Page 302 - Mechanics of Microelectromechanical Systems

5. Static response of MEMS 289
For the amplification scheme of Fig. 5.21 (b), point 3 will move due to
bending and axial deformations as follows:

The horizontal displacements and as well as the displacement
amplification a are given by Eqs. (5.67), (5.68) and (5.69), respectively. The
vertical displacement of point 1 in Fig. 5.21 (b) is:

Example 5.12
Assess the errors that appear in the amplification produced by the
microdevice of Fig. 5.21 (b) when neglecting the axial deformation of the
flexure hinge. Consider that the flexure has a constant rectangular cross-
section and that and

Solution:
When the axial deformation is accounted for, in addition to the bending-
produced deformation, the horizontal displacement at point 3 can be
calculated by means of Castigliano’s displacement theorem as:

and the slope at the flexure’s tip is:

For small displacements, the horizontal motions at points 1 and 2 can be
approximated as:

and the corresponding displacement amplification becomes: