An adaptor element for transmitting power between an output shaft of a motor and an input shaft of a driven machine comprises a substantially cylindrical body with a longitudinal hole on the surface of which is formed a longitudinally extending cavity for connection to the said output shaft, the said cavity in turn comprising a pair of substantially parallel lateral surfaces which can engage with corresponding bearing surfaces of a power transmission key. A distinctive feature of the invention is that the longitudinally extending cavity comprises substantially curved connecting surfaces between the said lateral surfaces , which are connected to each other to form a radial stop for the key, projecting towards the inside of the cavity. The main purpose of this is to decrease the maximum stresses on the cavity during power transmission, in order to eliminate risks of cracking and fatigue fracture of the body of the adaptor element.