The gantry robot of Prob. 10.26 is to travel a path for which the origin of the end effector O5 follows the straight line given by RO5 (t) = (120t +300)ˆi1 −150ˆj1

+(90t +225)kˆ 1 mm, with t varying from 0.0 to 4.0 s; the orientation of the end effector is to remain constant with kˆ 5 = −ˆj1

(vertically downward) and ˆi5 =ˆi1. Find expressions for the positions of each of the actuators, as functions of time, for this motion.