Hydraulic Chairs Mechanism

What mechanisms are used in raising or lowering chairs with hydraulic lifts?

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...based on Pascal's principle, which states that the pressure change is the same at all points in the liquid. The way that this operates is that with an applied force of magnitude Fi exerted on the input piston whose area is Ai (on the left), the incompressible liquid in the device exerts an upward force of magnitude Fo on the piston on the right (the output piston), that has an area Ao. The applied force, Fi and the exerted force, Fo produce a change in pressure in the liquid that is given by

So the output force Fo exerted on the load must be larger than the input force Fi, if Ao>Ai.
Also, if the input piston is moved downward a distance di, then the output piston will move upward a distance di such that the same volume V of the incompressible liquid is displaced at both pistons.

V = Aidi = Aodo

So what all of this means is that a given input ...