A polisher has an offset axis and a friction cam useful in a method of polishing that comprises a more random, elongated polishing pattern than known orbital polishers and is capable of portable use using a 9 volt battery. The method is capable of using lower contact pressures between fiber ends and a polishing surface and higher rates of rotation of the drive mechanism, reducing the polishing time for preparing fiber ends for applications. The polishing pattern changes when pressure is applied between a fiber end and the polishing surface. The fiber end provides one intermittent axis of rotation and the friction cam provides another intermittent axis of rotation.