**2.1. Grashof theorem**

In rigid body model of the MEMS amplifier, four-bar configuration is attained after vector loop equations are derived. Grashof theorem becomes significant to demonstrate the act of micro mechanism. Grashof theorem takes three cases into consideration and states that when both of beams are rocked it is called a double-rocker when both of beams are able to revolve, then it is called double-crank, when the short beam is able to rotate as the long one is rocked, then it is called a crank-rocker mechanism. To determine the moving limit of the micro mechanism, the relation between the lengths of beams turns out to be an important issue. Therefore, selecting the length of a beam plays a crucial role for the micro mechanism.

Due the fact that, x1, x2 are assumed as length of the shortest beam and length of the longest beam, respectively, as x3, x4 are the mean lengths of the beams. If x1+x2<= x3+x4, at least one of the beams can rotate and If x1+x2= x3+x4, the mechanism is activated and crank has limited rotation this feature enables beams to pass horizontal positions closely to each other achieving a high force amplifying.

**Figure 2.** Novel compliant MEMS Force Amplifier
