Hydraulic machine includes: a casing; a piston slidable therein and separating two chambers; hydraulic switching elements for supplying liquid to and for evacuating the chambers, including at least one connecting rod acting on a distribution member which can adopt two stable positions; and initiating elements having a pusher which, at the end of the piston stroke, can cause a sudden change in the position of the switching elements, under the action of an elastic member to reverse the stroke. Each end of the elastic member is secured to an articulation member respectively accommodated in a housing provided on the connecting rod and on another moving part, each housing being open in a direction substantially opposed to the direction of the force exerted by the elastic member, such that each articulation member can be removed from its open housing against the action of the force, thereby simplifying assembly and disassembly.