Optimal design of a piezo-actuated 2-DOF millimeter-range monolithic flexure mechanism with a pseudo-static model

Flexure-based displacement amplifiers are frequently used to magnify the small stroke of piezoelectric actuators. In this paper, a hybrid rhombus-lever multistage displacement amplifier with an improved boundary constraint is proposed to develop a parallel millimeter-range XY monolithic mechanism while retaining a relatively high dynamic frequency. A concise pseudo-static model developed by the authors is utilized to analyze the kinetostatic and dynamic performances of the designed flexure mechanism and then the geometric parameters are optimized in terms of both kinetostatics and dynamics. Different from the previous Lagrange-based dynamic methods for compliant mechanisms, cumbersome calculations of the kinetic and elastic energies as well as adopting Lagrange's equation are all avoided. With the proposed pseudo-static model, the kinetostatics and dynamics of the flexure mechanism can be analyzed concurrently in a programmed statics-similar way, suggesting its superiority for fast performance prediction and parameter optimization during the early stage of design. Finally, a prototype of the XY monolithic mechanism is manufactured and experimentally tested for evaluating its performances. Experimental results show that the designed flexure mechanism has a motion range in excess of 1.2 mm × 1.2 mm with a resonance frequency of 128 Hz. The cross-coupling error is measured to be less than 2%, indicating an acceptable decoupling performance.