RTYM1321 is designed for grinding irregular peripheries and hypotenuses on flat glass. The processed glass is adsorbed onto a vacuum sucker. A spinning disc or an independent satellite disc, which is driven by an auxilliar motor enables the grinder to work moveably on irregular edges of flat glass in a diameter between 700 and 2100mm, or 100 and 700mm. The speed of the spinning disc is adjustable. This machine can also perform semi-grinding on simple-shaped irregular glass. When grinding peripheries, coarse grinding, refine grinding, and polishing are alternatively done by three grinders. When grinding hypotenuses, the angle of the grinder on the bowel-shape wheel can be obliquely adjusted to fit the ground angle for grinding.