Page 178 - Mechanics of Microelectromechanical Systems

3. Microsuspensions 165
condition Eventually, the z-axis stiffness is calculated by considering
bending and torsion of the two compliant members (the cross-section is
considered constant) and its (quite complex) expression is:

with:

Example 3.12
A sagittal spring needs to be as insensitive as possible to the action of
external forces that act about the y-direction while maintaining a good
compliance about the motion direction. What is the inclination angle that
would accomplish these objectives for a given constant rectangular cross-
section ?

Solution:
The conditions of the problem require maximizing the following stiffness
ratio:

By using the definition Eqs. (3.98) and (3.101), the ratio of Eq. (3.105)
becomes:

and therefore the stiffness ratio is maximum when the inclination angle is
minimum, i.e. A practical solution will take a very small value of

2.7 Folded Beams

Another microspring configuration that is being utilized to spring-couple
to the translatory motion of a proof mass is shown in Fig. 3.36 where two