A crimping machine system including a set of crimping jaws placed in a circular array and defining a central axis; a flange structure configured to move in parallel with said central axis; a first power transmitting member equipped with inclined guide surfaces, placed between the jaws and the flange structure, and forcing the jaws to move radially towards the central axis; a circular structure configured to rotate around said central axis; and a second power transmitting member equipped with helical guide surfaces and placed between the circular structure and the flange structure, wherein while the circular structure rotates around the central axis, said power transmitting member is configured to force the flange structure to move in parallel with the central axis.