For the gantry robot shown, find the transformation matrix T15 relating the posture of the tool coordinate system to the ground coordinate system when the joint actuators are set to the values φ1 =

450 mm, φ2 = 180 mm, φ3 = 50 mm, and φ4 = 0.

Also, find the absolute position of the tool point that has coordinates x5 = y5 = 0, z5 = 45 mm.