2017-02-14 For several years, Oscillating knife cutting machine are used to cut and severe foamed materials etc. The band knives run over a plurality of knife deflecting pulleys and span freely in a cutting zone for a length of up to 2.5 m. Such a cutting machine is known, for example, from the applicant's documents DE 11 84 069 or DE 75 50 595. With such cutting machines, however, it is necessary to return the band knife above the material so that a large frame is required for the circulating band knife. A Oscillating knife cutting machine is known from DE 101 29 909, in which the band knife is twisted by means of a knife rotating head, so as to perform contour cutting.