Page 1 of 4 Semester One 2020 Assessment Notice Faculty of Engineering ASSESSMENT DETAILS Unit code(s) TRC4800/MEC4456 Title of assessment Final Assessment Assessment type Take-Home Exam Assessment duration 3 hours 10 mins Materials required Hardware and software to submit written or typed answers as a single PDF for file submission ACADEMIC INTEGRITY Intentional plagiarism or collusion amounts to cheating under Monash University Council Regulations (Part 7). Plagiarism: Plagiarism means to take and use another person’s ideas and or manner of expressing them and to pass these off as one’s own by failing to give appropriate acknowledgement, including the use of material from any source, staff, students or the internet, published and unpublished works. Collusion: Collusion means unauthorised collaboration on assessable written, oral or practical work with another person. Where there are reasonable grounds for believing that intentional plagiarism or collusion has occurred, this will be reported to the Associate Dean (Education) or nominee, who may disallow the work concerned by prohibiting assessment or refer the matter to the Faculty Discipline Panel for a hearing. During an assessment, you must not have access to any item/material that has not been listed in the materials required section above. Student Statement: ● I have read the university’s Student Academic Integrity Policy and Procedures. ● I understand the consequences of engaging in plagiarism and collusion as described in Part 7 of the Monash University (Council)Regulations (academic misconduct). ● I have taken proper care to safeguard this work and made all reasonable efforts to ensure it could not be copied. No part of this assessment has been previously submitted as part of another unit/course. ● I acknowledge and agree that the assessor of this assessment may for the purposes of assessment, reproduce the assessment and: i. provide to another member of faculty and any external marker; and/or ii. submit it to a text matching/originality checking software; and/or iii. submit it to a text matching/originality checking software which may then retain a copy of the assignment on its database for the purpose of future plagiarism checking. ● I certify that in completing this assessment I have not plagiarised the work of others, participated in unauthorised collaboration or otherwise breached the academic integrity requirements in the Student Academic Integrity Policy. In completing this assessment task you agree to the statements above. If you do not agree to the Student Statement, please submit directly to your Unit Coordinator by the due date, providing a written explanation of which aspect of the Student Statement you do not agree with and why. Page 2 of 4 Monash University (Clayton Campus) TRC4800/MEC4456 Robotics Take-Home Exam  This exam has 8 questions (3 pages + 1 assessment notice) for a total of 60 marks.  Attempt all questions.  This is an open-resource exam (i.e. open book, open web).  You may use computer programs and/or calculators to help answer the questions.  The outputs of your computer programs can be used directly as part of your answer, while your procedure of solving problems must be presented.  If you believe there is an omission in a question, make clear what it is, add any adjustment(s) and/or assumption(s) you deem necessary and proceed.  This exam requires submission of your working as a single PDF file before end of the exam. Write the page number at the top of each page. Start each question on a new page. Note: All of the following questions refer to the Robot given in Fig. 1. Mass centres of linkages are located at the end of the links and indicated by a circle with a cross and a parameter of . The joint space is represented by = [1 2 3] Only point masses of the robotic links are considered. Unless prompted otherwise, give all solutions in analytical form. Fig 1. RPR Robot Page 3 of 4 Question 1 [10 Marks] a. [4 Marks] Draw attached frames to the links according to the Denavit-Hartenberg (DH) notations. You can draw the frames using a computer or by hand. Make sure the drawing of the robot with the attached frames is submitted with the answer. b. [4 Marks] Formulate a DH table for the robot. Indicate the actuated variables. c. [2 Marks] For frames with a P or R joint, what does the Z-axis represent in DH notation? Question 2 [5 Marks] a. [2 Marks] Derive the transformation matrix, 1 0 , 2 1 , 3 2 and 3 0 . b. [1 Mark] If the end effector position is given by 3 = [3 0 0] , determine the position of the end effector with respect to frame 0. c. [1 Mark] Derive the transformation matrix 0 3 . d. [1 Mark] Given the Point B, measured in frame 1, 1 = [1 1 0]. Calculate 3 . Question 3 [12 Marks] a. [7 Marks] Derive inverse kinematic solutions of the end effector, 0 . Identify how many valid solutions there are in total. b. [2 Marks] What is a practical use of inverse kinematics? c. [1 Mark] Given the point 0 = [0.247 −0.106 0.523], determine the numerical values for the joints for the robot to reach this position, where, 1 = 0.35, 3 = 0.2, d. [2 Mark] Which solution(s) would you use for the physical robot and why? Question 4 [6 Marks] a. [3 Marks] Derive the Jacobian of this robot for the position of the end effector, 0 , measured in frame 0, 0 . b. [2 Marks] Derive the Jacobian for this end effector, measured in frame 3, 3 . c. [1 Mark] Given joint velocities, ̇ = [0.5rad/s 1/ −0.3rad/s] and joint positions, = [0.785 0.2 1.22], find the numerical velocity of the end effector measured in frame 0, where, 1 = 0.35, 3 = 0.2, Question 5 [4 Marks] a. [3 Marks] Given an external force vector, = [ ] exerted on the end effector, derive the joint torques and forces required to resist this external force. b. [1 Mark] Given, = [1 −2 4], = [0.785 0.2 1.22], derive the numeric joint torques and forces required to resist this external force, where, 1 = 0.35, 3 = 0.2, Page 4 of 4 Question 6 [10 Marks] a. [8 Marks] Using the Newton-Euler method, derive the dynamics of this robot. Show the equation used and analytic solution for each outward iteration. Show the final dynamic equations in matrix format. Assume only points masses and no external force or moment on the end effector. b. [2 Marks] Give an example of when you would use: a. Newton Euler Method b. Lagrangian Method Question 7 [8 Marks] a. [6 marks] Use cubic splines to generate a smooth trajectory in Joint Space, given the following points in task space.  = [0.247 −0.106 0.523] at = 0s  = [0.364 −0.170 0.547] at = 2s  = [0.303 −0.028 0.543] at = 4s  = [0.168 0.044 0.491] at = 6s For the joint space solution of use the value closest to; 1 = 45 , 2 = 0.25, 3 = 60 . Outline the method you used to solve this problem and show the equations for the full trajectory. Given joint limits of 0 to 90 degrees for joints 1 and 3, justify your choices of solution in the joint space. The units of your coefficients should be in degrees and metres. b. [2 Marks] Give an example of when you would use: 1. Joint Space Trajectory Planning 2. Task Space Trajectory Planning Question 8 [5 Marks] Design a PID controller with gravity compensation. a. [2 Marks] Define the fixed-reference equation (). b. [2 Marks] Illustrate the complete block diagram of your control system assuming a fixed reference. c. [1 Mark] Indicate the feedforward and feedback components of the Computer Torque Control (CTC) law and explain their roles. END OF EXAM PAPER






























































































































































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