**5. Conclusion**

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

2 2

 

2 2

 

6 6 66 6 6 6 \* sin \* \* cos \* *Ar r w cy c <sup>c</sup>* 

6 6 66 6 6 6 \* cos \* \* sin \* *Acx c <sup>c</sup> r rw* 

.. ..

5 6 6 66 6 6 5 5 5 5 5 5 \* sin \* \* cos \* \* sin \* \* cos \* *Ac y <sup>c</sup> <sup>c</sup> r r wr*

5 6 6 66 2 2 5 5 5 5 5 5 \* cos \* \* sin \* \* cos \* \* sin \* *Ac x <sup>c</sup> <sup>c</sup> r r wr*

The micro mechanism operates under constant angular velocity, 0.01 [rad/s], the slider crank starts increasing and reaches to its maximum value, 200 micron, meaning that the first stage slider crank is fully opened at 3.20 sec. then the first crank angle pass from 0° and slider begins to get close to its initial position and R1 decreases as shown Fig. 18. According to both crank angles, Θ2 and (90-Θ6), the output force increases or decreases. In the first section of the Foutput vs. time curve, first, both crank angles decrease, and two slider cranks start to open and at small crank angles, Foutput sharply increase and at 3.20 sec Θ2 is equal to 0.0013°

 

> 

(64)

 

> 

2 5 <sup>5</sup> *<sup>c</sup> Ac R R* (66)

(65)

*r w* (67)

*r w* (68)

<sup>2</sup>

<sup>2</sup>

The center of mass acceleration of beam 5 along x and y direction;

**Figure 18.** Displacement of slider and output force versus time

**4.4. Force and dynamic analysis of the micro mechanism** 

The MEMS force amplifier designed in this study is shown to provide high output to input ratio.

By quasi-static analysis, 5090 force amplifying is achieved as the first crank angle, Θ2, rotates 10° and passes from its horizontal position and (90°-Θ6) rotates 1.85° and continues to decrease.

The maximum amplifying ratio changes based on the initial position of the micro mechanism. So, the toggle of the micro mechanism has a crucial role to get high force output and high force amplification. If the mechanism's initial position is adjusted properly as both crank angles pass 0° at the same time, the force output and consequently force amplification go to infinity.

If pseudo rigid body of the compliant MEMS force amplifier having elastic hinges is modeled as a further study, it would provide us to get much more close response to the micro mechanism's real behavior. This novel MEMS amplifier design achieves high force amplifying due to its geometric design.

By dynamic analysis, high output force is achieved as the micro mechanism operates under 0.01 [rad/s] constant angular velocity of beam 6 at 3.20 sec and at about fully open position of first crank angle.

By Simulink, the simulation displays dynamic behavior of the micro compliant mechanism and it is claimed that second stage crank angle rotates 4.01°, whereas first stage crank angle, Θ2, rotates 19.92°.

