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Gimbal lock

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In gyroscopic devices controlled by Euler mechanics or Euler angles, gimbal lock is caused by the alignment of two of the three gimbals together so that one of the rotation references (pitch/yaw/roll, often yaw) is cancelled. This would require a reset of the gimbals using an outside reference. It may also be described as the situation when all three gyros hit the limits of their ability to move within the sensing mechanism - they hit hard stops and stop moving around.

For example, an airplane uses three references, pitch (angle up/down), yaw (angle left/right on a vertical axis) and roll (angle left/right on the horizontal axis). If an airplane heads straight up or down (change of pitch), one other reference (the yaw) is cancelled, one loses a dimension of rotation, because there is always a value for one angle of rotation that yields infinite values of the other two angles (in this case, the yaw). A solution to this problem is the implementation of an extra gimbal in the INS-platform. This reduces the statistical chance of gimbal lock to almost zero.

Compare a similar problem with tangents on triangles -- say one has a right triangle ABC, with angle ACB=90°. Consider angle BAC. tan(BAC) = BC/AC, but BAC is less than 90°. We can make angle BAC closer and closer to 90 degrees by increasing the length of BC, but as we keep doing this, AC stays the same so the ratio BC/AC gets infinitely large. So tan(90°) has no geometric meaning. Two legs of the triangle become infinitely long and never meet one another.

Another real world comparison is latitude and longitude. At the poles (latitude 90° north or south), the definition of longitude becomes meaningless (as all longitude lines meet at a point or singularity).

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