An Arecibo radio telescope-like optical telescope is under development which will operate in semitransit mode for spectroscopic survey work, using a five-axis servomechanism in the telescope's upper section to track an object's image locus on the focal sphere. Once the telescope is in the requisite azimuth position, a transit time for each object relative to the telescope structure can be determined and a strategy devised for driving the fiber-carrying optical head into conjunction with the image focus. The trigonometric mapping between the hour angle and declination functions of each object, on the one hand, and the five coordinates of the tracking device in the telescope's upper section, on the other, is a special transformation applicable to all telescopes of this type.
Frank B. Ray,
"Spectroscopic survey telescope design: II. Tracking geometry", Proc. SPIE 1236, Advanced Technology Optical Telescopes IV, (1 July 1990); doi: 10.1117/12.19252; https://doi.org/10.1117/12.19252