Page 313 - Mechanics of Microelectromechanical Systems

300 Chapter 5
By combining Eqs. (5.97) and Eq. (5.95) gives the output displacement
which is produced by application of the force F at the input port 1, namely:

The displacement amplification is found by means of Eqs. (5.91), (5.92) and
(5.98) as:

Example 5.15
Check whether the input stiffness output stiffness and
displacement amplification a of the quarter-model of a microdevice with four
straight hinges, as the one pictured in Fig. 5.26, satisfy the condition of Eq.
(5.89), which is valid for a similar device with pure rotation joints.

Solution:
If one combines Eqs. (5.93), (5.96) and (5.99), the condition posed in Eq.
(5.89) is only possible when:

which is equivalent to the particular value of the inclination angle:

Example 5.16
Based on the equations giving the input and output stiffness and the
displacement amplification for a quarter-model amplification microdevice,
find those amounts that correspond to the full, four-flexure microdevice.

Solution:
The full microdevice comprises four flexures and its spring-based model
is shown in Fig. 5.36 (a). There are two branches between the nodal points A
and B, the upper one and the lower one, each formed of two identical springs
connected in series. The equivalent spring stiffness for each branch is
according to the series connection rule, presented in this chapter. As a
consequence, the equivalent spring shown in Fig. 36 (b) results from