Forward kinematics

First transform

T01 = T[DH, 0, 1] ; T01 // TraditionalForm

( cos(θ1) -sin(θ1) 0 0 ) s ... 0 1 0 0 0 0 1

Second transform

T12 = T[DH, 1, 2] ; T12 // TraditionalForm

( cos(θ2) -sin(θ2) 0 L1 ) s ... 0 1 0 0 0 0 1

Last transform (to end-effector)

T23 = T[DH, 2, 3] ; T23 // TraditionalForm

( 1 0 0 L2 ) 0 1 0 0 0 0 1 0 0 0 0 1

Complete transform

T03 = T[DH, 0, 3] // Simplify ; T03 // TraditionalForm

( cos(θ1 + θ2) -sin(θ1 + θ2) ... 0 0 1

Created by Mathematica  (October 1, 2003)