PURPOSE: To excellently chamfer and polish both corner edge faces by providing a machining contact pressure between the both corner edges of a plate material and a rotary grinding wheel by means of a balance plumb bob body.

CONSTITUTION: A plate material G as an object to be machined is held in a holding rotary mechanism 5 so as to be vertically rotated at a low speed, while a supporting member 4 is allowed to be lowered oscillatingly without any strain by means of an upward/downward moving mechanism 29, so that both corer edges F, F of the plate material G are brought into pressure contact with a pair of rotary grinding wheels T, T rotating at a high speed. Machining contact pressures between both of the corner edges F, F of the plate material G and inclined machining surfaces T1, T2 of the rotary grinding wheels T, T are balanced by means of a balance weight body 27. As no strain is applied to the supporting member 4, the supporting member 4 is oscillated vertically according to a change in a distance from the center of rotation to the corner edge F in the plate material G while the plate material G is brought into contact with the rotary grinding wheel T so as to be rotated, and in this way, chamfering is carried out. Therefore, both corner edges F, F are continuously and excellently chamfered.