GUC
MATH103
For Engineering
Winter 2015
Lecture # 1
1
Instructor and Textbooks
Lecturer: Dr. Hany El-Sharkawy
Office:
C3.106
E- mail: [email protected]
Textbooks:
Lecture notes your main source
I- Available on the INTRAnet via:
V:\Faculties\Basic
Department of Mathematics
Dr. Tarek Emam
Mathematics
for Management Sciences (Math 101)
Assignments Nr. 9
Name :
Application Nr.
Group:
Note: Exercises labeled (I) are to be solved by Instructors in classes. Exercises labeled
(II) are to be solved by stud
Department of Mathematics
Dr. Tarek Emam
Mathematics
for Management Sciences (Math 101)
Assignments Nr. 8
Name :
Application Nr.
Group:
Note: Exercises labeled (I) are to be solved by Instructors in classes. Exercises labeled
(II) are to be solved by stud
Department of Mathematics
Dr. Tarek Emam
Mathematics
for Management Sciences (Math 101)
Assignments Nr. 7
Name :
Application Nr.
Group: M
Note: Exercises labeled (I) are to be solved by Instructors in classes. Exercises labeled
(II) are to be solved by st
Department of Mathematics
Dr. Tarek Emam
Mathematics
for Management Sciences (Math 101)
Assignments Nr. 6
Name :
Application Nr.
Group:
Note: Exercises labeled (I) are to be solved by Instructors in classes. Exercises labeled
(II) are to be solved by stud
Department of Mathematics
Dr. Tarek Emam
Mathematics
for Management Sciences (Math 101)
Assignments Nr. 5
Name :
Application Nr.
Group:
Note: Exercises labeled (I) are to be solved by Instructors in classes. Exercises labeled
(II) are to be solved by stud
Department of Mathematics
Dr. Tarek Emam
Mathematics
for Management Sciences (Math 101)
Assignments Nr. 4
Name :
Application Nr.
Group:
Note: Exercises labeled (I) are to be solved by Instructors in classes. Exercises labeled
(II) are to be solved by stud
Department of Mathematics
Dr. Tarek Emam
Mathematics
for Management Sciences (Math 101)
Assignments Nr. 3
Name :
Application Nr.
Group: M
Note: Exercises labeled (I) are to be solved by Instructors in classes. Exercises labeled
(II) are to be solved by st
Department of Mathematics
Dr. Tarek Emam
Mathematics
for Management Sciences (Math 101)
Assignments Nr. 2
Name :
Application Nr.
Group: M
Note: Exercises labeled (I) are to be solved by Instructors in classes. Exercises labeled
(II) are to be solved by st
Department of Mathematics
Dr. Tarek Emam
Mathematics
for Management Sciences (Math 101)
Assignments Nr. 1
Name :
Application Nr.
Group: T
Note: Exercises labeled (I) are to be solved by Instructors in classes. Exercises labeled
(II) are to be solved by st
Robotics
Islam S. M. Khalil
German University in Cairo
Islam S. M. Khalil
Hill Climbing using Newton-Raphson Method
Outline
Hill climbing
Newton-Raphson method
Newton-Raphson in optimization
Islam S. M. Khalil
Hill Climbing using Newton-Raphson Method
Hil
Robotics
Islam S. M. Khalil
German University in Cairo
October 1, 2016
Islam S. M. Khalil
Kinematics
Position and Orientation of Rigid Bodies
Position: A pAB R31 in A.
Orientation: A RB R33 in A.
RT = R1 A RB B RA = I | R |= +1
A B
R = A xB A yB A zB
xA y
1
Modeling of a Pantograph Haptic Device
Islam S. M. Khalil and Mohamed Abu Seif
Kinematics of the Pantograph Haptic Device
The pantograph haptic device consists of 5 links with lengths li for i = 1, . . . , 5. First, we assign frames
of reference to each
Robotics
Islam S. M. Khalil
German University in Cairo
September 18, 2016
Islam S. M. Khalil
Kinematics
Vector Functions
A vector v in a reference frame A depends on a scalar verifiable q.
We can say that v is a vector function of q in A. Otherwise, v is
Robotics
Islam S. M. Khalil
German University in Cairo
September 19, 2016
Islam S. M. Khalil
Kinematics
Angular Velocity
Let bl , b2 , and b3 form a right-handed set of mutually
perpendicular unit vectors fixed in a rigid body B moving in a
reference fram
Robotics
Islam S. M. Khalil
German University in Cairo
Islam S. M. Khalil
Homogeneous Transformations
ZX 0 Z 00 Euler angles
Rotation around Z -axis
cos sin 0
Rz () = sin cos 0
0
0
1
Rotation around X 0 -axis
1
0
0
Rx 0 () = 0 cos sin
0 sin cos
Rotation
Robotics
Islam S. M. Khalil
German University in Cairo
September 6, 2016
Islam S. M. Khalil
Kinematics
Outline
Motivation
Agenda
Generalized pseudoinverse
Over- and under-determined systems
Islam S. M. Khalil
Kinematics
Motivation
Autonomous Robotic Syste
a < U ( Department of Mathematics
0 Dr. Tarek Emam
German University in Cairo
I Mathematics
for Management Sciences (Math 101) . _
Assignments Nr. 9
Name : Application Nr. - Group:
3
Note: Exercises labeled (I) are to be solved by Instructo
Department of Mathematics
Dr. Tarek Emam
@GUC
German University in Cairo
Mathematics 1
for Management Sciences (Math 101)
Assignme'hftis Nr. 8
Name : pplication Nr. Group:
Note: Exercises labeled (I) are to be solved byrllristtuctors in clas