Page 281 - Mechanics of Microelectromechanical Systems
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268 Chapter 5
By assuming that the acceleration of the monitored system acts
perpendicularly to the flexure-hinge microaccelerometer, it is possible to
evaluate this acceleration by means of a measured amount, such as the
deflection or the slope of the deformed flexure as shown next. It can be
considered that the inertia force acts at point 2, the center of the proof mass –
Fig. 5.4 (a), which means the flexure hinge is loaded at its tip 3 by the inertia
force and the moment The slope and deflection at point 3 can be found
by using the compliance formulation of Chapter 2 as:
where the compliances above define any of the flexure microhinges that have
been analyzed in Chapter 2. The inertia force and moment are:
The unknown acceleration a can be determined when either the slope or the
deflection of Eqs. (5.10) can be measured directly (experimentally), namely:
or:
Example 5.2
Determine the external acceleration by means of a flexure-hinge
microaccelerometer (as the one sketched in Fig. 5.4 (a)) whose gap is
measured electrostatically.
Solution:
An elementary electrostatic force can be formulated that corresponds
to a length dx (not shown in Fig. 5.4 (b)) and to the gap g(x). This force is:
The variable gap g(x), as shown in Fig. 5.4 (b), is:
