Apparatus for converting between rotary motion and linear motion includes a rotatable piece being rotatable about an axis; at least one member having a linking surface facing the rotatable piece and arranged for movement relative to the axis of the piece; and a means for linking the linking surface of the respective member and the surface of the rotatable piece, so that rotational motion of the rotatable piece causes linear movement of the at least one member, and/or linear movement of the at least one member causes rotational motion of the rotatable piece. A sawing device may include said apparatus for cutting by repetitive reciprocating cutting action. A saw blade may be configured for such a sawing device.