The homogeneous transformation matrix
will be constructed by combining two simpler transformations. The
transformation
 |
(3.54) |
causes a rotation of
about the
-axis, and a
translation of
along the
-axis. Notice that the rotation
by
and translation by
commute because both operations
occur with respect to the same axis,
. The combined operation of
a translation and rotation with respect to the same axis is referred
to as a screw (as in the motion of a
screw through a nut). The effect of
can thus be considered as a
screw about the
-axis. The second transformation is
 |
(3.55) |
which can be considered as a screw about the
-axis. A
rotation of
about the
-axis and a translation
of
are performed.
Steven M LaValle
2020-08-14