A method for applying disinfectant to the teats of a dairy livestock includes determining that a stall of a rotary milking platform housing a dairy livestock is located adjacent to a track that has a carriage carrying a robotic arm. The method continues by communicating a first signal that causes operation of a first actuator such that the carriage moves along the track in relation to the rotary milking platform and independent of any physical coupling between the carriage and the rotary milking platform and in a direction corresponding to a direction of rotation of the rotary milking platform. The method concludes by communicating one or more additional signals that causes operation of one or more actuators of the robotic arm such that at least a portion of the robotic arm extends between the hind legs of a dairy livestock.