**1. Introduction**

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MEMS are micro electromechanical systems having component sizes varying from 1 micrometer to 1 millimeter and provide specific engineering operations. MEMS are used as a micro sensor, micro actuator, micro accelerometer etc. and also have tendency to function rapidly due to having low inertia moment and affected less by disturbances coming from environment due to their small size (Hsu, 2002).

Compliant mechanisms having an ability to transmit motion and energy via their flexible hinges and/or flexible components instead of joints and rigid components, perform large deflections (Sreekumar et al, 2008). The large deflections of compliant mechanisms instead of rigid-body mechanisms depend on applied force that causes a much more complexity to nonlinear analysis (Ashok, 2000). Moreover, the geometry of several flexure hinges are modeled as torsion springs in its pseudo-rigid-body mechanisms (Howell, 2001). Flexible segments of compliant mechanism store and transfer energy when it is functioning (Howell, 2001; Tantanawat & S. Kota, 2007). Flexible links having small cross sections instead of traditional joints provide acting of mechanism due to its very low moment of inertia (Howell, 2001; Lobontiu et al, 2001).

Compliant four-link mechanism is designed as seen in Fig. 1 achieving force or displacement application according to the output spring constant and also, studied on size optimization to achieve maximum mechanical or geometric benefit at specific spring constants (Parkinson et al, 2001). Large displacement amplifier integrated with comb drive achieves 100 times amplifying of comb drive displacement by means of its design is modeled (Li et al, 2005).

© 2012 Kosa et al., licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2012 Kosa et al., licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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

Compliant MEMS have been used as a force amplifier in micro actuators and micromechanisms (Parkinson et al, 2001).

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; Huang & Lan, 2006) induced forces.

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 behavior (Jensen et al, 2004).

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

$$\mathbf{MA} \triangleq \mathbf{F}\_{\text{out}} / \mathbf{F}\_{\text{in}} \tag{1}$$

$$\mathbf{G} \mathbf{A} \mathbf{=} \mathbf{d}\_{out} / \mathbf{d}\_{in} \tag{2}$$

The energy is conserved during the motion transfer of compliant micro mechanism indicating that the increase in the output force causes decrease in the output displacement and vice versa. So, both mechanical and geometric benefits are significant to provide input to the micro actuators in MEMS applications (Kosa et al, 2010).

Optimization of compliant mechanisms such as topology and size optimization is a challenging issue. In topology optimization, it is critical to design a suitable functional configuration of the mechanism to provide desired output motion under applied forces while in size optimization, it is important to achieve desired force or displacement amplification so as to operate under maximum loads (Kota et al, 2001).

In this study, novel compliant MEMS force amplifier is designed and simulated by modeling its rigid body mechanism by Matlab/Simulink to determine the dynamic and quasi-static behavior. Kinematic approach is investigated and kinematic equations are derived and velocity and acceleration analysis of the micro mechanism are modeled. Dynamic response of MEMS amplifier is validated at a constant angular velocity and it is concluded that force amplification reaches to infinity at zero-crank angle. It is achieved that force amplification ratio reaches 5093, as the first stage crank angle, Θ2 passes from 0° in quasi-static simulation.
