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4. Microtransduction: actuation and sensing 201
Eqs. (4.20) and (4.21) can be combined into:
Equation (4.23) is plotted in Fig. 4.23, which shows the non-linear
relationship between the normalized force and the normalized displacement.
It can be seen that the attraction force is 100 times larger than the initial-gap
force when the gap is 10% of the initial value.
In many practical applications, several identical pairs of transverse
actuators are used in order to increase the total force, and this principle is
exemplified in the picture of the MUMPs microdevice shown in Fig. 4.21
where two fixed digits were placed in the space created by two mobile ones.
Another solution is sketched in Fig. 4.24 where one digit of the movable part
is placed closer to one digit of the fixed counterpart, in such a way that the
attraction force generated by the resulting gap is larger than the opposite
force that is produced through the larger gap between the mobile digit and
the other neighboring fixed digit.
Figure 4.24 Digitated arrangement in a transverse electrostatic actuator
The resulting force in this case is simply the difference between the two force
components, namely:
