Two-port network models for compliant rhomboidal strain amplifiers

Piezoelectric stack actuators have the advantages of zero backlash and no acoustic noise, but their stroke is too small to actuate robotic links directly. Because the force available is often more than the required, the stroke of the piezoelectric stack can be amplified by a compliant mechanism at the expense of force. It is not always clear what the geometry of this compliant mechanism should be. Compliant mechanisms have parallels in biology in that they describe two-way interactions between the actuator and the environment. In this paper, we employ the concept of a two-port network model from circuit theory to describe this two-way interaction and present a method to obtain each element of the two-port model as an analytical function of physical geometric parameters for a wide class of geometries. This method makes use of Castigliano's theorem and Euler-Bernoulli linearly elastic beam theory. To our knowledge, this is the first two-port representation of a compliant mechanism that is based on analytical expressions of geometric parameters. This analytical model agrees well with finite-element method calculations. We also examine a representative case experimentally and achieve accuracies better than 18%.