itself can be so represented, but analogies are of greatest use in electromechanical systems where there is a connection between mechanical and electrical parts. Mechanical–electrical analogies are used to represent the function of a mechanical system as an equivalent electrical system by drawing analogies between mechanical and electrical parameters. In the mobility analogy the topology of networks is preserved, a mechanical network diagram has the same topology as its analogous electrical network diagram. The mobility analogy does not preserve this analogy between impedances across domains, but it does have another advantage over the impedance analogy. For instance force/velocity is mechanical impedance. In the impedance analogy, the ratio of the power conjugate variables is always a quantity analogous to electrical impedance. Another variation is required for acoustical systems here pressure and voltage are made analogous (impedance analogy). It is perfectly possible that both versions of the analogy are needed in, say, a system that includes rotating and reciprocating parts, in which case a force-torque analogy is required within the mechanical domain and a force-torque-voltage analogy to the electrical domain. In the impedance analogy, instead of force, torque is made analogous to voltage. Variations of these analogies are used for rotating mechanical systems, such as in electric motors. In the impedance analogy, for instance, this results in force and velocity being analogous to voltage and current respectively. These are variables which when multiplied together have units of power. A common choice is to make pairs of power conjugate variables analogous. By itself, that is not enough to fully define the analogy, a second variable must be chosen. The impedance analogy makes force and voltage analogous while the mobility analogy makes force and current analogous. There is no one, unique way of doing this numerous analogies are theoretically possible, but there are two analogies that are widely used: the impedance analogy and the mobility analogy. Mechanical–electrical analogies are developed by finding relationships between variables in one domain that have a mathematical form identical to variables in the other domain. For this reason domain-neutral terminology is preferred when developing network diagrams for control systems. A given system being represented by an electrical analogy may conceivably have no electrical parts at all. Electrical analogies are particularly used by transducer designers, by their nature they cross energy domains, and in control systems, whose sensors and actuators will typically be domain-crossing transducers. It has the major advantage that the entire system can be represented in a unified, coherent way. Nowadays, analysis by analogy is a standard design tool wherever more than one energy domain is involved. However, the technique can be used to solve purely mechanical problems, and can also be extended into other, unrelated, energy domains. This approach is especially useful in the design of mechanical filters-these use mechanical devices to implement an electrical function. Theoretical developments in the electrical domain that were particularly useful were the representation of an electrical network as an abstract topological diagram (the circuit diagram) using the lumped element model and the ability of network analysis to synthesise a network to meet a prescribed frequency function. However, as electrical network analysis matured it was found that certain mechanical problems could more easily be solved through an electrical analogy. James Clerk Maxwell introduced analogies of this sort in the 19th century. At first, such analogies were used in reverse to help explain electrical phenomena in familiar mechanical terms. Mechanical–electrical analogies are the representation of mechanical systems as electrical networks. For other uses, see Analogy (disambiguation).
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