Countermeshing Gear Discriminator

One example of a surface micromachined mechanism is the countermeshing gear discriminator that was invented by Polosky et al. (1998). This device has two large wheels with coded gear teeth. Counter-rotation pawls restrain each wheel so that it can rotate counterclockwise and is prevented from rotating clockwise.

The wheels have three levels of teeth that are designed so they will interfere if the wheels are rotated in the incorrect sequence. Only the correct sequence of drive signals will allow the wheels to rotate and open an optical shutter. If mechanical interference occurs, the mechanism is immobilized in the counterclock-wise direction by the interfering gear teeth and by the counter-rotation pawls in the clockcounterclock-wise direction.

A drawing of the device and a close-up of the teeth are shown in Figures 4.24 and 4.25, respectively. The wheels have three levels of intermeshing gear teeth that will allow only one sequence of rotations out of the more than the 16 million that are possible. Because the gear teeth on one level are not intended to interfere with gear teeth on another level and because the actuators must remain meshed with the code wheels, the vertical displacement of the code wheels must be restricted. This was accomplished with dim-ples on the underside of the coded wheels that limited the vertical displacement to 0.5µm. Warpage of the large 1.9-mm-diameter coded wheels is reduced by adding ribs with an additional layer of polysilicon.

The large coded wheels are prevented from rotating backward by the counter-rotation pawls. These devices must be compliant in one direction and capable of preventing rotation in the other direction. The next example discusses counter-rotation pawls.

FIGURE 4.23 A surface micromachine encapsulated by a piece of glass. Comb-drives can be seen through the right side of the mechanically machined cap. This process can be accomplished either on a die or wafer basis. (Photograph courtesy of A. Oliver, Sandia National Laboratories).

Example

Figure 4.26 shows a counter-rotation pawl. The spring is 180µm long from the anchor to a stop (labeled as l) and 20µm long from the stop to the end of the flexible portion (denoted asa), with a width of 2µm and a thickness of 3µm. The Young’s modulus is 155 GPa. Assume that the tooth on the free end of FIGURE 4.24 The countermeshing gear discriminator. The two code wheels are the large gears with five spokes in the center of the drawing; the counter-rotation pawls are connected to the comb-drives; and the long beams in the upper right and lower left portion of the photograph. (Drawing courtesy of M.A. Polosky, Sandia National Laboratories.)

FIGURE 4.25 Teeth in the countermeshing gear discriminator. The gear tooth on the left is on the top level of polysil-icon and the gear tooth on the right is on the bottom layer. If the gears do not tilt or warp, the teeth should pass with-out interfering with each other. (Photograph courtesy of Sandia National Laboratories.)

the beam does not affect the stiffness and that the width of the stop is negligible. Find the spring constant of the pawl if the gear is rotated in the counterclockwise direction. Comment on the spring constant if the gear is rotated in the clockwise direction.

In the counterclockwise direction, the spring constantkis:

k 0.12 N/m

using a length laof 200µm. In the clockwise direction, it is tempting to redefine the spring length as 20µm. The resulting spring constant is 116 N/m. Unfortunately, this is an oversimplification because the beam will deform around the stop. The exact equation is in Timoshenko’s Strength of Materials [Timoshenko, 1958] and in Equation 4.41:

k 1

冢 冣 ^(4.41)

This equation results in a spring constant of 15 N/m, which is still very stiff but not as stiff as the results of the oversimplified calculation.

4.6.2 Microengine

One important element of many polysilicon mechanism designs is themicroengine. This device, described by Garcia and Sniegowski (1995) and shown in Figures 4.27 to 4.29, uses an electrostatic comb-drive

a²l 4EI a³

3EI Ew³t 4L³

1 a

FIGURE 4.26 Example of a simple counter-rotation pawl. The stop is assumed to have a width of 0.

connected to a pinion gear by a slider-crank mechanism with a second comb-drive to move the pinion past the top and bottom dead center. Two comb-drives are necessary because the torque on a pinion pro-duced by a single actuator has a dependence on angle and is given by the following equation:

TorqueF₀r|sin(θ)| (4.42)

X

Y

FIGURE 4.27 Mechanical representation of a microengine.

FIGURE 4.28 Drawing of a microengine. The actuator measures 2.2 mm2.2 mm and produces approximately 55 pN-m of torque.

whereF₀is the force of the comb-drive,θdescribes the angle between hub of the output gear and the link-age, andris the distance between the hub and the linkage. The torque produced by the “Y” actuator has a similar dependence on angle. The inertia of the rotating pinion gear is not great enough to rotate the gear past the top and bottom dead center. One important feature of this device is that the conversion from linear motion to rotary motion requires the beams between the actuator and the driven gear to bend. The bending is permitted by a polysilicon linkage that is 40µm in length and 1.5µm in width with a thickness of 2.5µm.

Example

The comb-drive labeled “X” inFigure 4.27 has an actuator arm that must bend 17µm in the lateral direction as the gear rotates from 0° to 90°. The gear is connected to the comb-drive via a 50-µm-wide beam that is 500µm long in series with a thin flexible link that is 1.5µm wide and 45µm long. The thin link is connected to the comb-drive actuator and both beams have a Young’s modulus of 155 GPa. Given that both beams are 2.5µm thick, approximately how much force does it take to bend to the flexible link-age to rotate the gear from q0 to q90° if friction and surface forces are neglected? A drawing of this linkage is shown in Figure 4.29.

Assume that each segment is a cantilever beam spring that has one end fixed while the other end is undergoing a small deflection. For each beam:

y_max (4.43)

and

k (4.44)

Recall that for rectangular cross sections:

I (4.14)

Using substitution, the equivalent spring constant for the long beam is:

k 155 GPa(2.5µm)(50µm)³ 97 NⲐm 4(500µm)³

Etw³ 4L³

tw³ 12

3EI L³ y_MAXP

PL³ 3EI

Linkage connection Flexible links

Hub

FIGURE 4.29 Detail ofFigure 4.28 showing the thin linkages that connect the comb-drives to the gear.

and for the short beam:

k 3.6 N/m

By Equation 4.35, the equivalent spring rate is:

3.5 N/m

We can employ some simple trigonometry and calculus to determine the needed deflection of the flex-ure. From the section on cantilever beam springs:

y

(

)

Because the majority of the bending occurs in the thin flexible link the desired slope of the flexible link at its end is:

(

)

For the case of the small flexible link,Iis equal to:

I 710²⁵m⁴

BecausexL45µm,Pcan be calculated as:

P 6155 GPa7.010²⁵m⁴ 3.4µN