1.Write a MATLAB program to calculate the homogeneous transformation matrix when the user enters Z-Y-X Euler angles −− and the position vector . Test for two examples:
I) =100, =200 , =300 and ={1 2 3}
II) For =200 (= =00 ) and ={3 0 1}

2.This exercise focuses on DH parameters and on the forward-pose (position and orientation) kinematics transformation for the planar 3-DOF, 3R robot whose DH parameter table is given in Figure 1 with the following fixed-length parameters, 1=4, 2=3 and 3=2 (m).
Figure (1)
I) Derive the neighboring homogeneous transformation matrices −1 , i =1,2,3. These are functions of the joint-angle variables , i=1,2,3.
II) Use Symbolic MATLAB to derive the forward-pose kinematics solution 30 and 0 symbolically (as a function of ). Abbreviate your answer, using =sin (), =cos() and so on. Also, there is a ( 1+2+3) simplification, by using sum-of-angle formulas, that is due to the parallel axes. Calculate the forward-pose kinematics results (both 30 and 0 ) via MATLAB for the following input cases
a. Θ={1 2 3}={0 0 0}
b. Θ={100 200 300}
c. Θ={900 900 900}