Abstract: Surface abrading machines such as lapping machines of the type that lap both surfaces of the works, such as semiconductor wafers, using an upper lap and a lower lap between which such works are positioned by means of holders. The design object is to enhance the accuracy of lapping by reducing to a minimum the rotation of holders, thereby reducing the speed difference at different points of the holders and, therefore, the works carried thereby. When a central gear 18, which constitutes a work holding mechanism, is moved by the rotation of an eccentric cam 15 mounted over a drive shaft 3, an internal gear 28 supported inside a support ring, which is a pin gear 27, like a differential gear revolves at a low speed along the support ring 27 while being moved like the central gear 18 through the holders 30 placed between and engaged with the internal gear 28 and the central gear 18.