Abstract: An apparatus for grinding or polishing an article having a cylindrical curved surface comprises a turn table attached at an end of a rotary shaft by a pin joint and turned to a predetermined direction by the rotary shaft; a grinding means for grinding or polishing the article set on the turn table; a cam provided around the rotary shaft of the turn table; a cam roller contacting the cam; whereby the turn table is rocked around the pin joint by the cam and the cam roller; and the curved surface of the article is uniformly ground or polished by setting the article on the turn table so as to substantially arrange the cylindrical axis direction Y--Y of the article in the pin joint direction.