Gimbal Lock

When representing rotation with Euler angles, one angle reaching 90° makes two rotation axes coincide, losing a degree of freedom.

Gimbal lock was originally a mechanical problem: when a three-ring nested gimbal reaches a certain angle, two of its rotation axes become parallel, and the mounted platform loses its ability to rotate in one direction. The same phenomenon shows up mathematically when orientation is represented with Euler angles or roll-pitch-yaw angles: when pitch reaches ±90°, yaw and roll end up rotating about the same axis, so adjusting either one has the same effect, and certain small rotations nearby can't be expressed as a small change in the angles at all — interpolation and differentiation both develop discontinuities near this point. The inertial measurement platform on Apollo 11 was limited by exactly this: by design, the platform would lock once pitch neared 85°, requiring the crew to manually steer the spacecraft away from that attitude. The standard fix in robotics is to store and compute orientation with quaternions, rotation matrices, or a 6D rotation representation, and reserve Euler angles for human-readable display only; a policy trained to regress Euler angles directly can also learn discontinuous actions near these singular points.

ExampleControlling an arm's end-effector orientation with roll-pitch-yaw angles, setting pitch to 90° reveals that adjusting yaw and adjusting roll both rotate the gripper about the same axis — achieving a small rotation in the other direction requires all three angles to jump by a large amount at once.

Also called

Gimbal Lock Singularity

Related

Euler Angles · Roll-Pitch-Yaw (RPY) · Quaternion · 6D Rotation Representation · Rotation Matrix · Singular Configuration (Kinematic Singularity)

Sources

Gimbal lock - Wikipedia