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What is a commutator?

What is a commutator? Here are some definitions.

Noun
  1. An electrical switch, in a generator or motor, that periodically reverses the direction of an electric current.
  2. (group theory) A binary map in a given group G, given by [g, h] = ghg−1h−1, where g and h are elements of G, which yields the group's identity if and only if the group operation commutes for g and h.
  3. (ring theory) A binary map in a given ring R, given by [a, b] = ab − ba, where a and b are elements of R, which yields the ring's zero element if and only if the multiplication operation commutes for a and b.
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Examples
The commutator must switch current to the correct drive magnets in the correct direction at the correct time in order to produce desired rotor movement.
One part supports the slider means H1-H5 and the other part functions as an equipoise to facilitate or enhance the rotating movement of the commutator arm.
One of the places you need them is in modern small motors which don't have a commutator.
Note how the commutator reverses the current each time the coil turns halfway.
He went on to build an electric motor in 1832 and invented the commutator, an integral part of most modern electric motors.
Take the armature off the motor and connect the commutator wires to a dry cell battery.

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