Page 182 - Mechanics of Microelectromechanical Systems

3. Microsuspensions 169

and for the given moment of inertia and Young’s modulus, the stiffness
depends on and c, as shown in Fig. 3.38. The stiffness decreases with
and c increasing. For the values of and the solution is c = 0.94, and
therefore the length of the short leg is

Example 3.14
A sagittal suspension and a folded-beam spring can be inscribed within
the same a x b rectangular area What are their
stiffnesses about the motion direction, in the case both designs have the same
cross-section of their compliant members ? Consider that and
for the sagittal spring, and that for the folded-beam suspension.

Solution:
When both designs are inscribed in the given rectangular area, the main
dimensions of the sagittal suspension are related by the following
relationships:

which yield The conditions for the folded-beam design are:

and they result in:

Figure 3.39 stiffness ratio of sagittal spring versus folded-beam spring