What is the principal functions of hydraulics surrounded by a machinery?
to move parts
I agree that it is to move parts and to transmit motive power. However, I submit that one of its primary advantages is that it can multiply force by using the effects of fluid dynamics. This is why you see hydraulics used in applications where intensely high loads are required (aircraft control surface actuation, bulldozers, moving huge counterweights, etc).
To transmit motive power, both linear and rotational, to moving components using pressurized fluid.