Dynamic modeling of 3-DOF pyramidal-shaped piezo-driven mechanism

A new pyramidal shaped 3-DOF piezo-driven mechanism is proposed, modeled, manufactured and tested. The mechanism, made of aluminum alloy (2024-T3), is equipped with three piezoelectric elements that are separated by 120° angle. This mechanism is designed to deliver elliptical motion in 3-D planes with minimum numbers of actuators subject to different frequencies and phase differences applied to the piezoelectric elements. The design procedure is driven based on modal analysis through Finite Element Method (FEM) to ensure that the relevant mode shapes at different planes take place at almost identical frequency. Furthermore, the dynamic modeling of the mechanism is carried out to show that the designated structure is able to provide different types of motions at different sets of phase differences applied to the three piezoelectric elements. Through dynamic modeling, the response at the tip of the mechanism (end effector) is estimated with regard to two types of displacement inputs imposed by piezoceramics at the contact point where the head of the piezoelectric actuators meets the structure of the mechanism. The two types of displacement inputs are calculated using the new methodology in terms of constitutive equations utilized for modeling the piezoelectric actuators. These inputs, known as the linear pure sinusoidal input and the nonlinear hysteretic input, are applied to the contact point in order to compare the response on tip of the mechanism to both linear and nonlinear signals.