The novel contribution in this manuscript is an expansion of the current state-of-the-art in the geometric installation of control moment gyroscopes beyond the benchmark symmetric skewed arrays and the four asymmetric arrays presented in recent literature. The benchmark pyramid symmetrically skewed at 54.73 degrees mandates significant attention to singularity avoidance, escape, and penetration, while the most recent four asymmetric arrays are strictly useful in instances where space is available to mount at least one gyro orthogonal to the others. Skewed arrays of gyros and the research-benchmark are introduced, followed by the present-day box-90 and “roof” configurations, where the roof configuration is the first prevalently used asymmetric geometry. Six other asymmetric options in the most recent literature are introduced, where four of the six options are obviously quite useful. From this inspiration, several dozen discrete options for asymmetric installations are critically evaluated using two figures of merit: maximum momentum (saturation) and maximum singularity-free momentum. Furthermore, continuous surface plots are presented to provide readers with countless (infinite) options for geometric installations. The manuscript firmly establishes many useful options for engineers who learn that the physical space on their spacecraft is insufficient to permit standard installations.

Modification of rigid body angular momentum permits controlled rotational maneuvers, and one common momentum-exchange actuator contains challenging mathematical singularities that occur when the actuator geometrically aligns perpendicularly to the commanded torque direction. Substantial research has arisen toward singularity avoidance, singularity escape (when avoidance fails), and singularity penetration which permits safe flight through regions of singularity. The latter two in particular, singularity escape and penetration require mathematical calculations of singular and near-singular quantities (very large numbers) using constituent numbers that are sometimes very small. This dichotomy leads to interesting peculiarities in some specific geometries. This short communication critically evaluates three often spoke postulates for defining singularity and the axioms that accompany the postulates. Researchers using disparate postulates arrive at contradictory conclusions about singularities, and we examine these peculiarities, leading to a few conclusions. Singular conditions must never be declared in the abstract without consideration for the commanded maneuver (e.g. the claim “the CMG system is singular”). Seeking the true angular momentum capability at near-planar skew angles, this research concludes that performance prediction is difficult installations at low skew angles should be avoided whenever permissible to enhance abilities of mathematical calculations. It will be shown that maximum momentum performance is easily predicted at very high and very low skew angles, and performance will be shown to be lowest at mid-values of skew angle. Meanwhile, maximum singularity-free performance remains elusive at even modestly low skew-angles.