Modern production rates require more flexibility, productivity and accuracy of systems forautomatic orientation of production objects (SAOPO). SAOPO represent a specific technological environment of functionally interacting sets of automatic orientation devices (OD) and PO. The necessary conditions for increasing the flexibility, productivity and accuracy of SAOPO are the determination of OD optimal models in terms of the balance between the probable effects and costs of their use, as well as the functional compatibility of the OD with PO for their automatic orientation, and compatibility with other technological equipment. Modern PO represent software and hardware and are characterized by significant variability in structure, functionality and dynamic properties regarding the implementation of PO automatic orientation. The automated solution of these tasks is carried out by a previously developed information and computer system for automated modeling of SAOPO. The basis of the ICS functioning for the SAOPO automated modeling is mathematical models of the SAOPO elements. A mathematical model of the OD functional capabilities and dynamic characteristics is described, which is based on the mathematical apparatus of quaternions. The correspondence between previously developed quaternion models for determining the geometric parameters of the PO orienting movements and the first developed mathematical model of the orientating function components is established. The results of theoretical research and computer modeling are presented. The operability and efficiency of the developed quaternion model are shown. The obtained results are significant and show that the productivity and the speed of the work performed increase by approximately 40%. The social effect is important as well, it is manifested in the reduction of fatigue and the intellectual load on workers.