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