The lubrication, cooling, etc., of a machine which cannot run flooded with fluid, or almost so, presents a problem when the machine is subject to changes of orientation, because the intake pipe of a fluid delivery pump or the like is starved except for one attitude of the machine when the pipe end is at the bottom. This problem is solved by the provision of a rotary sump in the form of an annular channel with inturned side walls. The fluid pick-up dips into the body of fluid maintained in the channel by centrifugal force and may be connected to a pump inlet or may be self pressurizing by exploiting the ram effect. The submerged end of the pick-up may be of hydrofoil section to counteract fluid starvation by the plowing of a channel in the fluid. As far as possible, the channel surrounds rotary parts of the machine, to gather fluid flung off by them, the examples described being toroidal race rolling friction variable ratio transmission units. Rotating parts not so enclosed are surrounded parts of the casing, shaped to direct fluid towards the rotary sump. The sump may be replenished from a fluid supply maintained at a predetermined pressure applied to a duct dipping into the fluid in the rotary sump to a depth where the centrifugal head of the fluid equals the predetermined pressure for chosen conditions of sump speed etc. If the sump level falls, the centrifugal head is insufficient to prevent fluid entering the sump through the replenishment duct. Otherwise the pressure at the duct outlet is either in balance or the centrifugal head exceeds the predetermined pressure. A closed-circuit assembly of machines is illustrated, having a driven machine running flooded with fluid with a scavenge pump providing the pressure for the replenishment duct of the rotary sump. A fluid cooler may be inserted in the circuit.