Page 272 - Mechanical design of microresonators _ modeling and applications

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Resonant Micromechanical Systems

Resonant Micromechanical Systems 271
rod

ac vr
collar

ω

Figure 5.46 Collar sliding on a rotating rod as an example of the Coriolis effect.

V
İ = d (5.112)
0 31 t
1
where d 31 is the charge constant. When an ac voltage of the form:

V = V sin (Ȧt) (5.113)
0
is applied across the piezoelectric material, a sinusoidal force can be
generated which is applied at the free tip, whose amplitude is
4d 31
F = fV 0 (5.114)
0
lt
1
5.5 Resonant Microgyroscopes

Gyroscopes in the macroworld are bodies with a fixed position which
can freely rotate about three independent axes under the action of ex-
ternal forces and moments. In the micro- and nanodomain, gyroscopes
are mostly utilized as sensors of an externally applied angular velocity.
Applications of microgyroscopes include automobile control, inertial
navigation, platform stabilization, motion compensation in video cam-
eras, inertial mouse devices in computers, virtual reality devices,
robotics, and surgical instruments, as indicated by Fujita, Maenaka,
17
15
16
14
and Maeda; Li et al.; Yang et al.; Kawai et al.; Geiger et al.; 18
4
19
Degani et al.; Nakano, Toriyama, and Sugiyama; Ajazi and Najafi; 20
22
21
Yazdi, Ayazi, and Najafi; or Park et al.; to cite just a few of the works
dedicated to microgyroscopes.
The operating principle of gyroscopes is based on the Coriolis effect
which is illustrated in Fig. 5.46.
The collar slides on the rod with a relative velocity v r while the rod
undergoes a rotary motion with an angular speed Ȧ. It is known from
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