The Islamic University of Gaza – Faculty of Engineering
Graduate Program: Computer Eng.
Course: Robotics
ECOM 9305 "3 C.H."
Second Semester 2021-2022
Assignment No. 2 (8 points)
The MIT Mechanical Engineering is developing a dinosaur robot for a local science museum. Figure
1 shows a schematic of the robot, having three degrees of freedom. The joint angles θ 1, θ2 and θ3 are
̅̅̅̅= 1m. The head
all measured from the positive x axis fixed to the floor, and the link lengths are ̅̅̅̅
𝐴𝐵=𝑂𝐴
T
of the dinosaur is at Point E (xe,ye) , which is 3 meters from Joint 3 (Point B), and its orientation, ϕe is
measured from the positive x axis to line EH, the head centerline. Note that line EH bends down π/3
from line BE, as shown in the figure. Answer the following questions.
Figure 1 Overall structure of dinosaur robot
a) Obtain the position and orientation of the dinosaur head, p = (xe ye ϕe)T, as functions of
joint angles. (3 points)
b) Obtain the Jacobian matrix relating the head velocity 𝑝̇ = (𝑥̇ 𝑒 𝑦̇𝑒 𝜑̇ 𝑒 )𝑇 to joint velocities
𝑞̇ = (𝜃̇1 𝜃̇2 𝜃̇3 )𝑇 (3 points)
c) Obtain singular configurations using the above Jacobian in part b). First, mathematically
solve the singularity condition, interpret the result, and sketch singular configurations. (2
points)