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I understand how gimbal lock is a serious risk in case of CNG where the axis of rotation change in operation, and as they become coplanar you lose degrees of freedom, the respective axis duplicating given degree of freedom and losing another.

I still don't see how this could be a case with three reaction wheels installed perpendicular to each other. They always remain perpendicular, and the axis of rotation of the craft will never be parallel to more than one. Where, in what situation does gimbal lock occur with this sort of attitude control?

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  • $\begingroup$ I'm confused as well if the axes of the three wheels are not free to move. Can you give a reference to where this type of system was said to experience gimbal lock? $\endgroup$ – Organic Marble Oct 8 '18 at 16:38
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    $\begingroup$ @OrganicMarble: I recall the tetrahedral setup of reaction wheels to be described as superior due to immunity to gimbal lock (along with added redundancy) - somewhere on this site... I'd need to find it. $\endgroup$ – SF. Oct 8 '18 at 16:44
  • $\begingroup$ @SF. -- Perhaps you are referring to Optimal placement of 4 reaction wheels? The reason for using four reaction wheels is redundancy. It does not overcome the problem of saturation. Reaction wheels will become saturated if there's a persistent torque in one direction, regardless of how many reaction wheels are employed. $\endgroup$ – David Hammen Oct 11 '18 at 11:17
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Strictly speaking, the term "gimbal lock" is a misnomer when applied to either a reaction wheel assembly or a control moment gyro assembly: No gimbals get locked in either case. What can go wrong with both is a loss of control over one or more rotation degrees of freedom. This is exactly what happens with gimbal lock, so the term has been extended to the more generic case of loss of rotational degrees of freedom.

In the case of a reaction wheel assembly, control is lost when a reaction wheel would have to be rotated faster than some operational limit. These operational limits exist because violating them would result in a reduction of the wheel's lifetime, or possibly even in catastrophic failure. The wheel becomes "saturated" at this limit; something needs to be turn to slow it down.

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