Thrust reverser for an aircraft propulsion unit, this reverser comprising a fixed external structure, a movable external structure, at least one closure flap comprising a rear end articulated on the movable external structure, and a control mechanism configured to switch the reverser between: - a direct-thrust configuration wherein the movable external structure is in a closed position and the flap is in a retracted position so as to channel the flow of fluid in a conduit delimited radially outwards by the movable external structure, and - a thrust-reversal configuration wherein the movable external structure is in an open position leaving clear a radial opening, and wherein the flap is in a deployed position so as to divert at least a part (10B1) of said flow of fluid towards said radial opening, this reverser being characterised in that the control mechanism comprises at least one transmission member including first, second and third portions (51, 52, 53) connected together so as to form a triangle and extending respectively along first, second and third transmission directions (DR1, DR2, DR3) secant to one another, the first and second portions (51, 52) forming a vertex comprising a first cooperation element, the first and third portions (51, 53) forming a vertex comprising a second cooperation element, and the second and third portions (52, 53) forming a vertex comprising a third cooperation element, the transmission member being: - connected to the movable external structure by a first articulation cooperating with said first cooperation element so as to allow a rotation of the transmission member with respect to the movable external structure about a rotation axis of this first articulation, - connected to the fixed external structure by a first connection member, the transmission member being articulated on said first connection member by a second articulation cooperating with the second cooperation element, the first connection element being configured so as to rotate the transmission member about the rotation axis of the first articulation in a first direction when the movable external structure is moved towards the open position and in a second direction when the movable external structure is moved towards the closed position, - connected to the flap by a second connection member, the transmission member being articulated on said second connection member by a third articulation, cooperating with the third cooperation element, the second connection member being configured so as to move the flap towards the deployed position when the transmission member is moved in said first direction and towards the retracted position when the transmission member is moved in said second direction. - a direct-thrust configuration wherein the movable external structure is in a closed position and the flap is in a retracted position so as to channel the flow of fluid in a conduit delimited radially outwards by the movable external structure, and - a thrust-reversal configuration wherein the movable external structure is in an open position leaving clear a radial opening, and wherein the flap is in a deployed position so as to divert at least a part (10B1) of said flow of fluid towards said radial opening, - connected to the movable external structure by a first articulation cooperating with said first cooperation element so as to allow a rotation of the transmission member with respect to the movable external structure about a rotation axis of this first articulation, - connected to the fixed external structure by a first connection member, the transmission member being articulated on said first connection member by a second articulation cooperating with the second cooperation element, the first connection element being configured so as to rotate the transmission member about the rotation axis of the first articulation in a first direction when the movable external structure is moved towards the open position and in a second direction when the movable external structure is moved towards the closed position, - connected to the flap by a second connection member, the transmission member being articulated on said second connection member by a third articulation, cooperating with the third cooperation element, the second connection member being configured so as to move the flap towards the deployed position when the transmission member is moved in said first direction and towards the retracted position when the transmission member is moved in said second direction.