Abstract: In a torque transmitting coupling between a cylindrical shaft and a female member having a bore to receive the shaft, the shaft has a secant face and the female member has a connecting bolt bore which intersects the shaft bore and faces the secant face of the shaft. A connecting bolt in the bolt bore of the female member has a secant face which tightly engages the secant face of the shaft. In one embodiment, the shaft axis, secant faces of the shaft and bolt and the bolt bore are all parallel. In another embodiment the axis of the bolt bore is inclined at a small angle to the secant face, the bolt being of wedge form. A screw extending through a hole in the female member and screwed into a tapped hole in the bolt is rotatable to move the bolt axially and thereby wedge the secant face of the bolt against the secant face of the shaft. The secant faces of the shaft and bolt may have intermeshing longitudinally extending serrations.