A crankless reciprocating machine which is provided with a mechanism other than a conventional crank mechanism for converting a reciprocating motion into a rotary motion or vice versa. The mechanism comprises at least one pin firmly connected to a piston or pistons so as to be immovable relative thereto and extending radially outwardly therefrom, and an endless cam mounted in a fixed part or a rotating part, said pin and said cam operatively connecting the reciprocating motion of said piston or pistons with the rotary motion of said rotating part.