What are those mechanisms called which are designed to conduct electric current through a rotary shaft?
There are two main components that match your description "slips rings" (which your photo shows) and a "commutator". As others have majored on slip-rings I will comment mainly on the action of a commutator.
Slip Rings provide a continuous connection from rotor to the stationary environment so that whatever you apply to the leads appears inside the rotor. Slip rings are usually used when either AC or DCV is to be fed to or from a rotor in the same manner regardless of rotor position.
A Commutator also uses brushes acting on a rotating surface but the surface is divided into a number of sectors such that the signal (or power level voltage and current) that appears "inside" a given point on the rotor will vary with rotor position OR different parts of the interior are connected to a given output lead at different times.
A commutator is usually used either as
An AC to DC converter that takes AC voltages generated inside the rotor and applies them with polarity such that a positive voltage is always connected to the positive output lead.
Such an arrangement turns an AC alternator into a DC generator.
A DC to AC converter by changing the points inside the rotor to which the fixed external DC signal is connected so that the rotor "sees" an effective AC signal.
This is usually used in a motor to create a rotating magnetic field which "chases" the stationary magnetic field generated by the appropriately named field-windings.
Wikipedia - Commutator
- A commutator consists of a set of contact bars fixed to the rotating shaft of a machine, and connected to the armature windings. As the shaft rotates, the commutator reverses the flow of current in a winding. For a single armature winding, when the shaft has made one-half complete turn, the winding is now connected so that current flows through it in the opposite of the initial direction. In a motor, the armature current causes the fixed magnetic field to exert a rotational force, or a torque, on the winding to make it turn. In a generator, the mechanical torque applied to the shaft maintains the motion of the armature winding through the stationary magnetic field, inducing a current in the winding. In both the motor and generator case, the commutator periodically reverses the direction of current flow through the winding so that current flow in the circuit external to the machine continues in only one direction.