Page 194 - Mechanics of Microelectromechanical Systems

3. Microsuspensions 181
Problem 3.8
A basic serpentine spring of very thin cross-section (t << w) with a given
value of its long leg‚ has to be stiff about the out-of-the-plane (z) direction
and compliant in torsion. Select a length which will satisfy these
requirements. (Hint: Analyze the ratio).

Answer:
The ratio is maximum (which means the numerator is maximum and the
denominator is minimum) for a given when is minimum.

Problem 3.9
What is the main compliance of a linearly-scaled serpentine spring that
contains two units ? The length of the smaller unit’s long leg is
the shorter leg’s length is and E = 140 GPa.

Answer:
The compliance is the sum of the two units compliances;

Problem 3.10
Compare the two linear in-plane compliances of a bent beam serpentine
spring that is microfabricated of polysilicon with E = 130 GPa‚ G = 40 GPa‚

Answer:

Problem 3.11
Find the out-of-the-plane deflection of a bent beam serpentine spring
with E = 135 GPa‚ G = 42
GPa under the action of a force of Also calculate the deflection of
a similar bent beam spring with under the same loading and having all
other geometrical and material properties identical to the ones of the bent
beam serpentine spring.

Answer:
Stiffness of bent beam serpentine spring is 36.219 N/m.
Stiffness of bent beam spring is 11.808 N/m.

Problem 3.12
A configuration # 1 U-spring (with the boundary conditions of Fig. 3.12)
with and a sagittal spring (Figure 3.35)‚ both inscribed in the same
rectangular area are possible solutions for an application where
relatively high (definition) stiffness is required. Determine the best design
solution‚ when E = 140 GPa.