As the literature indicates, spiroid gears are characterized by a compact design and small space required for their installation, so they are used in modern drive systems of many means of transport. In practice, they constitute an alternative solution to worm gears. It is emphasized that in the case of this type of gear, the basic factors that have a direct impact on proper operation are the geometric parameters of the teeth and meshing cooperating with the worm disc wheel. The aim of this article is to evaluate selected geometry parameters that have a decisive impact on the amount of wear in the contact area of cooperating parts and the operating temperature, and thus on the durability and reliability of the gear. This work presents a method for determining and measuring the position of the cooperation trace of the worm coil and the teeth of the disc wheel using a numerical method based on CAD software. Model analyzes have shown that one of the key factors affecting the correct operation of the gear transmission is obtaining the correct shape and position of the trace of cooperation of parts in the meshing area during gear operation. In practice, the proposed method may be helpful in the process of designing this type of gear in terms of determining the correct geometric tolerances for the tooth profile and line, as well as the position of the longitudinal axis of the worm relative to the center of the ring wheel.