A planar unimorph-based actuator with large vertical displacement capability. II. Theory

A piezoelectric actuator utilizing a planar trellis-like arrangement of multiple unimorph elements is described which produces displacements perpendicular to the plane of the actuator. The unimorph elements are connected in series mechanically so that the vertical displacement of each unimorph element in the structure adds to the vertical displacements of the other elements, resulting in a large overall vertical displacement at the output of the actuator. A simple electromechanical model of the actuator is developed. The model consists of a voltage-actuated force source, which is the result of the piezoelectric properties of the unimorph bars that make up the actuator, in parallel mechanically with a stiff spring that models the elastic response, both bending and twisting, of the unimorph elements. The long moment arms inherent in the geometry of the actuator make a substantial contribution to the overall compliance of the actuator. The addition of stiffeners to the actuator can significantly reduce the effect of these moment arms, and thus substantially increase the stiffness of the actuator. As a result, the force generation capability of the actuator is significantly increased without affecting its displacement capability.