H7123-ROBOT DESIGN AND IMPLEMENTATION

Candidates must attempt THREE questions out of FOUR.

Question 1.

a) Calculate the Mobility of the spatial mechanism shown in Figure Q1a. Further, define idle degrees of freedom and identify how many idle degrees of freedom are in the mechanism

[6 marks]

b) You are given a set of six links. The lengths of the links are as follows: 6.3cm, 9.1cm,12.4cm,15.6cm,20cm,40.2cm Sketch a crank-rocker mechanism you can realize using a selection of four links from the set. [6 marks]

c) Sketch the reachable workspace and the dexterous workspace of the planar three link robot shown below in Figure Q1c. Calculate the areas of both the workspaces.

[6 marks]

d) Calculate the memory required for creating a 200× 300 pixel 8-bit RGB colour image. [2 marks]

Question 2.

a) Draw a pencil sketch showing a reference frame A and a frame B that represents 𝑅𝑜𝑡𝑦𝜃. Using the geometry, derive the 4X4 Homogenous Transformation Matrix for 𝑅𝑜𝑡𝑦𝜃. [4 marks]

b) Shown below in Figure Q2b is a 5-bar robot with the link AE rigidly fixed to the ground. The lengths of the links are as follows: AE=6cm, AB=BC=CD=DE=3cm. Th links AB and DE are driven by motors with respect to the ground link, AE. Assume there are no joint angle constraints and sketch the workspace of the end-effector, C. Explain the reasoning behind you answer.

[6 marks]

c) A 3-link articulated robot is shown below in Figure Q2c with link lengths L1=5, L2=5 and L3=5 units. The desired end-effector position is (2.5 ,2.5√3 , 10). Solve for the joint angles of the three revolute joints with the first joint angle in the 1 st quadrant. [10 marks]

Question 3.

a) The ZXZ Euler Angles Rotation matrix represents a frame obtained by the following transformations in succession: First rotate frame 1 about the z-axis by the angle 𝜙. Next rotate about the current x-axis by the angle 𝜃. Finally rotate about the current z-axis by the angle 𝜓 .Derive the rotation matrix for ZXZ Euler angles. [6 marks]

b) Solve for the two sets of ZXZ Euler angles { 𝜙, 𝜃, 𝜓} that result in the rotation matrix above. [8 marks]

c) A vector P is denoted with respect to frame {B} with orientation represented by the above rotation matrix 𝐵𝑅 𝐴 as [0,0,1]^T and with respect to frame {A} as [1,0,2]^T . Write the transformation matrix 𝐵𝑇 𝐴 . [6 marks]

Question 4.

a) Assume the link is of uniform cross-section with negligible breadth and width. Its mass is 0.1kg and the additional point mass attached to the link at point B is 1kg. Calculate the moment of inertia of the load about its rotational axis at point A. [4 marks]

b) If the gearbox has negligible inertia, and the inertia of the motor rotor is 1.5 × 10−5 kg.m2, what is the total inertia on the motor shaft? [4 marks]

c) The load undergoes constant acceleration from complete rest to an angular velocity of 15rpm in a duration of 0.25 s, runs at that angular velocity for 2.5 seconds and then undergoes constant deceleration to rest in 0.25 s. Draw the angular velocity vs time and angular acceleration vs time profiles for the motor. [6 marks]

d) If the frictional torque of the system is 0.005Nm, calculate the acceleration torque, run torque and deceleration torque that needs to be delivered by the motor. [6 marks]