A rewinding machine winds web material into a log. The machine has a winding drum that is rotatable about a center axis and about which the web material to be wound is directed. A continuous loop is spaced from the winding drum and with the winding drum defines a nip through which the web material is directed when winding the web material into the log. The continuous loop is configured to move in a direction generally opposite of a direction of the winding drum at the nip. The continuous loop is configured to change speed relative to a speed of the winding drum during winding the web material into the log about a lead edge of the web material. The continuous loop is positionable relative to the winding drum at the nip to accommodate winding the web material into the log about the lead edge of the web material and to sever the web material.