In this paper, a new type of arm-type friction damper with two links and three joints (two universal joints and a hinge) has been developed. The friction damper is able to suppress six modes of vibration of a machine, three in translational modes and three in rotational modes. The trial friction damper was made and the resisting force characteristics in the three translational directions were discussed theoretically and experimentally. The seismic responses of a two-degree-of-freedom system and a three-degree-of-freedom system consisting of a mass and four coil springs and supported by the friction damper were measured using a two-dimensional electrohydraulic type shaking table. The experimental results are compared with the calculated ones, and the effects of vibration suppression of the friction damper in two or three translational directions are discussed.