In this paper, the mechanism of a slotting spindle head for the implementation of rectilinear motion based on a rack and pinion is considered. A three-dimensional modeling procedure of the slotting head elements for a multioperational machine tool of the drilling-milling-boring type has been carried out. 3D models of the rack and pinion were built in the integrated CAD KOMPAS using its built-in geometric core. An assessment of the stress-strain state in the engagement zone is given using the finite element method. The concept of increasing the load capacity due to the proposed version of the teeth envelope surface with curved axoids is analyzed. An analytical apparatus for determining the basic design parameters of a rack and pinion transmission modified version is proposed. The calculation of the geometric parameters for the end profile of the gearing teeth is experimentally realized, taking into account the found value of the disk milling cutter diameter for teeth cutting by the copying method.