Page 176 - Mechanics of Microelectromechanical Systems
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3. Microsuspensions 163
A first-level design and modeling approach would be the one considering
constant cross-section compliant microhinges, but they could also be of a
different shape, such as corner-filleted or be a series combination of different
compliant segments in order to achieve specific design requirements. It is
considered here that both compliant links have the same constant cross-
section, and that only bending is taken into account.
By applying a force at point 1 in Fig. 3.34, the corresponding
displacement can be found which will enable determining the required
stiffness As previously mentioned, the reactions and need to be
calculated by solving the equations: and which are set up by
applying Castigliano’s displacement theorem.
Figure 3.34 Half-model of a sagittal spring for x-stiffness calculation
It can be shown that the stiffness about the motion direction of the half model
is:
By taking in Eq. (3.96) results in:
which is the stiffness for a U-spring formed of two parallel fixed-free beams
of length When the cross-section of the two identical compliant members
of Fig. 3.34 is variable, Equation (3.96) can be generalized to the form:
