2019-2020 / SPRING SEMESTER
Name Surname
Student ID
Student Department
Course name
Assessment
Date
Duration
Lecturer
:
:
:
:
:
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BEYKENT UNIVERSITY
Faculty of Engineering and Architecture
Introduction to Robotics
Final Exam (Take-Home)
21.06.2020
Student Signature:
24 Hours
Assist. Prof. Dr. Janset Dasdemir
Please ensure that your name appears on each booklet, together with the number of questions
attempted. You are allowed to use calculator.
Each question = 25 points
Question Number
Attempted
Marks Awarded
1
2
3
4
5
6
7
8
9
10
Total
Question 1. Verify the following equations by direct calculation. Please, do not use
numeric values.
a) 𝑆 𝑎 𝑝 = 𝑎×𝑝
b) 𝑅 𝑎×𝑏 = 𝑅𝑎×𝑅𝑏
Question 2: For a three degree of freedom manipulator, with first two joints revolute
and last joint prismatic, it is given that 𝑻𝟑 = 𝑨𝟏 𝑨𝟐 𝑨𝟑 where
𝐶!
𝑆
𝐴! = !
0
0
0
0
1
0
−𝑆!
𝐶!
0
0
0
0
2
1
𝐶!
𝑆
𝐴! = !
0
0
0
0
1
0
𝑆!
−𝐶!
0
0
0.3𝐶!
0.3𝑆!
0
1
1
0
𝐴! =
0
0
Derive the Jacobian matrix with respect to base coordinate frame.
0
1
0
0
0
0
1
0
0
0
𝑑!
1
Question 3: For a three degree of freedom manipulator, with first two joints revolute
and last joint prismatic, it is given that 𝑇! = 𝐴! 𝐴! 𝐴! where
𝐶!
𝑆
𝐴! = !
0
0
0
0
1
0
𝑆!
−𝐶!
0
0
0
0
2
1
𝐶!
𝑆
𝐴! = !
0
0
0
0
−1
0
−𝑆!
𝐶!
0
0
5𝐶!
5𝑆!
0
1
1
0
𝐴! =
0
0
0
1
0
0
0
0
1
0
0
0
𝑑!
1
Determine the joint variables if the manipulator orientation and position is desired to
be
0
0
𝑇! =
1
0
0
1
0
0
−1
0
0
0
−3
0
7
1
Question 4. For the given 3-DOF robot manipulator derive the forward kinematic
(𝑇! = 𝐴! 𝐴! 𝐴! ) using D-H convention.