All the primary inertia forces and/or moments generated by engines having three cylinders or less are not normally in balance by themselves and thus may be a great source of vibration for the frame supporting the engine. If the mass distribution of the crankwebs is selected in a proper manner, it is possible to determine arbitrarily the directions and the length ratio of principal axes of ellipses, which are obtained as Lissajous diagrams of inertia force and moment. This method can be effectively applied to reduce vibration in the frames. In this paper the appropriate inertia force and moment ellipse equations are developed and the analysis is outlined for optimizing the engine balance. Also the fundamental properties of the linear vibration systems excited by the elliptical forces as well as some experimental examples of elliptical excitation are detailed.