Abstract: A joint adaptable to a wide range of speed and torque conditions and articulable to a maximum predetermined angle .phi. of up to 30.degree. or greater includes a cylindrical socket with a major inner diameter complimentary to a predetermined diameter `d` and a preselected number `n` of longitudinal internal splines integrally and uniformly extending inwardly from the major diameter and centered on planes cyclically angularly disposed through a longitudinal axis of the socket and a ball with an exterior surface defined by rotation of a first circular arc about a longitudinal axis of the ball. The first arc point of origin is along a line defined by the intersection of a plane containing the first arc and the ball axis with a plane passing transversely through a midpoint on the ball axis. The first arc radius is determined as `r.sub.ball `=d (1.25-3 Tan .phi./2+2.25 Tan.sup.2 .phi./2)1/2 and the first arc point of origin is spaced from the ball axis by a distance `x.sub.ball `=d/2.