How does a linear acuator in flight control work?
There are several types of linear actuators. The main three types are Pneumatic, Lead Screw Driven, and Hydraulic Linear actuators. In addition there are also solenoids and stuff but the three main types are used in heavy mechanical applications.
The one in the picture looks like a Hydraulic Linear actuator. The way hydraulics work is that the pressurized non-compressible liquid is forced into a cylinder using a pump. The pressurized liquid then moves a sliding wall inside of the cylinder. The sliding wall is also connected to the main shaft. When the liquid is pushed from one side, the sliding wall inside of the cylinder moves as the liquid pushes onto it, thus moving the main rod in and outside depending on the configuration.
Hydraulic linear actuators are used for mechanisms that reqiuire precision and high force / torque. İn this case, we want the rudder to move on a hinge that is placed on the root of the rudder. The linear actuator is placed on an lever that is offset compared to the hinge. Then, when the linear actuator moves, the linear movement converts to rotational movement and rotates the rudder surface.
Here is an image to help.