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I was watching the video Gimble Lock - Explained, by videodumper, about the gimbal lock problem. I understood that during rotations it could happen that one DOF disappear. Looking at the middle part of the video (min 3.22) can be seen that two planes are stuck in only one plane. For this reason performing rotations along X axis is the same of performing rotations along Z axis.

Why are these two planes stuck together? For my imagination it does not seem so complicated to separate them and to continue having 3 DOFs. But I think that something eludes me...

Emilio Pisanty
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Enrico123
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1 Answers1

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The planes are not deliberately stuck together - they just happen to coincide when one rotation (by 90 degrees) has dragged one plane of rotation to coincide with another. After that, you can no longer distinguish between rotation about the two axes whose planes coincide - so you have gone from three degrees of freedom to just two.

When this happens, you can no longer describe an arbitrary motion for the next moment in time - there are certain directions of motion that cannot be described (if you think of rotation as a vector pointing "somewhere" in space, you cannot reach every direction in space with just two basis vectors).

Even when you "unlock", and there are once again three distinct directions, two of the basis vectors point in almost the same direction - which means that certain rotations can only be described by the superposition of very large (and nearly opposite) rotations about the two axes that are nearly parallel.

This just makes the problem of describing motion with these axes ill-conditioned. And that is what is called gimbal lock.

Emilio Pisanty
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Floris
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