A machine (1; 101) comprising: - a rotor (10; 110) having a preset number (n) of end zones; - a stator (20; 120) exhibiting a recess (21; 121) delimited by an inner surface (22a; 122a), the rotor (10; 110) being housed eccentrically inside said recess (21; 121) and being movable relative to the stator (20; 120) with a roto-orbital movement about an axis of the recess (21; 121); - a shaft (30; 130) having an eccentric portion (32; 132), the rotor (10; 110) being provided with a hole (12; 112), in which said eccentric portion (32; 132) is engaged, the rotor (10; 110) being so installed as to be free to rotate with respect to the eccentric portion (32; 132) of the shaft (30; 130), wherein each end zone of the rotor (10; 110) is provided with a rolling element (16; 116) suitable for rolling on said inner surface (22a; 122a), so as to remain in contact with said inner surface (22a; 122a) while the rotor (10; 110) is roto-orbiting about said axis, the rotor being delimited, transversely to said axis, by a face and by a further face opposite to one another, characterized in that the inner surface (22a; 122a) of the recess (21; 121) is defined, on a Cartesian plane perpendicular to said axis, by a curve traced by a preset point when a rolling circumference is rolling on a base circumference, outside the base circumference, said curve having the following equations: x = n − 1 R + R cos α − Ecos nα ± Rr cosarctg n − 1 R + R sin α − nEsin nα n − 1 R + R cos α − nEcos nα and y = n − 1 R + R sin α − Esin nα ± Rr sinarctg n − 1 R + R sin α − nEsin nα n − 1 R + R cos α − nEcos nα wherein: - n is an integer greater than or equal to one, equal to the number of end zones of the rotor (10, 110); - (n-1) R is the radius of the base circumference; - R is the radius of the rolling circumference; - Rr is the radius of each rolling element; - α is an angle which indicates the angular position of the rolling circumference with respect to the base circumference, which coincides with the angular position of the rotor (10; 110) about the axis of the recess (21; 121); - E is the distance of said preset point from the center of the rolling circumference, measured along a segment joining the center of the rolling circumference with the center of the base circumference when said angle (α) is equal to zero, said distance further expressing the eccentricity between the rotor (10; 110) and the stator (20; 120), the rotor (10; 110) being so installed as to be free to slide axially with respect to the eccentric portion (32; 132) of the shaft (30; 130), the machine (1;101) being provided with a balancing arrangement, configured for sending a pressurized fluid towards said face and towards said further face, so that the pressurized fluid exerts axially balanced forces on the rotor (10; 110). - a rotor (10; 110) having a preset number (n) of end zones; - a stator (20; 120) exhibiting a recess (21; 121) delimited by an inner surface (22a; 122a), the rotor (10; 110) being housed eccentrically inside said recess (21; 121) and being movable relative to the stator (20; 120) with a roto-orbital movement about an axis of the recess (21; 121); - a shaft (30; 130) having an eccentric portion (32; 132), the rotor (10; 110) being provided with a hole (12; 112), in which said eccentric portion (32; 132) is engaged, the rotor (10; 110) being so installed as to be free to rotate with respect to the eccentric portion (32; 132) of the shaft (30; 130), - n is an integer greater than or equal to one, equal to the number of end zones of the rotor (10, 110); - (n-1) R is the radius of the base circumference; - R is the radius of the rolling circumference; - Rr is the radius of each rolling element; - α is an angle which indicates the angular position of the rolling circumference with respect to the base circumference, which coincides with the angular position of the rotor (10; 110) about the axis of the recess (21; 121); - E is the distance of said preset point from the center of the rolling circumference, measured along a segment joining the center of the rolling circumference with the center of the base circumference when said angle (α) is equal to zero, said distance further expressing the eccentricity between the rotor (10; 110) and the stator (20; 120),