A mechanical system forming one of a cam follower or a rocker arm, the mechanical system comprising: a support element; a pin extending between two opposite ends along a first axis and supported by the support element; and a roller movable in rotation relative to the pin around the first axis and adapted to roll on a cam. At least one recess is formed within the pin or roller, wherein the at least one recess provides a lubricant reservoir at an interface between the pin and the roller. The mechanical system can be integrated into an injection pump or a valve actuator. The mechanical system is manufactured by forming the at least one recess within the pin or roller and assembling the parts together, wherein the recess provides a lubricant reservoir at an interface between the pin and the roller.