A rotary machine which comprises: a machine casing (25); a drive shaft mounted for rotation within the said casing; an eccentric (15) attached to the drive shaft and parallel to the axis of rotation of the drive shaft (10); a rotor (20), mounted for rotation on the said eccentric constrained to rotate in the same direction as the drive shaft performing one revolution to three revolutions of the drive shaft; a housing with a profile (28) constructed from a diametrically divided circle in which the two halves are displaced apart perpendicular to the line of division and the ends joined, tangentially, by two equal parallel lines to form a smooth closed curve; so that in operation the path traced by a point attached to the said rotor closely approximates to the housing profile.