A mechanical system, comprising a support element having an outer surface adapted to slide in a housing receiving the mechanical system, a pin extending along a first axis and comprising two opposite ends, each adapted to be fitted in the support element for radial and/or axial retention of the pin relative to the first axis, and a roller element movable in rotation relative to the pin around the first axis. The mechanical system comprises at least one outer insert positioned at the outer surface of the support element. The mechanical system can be integrated into either an injection pump or a valve actuator.