Page 314 - Mechanics of Microelectromechanical Systems

5. Static response of MEMS 301
combining two springs in parallel, each having the stiffness and its
stiffness is the sum of these two intermediate stiffnesses, namely:

Figure 5.36 Spring-based models: (a) Full four-flexure sagittal amplification microdevice
model; (b) Equivalent model

As a consequence, the input stiffness of the whole micromechanism is equal
to the stiffness of one quarter of it. Similar reasoning can be applied to
demonstrate that the total output stiffness is:

by following the left and right branches between points C and D in Fig. 5.36
(a).
The following reasoning can be developed in order to determine the
displacement amplification of the full microdevice. A simplified quarter-
model amplification device of the type discussed here is sketched in Fig. 5.37
(a), where the input and output displacements are shown (the thicker line
indicates the flexure in its final position). The corresponding full microdevice
model is shown in Fig. 5.37 (b).
When the full mechanism is analyzed, the input displacement is actually
applied from both sides, as indicated schematically in Fig. 5.37 (b) and the
output can also be collected at two ports about the direction perpendicular to
the input direction. As a consequence, the amplification of the whole
microdevice can be calculated as:

As the case was with the input and output stiffnesses, Eq. (5.104) indicates
that the displacement amplification of the entire sagittal micromechanism is
equal to the amplification produced by one quarter model.