Page 286 - Mechanics of Microelectromechanical Systems

5. Static response of MEMS 273
actuation when it will touch another fixed component and close an electrical
circuit (in a microswitch application) or through inertial acceleration (in a
microaccelerometer). Figure 5.8 (b) shows the equivalent spring model of the
MEMS design of Fig. 5.8 (a). The static response of this system is
characterized by the equation:

Example 5.4
Find the minimum actuation voltage that will move the central link a
distance (where in an electrical microswitch with two
identical flexure hinges, as the one sketched in Fig. 5.8 (a). Young’s modulus
is E = 160 GPa, the electrical permittivity is and the
actuation area is
(a) The flexure hinges are long and have constant rectangular cross-
section with
(b) The flexure hinges are right circularly-filleted with r = 1 and

Solution:
In both cases, the actuation voltage can be found by solving Eq. (5.20)
after substituting the electrostatic actuation force of Eq. (5.2).

(a) For the constant cross-section flexure hinge, the stiffness is and
therefore a voltage of U = 29.1 V is obtained by solving Eq. (5.20).

(b) For the right circularly-filleted flexure hinge, as the one shown in Fig.
2.14, Chapter 2, the stiffness is found by inverting the symmetric
compliance matrix which is formed of and of Eqs.
(2.72), (2.73) and (2.74), respectively. By using again Eq. (5.20), the voltage
corresponding to this design is U = 98.16 V.

3.2 Other Linear-Motion Microdevices

Several examples of two-spring linear-motion microdevices are
presented next. One class of linear-motion MEMS comprises microdevices
whose linear motion takes place in an x-y plane, as shown in Fig. 5.9 (a).
Adding to the active planar motion, the effects of gravity about the z-
direction (which is perpendicular to the x-y plane) might play an important,
although undesired, role.
In addition to the spring-type stiffness of the two suspensions about the
x-axis, the self weight of the central mass solicits the flexibility of the same
suspensions about the out-of-the-plane z-axis, as indicated in Fig 5.9 (b).
Various suspensions have been studied in Chapter 3 and their stiffnesses
about both the x- and z-axes have explicitly been given.