A coupling device for transmitting torque between an input shaft and an output shaft have respective opposing ends, includes a male element and a female element for engaging with one another. One of the input shaft and the output shaft includes, at the end, the male element, a cross-section of which has a generally polygonal outer shape. The other of the input shaft and the output shaft includes, at the end, the female element, a cross-section of which has a generally polygonal inner shape complementary to the polygonal outer shape of the male element. The male and female elements engage with one another by meshing with a first functional play between them, and the male element and the shaft on which the male element is mounted have a second functional play between them. The male element and the shaft engage each other by meshing with the second functional play.