A method for applying disinfectant to the teats of a dairy livestock comprises moving a robotic arm along a track in relation to a rotary milking platform housing a dairy livestock and independent of any physical coupling between the robotic arm and the rotary milking platform. The rotary milking platform has a substantially circular perimeter. The track is positioned outside the perimeter of the rotary milking platform. At least a portion of the track is straight and offset in relation to the rotary milking platform. The robotic arm comprises an arm member operable to pivot about an axis that is parallel to the track, and a spray tool attached to one end of the arm member. The method further comprises extending the robotic arm between the hind legs of the dairy livestock while the rotary milking platform rotates such that the spray tool is located at a spray position from which it may discharge disinfectant to the teats of the dairy livestock.