Article deals with safety-overrunning clutches for mechanical driving systems. New construction of safety-overrunning clutch with grooves sides inclined to semi-coupling radius has been proposed and studied in the article. It has practical importance for building, based on modular principles, machines. As the result of the theoretic researches, the expressions to calculate the main specific clutch characteristics have been obtained: rating torque, torques of beginning and ending of operation. On the basis of the mentioned researches, the expressions for estimation the clutch main operation characteristics have been obtained - rating torque exceeding coefficient, accuracy and sensitivity coefficients. On account of modeling and comparison with clutch where grooves sides are parallel to the radius made a number of important conclusions. The analysis performed demonstrates that clutches with inclined to radius grooves sides in general have higher operation characteristics compared with clutches with parallel to radius grooves sides, particularly higher accuracy coefficient and lower rating torque exceeding coefficient. Obtained results make it possible to recommend for highly loaded large-mass systems clutches with low values of grooves to clutch axe and grooves sides to radius inclination angles, because it provides balls contact with plane sides grooves surfaces.