PURPOSE: To make both hard and fragile materials into gyro machining so efficiently without entailing any chipping in an ideal manner by reducing a relative speed between an abrasive and a workpiece at the initial machining stage, and making the relative speed go up successively with the progress of machining.

CONSTITUTION: A rotating shaft of a work tank 11 and a revolving shaft of workpieces 4a-4m are made eccentric to each other. Accordingly, at the initial stage of machining, for example, at a position of the workpiece 4b, a radius of gyration in an abrasive 5 hitting on the workpiece becomes smaller, and a relative speed between the abrasive 5 and the workpiece 4b is small. Accordingly, any chipping in an edge of the workpiece 4b is no longer produced. Next, with a turret rotated and machining of the workpiece advanced, a radius of gyration in the abrasive 5 grows larger successively, so that the relative speed between the workpiece and the abrasive 5 is increased as well. Thus, these workpieces 4a-4m are efficiently machined without chipping.