the frame 12 of the weaving mechanism the second pulleys 9b of the two tackle assemblies 9 of the two devices a and b and pulley 10 are engaged by another cord 13 of which one of the ends 13a is attached to a fixed point 12a of the frame 12 while its other end 13b carries a snap 14 which constitutes the collar to which at least one heddle 15 is fixed a double tackle assembly is thus produced enabling the three desired positions of the collar 14 to be obtained namely a low position corresponding to the lower position of the warp yarns fig1 a horizontal or intermediate position thereof fig2 and a high or upper position of these yarns fig3 when the warp yarns are to be in low position fig1 the arms 1a of devices a and b are pressed so that knife 4a does not engage the corresponding barbs 1b when the griffe frame 4 rises similarly the hooks 2 are pressed so that barbs 2b are engaged by the knife 3a corresponding to the griffe frame 3 when it rises in this way the collar 14 remains in the low position and all the hooks 1d 2d of devices a and b rest on.