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# Vibrating structure gyroscope

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 Title: Vibrating structure gyroscope Author: World Heritage Encyclopedia Language: English Subject: Collection: Gyroscopes Publisher: World Heritage Encyclopedia Publication Date:

### Vibrating structure gyroscope

A vibrating structure gyroscope, standardised by IEEE as Coriolis vibratory gyroscope (CVG),[1] is a wide group of gyroscope using solid-state resonators of different shapes that functions much like the halteres of an insect.

The underlying physical principle is that a vibrating object tends to continue vibrating in the same plane as its support rotates. In the engineering literature, this type of device is also known as a Coriolis vibratory gyro because as the plane of oscillation is rotated, the response detected by the transducer results from the Coriolis term in its equations of motion ("Coriolis force").

Vibrating structure gyroscopes are simpler and cheaper than conventional rotating gyroscopes of similar accuracy. Miniature devices using this principle are a relatively inexpensive type of attitude indicator.

## Contents

• Theory of operation 1
• Implementations 2
• Piezoelectric gyroscopes 2.1
• Wine-glass resonator 2.2
• Cylindrical resonator gyroscope (CRG) 2.3
• Tuning fork gyroscope 2.4
• Vibrating wheel gyroscope 2.5
• MEMS gyroscopes 3
• Applications 4
• Spacecraft orientation 4.1
• Automotive 4.2
• Entertainment 4.3
• Photography 4.4
• Hobbies 4.5
• Industrial robotics 4.6
• Other 4.7
• References 5

## Theory of operation

Consider two proof masses vibrating in plane (as in the MEMS gyro) at frequency \scriptstyle\omega_r. Recall that the Coriolis effect induces an acceleration on the proof masses equal to \scriptstyle a_c = 2(v\times\Omega), where \scriptstyle v is a velocity and \scriptstyle\Omega is an angular rate of rotation. The in-plane velocity of the proof masses is given by: \scriptstyle X_{ip} \omega_r \cos(\omega_r t), if the in-plane position is given by \scriptstyle X_{ip} \sin(\omega_r t). The out-of-plane motion \scriptstyle y_{op}, induced by rotation, is given by:

y_{op} = \frac{F_c}{k_{op}} = \frac{2m\Omega X_{ip} \omega_r \cos(\omega_r t)}{k_{op}}

where

\scriptstyle m is a mass of the proof mass,
\scriptstyle k_{op} is a spring constant in the out of plane direction,
\scriptstyle\Omega is a magnitude of a rotation vector in the plane of and perpendicular to the driven proof mass motion.

In application to axi-symmetric thin-walled structures like beams and shells, Coriolis forces cause a

• Proceedings of Anniversary Workshop on Solid-State Gyroscopy (19–21 May 2008. Yalta, Ukraine). - Kyiv-Kharkiv. ATS of Ukraine. 2009. - ISBN 978-976-0-25248-5. See also the next meetings at: International Workshops on Solid-State Gyroscopy [1].
• Silicon Sensing - Case Study: Segway HT
• Apostolyuk V. Theory and Design of Micromechanical Vibratory Gyroscopes
• Prandi L., Antonello R., Oboe R., and Biganzoli F. Automatic Mode-Matching in MEMS Vibrating Gyroscopes Using Extremum Seeking Control //IEEE Transactions on Industrial Electronics. 2009. Vol.56. - P.3880-3891.. [2]
• Prandi L., Antonello R., Oboe R., Caminada C., and Biganzoli F. Open-Loop Compensation of the Quadrature Error in MEMS Vibrating Gyroscopes //Proceedings of 35th Annual Conference of the IEEE Industrial Electronics Society - IECON-2009. 2009. [3]