A mechanical system, forming a cam follower or a rocker arm, and 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. The support element includes at least a first part and a second separate part which, when fitted together, together delimit a lubricating groove on an external surface of the support element.