Page 164 - Mechanics of Microelectromechanical Systems

3. Microsuspensions 151
configuration # 1. Similarly, when the same Eqs. (3.60) through (3.65)
change into Eqs. (3.46) through (3.51), respectively, which define
configuration # 2. All these calculations confirm the correctness of the
equations derived here.
The out-of-the-plane stiffness for this configuration # 3 is:

Example 3.7
Decide which of the three U-spring configurations is the most compliant
about the main direction of motion when compliant members of all design
variants have the same rectangular cross-section and can be inscribed each in
the same rectangle of sides equal to and Also known are
and

Solution:
The compliances of the three U-spring configurations will be
compared by analyzing compliance ratios. It can be seen that while the first
two configurations have their compliances determined by the parameters
given in this example, the third configuration can have various compliances
because the radius R can take any value from 0 to
The following compliance ratios are discussed:

where the superscripts 1, 2 and 3 denote the first, second and third
configuration, respectively.
Figure 3.18 is the plot of the first ratio defined in Eqs. (3.73) as a
function of the radius R, in the case R / w > 10 for configuration # 3.
Similarly, Fig. 3.19 pictures the second ratio of Eq. (3.73). As Fig. 3.18
indicates it, the design configuration # 1 is more compliant than the design
configuration # 3, but they tend to be equal for small radii. Configuration # 2
is less compliant than configuration # 3, but for large radii, the two designs
have almost identical compliances. Similar plots are drawn in Figs. 3. 20 and
3.21 when R / w < 10 for configurations # 2 and # 3.