To reduce the angular velocity fluctuation of the input shaft to a machine, we deduced that a machine under the combined action of the inertia and the load may keep running smoothly if the equivalent kinetic energy (EKE) of the machine is constant during its operation. Furthermore, we introduced a novel type of flywheels with variable equivalent mass moment of inertia (VEMMoI) and without fixed connection with the input shaft to the machine. The kinetic energy fluctuation of the flywheel is used to dynamically decrease the EKE fluctuation of the original machine, thereby realizing smooth machine operation. Three types of flywheels with VEMMoI driven by a two-link dyad, a pair of noncircular gears and a planet cam respectively were designed as examples. The velocity fluctuation of the machine is significantly reduced. In the second and the third examples, in particular, the input shaft may rotate at a constant rate, since its angular velocity fluctuation is eliminated completely in principle.