The paper provides mathematics and physics considerations concerning a special class of electron spin manipulating structures for future Electron-Ion Collider (EIC) projects. These structures, which we call Universal Synchronous Spin Rotators (USSR), consist of a sequence of standard basic spin manipulating elements or cells built with two solenoids and one bending magnet between them. When integrated into the ring arcs, USSR structures do not affect the central particle orbit, and their spin transformation functions can be described by a linear mathematical model. In spite of being relatively simple, the model allows one to design spin rotators, which are able to perform spin direction changes from vertical to longitudinal and vice versa in significant continuous intervals of the electron energy. This makes USSR especially valuable tools for EIC nuclear physics experiments.
