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74 4. Building a Practical VR System
(coming out of the page, in the side view) by pushing the gyro down, the
result is an increased Coriolis force tending to make the gyro precess faster.
This extra force
f can be measured in the same way as the linear accelera-
tion force; it is related to the angular velocity = f ( f) of the gyro around
the z-axis. Integrating once gives the orientation about z relative to its
starting direction.
If a gyro is mounted in a force-sensing frame and the frame is rotated
in a direction that is not parallel with the axis of the gyro’s spin, the force
trying to turn the gyro will be proportional to the angular velocity. Inte-
grating the angular velocity will give a change in orientation, and thus if
we mount three gyros along mutually orthogonal axes, we can determine
the angular orientation of anything carrying the gyros. In practice, trad-
itional gyros, as depicted in Figure 4.17(b), are just too big for motion
tracking.
A clever alternative is to replace the spinning disc with a vibrating de-
vice that resembles a musical tuning fork. The vibrating fork is fabricated on
a microminiature scale using microelectromechanical system (MEMS) tech-
nology. It works because the in-out vibrations of the ends of the forks will
be affected by the same gyroscopic Coriolis force evident in a r otating gyro
whenever the fork is rotated around its base, as illustrated in Figure 4.18(a).
If the fork is rotated about its axis, the prongs will experience a force push-
ing them to vibrate perpendicular to the plane of the fork. The amplitu de
of this out-of-plane vibration is proportional to the input angular rate, and
it is sensed by capacitive or inductive or piezoelectric means to measure the
angular rate.
The prongs of the tuning fork are driven by an electrostatic, electromag-
netic or piezoelectric force to oscillate in the plane of the fork. This generates
an additional force on the end of the fork F =
× v, which occurs at right
angles to the direction of vibration and is directly related to the angular ve-
locity
with which the fork is being turned and the vector v, representing
the excited oscillation. By measuring the force and then integrating it, the
orientation can be obtained.
Together, three accelerometers and three gyros give the six measurements
we need from the real world in order to map it to the virtual one. That is,
(x, y, z) and roll, pitch and yaw. A mathematical formulation of the theory of
using gyros to measure orientation is given by Foxlin [8].
The requirement to integrate the signal in order to obtain the position
and orientation measures is the main source of error in inertial tracking. It
tends to cause drift unless the sensors are calibrated periodically. It works very