Page 317 - Mechanics of Microelectromechanical Systems

304 Chapter 5
The sine and cosine terms appear in Eq. (5.109) because of the inclination of
the force with respect to the local reference frame xy of Fig. 5.39. The
displacement about the vertical direction at point 4 results from
superimposing the local displacements at that point in the form:

where Y and X denote the global reference frame, as shown in Fig. 5.39. By
expressing the local displacement components at point 3, according to the
generic Eq. (1.127) of Chapter 1, the output stiffness can be formulated as:

The amplification factor is found by applying the force F at node 1 (as in
the case of finding the input displacement) and by determining the
corresponding displacement about the Y-direction at 4. In this case, a
horizontal reaction (not shown in Figs. 5.38 and 5.39) is set at node 4
such that The unknown bending moment at the same node can be
found as:

The vertical displacement at node 4 is determined by following the approach
previously described and by combining this displacement with which
was determined when formulating the input stiffness. The displacement
amplification becomes:

Another important aspect is assessing the way these displacement-
amplification micromechanisms interact with and can handle external loads
that are connected to the output port and are directed about the output
direction. A reduced quarter-model of the displacement amplification
microdevice is shown in Fig. 5.40, where the actuation force F is opposed by
the external (resistive) load