Page 290 - Mechanics of Microelectromechanical Systems

5. Static response of MEMS 277

Figure 5.11 Linear actuator working against spring

In many situations, linear actuators, such as thermal, work against one or
several springs that are designed to oppose the generated force/motion. An
example is sketched in Fig. 5.11, where a bar functions as an actuator as it
expands through thermal heating. Coupled to the thermal bar is a spring of
stiffness Application of a certain temperature increase will displace the
actuator-spring connection point to the right by a quantity as sketched in
the figure. This position is the result of the force equilibrium between the
actuation force (given generically in Chapter 4 in Eq. (4.7)) and the elastic
force developed in the spring, namely:

As discussed in Chapter 4, is the bloc force and the free displacement of
the actuator. The solution to Eq. (5.34) is:

The two characteristics, of the actuator and of the spring, are plotted in Fig.
5.12, and their intersection gives the value of Eq. (5.35).

Figure 5.12 Force-displacement characteristics of linear actuator and spring working in
series