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What is the quadrature counting as applied to process control applications?

Quadrature is a method which senses distance or amount and direction.  Applied primarily in 2 ways.  Quadrature encoders may be either direct coupled  to a motor through a flange amounted coupling or they may be used  with a measuring wheel that is directly connected to the encoder shaft itself.  If it is direct coupled to a motor, the encoder will track the motor`s operation, both motor shaft distance traveled and motor shaft direction, and report that information in the form of an electronic pulse train back to an electronic count control device.