Page 282 - Mechanics of Microelectromechanical Systems

5. Static response of MEMS 269
The total electrostatic force can be calculated by integrating Eq. (5.14) over
the length and by using Eqs. (5.10) and (5.11), namely:

This electrostatic force is equal to the inertia force that is generated by the
external acceleration and the mass of the proof mass, as given in the first Eq.
(5.11). The acceleration a can be determined by solving the third-degree
algebraic equation that results by equating Eq. (5.16) and the first Eq. (5.11).

2.3 Rotary Microdevices

Rotary actuation and sensing, together with appropriate suspensions, are
used in microgyroscopes for instance that are utilized to detecting changes in
the direction of rotation of navigational systems such as those implemented
in cars. The rotary portion of a microgyroscope consists at its minimum of
actuation, sensing and suspension. An example, similar to the one analyzed
by Geiger et al. [1], is sketched in Fig. 5.5, where two pairs of rotary
electrostatic actuators (connected in parallel) are disposed symmetrically to
ensure balancing of the microdevice. Two similar sensing pairs (also in
parallel connection) are disposed 90° with respect to the actuator units. The
outer mobile hub and the inner fixed post are connected by means of a spiral
spring.

Figure 5.5 Rotary electrostatic transduction with spiral-spring microsuspension