An apparatus for folding a product having a first portion and a second portion, and a fold axis (A-A), the apparatus comprising: a receiving roll configured to hold the first portion and the second portion of the product thereto and to release the first portion while continuing to hold the second portion of the product, the receiving roll having a drive assembly for rotating the receiving roll at variable surface speeds in a first direction of rotation; an oscillating member positioned adjacent the receiving roll, the oscillating member having a drive assembly for moving the oscillating member at variable surface speeds in the first direction of rotation and in a second direction, the oscillating member being configured to receive the first portion of the product from the receiving roll while moving in the second direction and at substantially the same surface speed as the receiving roll, wherein the oscillating member comprises an inner cylinder, an outer cylinder being rotatable by the drive assembly of the oscillating member about the inner cylinder, and a puck disposed on the outer cylinder, the puck having a plurality of apertures therein, the inner cylinder including a slotted segment having a plurality of slots in fluid communication with a vacuum source, the plurality of apertures in the puck being positioned to rotate into and out of alignment with the slots in the slotted segment of the inner cylinder; and a folding roll positioned adjacent to the receiving roll and the oscillating member, the folding roll having a drive assembly for rotating the folding roll at variable surface speeds in the second direction, the folding roll being configured to receive the first portion of the product from the oscillating member while the oscillating member is moving in the first direction and at substantially the same surface speed as the folding roll, the folding roll also being configured to transfer the first portion of the product from the folding roll to the receiving roll such that the product is folded generally along the fold axis (A-A) and the first portion is generally overlying the second portion. a receiving roll configured to hold the first portion and the second portion of the product thereto and to release the first portion while continuing to hold the second portion of the product, the receiving roll having a drive assembly for rotating the receiving roll at variable surface speeds in a first direction of rotation; an oscillating member positioned adjacent the receiving roll, the oscillating member having a drive assembly for moving the oscillating member at variable surface speeds in the first direction of rotation and in a second direction, the oscillating member being configured to receive the first portion of the product from the receiving roll while moving in the second direction and at substantially the same surface speed as the receiving roll, wherein the oscillating member comprises an inner cylinder, an outer cylinder being rotatable by the drive assembly of the oscillating member about the inner cylinder, and a puck disposed on the outer cylinder, the puck having a plurality of apertures therein, the inner cylinder including a slotted segment having a plurality of slots in fluid communication with a vacuum source, the plurality of apertures in the puck being positioned to rotate into and out of alignment with the slots in the slotted segment of the inner cylinder; and a folding roll positioned adjacent to the receiving roll and the oscillating member, the folding roll having a drive assembly for rotating the folding roll at variable surface speeds in the second direction, the folding roll being configured to receive the first portion of the product from the oscillating member while the oscillating member is moving in the first direction and at substantially the same surface speed as the folding roll, the folding roll also being configured to transfer the first portion of the product from the folding roll to the receiving roll such that the product is folded generally along the fold axis (A-A) and the first portion is generally overlying the second portion.