“…The theory of two in-plane modes of a ring excited by a single-phase drive was discussed (Cagatay et al, 2003; Koc et al, 2000, 2002; Peter, 1987; Sashida, 1982; Ueha et al, 1993). Tubular ultrasonic motors utilizing only one drive signal were developed (Aoyagi et al, 2002; Cagatay et al, 2003; Chen et al, 2015; Friend et al, 2003; Ishii et al, 1993; Koc et al, 2000, 2002; Ma et al, 2016; Takano et al, 1992, 1994, 1999; Tamura et al, 2010; Ueha et al, 1993); This motor has two orthogonal degenerative bending modes, and only one excitation signal was supplied to one PZT element at a frequency between the resonance frequencies of the two modes, activating both modes and providing oscillating movement. The rotation direction could be reversed by changing the voltage to the other PZT element.…”