Euler Angle

Gimbal Lock

Introduced by Steven M. Lavalle in his Virtual Reality lectures.

Gimbal lock is the loss of one degree of freedom in a three-dimensional, three-gimbal mechanism that occurs when the axes of two of the three gimbals are driven into a parallel configuration, “locking” the system into rotation in a degenerate two-dimensional space.

See Euler Angle for an example of when this happens ($\pi /2$ rotation).

Resources

• https://robotacademy.net.au/lesson/singularity-in-3d-rotation-angle-sequences/
  • had to watch a second time, but this video is so much better
• https://www.youtube.com/watch?v=zc8b2Jo7mno&ab_channel=GuerrillaCG

2023-09-29: Alright, I am getting confused again, because it seems that it was my intuition that if you have 2 same ways to encode an orientation, then you automatically have gimbal lock.

However, in Quaternions, the value and its value negated result in the same orientation…, i.e. $q=-q$

4D Space: Quaternions operate in 4D space and encode rotation as a single operation, not as sequential rotations around individual axes. This intrinsic nature avoids the conditions that lead to gimbal lock.