What is the name of the structures that pull a valve open and shut?

In the most generalized notion of a mechanical valve system, the open and shut operations are controlled by oblong lobes, called cams, that rotate on the axis of a connected shaft, called the camshaft. The rotation of the camshaft can be accomplished by any component that transfers mechanical energy, usually a moving belt or sequence of gears.
The cams and camshaft are mounted in a larger component called the engine block. Against each cam, the engine block pairs a small cylinder called a tappet. The tappets move up and down based on the rotational position of the oblong cams. Once the mechanical energy that begins in the belt or gears reaches the tappets, it's transferred to a rocker arm attached to each valve. It is the arm's rocking motion that depresses and releases the one or more valves, opening and shutting the flow channel.