For another real-world model, let's try to rotate a gimbal locked a cylinder from a vertical position to a horizontal one. Problems like this come up all the time in complex animations, as orientations change so often, that gimbal lock is bound to come up eventually.
This is important as it is a very simple example, yet it highlights one of the major issues with Euler angles and gimbal lock, unexpected animation paths.
It's somethat difficult to see (you can tell if you look at how diagonal the cylinder looks about halfway through the animation), but due to gimbal lock the cylinder takes a slightly curved path, as the axis that would normally allow direct rotation is locked.
Slight issues like this might seem trivial, but in complex animations they can be significantly disorienting, especially when objects flip 180 degrees unexpectedly (which I haven't been able to replicate myself, but which I have seen happen in more complex animations).
Note: the numbers (and calculations) aren't really important because the issue is not in the gimbal lock itself, but the frame interpolation.
However they are located here
Gimbal Lock Version
The quaternion version is using Spherical Linear Interpolation or Slerp, which is a cool algorithm which allows "constant-speed motion" with quaternion rotations, and which does not suffer from gimbal lock style issues (as linear interpoliation over quaternions, unlike linear interpolation over Euler angles, does not lead to points of visual discontinuity).
- Another video showing gimbal lock I made is located here