to determine the movements of the heald frames under the control of the reading unit a and comprises vertical control rods 5 controlled by horizontal needles 6 subjected to the actions of the rockers 4 and of return springs 7 in order to establish and remove the engagement with lifting blades 9 by way of upper end hook portions 8 it also comprises hooks 10 pivoted at 10 39 to the ends of rocker levers 11 which in their turn are pivoted at 11 39 to the centre of transmission levers 12 which operate lever systems 13 for controlling the heald frames the vertical rods 5 engage with the hooks 10 in order to raise them and lower them in accordance with commands received from the rockers 4 of the reading unit a the hooks 10 engage with fixed knives 14 and mobile knives 15 in order to control the rocker levers 11 engagement with the fixed knives 14 occurs when the rods 5 raise the hooks under the control of the lifting blades 9 with which the hook portions 8 cooperate engagement with the mobile knives 15 occurs when the rods 5 do not exert positive force on the hooks the movements impressed by the rocker levers 11 and transmission levers 12 on the lever systems 13 and thus on the heald frames leading to the formation of the shed derive from the combination of these engagements and the law governing the movement of the mobile knives 15 it should be noted that in reality the fixed knives 14 have only their axes fixed in the sense that they undergo oscillations about this latter for the purpose of facilitating their engagement with the hooks in contrast besides undergoing similar oscillation about their axes again to facilitate engagement.