A pulling mechanism for controlling the heald frames of a loom equipped with a shedding machine includes a set of connecting rods and oscillating levers (72) coupled to the set of connecting rods, for each heald frame, for returning a movement of the shedding machine to the heald frame. The pulling mechanism includes at least one measuring portion (72C), equipped with a target (100) configured to interact with a sensor (110). For easier mounting and dismounting of the targets on the measuring portions, each measuring portion is provided on a peripheral wall of one of the oscillating levers (72), or a stabilizer of the pulling mechanism, the target being reversibly mounted on the measuring portion (72C).