Tool-holding device for a machining tool and method for locking a tool into a tool-holder

A machining tool, comprising a retaining element provided with a pair of mutually cooperating jaws and a female seat between said jaws for a male engaging portion of a machining tip, said jaws being capable of taking a locking configuration, in which the engaging portion of the tip is firmly locked within the seat of the retaining element, and a disengaged configuration in which said engaging portion of the tip can be detached from the retaining element, wherein the tip and the female seat are configured so as to allow a snap insertion into the locking configuration of the tip within the female seat along a direction parallel to bases of the retaining element, wherein the jaws are resiliently connected at a connection end of the retaining element and the female seat is provided between the jaws at an end of the retaining element opposite to said connection end, wherein the snap insertion is brought about by an elastic force at the connection end as well as by shapes of the tip and the female seat, said elastic force causing retaining of the tip within the retaining element before the retaining element is locked in a receiving part of the machine tool, and wherein the retaining element includes an elastic element arranged astride of the two jaws and determining an elastic return of the jaws towards each other.