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The study determines the most suitable pattern of alignment and fixing of low-rigidity shafts; it also presents factors that determine such choice. The part is fixed both by force closing and kinematic closing. A new method for machining low rigidity shafts is developed to control the elastic-deformable state of these shafts in a technological system and to produce parts with the required accuracy during turning. To implement this new developed method for low rigidity shafts, an apparatus is designed. The apparatus allows to increase the rigidity of shafts during machining by the application of axial tensile force to the workpiece. Rational prime costs of preparing technological alignment centers at the stage of production preparation are determined; knowing these costs, it is possible to select a suitable machining technology for low rigidity shafts, to produce a technology-oriented design, and to reduce the costs of machining these shafts.