As previously mentioned, the FARO arm data describes the location
of the probe holder (H) together with its orientation
(
,
,
) with respect to a coordinate system attached
to the base of the arm (B). The angles correspond to the Euler's
angles in the z-x-z convention
[23]. The tip position vector 
in the arm's base (B) coordinate system is given by
where
and
The homogeneous matrix is written with a notation similar to that in previous section
A separate set of measurements obtained as the probe was rotated about
a fixed endpoint was acquired in the same manner as in previous
section. Since, during this motion, the tip of the probe was
stationary, the vector 
was found by minimizing the
standard deviation of the set of tip positions calculated using the
inverse of the equation:
This value of 
was then used in BTH to find
the position of the probe's tip (
) from the probe
holder position and orientation calibration measurements.
