Piezoelectric motors use the inverse piezoelectric effect, where microscopically small periodical displacements are transferred to continuous or stepping rotary or linear movements through frictional coupling between a displacement generator (stator) and a moving (slider) element. Although many piezoelectric motor designs have various drive and operating principles, microscopic displacements at the interface of a stator and a slider can have two components: tangential and normal. The displacement in the tangential direction has a corresponding force working against the friction force. The function of the displacement in the normal direction is to increase or decrease friction force between a stator and a slider. Simply, the generated force alters the friction force due to a displacement in the normal direction, and the force creates movement due to a displacement in the tangential direction. In this paper, we first describe how the two types of microscopic tangential and normal displacements at the interface are combined in the structures of different piezoelectric motors. We then present a new resonance-drive type piezoelectric motor, where an octagonal plate, with two eyelets in the middle of the two main surfaces, is used as the stator. Metallization electrodes divide top and bottom surfaces into two equal regions orthogonally, and the two driving signals are applied between the surfaces of the top and the bottom electrodes. By controlling the magnitude, frequency and phase shift of the driving signals, microscopic tangential and normal displacements in almost any form can be generated. Independently controlled microscopic tangential and normal displacements at the interface of the stator and the slider make the motor have lower speed-control input (driving voltage) nonlinearity. A test linear motor was built by using an octagonal piezoelectric plate. It has a length of 25.0 mm (the distance between any of two parallel side surfaces) and a thickness of 3.0 mm, which can produce an output force of 20 N.