The SCARA robot of Prob. 10.24 is to be guided along a path for which the origin of the end effector O5 follows the straight line given by RO5 (t) = (1.6t +4.0)ˆi1 +(1.2t +3.0)ˆj1 +2.0kˆ 1 in, with t varying from 0.0 to 5.0 s; the orientation of the end effector is to remain constant with kˆ 5 =

−kˆ 1 (vertically downward) and ˆi5 radially outward from the base of the robot. Find expressions for how each of the actuators must be driven, as functions of time, to achieve this motion.