Electrostatic actuators

Equation 4.

When the plates of the capacitor move towards each other, the work done by the attractive force between them can can be computed as the change in U with distance (x). The force can be computed by equation 5.

Equation 5.

Note that only attractive forces can be generated in this instance. Also, to generate large forces (which will do the useful work of the device), a large change of capacitance with distance is required. This has lead to the development of electrostatic comb drives (figure 12a).

Figure 12.

Comb Drives. These are particularly popular with surface micromachined devices. They consist of many interdigitated fingers (figure 12a). When a voltage is applied an attractive force is developed between the fingers, which move together (figure 12b). The increase in capacitance is proportional to the number of fingers; so to generate large forces, large numbers of fingers are required. One potential problem with this device is that if the lateral gaps between the fingers are not the same on both sides (or if the device is jogged), then it is possible for the fingers to move at right angles to the intended direction of motion and stick together until the voltage is switched off (and in the worst scenario, they will remain stuck even then).

Wobble motors are so called because of the rolling action by which they operate. Figure 13a,b shows a surface micromachined wobble motor design. The rotor is a circular disk. In operation the electrodes beneath it are switched on and off one after another. The disk is attracted to each electrode in turn; the edge of the disk contacting the insulator over the electrode. In this manner it rolls slowly around in a circle; making one revolution to many revolutions of the stator voltage. Problems can arise if the insulating materials on the stator electrodes wear rapidly, or stick to the rotor. Also, if the rotor and bearing aren't circular (this is possible since many CAD packages draw circles as many sided polygons), then the rotor can get stuck on its first revolution.

Figure 13.

A problem with surface micromachined motors is that they have very small vertical dimensions, so it is difficult to achieve large changes of capacitance with motion of the rotor. LIGA techniques can be used to overcome this problem - for instance the wobble motor shown in figure 13c,d, where the cylindrical rotor rolls around the stator.

[Electrostatic Comb Driven Resonator (image from MCNC - 39k).]
[Wobble Motor (image from MCNC - 68k).]
[Operating Wobble Motor (mpeg video from MCNC - 157k).]