从阿波罗13到gimbal lock，哈哈，各位请慢用……

WHAT IS GIMBAL LOCK?

================== ONE 华丽的分割线=======================

Newsgroups: sci.space.shuttle
From: Henry Spencer
Subject: Re: What is "gimble lock" in Apollo 13
Date: Sat, 30 Dec 1995 18:09:53 GMT 
 
In article <30E472AC.6D67 writes:

>It's obviously a bad thing.  Can someone give me an explanation?
It's hard to do in a few words...

Old-style inertial-guidance systems used a "stable platform", held in a
fixed orientation in space by gyros.  To do this, the connection between
platform and spacecraft needs to be able to rotate in several directions
at once.  This is done by putting several gimbals in between platform and
spacecraft, each one a ring which rotates on pivots supported by the
next-biggest ring and in turn supports the pivots for the next-smallest
ring.

Three gimbals is the minimum for free movement in any direction, since
there are three axes on which rotation can occur.  However, if the gimbals
are moved suitably, you can line up the innermost pivots with the
outermost pivots... in which case those two can only handle one axis, and
so there is an axis which neither those two nor the third can handle.  If
there is then a rotation around that axis, the result is loss of the
platform's stable orientation.  That's gimbal lock. 
 
Adding a fourth gimbal gives enough extra freedom of motion that the
problem goes away.  However, each gimbal also adds complexity, bulk, and
weight.  For Apollo, the decision was to use only three gimbals and rely
on the astronauts to avoid sequences of rotations that would produce
gimbal lock.  This was normally not a problem, but became a troublesome
complication when Apollo 13 had attitude-control difficulties after the
tank rupture.
--
Look, look, see Windows 95.  Buy, lemmings, buy!   |       Henry Spencer
Pay no attention to that cliff ahead...            |   henry@zoo.toronto.edu

================== TWO 华丽的分割线=======================

Question: What is meant by the term gimbal lock?

--------------------------------------------------------------------------------
Message:
I was recently watching the movie Apollo 13 and noticed that the
astronauts were frequently complaining of going into "gimbal lock". 
What does that mean exactly?  I assume it has something to do with
tumbling out of control in all three planes or a state in which the
gyroscopes fail to stabilize the spacecraft.  Any illumination on the
subject would be appreciated.

George F.
--------------------------------------------------------------------------------

Answer: What is meant by the term gimbal lock?
Posted By: Adrian Popa, Directors Office, Hughes Research Laboratories
Area of science: Engineering
--------------------------------------------------------------------------------
Message:
Greetings:

A gyroscopic stabilized instrument in a spacecraft is designed to maintain a specific reference direction (vector) in three dimensional space so that the pilots or other automatic control mechanisms can determine from the instrument in what spatial direction the vehicle is oriented relative to the reference direction and make corrections to the systems if required.. For example the solar cell arrays on the MIR space station must always face the sun to generate maximum battery charging power. A control gyro is referenced toward the sun so that no matter how the space station maneuvers, the control systems or the pilots can determine what corrections to the vehicle orientation or solar cell panels or both are required to keep the solar panels pointed toward the sun. .This would be a continuous, boring and time wasting job for an astronaut so automatic controls are designed to perform the sun tracking job 24 hours a day even when the spacecraft is in the earth's shadow so that the solar arrays are always correctly aimed toward the sun when the spacecraft emerges from the earth's shadow.

When a spacecraft makes a maneuver that a gyrostabilized instrument cannot follow, the situation is called a gimbal lock and the gyroscope looses the reference direction and it begins to tumble out of control (the spacecraft may also begin to tumble) and the instrument (and perhaps the spacecraft) must be reset in the reference direction and the sun re acquired. This correction may take a few minutes, hours or days depending on the system design and the cause of the gimbal lock problem.

How a gimbal lock occurs is a three dimensional problem that I will try to describe in words; however, it would be better to have a model to experimentally follow my discussion.

