Homework answers / question archive / MNE482/MNE591-02 (Fall 2021) HW Assignment 5 (Total:  100 points + 30 extra credits) 1) Solve the inverse kinematics problems for each robotic arm with three degrees of freedom shown below using the desired position of the end-effector, [xd, yd, zd]T and the given ?30, the transformation matrix

MNE482/MNE591-02 (Fall 2021) HW Assignment 5 (Total:  100 points + 30 extra credits) 1) Solve the inverse kinematics problems for each robotic arm with three degrees of freedom shown below using the desired position of the end-effector, [xd, yd, zd]T and the given ?30, the transformation matrix

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MNE482/MNE591-02 (Fall 2021)

2. (a) Solve the inverse kinematics problem for the LabVolt 5150 robot arm using both analytical and geometric approaches. (i.e. two-step approach by dividing the robot arm into two parts, {Base to Wrist} and {Wrist to End-effector}.)                            (40 pts) 

 

 

		LabVolt 5150
Joint # (i)	ai [mm]	αi [° or radian]	di [mm]	θi [° or radian]
1 ( {0} -> {1} )	0	90° or π/2	255.5	θ1var
2 ( {1} -> {2} )	190	0	0	θ2var
3 ( {2} -> {3} )	190	0	0	θ3var
4 ( {3} -> {4} )	0	90° or π/2	0	θ4var
5 ( {4} -> {5} )	0	0	115	θ5var

 

 

(b) Determine possible joint variable sets, θ_i^var (i=1,2,3,4, and 5) as numbers satisfying the desired transformation matrix given below.). You may use Matlab or other programing tools with providing your

              own source code.                                                                                                                                                       (20 pts)

        

                                                                              0.7866       −0.0795    0.6124                                                                            377.4677

                                        (?05)??????? = [−00.5000.3624                                                     −−00..50008624    −00.3536.7071                                                  217269..93111827]

                                                                                     0                    0                   0                                                                                                           1

 

 

3. (Optional for Extra Credit) Confirm the table below using the ‘ikine’ function in the Matlab robotics toolbox and the LabVolt model built by ‘SerialLink’ from Assignment 4). (Hint: Since LabVolt5150 is a 5DoF manipulator, you need to use ‘mask’ when you use the ‘ikine’ function. Read how to use ‘mask’ by typing ‘help SerialLink/ikine’ on the Matlab command window.)                (30 points)

 

From Measurements (or Simulation Program)							Matlab Result
Sets	θ1	θ2	θ3	θ4	θ5	X	Y	Z
IC	0°	0	0°	0°	0°	380.00	0	140.55
Xmax	0°	0	0°	90°	0°	495.00	0	255.50
Ymax	90°	0	0°	90°	0°	0	495.00	255.50
Zmax	0°	90	0°	90°	0°	0	0	750.50
1	30°	45°	-90°	45°	90°	232.70	134.35	140.50
2	-27°	15°	24°	28°	-6°	389.41	-198.41	379.31
3	15°	-15°	42°	61°	42°	451.81	121.06	288.57