Figure 1 shows a Motoman MH3F robot. This is a computer controlled six-joint robot, driven by six
DC servomotors. The geometrical parameters of the MH3F are given in Figure 1(b).
Figure 1. An MH3F robot. (a) A photo of the MH3F robot1
. (b) a sketch of the MH3F robot with geometrical
parameters2
Students are required to work individually to obtain the forward kinematic equations of the MH3F robot.
Students will use Denavit-Hartenberg (DH) representation to establish the 7 coordinate frames
(including the base coordinate system X0Y0Z0) of the robot.
Students should complete the following tasks for submission (the total mark of this assignment is 86
points):
- Number all links and joints of the MH3F as shown in Figure 1 (b) and establish (by drawing) DH
coordinate frames for all links. You can also copy the figures from this assignment sheet and
draw your own DH coordinates. (14 mark) - Identify all DH parameters and write into a table format as below: (24 marks)
MH3F robot DH parameters
Joint i qi di ai ai
1
2
3
4
5
6 - Obtain the forward kinematic equations of the robot (
0
A6) in the matrix form using the link and
joint parameters that you have already identified (no need to expand the multiplication)
(8 marks)
1 https://www.motoman.com/industrial-robots/mh3f 2 http://www.wtech.com.tw/public/download/manual/yaskawa/MH3F.pdf
Joint 1
Joint 2
Joint 3
Joint 4
Joint 5
Joint 6
MECH4004 - Robotics
Due: 23:59 Sunday 12 December 2021 - Use MATLAB to calculate the robot end-effector’s position, i.e., the origin of the coordinate
frame 6 of the robot, for the following joint positions:
(20 marks)
Case
q 1 2 3 4
1 0 (rad) p/2 (rad) 0 (rad) p/2 (rad)
2 0 (rad) 0 (rad) -p/2 (rad) 0 (rad)
3 0 (rad) p/2 (rad) p/2 (rad) p (rad)
4 0 (rad) 0 (rad) 0 (rad) 0 (rad)
5 0 (rad) 0 (rad) 0 (rad) 0 (rad)
6 0 (rad) 0 (rad) 0 (rad) 0 (rad) - When six joints are moving simultaneously, write a MATLAB program to determine and plot the
robot end-effector’s position in a 3-dimensional plot (time t is 0 to 5 seconds at 0.2 second
interval). The program should plot the movement of the end-effector in 3D (XYZ), and in XY,
XZ, and YZ planes. The six joints are moving according to the following trajectories:
(rad)
(rad)
(rad)
(20 marks)
In the written report, students can submit handwritten results for tasks 1 – 4. For task 5, students should
submit a computer plot that shows the positions of the end-effector of the robot. Students should also
submit the MATLAB programs for both tasks 4 and 5 on vUWS.
θ1 = −2(1− 0.1t)
θ2 = 2(1− 0.04t)
θ3 = 3(1− 0.2t)
θ4 =θ1
θ5 =θ2
θ6 =θ3
Sample Solution