Article deals with safety-overrunning clutches for mechanical transmissions. Modern design of safetyoverrunning clutch with grooves sides inclined to semi-coupling radius has been described and researched in the article. It has practical value for creation modular-type machines. On the basis of the theoretic studies, the expressions for obtaining the main specific operation parameters have been proposed: rating torque, beginning and ending operation torques. As the result of the studies, the equations for estimation the clutch main operation characteristics have been received -rating torque exceeding coefficient, coefficients of clutch accuracy and sensitivity. 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 and through this allows to decrease contact stresses compared with clutches with grooves sides parallel to radius; allows to provide high load capacity with low rating torque exceeding in overload mode; in clutches with inclined to radius grooves sides friction impact manifests less in operation with high rotation frequency.