Micro-electromechanical system (MEMS) vibratory gyroscopes are inertial sensors for measuring angular velocity based on a micro-machined proof-mass that can detect rotating-induced inertial force (i.e., Coriolis force). During the past several decades, great advancement has been achieved in the fields of design and fabrication of MEMS vibratory gyroscopes, however, little investigation on understanding and improving their measurement range could be found in the literature. We find that most of the commercial single-axis force-rebalance MEMS vibratory gyroscopes have a measurement range of the order 10^2 . A question naturally arises: is there any physical reasoning to the limit of the measurement range? To answer this question, we propose a theoretical method to investigate the limit by creating a mathematical model for typical single-axis force-rebalance MEMS vibratory gyroscopes. A deeper analysis gives the answer to the question, for the first time.
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