pneumatic cylinder 85 having horizontal axis and mounted on a support 86 which is in turn supported by the rod of an underlying pneumatic cylinder 87 having vertical axis the said support 86 is rotatively anchored to the rod of the vertical cylinder 87 and associated to a relevant driving member not shown in the figures of the attached drawings moreover advantageously the vertical cylinder 87 of the means for positioning the baskets 6 in correspondence of the units 4 is mounted on a motor driven carriage 88 sliding under control onto a horizontal guide 89 located in proximity of the units 4 and developing parallel to them owing to the thus ensured handling capability of the arm 8 it is possible to pick up the baskets 6 from one or more shelves 60 on which they are positioned awaiting to reach the destination units 4 to deliver them to the respective units 4 and to remove them therefrom at the end of the cycle for dyeing the materials held therein and lying them back in the respective initial positions in case only one shelf 60 is used for the baskets 6 there is no need of rotating the arm 8 and accordingly the horizontal cylinder 85 may be fixed.