Mechanism for transforming rotating to reciprocating motion, or vice versa, comprising a first annular component (1) and a second annular component (3) coaxially located, the first beside the second, along a longitudinal axis (ΔA), wherein both are able to rotate around the longitudinal axis and to reciprocate along the longitudinal axis, wherein aide (A) of the first annular component (1) adjacent to the second annular component (3) is in continuous contact, in at least one point, with the neighbouring side (Γα) of the second annular component (3), such that the second annular component (3) is able to rotate relative to the first annular component (1) in continuous contact in at least one point with the adjacent side (A) of the first annular component (1), wherein the contacting sides are undulated surfaces (A, Γα), such that if the first annular component (1) and the second annular component (3) are forced into rotational motion relative to each other, remaining the same time in continuous contact, then every point of the undulated surfaces (A, Γα) will trace, relative to the other, an undulated trajectory and at the same will also execute, relative to the other, reciprocating motion.