This paper presents elliptical rolling contact joints in compression as an alternative to circular rolling contact and conventional revolute joints where high quality force transmission—low friction and backlash—with variable output are desired. Parameters specific to the joint and its position are defined in terms of relative link angles and elliptical surface geometry. These relationships allow elliptical rolling contact joints to be incorporated in vector loop summations used in kinematic analysis. Notably, elliptical rolling contact is developed as the more general case of which circular rolling contact is a subset. Elliptical rolling contact joints are shown to offer several benefits over circular rolling contact, including reduced Hertz contact stresses, variable output velocity, maximum use of contact interface by distributing small rotations across surfaces of small curvature, reduced forces on constraining members, and no-slip pure rolling provided by either connecting links or flexures, without the need for gear teeth or friction.