You can use the Transform tool on a keyframe of the Animation Curves docker, using an animated transform mask. Then the transform (only Free Transform can be used) will be interpolated along the frames during playback.
See this animation as an example of what animation curves can do:
Paint in haste, erase at leisure
Note: That is not a ‘recorded’ movement, it’s a ‘controlled’ movement where you tell it where to move/rotate/etc at which keyframe, then it interpolates between the keyframes for each frame of playback.