Game Development Reference
In-Depth Information
Figure 6.1 Electromagnetic field around a coil
values of the created magnetic field B in polar coordinates are r and θ in a plane
containing the axis of the coil (Figure 6.1).
µ o NIR 2 cos( θ ) / 2 r 3
B r =
(6.2)
and
B θ = µ o NIR 2 sin( θ ) / 4 r 3
(6.3)
with geometric positions: r
R and r
L , coil of N windings, of radius R and length L ,
vacuum permeability µ o , wavelength λ
With a coil of the transmitter, we create an alternating magnetic field, whose
strength depends on r and θ . The direction and strength of this field are determined
with the three orthogonally aligned coils of the receiver as they receive the measured
electric currents, depending on r and θ . Similarly, we create two magnetic fields with
the other two orthogonally aligned coils of the transmitter (Figure 6.2). One might
think that to determine the 6 DOF of the receiver, we separately create a magnetic field
with each coil, each at a different time. In that case, we would have a system of non
linear equations which will be difficult to linearise. To get around this difficulty, in
practice, the transmitter creates a field in the assumed direction of the receiver and in
the two corresponding orthogonal directions, at two different moments. Linearising
the equation system becomes easy in these conditions. The method for calculating the
6 degrees of freedom of the receiver is given in annexe at the end of this chapter.
The electronic unit, which controls the entire set, has the following functions:
Alternating current power supply, having a carrier frequency close to 10KHz, to
the three coils of the transmitter;
Measurement of currents circulating in the receiver coils;