ÍNDICE DE SOSTENIBILIDAD

3.3 Pivot Pivot and and Output Output System System Configuration Configuration

Figure 3.6 is an interesting plot which shows how the amplification factor varies Figure 3.6 is an interesting plot which shows how the amplification factor varies with the angle between the pivot beam and the lever arm. It is found that the with the angle between the pivot beam and the lever arm. It is found that the amplification factor is maximum when the angle between the pivot beam and the lever  amplification factor is maximum when the angle between the pivot beam and the lever   beam

 beam is is at at 90 90 degrees. degrees. At At 270 270 degrees, degrees, the the amplification amplification factor factor is is slightly slightly smaller smaller thanthan that at 90 degrees. When the pivot is at the same or opposite side of the output system, that at 90 degrees. When the pivot is at the same or opposite side of the output system, the mechanism is deflected differently.

the mechanism is deflected differently.

Sometimes, the micro-fabrication technology constraints will determine the Sometimes, the micro-fabrication technology constraints will determine the leverage mechanism configuration, whether the pivot and the output system can be leverage mechanism configuration, whether the pivot and the output system can be  placed

 placed on on the the same side same side or or different sides different sides of the of the lever alever arm, e.g., rm, e.g., SOI-MEMS technologySOI-MEMS technology only allows an outside anchor. Figure 3.7 shows the Model I pivot where the pivot and  only allows an outside anchor. Figure 3.7 shows the Model I pivot where the pivot and  output system are on (a) the same side and (b) opposite sides of the lever arm. Table 3.2 output system are on (a) the same side and (b) opposite sides of the lever arm. Table 3.2 lists the results from SUGAR simulation for a comparison between the two cases. The lists the results from SUGAR simulation for a comparison between the two cases. The horizontal displacements are significantly different and the force direction changes. Also horizontal displacements are significantly different and the force direction changes. Also different are the rotation angles. Those differences cause slight amplification factor  different are the rotation angles. Those differences cause slight amplification factor  change for the single-stage leverage mechanism.

change for the single-stage leverage mechanism.

Figure 3.8 shows the shape of the deflected pivot beam when the pivot and the Figure 3.8 shows the shape of the deflected pivot beam when the pivot and the output system are on different sides of the lever beam. Although the effect of the lever  output system are on different sides of the lever beam. Although the effect of the lever  configuration on the amplification factor of a single-stage microleverage mechanism is configuration on the amplification factor of a single-stage microleverage mechanism is insignificant, the effect becomes much more pronounced in a two-stage microleverage insignificant, the effect becomes much more pronounced in a two-stage microleverage

mechanism. For a second-kind lever, the 2

mechanism. For a second-kind lever, the 2 D D microlever has a lower amplification factor microlever has a lower amplification factor  than 2

than 2S S , as explained in , as explained in detail in later detail in later Chapters. Chapters. The deflections of The deflections of pivot and connectionpivot and connection  beams

 beams are are simulated simulated with with SUGAR SUGAR and and plotted plotted in in Fig. Fig. 3.9. 3.9. For For illustrative illustrative purposes, purposes, thethe scale of the vertical axis (location on a beam) is 10

scale of the vertical axis (location on a beam) is 10⁶⁶ times that of the horizontal axistimes that of the horizontal axis (deflection). When the connection beam and the pivot are on different sides of the lever  (deflection). When the connection beam and the pivot are on different sides of the lever  arm, the shape of connection beam under loading is interesting, noting that they would  arm, the shape of connection beam under loading is interesting, noting that they would  have been bent in the same fashion if they had been on the same side of the lever arm.

have been bent in the same fashion if they had been on the same side of the lever arm.

Because of the increased resistance to rotation when the pivot and output connection Because of the increased resistance to rotation when the pivot and output connection  beam are on different sides of a lever arm, the amplification factor is reduced.

 beam are on different sides of a lever arm, the amplification factor is reduced.

Input Input L

L ll

Output System Output System Pivot

Pivot 1

1

2 2

3

3 44 55

6 6

7 7 (a)

(a) VVertertical ical PPivivotot

Input Input L

L ll

Output System Output System

Pivot Pivot 1

1 22

3

3 44 55

6 6

7 7 (b) Horizont

(b) Horizontal Pal Pivotivot

Input Input L

L ll

Output S Output Syystemstem Pivot

Pivot 1

1

2 2

3

3 44 55

6 6

7 7 (C

(C) ) CombCombined ined PPivotivot

11 11

Fig. 3.4

Fig. 3.4 Different Different Pivot MPivot Models.odels.

0 Length of Pivot Beam, micron

Length of Pivot Beam, micron

All dimensions

Fig. 3.5 3.5 Comparison Comparison of of the the amplification amplification factors factors of of three three Models Models as as a a function function of of thethe  pivot beam length. Angle Between Pivot and Lever Arm

Angle Between Pivot and Lever Arm

All dimension

Pivot Model I, II, aI, II, and In-betweennd In-between Lever Ratio 21:1

Lever Ratio 21:1

Model II Model II Model I

Model I Model IModel I

Fig. 3.

Fig. 3. 6 6 Effect of Effect of pivot beam pivot beam with diffwith different angles erent angles on the on the amplification amplification factor.factor.

(a)

(a) PPivot ivot at at the the samesame sid

side as outpue as outputt

Input Input Pivot

Pivot

Output System Output System

(b)

(b) PPivot ivot at at the the differentdifferent sid

side as outpue as outputt

Input Input Pivot

Pivot

Output System Output System

Fig.

Fig. 3.7 3.7 A second-kind leverage A second-kind leverage mechanism with the pivot anmechanism with the pivot and output systemd output system (connection beam) (a) on the

(connection beam) (a) on the same side and (b) different sides of the same side and (b) different sides of the lever arm.lever arm.

0 Horizontal Displacement, 1E-6 micron Horizontal Displacement, 1E-6 micron

Second-Kind lever with single Second-Kind lever with single

beam as output beam as output  All dimensions in  All dimensions in micronsmicrons

L = 210

Fig 3.8 The shape of a deflected pivot located on the opposite The shape of a deflected pivot located on the opposite side of the lever arm.side of the lever arm.

0

Horizontal Displacement, 1E-6 Horizontal Displacement, 1E-6 micronmicron Horizontal Displacement

Horizontal Displacement, 1E, 1E-6 micron-6 micron

Fig 3.9

Fig 3.9 The deflection of The deflection of pivot and connection pivot and connection beams of beams of a 2D a 2D microlever.microlever.

CHAPTER 4

CHAPTER 4