This paper presents two distinct manoeuvres allowing an articulated robot in free fall to change its orientation using closed paths in the joint space. It is shown through dynamics simulations that the magnitude of the net rotation is dependent upon the amplitude of the angular displacement of the joints. With realistic joint limitations, the robot, which includes rotary actuators only, can perform a 180-degree reorientation about its longitudinal axis, similar to the cat righting reflex. The second manoeuvre allows the robot to accomplish rotations of smaller magnitude about a different axis. A physical prototype and a VICON motion tracking system are used to experimentally validate the simulation results. Finally, it is shown that the two manoeuvres, which yield rotations about fixed axes, can be repeated and alternated to enable the robot to reach any arbitrary 3D orientation.