This paper presents the mobility augmentation method to provide omnidirectional mobility to nonomnidirectional wheeled bases. First, the kinematic model of a nonomnidirectional wheeled base and a link combined by an extra revolute/prismatic joint to the base is derived in a matrix-vector form. Then it is shown that, if the kinematic model satisfies some structural conditions, the link motion can be omnidirectional. The structural conditions for omnidirectional motion are derived and several examples are provided to demonstrate the method.