Three basic type of dc motor?

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For DC:

Permanent magnet brush motor; (uses fixed magnets for stator fields); toys and automotive use

Shunt field motor; (field winding has many turns of fine wire in parallel with armature) small machines;

Series field motor; (field winding has few turns of heavy wire in series with armature); high speed, high torque;

Compound field motor; (has both series and shunt fields); large machinery, general purpose workhorses;

Brushless DC motors (use electronics to switch stator windings on and off, and have permanent magnet rotors) small fans and light loads.

For single phase AC:

Split Phase induction motor (2 different windings connected to supply, cage type rotor) low torque, general purpose;

Capacitor Start induction motor; (As per split phase, but with capacitor in series with starting winding) high starting torque, general purpose;

Capacitor start, Capacitor run induction motor; (as per capacitor start, but different capacitors used for starting and running) high starting and running torque, quietest running;

Shaded pole induction motor; (run winding and copper or aluminium ring around part of iron core of stator) small, cheap motors, low torque;

Universal motor; (as per series DC motor above) high torque, high speed, poor speed stability.

For 2 or 3 phase AC (star or delta connected)

Polyphase induction motor (2 or 3 identical windings on stator, cage rotor) general purpose;

Wound rotor induction motor (2 or 3 identical windings on stator, wound rotor connected in star to 3 sliprings and external resistance unit) very high starting torque, low starting current;

Synchronous motor; (standard stator, and wound rotor connected to DC supply for 'excitation' of rotor field) constant speed, power factor correction.