I have a fundamental misunderstanding about the role of gimbals and gyroscopes in determination of angular rotation rates (in inertial measurement units). A set of three gimbals enables an object mounted on it's innermost gimbal to assume an arbitart orientation in space. Viewed differently, a three axis gimbals set enables full freedom (3 degrees of freedom) of relative motion between the object mounted on them and it's support, what paves the way for the design of stabilized platforms.

In particular, one can mount three orthogonal gyroscopes on a gimballed stabilized platform, so that the gimbals isolate the gyros from any external torques and the three gyros will maintain a fixed orientation relative to the inertial space.

Up to this point, i agree with the chains of reasoning. What i don't understand is why one can't simply incorporate angle sensors in order to measure the angles between the axes of the gyros and spacecraft axes?

I now quote the wikipedia article on "gimbal":

In inertial navigation, as applied to ships and submarines, a minimum of three gimbals are needed to allow an inertial navigation system (stable table) to remain fixed in inertial space, compensating for changes in the ship's yaw, pitch, and roll. In this application, the inertial measurement unit (IMU) is equipped with three orthogonally mounted gyros to sense rotation about all axes in three-dimensional space. The gyro outputs are kept to a null through drive motors on each gimbal axis, to maintain the orientation of the IMU. To accomplish this, the gyro error signals are passed through "resolvers" mounted on the three gimbals, roll, pitch and yaw. These resolvers perform an automatic matrix transformation according to each gimbal angle, so that the required torques are delivered to the appropriate gimbal axis. The yaw torques must be resolved by roll and pitch transformations. The gimbal angle is never measured. Similar sensing platforms are used on aircraft.

So if the initial purpose of the stabilizes gimballed platform was to isolate the gyros from any external torques, why do we now need a complicated drive motors system and a matrix calculator in order to apply torques to the components of this platform?

My question might result from a lack of knowledge on practical engineering issues, or maybe from a basic misunderstanding of the mechanics involved here. Anyway, my attempts at reading other sources than wikipedia didn't help me a lot, so i'll be glad to get an exhaustive answer.

  • $\begingroup$ The gyros are tiny and play no direct role is maintaining the orientation of the platform (they aren't flywheels). Some are just laser beams. So all they do is sense a change. These sense signals are processed and the gimbals stepped to null the changes. $\endgroup$
    – Phil Sweet
    May 3 '19 at 20:09
  • $\begingroup$ @Phil - you should post this as an answer so that it canbe voted ... $\endgroup$ Dec 29 '19 at 10:26

The matrix calculator sounds fancy, untill you realize that this is one of the earliest things engineers learn in uni and is realy just a way of avoid using sinus and cosinus ad nauseum*. A control system needs to be present ayway and the computations needed arent really all that hard, they just sound fancy.

Now the gimbal system has a nasty problem. If you turn it to a certain orientation it ceases to work. Since the disks need to be fed with energy anyway or they would cease to eventually rotating. You would need motors anyway to counteract friction. But you can actually read the energy changes and keep the gyro in base position. This then will never end up having to deal diminished degrees of freedom leading eventually to gimbval lock.

In a way this is technically simpler the letting the gimbal free float and reading angles. Even if you were to read angles directly im not sure you could or even would want to skip the matrix calculator.

* Although, most students dont realize it at this point that engineering math is not about doing computations like in earlier school stages. So freshmen tend to learn abhor matrices since they are superficially labour intensive. Not realizing yet that labour intensive is way better than hard or complicated (which is what they equate labour intensive with). Labour intensive just simply means can be done by a machine. This frees you to think on higher order things. But then freshmen arent engineers, yet.

Oh and also its numerically more stable.


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