A mechanical system, forming 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. The support element includes an inner cavity in which the roller is at least partially arranged and which is adapted to contain an oil bath for lubricating the roller. Examples of applications for the mechanical system include a follower device, an injection pump or a valve actuator.