Page 115 - Introduction to Autonomous Mobile Robots

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Figure 4.4 Chapter 4
Two-axis mechanical gyroscope.

Gyroscopes can be classified in two categories, mechanical gyroscopes and optical gyro-
scopes.

Mechanical gyroscopes. The concept of a mechanical gyroscope relies on the inertial
properties of a fast-spinning rotor. The property of interest is known as the gyroscopic pre-
cession. If you try to rotate a fast-spinning wheel around its vertical axis, you will feel a
harsh reaction in the horizontal axis. This is due to the angular momentum associated with
a spinning wheel and will keep the axis of the gyroscope inertially stable. The reactive
torque τ and thus the tracking stability with the inertial frame are proportional to the spin-
ω
ning speed , the precession speed Ω , and the wheel’s inertia . I

τ = IωΩ (4.5)

By arranging a spinning wheel, as seen in figure 4.4, no torque can be transmitted from
the outer pivot to the wheel axis. The spinning axis will therefore be space-stable (i.e., fixed
in an inertial reference frame). Nevertheless, the remaining friction in the bearings of the
gyro axis introduce small torques, thus limiting the long-term space stability and introduc-
ing small errors over time. A high quality mechanical gyroscope can cost up to $100,000
and has an angular drift of about 0.1 degrees in 6 hours.
For navigation, the spinning axis has to be initially selected. If the spinning axis is
aligned with the north-south meridian, the earth’s rotation has no effect on the gyro’s hor-
izontal axis. If it points east-west, the horizontal axis reads the earth rotation.