Page 319 - Mechanics of Microelectromechanical Systems

306 Chapter 5
Figure 5.41 shows an example where two identical units are used to
actuate a central unit. The two different units have potentially different
stiffness and amplification properties. The input forces actuate the two
side amplification devices in the way suggested in Fig. 5.41, and their output
serves as input to the middle amplification microdevice, which produces
the bi-directional doubly-amplified output displacements Knowing the
amount of actuation force it is of interest to determine the output
displacement The subscript 1 will be used to denote the side input
actuators and the subscript 2 will stand for the middle amplification unit. The
displacement amplifications produced by the two units are:

However, the input displacement to the middle unit is the output
displacement produced by the first unit and therefore the two Eqs.
(5.116) combine into:

The input displacement can be expressed as:

The input stiffness of the side amplification device is connected to the
stiffness at its output port about the output direction, as shown previously. In
the present case, the stiffness at the output port of the side device is
composed of the output stiffness of this device, coupled in parallel to the
input stiffness of the middle microdevice, and therefore, the following
equation applies (the minus sign of the original Eq. (5.89) is ignored):

By combining Eqs. (5.117), (5.118) and (5.119), yields the absolute output
displacement, namely:

In order to increase the output displacement, the amplification of the middle
microdevice needs to be high, whereas the amplification of the side
microdevices has to be relatively small. Also the output stiffness of the side