Has there ever been shown in Star Wars (canon or Legends, but canon preferably) a lightsaber where the emitter can move position? That is to say, that the 'head' of the lightsaber is hinged or in some other way can be moved to change the angle of the blade relative to the handle? I know that there is an example of a saber staff that hinges in the middle, however I'm more interested in cases where the moving component is as close to the blade as possible.
The Inquisitor Lightsaber from Star Wars: Rebels
I'm not sure if you'll count this as hinged, but it can certainly move the angle of the blade. In fact, it's a hand-held General Grievous, being capable of spinning in circles.
The hilt stays in position while the blade itself spins around the edge of the circle, which suggests the emitter is not directly attached to the hilt.
Their internal workings permit the plasma blades' containment field to be pliable, thus allowing for dozens of small emitters to create thin and flexible blades that could reach several meters in length. Lightwhips' blades were weaker than a typical lightsaber's, and as such had limited cutting capabilities. However, whips were able to capture or entangle opponents.
That's about as 'hinged' or independent from handle as it gets!