Geometric Transformations
Course Syllabus
| Course Code: | ΕΠ9 |
| Semester: | Elective courses – Spring semester |
| ECTS units: | 3 |
| Weekly Teaching Hours: | 3 |
| Course Page: | https://eclass.duth.gr/courses/TME300/ |
| Instructors: | TAOUKTSOGLOU ANASTASIA |
Course Description
The main purpose of this course is to provide the student with the necessary and necessary “language” in order to be able to understand, interpret, evaluate and describe both the concepts and phenomena that will be encountered in the curriculum of the Department’s courses, as well as to solve specific problems in the science of Production Engineering and Management.
In the first part of the course, students are introduced to the concept of geometric transformation. They study basic transformations of the plane and space. They learn to express transformations as a product of matrices and appreciate methods of linear algebra devised for this purpose: Homogeneous coordinates, LU-factorization, matrices with blocks. The expression of geometric transformations in matrix form favours computer programming of any of the motion. In the second part of the course, students are introduced to the study of motion, the relative motion of coordinate systems, the calculation of velocity and acceleration of one system with respect to another. Finally, they program in Mathematica, Matlab and Geogebra real motions, which are applied in industrial production.
Purpose of the course
Successful completion of the Geometric Transformations course will enable students to develop their skills in order to be able to:
- apply in practice knowledge of Linear Algebra and Mathematical Analysis to problems in Kinematics, Mechanics and Robotics,
- know and apply the basic geometric transformations of the plane and space,
- apply matrix theory in order to express and program on the computer the geometric transformations,
- apply the geometric transformations in order to determine the position of the end of a robotic arm, to study the relative motion of coordinate systems, to calculate the speed and acceleration of motion of one system relative to another,
- to apply LU-factorization and block diagonalization to practical applications,
- to program algorithms on the computer, learned in theory in Mathematica and Matlab,
- recognize geometric transformations applied to mathematical models supporting decision processes in industrial management and production in general.
