Abstract: The universal joint includes an outer joint member having a rotational axis and three guide grooves extending parallel to its rotational axis. The three guide grooves are equally circumferentially spaced about the axis and each has opposed side portions. The universal joint also includes an inner joint member disposed inside the outer member. The inner joint member has a rotational axis and three arms equally spaced about this rotational axis extending radially into the guide grooves of the outer joint member. Each aim carries a roller having an external surface which engages the opposed side portions of the guide groove into which the arm extends. The roller is constrained to roll along the guide groove and each roller being able to rotate about, move lengthwise of, and tilt relative to the arm by which it is carried.