Nonuniform articles, such as potatoes, are cut into uniform pieces by subjecting the articles to a centrifugal force for orienting each article along its longitudinal axis, transferring tangentially each oriented article to a conveyor defining a conveying path for forming a single row of articles moving in a conveying direction and oriented with their longitudinal axes parallel to the conveying path, feeding the single row of articles past a plurality of measuring stations, measuring a longitudinal length for each article passing a measuring station, removing from the conveyor each article having a longitudinal length greater than a length predetermined for the respective measuring station, and cutting each article into uniform pieces. Apparatus for performing the method has a cylindrical wall defining an opening for the transfer of the articles to the conveyor and a cone-shaped disc mounted for rotation and arranged within the cylindrical wall for supplying the centrifugal force. A plurality of sensing devices is used to measure the length of the passing articles, and a plurality of associated plungers is provided to remove the articles from the conveyor and move the articles into a cutting assembly. The sensing devices are arranged in the conveying direction to remove articles having progressively shorter longitudinal lengths.