Abstract: A circular column,s completely rolling in a free circular concave trough on a smooth horizontal plane is investigated.the track equation of the circular column,s mass center and any point on the circular column,s edge in inertial frame of reference is deduced, the strict isochronism vibration condition is given,and the tracks is sketched by a computer; the period of vibration when the circular column is completely rolling is calculated,and the period of vibration when the circular column is completely rolling to when the circular column is completely glide are compared.