Abstract: An apparatus for successively grinding the edges of a series of like, sheetlike articles, such as glass sheets, and especially irregularly shaped glass articles such as automotive windows. The apparatus includes a frame, a table rotatably secured to the frame, a clamp for clamping an article on the table, and a template of the article carried by the table, but at an elevation below that of the article. The apparatus also has a swing arm assembly which carries a spindle near its outer free end, an inner end of the swing arm assembly being pivotally secured to the frame, the swing arm assembly being movable in a plane to move the spindle toward or away from the table. The spindle of the swing arm assembly has a rotatable grinding wheel which is positioned to engage the edge of an article on the table and a motor drive for rotating the grinding wheel. The spindle further has a cam follower which is positioned to engage the edge of the template when the grinding wheel engages the article.