3. This is a 3 DOF spatial robot with 2 rotational joints and 1 translational joint in the reference pose. [3 marks] Yo B dz Please answer the follow questions using the DH method: a) Define all the required coordinate systems associated with each joint and derive link parameters based on the DH method. [y-axis direction is given; you have to assume the other axes directions] (0.5 mark) b) Derive the transformation matrix between the end-effector and the base coordinate system ³Ho. (1.5 mark) c) Calculate the coordinates of the point C and draw the corresponding configurations based on the values of parameters and variables given: 1₁ = 12 = 13= 6, 0₁ =30°, 0₂2 = 60° and assume d3 (1 marks).

Question 3 (10 marks) A coordinate frame {B} is located at the base of a robot manipulator. Frame {C} describes the position and orientation of a depth camera that was originally coincident with {B} then translated - 1 unit in g, translated 2 units in Pg, translated 3 units in 2g; the resulting frame is denoted by {C'}. The frame is then rotated about & by 45° into a new frame {C"}. The final transform is rotated about fe by -45° into the frame {C}. The camera detects an object having coordinates P = [1.0 1.0 1.01. (a) Determine PCORG (b) Formulate the homogeneous transformation T. (c) Calculate the object coordinates in frame (B), i.e., BP. You can use hand calculation or computer calculation (by PYTHON or MATLAB). Please provide your source code if you use computer calculation.

Question 1 (10 marks) Figure Q1 shows a coordinate frame {A}. Here X is pointing out of page according to the right- hand rule. The frame {A} is rotated by 0 = -30° about into a new coordinate frame {B}. ŽA {A} Figure 01 (a) Plot a figure to schematically illustrate the coordinate frame {B} based on the illustration given in Figure Q1. (b) List formula to calculate the rotation matrix R and present the numerical result. (c) Demonstrate that the R matrix is orthonormal by calculation. (d) A position vector is expressed in {A} as ^P = [012]. Calculate its position in {B}, i.e., BP. (e) A position vector is expressed in {B} as BP = [012]. Calculate its position in {A}, i.e., AP. (f) Calculate determinant of R, i.e., R.

Question 5 (16 marks) Consider a typical arm two-link kinematic chain shown in Figure Q5. The first joint is a revolute joint. The second joint is a prismatic joint; it moves in a direction normal to the axis of the first joint. The frames are assigned as shown in the figure. SINGAPORS UNIVERSITY OF SOCIAL SCIENCES (US) CAS401 (d) (c) End Effector- 2 Joint 1 V 100 Figure O (2) Determine the Denavit-Hartenberg (DH) parameters, and list the results in the table. 8₁ Table (5 d₂ Page 110 Tutor-Marked ment Joint 2 Describe how you obtained a, and 8, in the table. Appraise the assignment of Frame (1) shown in the figure. Appraise the assignment of Frame (2) shown in the figure. Formulate the kinematic equations for T If the coordinates of the end effect in Frame (0) is given in "P- [x y 0]", analyse the inverse kinematic problem to obtain the control parameter d in terms of the coordinates

● Detail the solutions steps to get full marks, assume coordinate axes and numerical values of the given variables independently so that there is no intentional match between the solutions of two students, otherwise, both students will receive 'o' marks. • You need to define coordinate systems and all the parameters precisely so that there is no ambiguity in interpreting your answers. 1. For the arm with three degrees of freedom shown in the figure, please answer all the questions below: [4 marks] Yo 0₁ L₁ L3 12 0₂ 0₂ a) Define all the required coordinate systems associated with each joint based on the DH method. [y-axis direction is given; you have to assume the other axes directions] (0.5 mark) b) Derive link parameters based on the answer in a). (DH method!) (0.5 marks) c) Derive the kinematic equations for ³H, based on the answer in b). (1.5 marks) d) Solve the forward kinematics problem using the following input data: L₁ = 4, L2= 2, L3= 1 (m), and Ⓒ = {0₁, 0₂, 03} = {-----} assume the numerical values of the angles less than 90 degrees. (1 mark) e) Check your result in d) by sketching the robot configuration as a line diagram to represent robot links. (0.5 marks).

2. As shown in the figure, it is a 3 DOF planar robot with 3 rotational joints. [3 marks] a) Define all the required coordinate systems associated with each joint and derive link parameters based on the DH method. [y-axis direction is given; you have to assume the other axes directions] (0.5 mark) b) Derive the kinematic equations for H3 based on the answer in a). (0.5 marks) c) Solve the forward kinematics problem using the following input data: L₁= 2, L2= 1, L3= 0.5 (m), = {01, 02, 03}T, assume 0₁<10, 15<0₂<50, and 03<0. (1 marks) d) Check your result in c) by sketching the robot configuration. (1 marks) 02 is The coordinate systems of the three-link planar arm

Question 7 (25 marks) Recent developments in robotics and related technologies such as artificial intelligence, computer vision, internet of things and 5G communication have strongly motivated robot applications. In Singapore, the commercialised applications and the pilot projects are transforming the economy and improving lives. The nation's interest in robotics is part of its effort to become a knowledge-based, innovative, and smart nation. The local aerospace companies are aggressively looking for robotics and automation engineers to seize new growth opportunities in digital services, autonomous technologies and sustainability [1]. Various robotics technologies are being adopted and developed in the aerospace industry to enhance its competitiveness as a global aircraft MRO provider. A common trend is to develop new technologies in a robot arm platform to increase automation [2]. In addition to the traditional applications of robot arms, several recent examples of the robot applications in the industry and society are Drone for air delivery [3, 4] • Drone for aircraft inspection [5] • Drone for building inspection [6] • Autonomous vehicle for last-mile delivery [7,8] • Autonomous vehicle for surveillance [9] • Self-driving vehicle for urban transportation [10, 11, 12] • Indoor mobile robot for service [13] • Quadruped robot for surveillance and service [14. 15] • • Robot arm for coffee maker [16, 17] Unmanned cashless store powered by AI and robotics [18] Robot arm equipped with payload for aircraft engine inspection [19] Quadruped robot for surveillance [20] Quadruped robot for MRT train inspection [21] Robotics will profoundly reshape our society in the years ahead. With the development of new technologies, novel robotic systems will assist human beings, typically by performing a job that is dirty, tedious, distant, dangerous or repetitive. In this open-ended question, you are required to apply the knowledge from EAS401, literature review, and your working experience to study technical aspects in the development of a robotic system for an industrial or social application. This system can be related to your job roles, daily life, a start-up plan, or a personal interest. It can be your motivation to contribute to society. In this question, you are required to present a proposal to design the robotic system. In TMA02, you will be further required to present some thoughts on how you can take advantage of Webots to develop a prototype of your proposal. The requirements of this question are listed below: • Identify the robotic system and the targeted application for your study. Present a title (topic) to indicate your proposed system and targeted application. The length of title should be within 30 words, for example, Development of a Robotic System for Aircraft/nIn this question, you are required to present a proposal to design the robotic system. In TMA02, you will be further required to present some thoughts on how you can take advantage of Webots to develop a prototype of your proposal. The requirements of this question are listed below: • Identify the robotic system and the targeted application for your study. Present a title (topic) to indicate your proposed system and targeted application. The length of title should be within 30 words, for example, Development of a Robotic System for Aircraft SINGAPORE UNIVERSITY OF SOCIAL SCIENCES (SUSS) EAS401 Page 8 of 10 Tutor-Marked Assignment 01 Engine Inspection in Maintenance, Proposal of an Unmanned Aerial System (UAS) for Autonomous Flight in Building Façade Inspection. • Conduct a literature review to examine emerging robotics technologies and application cases related to your study, present a design by word description and schematic illustrations, appraise the technologies employed to develop the robotic system. • A typical robotic system consists of kinematic mechanism, actuation system, perception system, computing system, communication system, power supply system, computing codes including control algorithms, and payload. Your design should consider the essential parts of the system. • In your presentation, you can assume background of targeted readers, e.g., a senior management team in your company, a government funding agency, an investor from venture capital, or your course lecturer. • Limit the maximum length of this section to 1500 words. • You are required to cite the references in your study. Direct adoption of contents from an open resource or an Al generative resource is strictly prohibited.

Problem 6 (17 marks) Consider an RPR plannar robot shown in Figure Q6. The robotic system has three-degrees of freedom; the joint variables are 8,, d, and 8. It is noted that the dimension L₁ is fixed and the dimension d, is used to denote the movement of prismatic Joint 2. For kinematic analysis, Frame (0) is the base frame; the base coordinate system ŽŸŻ, is shown SINGAPORS UNIVERSITY OF SOCIAL SCIENCES (USS) EAS401 (b) in the figure with the 2, axis pointing out of the paper. Frame (3) is located at the axis of Joint 3 which is the wrist of this robotic system. d₂ Figure 06 Assign link frames to the robot arm. Appraise the consideration(s) in assigning frame (2). Obtain the Denavit-Hartenberg (DH) parameters from kinematic analysis. List your results in the following table. IT- Table 06 Tutor-Marked Assignment Formulate the transformation that relates frame (3) to frame (0), i.c. T. 0 0 Page 10 [fo -500x3 C0y Analyse inverse kinematics to obtain relations for joint variables in terms of known position and orientation of the origin of frame (3) d₂ 0 10 0 01