Coreless DC motors

Nothing in the design of any of the motors described above requires that the iron (steel) portions of the rotor actually rotate; torque is exerted only on the windings of the electromagnets. Taking advantage of this fact is the coreless DC motor, a specialized form of a brush DC motor. Optimized for rapid acceleration, these motors have a rotor that is constructed without any iron core. The rotor can take the form of a winding-filled cylinder inside the stator magnets, a basket surrounding the stator magnets, or a flat pancake (possibly formed on a printed wiring board) running between upper and lower stator magnets. The windings are typically stabilized by being impregnated with epoxy resins.
Because the rotor is much lighter in weight (mass) than a conventional rotor formed from copper windings on steel laminations, the rotor can accelerate much more rapidly, often achieving a mechanical time constant under 1 ms. This is especially true if the windings use aluminum rather than the heavier copper. But because there is no metal mass in the rotor to act as a heat sink, even small coreless motors must often be cooled by forced air.
These motors were commonly used to drive the capstan(s) of magnetic tape drives and are still widely used in high-performance servo-controlled systems.

Linear motors
A linear motor is essentially an electric motor that has been "unrolled" so that, instead of producing a torque (rotation), it produces a linear force along its length by setting up a traveling electromagnetic field.
Linear motors are most commonly induction motors or stepper motors. You can find a linear motor in a maglev (Transrapid) train, where the train "flies" over the ground.

Doubly-fed electric motor
Doubly-fed electric motors or Doubly-Fed Electric Machines have two multiphase windings, with at least one of the winding sets electronically controlled for synchronous operation from sub-synchronous to super synchronous speeds. As a result, doubly-fed electric motors are synchronous machines with an effective constant torque speed range that is twice synchronous speed for a given frequency of excitation. This is twice the constant torque speed range as Singly-Fed Electric Machines, which have only one active winding set. In theory, this attribute has attractive cost, size, and efficiency ramifications compared to Singly-Fed Electric Machines but Doubly-fed motors are difficult to realize in practice.
The Wound-Rotor Doubly-Fed Electric Machines, the Brushless Wound-Rotor Doubly-Fed Electric Machine, and the so-called Brushless Doubly-Fed Electric Machines are the only examples of synchronous doubly-fed electric machines.

Singly-fed electric motor
Singly-fed electric motors or Singly-Fed Electric Machines incorporate a single multiphase winding set that actively participate in the energy conversion process (i.e., singly-fed). Singly-fed electric machines operate under either Induction (i.e., Asynchronous) or Synchronous principles. The active winding set can be electronically controlled for optimum performance. Induction machines exhibit startup torque and can operate as standalone machines but Synchronous machines must have auxiliary means for startup and practical operation, such as an electronic controller. Singly-fed electric machines have an effective constant torque speed range up to synchronous speed for a given excitation frequency.
The Induction (Asynchronous) motors (i.e., squirrel cage rotor or wound rotor), Synchronous motors (i.e., field-excited, Permanent Magnet or brushless DC motors, Reluctance motors, etc.), which are discussed on this page, are examples of Singly-fed motors. By far, Singly-fed motors are the predominantly installed type of motors.