In the paper we consider an approximate transmission. The work is aimed at development of gear-powered transmission on parallel axes, which is RF patent-protected. The paper justifies a relevance of the synthesis of new kinds of engagement with the simplified geometry of the contacting condition. A typical solution for powered mechanisms received by F. L. Livinin and his disciples is characterized.

The paper describes the arrangement of the coordinate systems used to obtain the function of the position of the gear-powered transmission consisting of two wheels with fifteen leads. For them, also the coordinates of the contact points are obtained, and errors of function of the position in tooth changeover are calculated. To obtain the function position was used a method of matrix transformation and equality of radius and unit normal vectors at the contact point. This transmission can be used in mechanical and instrumentation engineering, and other sectors of the economy. Both reducers and multipliers can be made on its basis. It has high manufacturability (with no special equipment required for its production), and a displacement function is close to linear.

This article describes the influence of the axle spacing error on the quality of the transmission characteristics. The paper presents the graphic based relationships and tabular estimates for nominal axle spacing and offsets within 0.2 mm. This error of axle spacing is significant for gearing. From the results of this work we can say that the transmission is almost insensitive to errors of axle spacing. Engagement occurs without an exit of contact point on the lead edge. To solve the obtained system of equations, the numerical methods of the software MathCAD package have been applied.

In the future, the authors expect to consider other possible manufacturing and mounting errors of gear-powered transmission (such as the error of the step, misalignment, etc.) to assess their impact on the quality of engagement.