This paper describes the dynamics of a microelectromechanical rate gyro whose operation depends on nonlinear parametric resonant response. The basic idea behind this and other similar gyros is that a proof mass is free to move in a plane such that the perpendicular directions of motion are ideally mechanically uncoupled. In one direction, the drive mode, the mass is parametrically driven such that it undergoes a nonlinear resonant response. When rotated about an axis perpendicular to the plane of motion, Coriolis effects couple this drive mode to the other direction, the sense mode, whose response is then measured and calibrated with the rotation rate. Traditional rate gyros of this type require precise matching of the drive and sense linear natural frequencies in order to optimally amplify the sense response. By making use of the wide frequency range of the nonlinear resonant response, many of the difficulties associated with this tuning problem can be avoided. In this paper we emphasize results from a simple two degree-of-freedom micro-electro-mechanical system model that allows one to predict and design the rate response of the gyro by selection of system parameters.

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