The common two-axis azimuth-elevation gimbaled pedestal has a full-hemispheric, horizon-to-zenith field of regard. This pedestal has no kinematic difficulties at low elevation angles. In this position, the line-of-sight of the mounted sensor is perpendicular to both the azimuth and elevation gimbal axes, which thus provide two orthogonal degrees of freedom. However, as the line-of-sight approaches zenith, the sensor axis nears alignment with the azimuth axis. The azimuth axis thus loses its ability to move the line-of-sight orthogonally to the sweep of the elevation axis. This condition is known as gimbal lock and the position range in which dynamic difficulties occur is called keyhole. The keyhole region is a solid cone centered around the zenith axis. The onset of dynamics difficulties is a continuum from horizon to zenith, and as such defining the keyhole region is arbitrary. However, dynamic difficulties become rapidly pronounced somewhere between 70 and 80 degrees, so it is generally agreed that the keyhole region starts in this range. This paper provides a comprehensive analysis of the keyhole region. While performance problems at keyhole are well known (high torque, acceleration, and speed requirements), certain dynamic effects actually reduce in keyhole, such that for some systems the range of worst-case performance is actually outside the keyhole region. Gimbal geometry is introduced and pointing equations derived using vector methodology. Kinematic equations are then developed, with a focus on the requirements of line-of-sight stabilization for vehicle-mounted systems. Examples and simulation results are provided to illuminate the issue.
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