**2. Mechanism design**

90 MATLAB – A Fundamental Tool for Scientific Computing and Engineering Applications – Volume 1

**Figure 1.** Schematic view of force or displacement amplifier' mechanism

mechanisms (Parkinson et al, 2001).

Huang & Lan, 2006) induced forces.

behavior (Jensen et al, 2004).

Compliant MEMS have been used as a force amplifier in micro actuators and micro-

They are preferred since there is no need for assembly, no energy loss due to absence of friction, thus requiring no need for lubrication all of which providing high precision (Kosa et al, 2010). Besides, compliant micro mechanisms could be activated by mechanically (Han et al, 2007; Krishnan & Ananthasuresh, 2008), electro statically (Français et al, 2005; Millet et al, 2004), thermally (Lai et al, 2004; Terre & Shkel, 2004) or electrical (Gomm et al, 2002;

Moreover, compliant MEMS having two or three clear stable states as named bi-stable or tristable behavior respectively were used in micro valve, micro switch, micro clasps applications (Chen et al, 2009; Jensen et al, 2001; Jensen & Howell, 2003; Nathan & Howell, 2003; Wilcox & Howell, 2005). For instance, Jensen designed several mechanisms such as double slider crank, slider-rocker mechanisms and explained the theory of bi-stable

Recent studies on compliant mechanisms are focused on novel designs (Kosa et al, 2010), new developed methodologies and optimization in topology (Chour & Jyhjei, 2006; Krishnan & Ananthasuresh, 2008; Pedersen & Seshia, 2004), size and shape (Krishnan & Ananthasuresh, 2008) or the use of finite element methods (Jensen et al, 2001). Compliant micro mechanisms enable mechanical or geometric benefit meaning that the ratio of output force to input force and the ratio of output displacement to input displacement, respectively, and both mechanical

MA=Fout/Fin (1)

GA=dout/din (2)

and geometric advantage (MA and GA, respectively) are formulized as follows;

Compliant MEMS force amplifier's configuration is schematically shown in Fig. 2. Micro amplifier is composed of two slider-crank mechanisms. The two stage slider-crank amplifier provides force amplifying by means of its novel design. Its aim is to perform high output force at point B under low input forces. Two stages provide much more amplification compare to one stage. For both stages, rigid beams are linked by single thin flexible beams having a width of 3 µm. These flexible beams make the micro mechanism motion possible under operating forces. The micro mechanism stores energy and transfers force by elastic deformation of flexible beams linking rigid beams as both stage-slider cranks get close zero degree crank angle. Afterwards, input force is removed and micro amplifier springs back to its original position by means of flexible links having large deflections.

The beams in first stage have a length of 100 µm and width of 25 µm as the beams in second stage have a length of 800 µm and width of 25 µm, as all beams have rectangular cross sectional area. The depths of all beams are chosen as 25µm limited by SOI-MUMPs (Silicon on Insulator Multi User MEMS Process) manufacturing technology (Cohen et al, 2009).
