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

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 2012-04-20