Deflection of an eccentric tooth of a comb drive in an electrostatic field

The elastic deflection of a comb drive tooth in an electrostatic field is considered. The tooth can be symmetrically located between two rigid teeth of the matching comb, in which case the problem reduces to a pure bifurcation problem for which the critical voltage can be determined. Alternatively, due to an ap- proximate straight-line mechanism, the tooth can have a uniform initial lateral displacement and a smooth curve of equilibria is found which has a limit point, after which pull-in occurs. An assumed deflection shape and a series expansion of the electrostatic capacity yield the deflection curves for the case with a uniform initial lateral displacement. This shows that pull-in occurs at a voltage that is reduced by a factor that is about pro- portional to the two-third power of the relative lateral initial dis- placement. The theoretical results have been experimentally tested. The results show a qualitative agreement, but the experimental de- flections are larger and the pull-in voltages are lower. These differences can be explained from neglected fringe fields and de- viations from the nominal shape.