To help understand the gimbal lock condition I'm going to turn the problem around and have the gimbals track a moving object relative to a fixed reference plane. A camera tripod, a surveyor's telescope and tracking radar antennas use two axis gimbal systems that are called AZ-EL mount s (Azimuth-Elevation). Let's use the surveyor's telescope for our thought experiments. The top of the tripod holding the telescope is leveled with the horizon (reference plane) so that a vertical rotation axis (Azmithual axis) is perfectly vertical (normal) to the ground plane. The telescope can then be rotated around 360 degrees in azimuth so that it can scan the horizon in all the directions of the compass.. Zero degrees azimuth is usually set toward a heading of true north. A second horizontal axis parallel to the ground plane, the elevation axis, enables the telescope to be rotated in elevation upward or downward from the horizon. The horizon is usually set at zero degrees and the telescope can be rotated +90 degrees upward in elevation so that it is looking straight up toward the zenith or rotated -90 degrees downward so that it is looking vertically at the ground plane. Some surveyor telescopes (including the one we are using in our experiment) are designed be able to be rotated over the top to set points on the horizon in the opposite,180 degrees apart, directions in azimuth (e.g. North east over the top to south west). In the AZ-EL system every point in the sky (and the ground) can be referenced by only ONE unique pair of azimuth and elevation readings. For example an azimuth of 90 degrees and elevation of 45 degrees specifies a point exactly due east of the telescope and in a skyward direction half way up toward the zenith.

Now let's say that we detect a high flying aircraft, one we cannot see without the telescope, near the horizon, due east from the telescope (AZ = 90 degrees, EL = 10 degrees) and we follow it (track it) as it comes directly toward us. The azimuth angle stays at 90 degrees and the elevation angle slowly increases. As the aircraft comes closer the elevation angle increases more rapidly and the azimuth direction begins to rotate toward the north. As the elevation angle reaches 85 degrees the aircraft passes us slightly to the north of and we quickly track it by rotating the azimuth angle through 180 degrees to 270 degrees and we continue to track the aircraft as the elevation angle decreases and the aircraft finally reaches the western horizon (AZ=270 degrees, EL = 0 degrees).

Now let's repeat the experiment with a slight change. We detect a high flying aircraft, near the horizon, due east from the telescope (AZ = 90 degrees, EL = 10 degrees) and we follow it (track it) as it comes directly toward us. The azimuth angle stays at 90 degrees and the elevation angle slowly increases. As the aircraft comes closer the elevation angle increases more rapidly and just as the aircraft reaches an elevation of 90 degrees (exactly overhead), it makes a sharp turn due south. We find that we cannot quickly move the telescope toward the south because the elevation angle is exactly +90 degrees so we loose sight (loose track) of the aircraft . We have GIMBAL LOCK! (or GimbleLock) Because humans have good brains, we quickly realize that we must rotate the azimuth axis toward the south and search for the airplane downward in elevation because it probably will be flying away from us. We may or may not find the aircraft again as we try to re acquire the target. It may be flying a tight circle directly over us!

Two axis gimbal systems, set up in the way we set up the surveyor's telescope, have two regions for potential grid lock, exactly vertical, straight up or straight down! Radar (and satellite tracking antennas) often loose track (gimbal lock) on vehicles flying directly overhead (even a few degrees away from exactly over head) and the targets must be re acquired by the tracking computer or more often manually by the radar operator! Fortunately aircraft rarely fly exactly over head and depending on the gimbal design and size, flying just a few degrees to the side of overhead we will just miss the gimbal lock condition.

To over come the gimbal lock problem a third axis gimbal can be added to the system with it's axis often set 90 degrees (orthogonal to) the elevation axis. For several reasons this is not practical for large systems such as radar antennas, but 3 axis gimbals can be used in instruments such as gyro horizon indicators in aircraft. With a three axis system every point in the sky can be specified by many different settings of the three gimbals. The 3 axis system also overcomes the zenith gimbal lock problem (both up and down)..

However; the 3 axis system can become gimbal locked in many spatial directions if two of the gimbal axes become aligned (parallel) in the SAME SPATIAL DIRECTION! Thus it requires a computer to monitor and slightly adjust the relative positions of the gimbals to ensure that two of the gimbals axes never become aligned.

With monitoring, the reference axis on a 3 axes gyro stabilized instrument can be oriented in any spatial direction, relative to the vehicles spatial direction, without gimbal lock.! However, if the computer fails , as has been happening in the MIR space station, the gyros can still operate; however, there always is the potential for reaching a spatial orientation for gimbal lock to occur,. This has been happening on MIR and as the space station tumbles the astronauts must realign the system manually and re acquire the sun or a star reference, loosing many hours of battery charging time and causing them to have to shut down many electrical systems to save battery power for critical life support and flight systems.

You may have to make a cardboard model of a three gimbal configuration to understand gyro lock in the 3-axes system, I did!

Best regards, your Mad Scientist
Adrian Popa