The arc teeth cylindrical gear is under study. The arc teeth are cut with a circular cutter head by the periodic generating method. Using the theory of spatial gearing by meshing, mathematical models of the arc teeth cylindrical gear shaping process have been built. Arc teeth meshing has been regarded in the presence of a gear twist angle and misalignment angle as well as gear axial displacement. Based on solving the inverse problem of the theory of gearing by meshing, algorithms and software have been developed to calculate the coordinates of the arc teeth points of contact, principal relative curvatures at these points for various meshing phases during the gearing operation in the conditions of errors in the pinion and wheel relative position. A variant of an arc teeth cylindrical gear has been proposed, in which one of its elements, a wheel, for instance, is composite, consisting of two mirror geometry arc teeth half-wheels. In the proposed gear, arc teeth meshing is implemented in two contact areas located symmetrically relative to the middle of the arc tooth. An algorithm which ensures the location of the half-wheel pressure spot centers in the middle of their arc teeth has been developed to solve the problem of determining the required half-wheel axial displacements. The half-wheels arrangement on the shaft with the possibility of axial movement provides half-wheels self-adjustment and error compensation for proper gear performance. The study results of the position of active paths of action and arc teeth contact patterns in a self-adjusting gear in the absence and presence of errors in the pinion and wheel relative position are presented.