When working with animating a rig, quaternions are often used for rotations. However sometimes we need to clear rotation along given local axis of a joint. With quaternions it's not as simple as just clearing out one component of the quaternion. Doing this will clear out the rotation along that axis, but it will also affect rotation along other axes since the W value of quaternion is interdependent on all three axes.
Take Blender3D as example. You can key a euler rotation for a given joint. If you then are not satisfied with rotation along say Y axis, you could just remove Y rotation channel for the whole animation. With quaternions this does not work as well.
How do animators and riggers handle this problem?