Which of the following kinds of valves should be used in a hydraulic system to change the direction of motion of the cylinder?

The use of a Directional Control Valve (DCV) is essential in hydraulic systems when it comes to changing the direction of motion of a cylinder. A DCV directs the flow of hydraulic fluid through different routes within the system, allowing the operator to control the actuation direction of hydraulic actuators, such as cylinders.

Directional Control Valves can be configured in various ways, such as two-position or three-position designs, enabling precision in directing the fluid flow to either extend or retract the cylinder. This ability to manage flow paths is crucial for the effective operation of hydraulic machinery, as it determines how and when the cylinder moves.

In contrast, a Pressure Relief Valve serves a different purpose by protecting the hydraulic system from exceeding safe pressure limits, thereby preventing potential damage. A Flow Control Valve regulates the speed of fluid flow but does not change the direction of that flow. Check Valves allow fluid to flow in only one direction to prevent backflow, which is not relevant to directing motion. Hence, the specific function of redirecting hydraulic flow to control the cylinder's movement is the primary reason a Directional Control Valve is the correct choice for this application.