Abstract: A tap-driving chuck, having a driven shaft and a driving sleeve spaced co-axially from the shaft to provide an annular space closed at one end by an annular flange extending from the sleeve. Several circumferentially-spaced balls are positioned in the annular space and are urged by a spring into shallow depressions formed in the annular flange. The balls are each located in slots in a circumferential edge of a flange on the shaft. A driving torque applied to the sleeve is transmitted by the balls to the shaft only while the balls are urged by the spring into the depressions. The balls are lifted against the spring force out of the depressions when the torque being transmitted reaches an upper limiting value, the sleeve then turning idly past the balls.