Abstract: A device for moving a back rest in weaving machines includes two movable supporting mechanisms between which the back rest is mounted, an eccentric for moving the supporting mechanisms and whose eccentricity can be modified, and a driving wheel for driving the eccentric. A mechanism provided between the driving wheel and the eccentric permits a continuous setting of the phase of the eccentric in relation to the driving wheel. The mechanism includes a seating formed in the driving wheel, an element which fits in the seating and which can be axially turned in relation to the driving wheel to which the eccentric is coupled, and a clamp for clamping the element at any required angular position in the seating.