Abstract: A coupling for splining together first and second shafts which may be inner and outer, co-axial annular members, abutting co-axial annular members, or intermeshing gears on parallel shafts. One embodiment is a coupling for splining together inner and outer annular members having corresponding inner and outer cylindrical surfaces concentrically disposed about an axis and having splines which are generally circumferentially disposed on the cylindrical surfaces along an axial length of at least one of the members such that the splines having a varying pitch so as to be curved with respect to the axis. The pitch is defined by a function which varies parabolically with respect to a shaft axis and, in a more particular embodiment, the function has a non-zero fixed pitch component and a parabolic component so that the shape of the splines are both helical and parabolic.