The mechanism comprises a body, a drive member movable in the body, a main spring that is loaded when a dose is set and is released for moving the drive member during a delivery of a dose, and a movable trigger inhibiting a movement of the drive member, a movement of the trigger releasing the main spring and the drive member. The trigger is moved from a start position to an end position relative to the body during a setting of a dose, the end position having a distance from the start position that increases as the dose set increases.