Closed-form equations for the vibrations of a flexure-based Scott-Russell mechanism

This paper presents the closed-form equations for the vibrations of a flexure-based Scott-Russell mechanism driven by a piezoelectric actuator. This mechanism is used for the nano-manipulation. To overcome the displacement limitation of the piezoelectric actuator, the proposed Scott-Russell mechanism is also used to enlarge the working range of the entire system with high positioning accuracy. With consideration for the effect of the driving circuit, the dynamic model of the flexure-based Scott-Russell mechanism is established. The closed-form transient response of the flexure-based Scott-Russell mechanism to the slope command signal is derived based on the Laplace transform method. The influence of the rising time on the dynamic characteristics of the mechanism is investigated. Compared with the step signal, the slope command signal can generate vibration-free motion and thus improve the dynamic performance of the flexure-based Scott-Russell mechanism.