Although the liquid balancer has nearly a century of having been introduced by the French inventor Maurice LeBlanc, little information is available on the dynamic performance of this kind of device. Four main topics are investigated in this dissertation;(1) the unbalance response, (2) the stability characteristics, (3) the baffles curvature to modify the fluid-solid interaction and improve the dynamic performance, and (4) a hybrid two-plane balancing system for reduction of rotor dynamic forces, moments and support stresses in a vertical-axis washing machine. Experimental results indicate that the baffle-liquid interaction renders fluid modes of vibration of circumferential and axial type. This complex swirl flow is comprised of two inertial waves; one of such waves is synchronous with the rigid body motion, while the other is a fluid backward traveling wave, thus enhancing the system damping capability. An analytical dynamic model of the unbalanced response is derived and correlated with fluid flow visualization experiments and vibration measurements. It is shown that a flexible rotor employing a vi LeBlanc balancer has remarkable increase in the threshold speed of instability for aerodynamic cross-coupling and rotor internal friction damping. Further experiments are performed on a balance ring for washing machines varying the amount of baffles and also with curved baffles or "blades" to modify the fluid-solid interaction. Dynamic equations of motion for a fluid particle are introduced and solved to arrive to and optimum curvature. This novel design enables the washing machine drum to run at higher speeds, and reducing the centrifugal cycle while increasing the centrifugal force applied to the objects being washed. Finally, besides the conventional liquid balance ring placed on top of the rotating basket, a ball-balance ring was fitted to the lower part of such basket, such that a two-plane balancing is achieved by the combination of both types of devices. The advantages of including a second lower balance ring are mainly, the minimum space required to house it into the basket bottom, cost-effectiveness, and good dynamic performance achieved by reducing the unbalance forces, moments, and support stresses present on the rotating system. vii DISCLAIMER This dissertation is written in the English language for convenience to the author, and in agreement with the advisory committee. The aforesaid because the products of this research, namely; technical papers and patents, have been originally written in English and submitted to ASME 1 Conferences, ASME Journal of Vibration and Acoustics, Journal of Shock and Vibration, and the United States Patent Office with due proof review. Although every effort has been made in writing well this thesis, the author is not a native English speaker, therefore he apologizes for any typographical errors, misspellings, incorrect phrasings, or just plain wrong use of the English language. The author also believes that in writing this thesis in English, it will also be worldwide more acc...