Characteristic analysis and shape optimal design of a ring-type traveling wave ultrasonic motor Jong-Suk Ro, Kyung-Pyo Yi, Tae-Kyung Chung and Hyun-Kyo Jung Eur. Phys. J. Appl. Phys., 63 1 (2013) 10901 Published online: 05 July 2013 DOI: 10.1051/epjap/2013130069