Grinding unit for grinding at least one knife (Kn.1, Kn.2,...), wherein the grinding unit comprises - a grinding head, - a grinding head holder (3.1, 3.2, 33.1, 33.2) holding the grinding head, - a grinding head rotating drive (7.2), - a grinding head shifting drive (7.1), and - a guiding assembly (4.1, 4.2, 5.1, 5.2), wherein the grinding head comprises - a grinding head shaft extending along a grinding head shaft axis and - at least one grinding body (1.1, 1.2,...) rigidly mounted on the shaft, wherein the or every grinding body (1.1, 1.2,...) is arranged to touch at least one knife (Kn.1, Kn.2,...) to be ground, wherein the grinding head rotating drive (7.2) is arranged to rotate the grinding head shaft, thereby causing the or every grinding body (1.1, 1.2,...) to be rotated on the grinding head shaft, wherein the grinding head shifting drive (7.1) is arranged to shift the rotated grinding head shaft with respect to the head holder (3.1, 3.2, 33.1, 33.2), thereby causing the rotated grinding head to be shifted in a direction perpendicular to the grinding head shaft axis, and wherein the guiding assembly (4.1, 4.2, 5.1, 5.2) is arranged to guide the shifted grinding head along a given trajectory, characterized in that the guiding assembly (4.1, 4.2, 5.1, 5.2) provides at least one grinding head shaft guiding surface (37.1, 37.2), the guiding assembly (4.1, 4.2, 5.1, 5.2) comprises at least one longitudinal guiding slot (4.1, 4.2), wherein the or every guiding slot (4.1, 4.2) - is inserted into the grinding head holder (3.1, 3.2, 33.1, 33.2) and - provides the or at least one grinding head shaft guiding surface (37.1, 37.2) and wherein the grinding head shaft protrudes through the or each guiding slot (4.1, 4.2) inserted into the grinding head holder (3.1, 3.2, 33.1, 33.2). wherein the rotated and shifted grinding head shaft stays in contact with the or at least one grinding head shaft guiding surface (37.1, 37.2) and wherein the or at least one grinding head shaft guiding surface (37.1, 37.2) guides the rotated and shifted grinding head shaft with respect to the grinding head holder (3.1, 3.2, 33.1, 33.2) along the given trajectory. wherein the grinding unit comprises - a grinding head, - a grinding head holder (3.1, 3.2, 33.1, 33.2) holding the grinding head, - a grinding head rotating drive (7.2), - a grinding head shifting drive (7.1), and - a guiding assembly (4.1, 4.2, 5.1, 5.2), - a grinding head, - a grinding head holder (3.1, 3.2, 33.1, 33.2) holding the grinding head, - a grinding head rotating drive (7.2), - a grinding head shifting drive (7.1), and - a guiding assembly (4.1, 4.2, 5.1, 5.2), wherein the grinding head comprises - a grinding head shaft extending along a grinding head shaft axis and - at least one grinding body (1.1, 1.2,...) rigidly mounted on the shaft, - a grinding head shaft extending along a grinding head shaft axis and - at least one grinding body (1.1, 1.2,...) rigidly mounted on the shaft, wherein the or every grinding body (1.1, 1.2,...) is arranged to touch at least one knife (Kn.1, Kn.2,...) to be ground, wherein the grinding head rotating drive (7.2) is arranged to rotate the grinding head shaft, thereby causing the or every grinding body (1.1, 1.2,...) to be rotated on the grinding head shaft, wherein the grinding head shifting drive (7.1) is arranged to shift the rotated grinding head shaft with respect to the head holder (3.1, 3.2, 33.1, 33.2), thereby causing the rotated grinding head to be shifted in a direction perpendicular to the grinding head shaft axis, and wherein the guiding assembly (4.1, 4.2, 5.1, 5.2) is arranged to guide the shifted grinding head along a given trajectory, characterized in that the guiding assembly (4.1, 4.2, 5.1, 5.2) provides at least one grinding head shaft guiding surface (37.1, 37.2), the guiding assembly (4.1, 4.2, 5.1, 5.2) comprises at least one longitudinal guiding slot (4.1, 4.2), wherein the or every guiding slot (4.1, 4.2) - is inserted into the grinding head holder (3.1, 3.2, 33.1, 33.2) and - provides the or at least one grinding head shaft guiding surface (37.1, 37.2) and - is inserted into the grinding head holder (3.1, 3.2, 33.1, 33.2) and - provides the or at least one grinding head shaft guiding surface (37.1, 37.2) and wherein the grinding head shaft protrudes through the or each guiding slot (4.1, 4.2) inserted into the grinding head holder (3.1, 3.2, 33.1, 33.2). wherein the rotated and shifted grinding head shaft stays in contact with the or at least one grinding head shaft guiding surface (37.1, 37.2) and wherein the or at least one grinding head shaft guiding surface (37.1, 37.2) guides the rotated and shifted grinding head shaft with respect to the grinding head holder (3.1, 3.2, 33.1, 33.2) along the given trajectory.