For the SCARA robot, 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 = 30◦,

φ2 = −60◦, φ3 = 2 in, and φ4 = 0. Also find the absolute position of the tool point that has coordinates x5 = y5 = 0, z5 = 1.5 in.

Figure P10.24 a12 = a23 = 10 in, a34 = a45 = 0, α12 =

α34 = α45 = 0, α23 = 180◦, θ12 = φ1, θ23 = φ2, θ34 =

0, θ45 = φ4, s12 = 12 in, s23 = 0, s34 = φ3, and s45 = 2 in.