A transmission assembly including a transmission member and an oil distribution system. The transmission member includes a rotary pivot, and a pivot portion for pivoting about the rotary pivot; the oil distribution system is to receive oil feed and to transfer it to an oil reception chamber of the rotary pivot; the rotary pivot includes injection orifices putting the oil reception chamber into fluid flow communication with the gap between the rotary pivot and the pivot portion to form a fluid bearing; and the transmission assembly is for injecting oil into the gap at a first pressure into an outer portion of the gap, and at a second pressure into an inner portion of the gap, the second injection pressure being different from the first injection pressure.