# How do rate gyros measure yaw, roll and pitch rates?

I need some help in understanding how rate gyros are used for measuring rotation rates about the yaw, roll, and pitch directions.

Suppose a gyro is used for measuring roll rate. How should the spin axis and input axis be oriented to get the rate in output axis.

In this figure, ζ is the input axis, η is the output axis, and the spin axis is obvious.

If the vehicle is rotated around the axis ζ (the input axis) with an angular velocity ωζ, the frame will rotate around the axis η (the output axis) to an angle β. The dependence of this angle on ωζ is given by the equation β = ωζH/c, where H is the moment of momentum of the gyroscope and c is a coefficient that depends on the stiffness of the spring and on the location of the point where the spring is attached. The values of β are read from the potentiometer; they define the magnitude of ωζ.

So the input axis (when the vehicle is not rotating) should be set up to point along the vehicle axis about which you wish to measure the rotation. For roll rate, it should point along the vehicle's X axis.

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