This paper discusses the effects of substrate motions on the performance of microgyroscopes modeled as suspended beams with a tip mass. The substrate movements can be motions along as well as rotations around the three axes. Using Extended Hamiltonian Principle and Galerkin approximation, the equations of the motion of the beam are analytically derived. In these equations, the effects of beam distributed mass, tip mass, angular accelerations, centripetal and coriolis accelerations are clearly apparent. The effect of electrostatic forces inducing the excitation vibrations are considered as linear functions of beam displacement. The response of the system to different inputs is studied and the system sensitivity to input parameter changes are examined. Finally, the sources of error in the measurement of rotation rate input are recognized. The study demonstrated the importance of errors caused by cross axes inputs on the gyroscope output measurements and overall performance.

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