Kinematic modelling of a MH3F robot

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):

  1. 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)
  2. 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
  3. 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
  4. 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)
  5. 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