The development and manufacturing of gear pairs is determined by a system combining the kinematic basis of the relative motions between workpiece and tool with the necessary production technology. This system unites the two subsystems of theory and technology. Via a multitude of parameters, gears can be assigned to different classes according to the range of existence. The paper describes a mathematical model for determining the range of existence for the general kinematic scheme of gear shaping. This model is based on an analysis of the existing kinematic schemes of theoretical and real shaping. Based on a morphological approach, individual kinematic shaping schemes are classified, and their mathematical models are developed. The shaping schemes, as well as the necessary translational and rotational motion matrices, are exemplarily presented for a gear manufacturing machine using the shaping principle. The modern approaches to the principles of designing equipment and instrumentation systems for gear manufacturing are presented. Methodical basics for selecting the optimal machine configuration depending on the technical and economic requirements for the machining and form of a gear's tooth profile are stated. The system for theoretical and technological optimization synthesis of instrumentation systems for gear manufacturing is presented.