How does a landing gear work?

No.

This question probably stems from a misunderstanding of a term. Likely came from the fact that the undercarriage of an aircraft is often referred to, at least in the U.S. as Landing Gear.

Answer 2Aircraft landing gears can have gears similar to a car's rack and pinion steering mechanism that turns the lower piston of the Nose landing gear. The rack and pinion would be operated with hydraulic pressure. Reference Airbus airliners.

The first answer seems to refer to the retract mechanism. Most gears are retracted and extended using some hydraulic power and the kinematic design of the strut and its links and pivot points.

The Concord had a mechanism that pulled up the Main landing gear to make it shorter just before it rotated into the wheel well during Retraction. Otherwise, the gear was too long to go inside the wheel well. I'm not sure exactly how this worked but I think it was with the use of a mechanical linkage that may have used a bell crank or a gear.

I don't know of any Landing Gear that uses a ball-screw actuator to retract and extend it, which is commonly used for flight controls.