Course detail

Modeling and Simulations II

FSI-RKDAcad. year: 2025/2026

The course deals with the kinematics and dynamics modeling of controlled mechatronic systems. Previous knowledge of mechanics is developed, mainly with a focus on numerical solutions to problems on computers. Mechanisms are considered rigid multi-body systems. Exercises run on computers using MATLAB. The forward and inverse kinematic model is solved using analytical and numerical methods. Numerical methods are also studied from a general point of view, as a tool for solving sets of nonlinear equations and optimization tasks. The dynamic model is built using Newton's method, Lagrange equations, and automatically (MATLAB/SimMechanics). Modeling of electrical and regulation structures such as submodels of complex models are also discussed.

Language of instruction

Czech

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

doc. Ing. Robert Grepl, Ph.D.

Department

Institute of Solid Mechanics, Mechatronics and Biomechanics (ÚMTMB)

Entry knowledge

Vector algebra. Matrix algebra. Fundamentals of kinematics and dynamics. Method of relaxation and Lagrange's equations. MATLAB/Simulink programming.

Rules for evaluation and completion of the course

The course assessment is based on a standard 0-100 point scale. During the semester, students take a midterm test and a graded credit. The midterm test is graded with a maximum of 30 points. The graded credit is assessed with a maximum of 70 points, of which 30 points can be obtained for theoretical questions and 40 points for practical tasks on a PC similar to the exercises. The overall grade is a combination of the points from both parts.

Attendance at the exercise is compulsory. The learning review is carried out at the practical.

Aims

During the course, students will be introduced to modern approaches to solving problems of kinematics and dynamics of mechanisms. The course focuses on the control of real machines and their simulation models, with a key emphasis on the use of computer support. Theoretical knowledge will be applied to the solution of a specific problem in a semester project.

Upon completion of the course, students will be able to:

construct and solve direct (analytical) and inverse (analytical and numerical) kinematic models of any open kinematic chain, assess the suitability of a particular method for kinematics modelling, construct and solve analytical dynamic models of simpler mechanical systems, and orient themselves in the problems of numerical modelling of complex mechatronic systems.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Corke,P.I.: A Robotics Toolbox for Matlab, IEEE Robotics and Automation Magazine, pp.24–32, 1996
Murray, R. M.; Sastry, S. S. & Zexiang, L. A Mathematical Introduction to Robotic Manipulation CRC Press, Inc., 1994
Sciavicco, L.; Siciliano, B. & Sciavicco, B. Modelling and Control of Robot Manipulators Springer-Verlag New York, Inc., 2000
Spong, M. W.; Hutchinson, S. & Vidyasagar, M. Robot Modeling and Control Wiley, 2005

Recommended reading

Grepl, R. Kinematika a dynamika mechatronických systémů CERM, Akademické nakladatelství, 2007
Grepl, R. Modelování mechatronických systémů v Matlab/SimMechanics BEN - technická literatura, 2007
Kratochvíl, C., Slavík, J.: Mechanika těles-dynamika, PC-DIR, skriptum VUT Brno, 1997
Valášek M. a kol.: Mechatronika, Vydavatelství ČVUT Praha, 1995

Classification of course in study plans

  • Programme N-MET-P Master's 1 year of study, winter semester, compulsory

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

doc. Ing. Robert Grepl, Ph.D.

Syllabus

  1. Direct and inverse kinematics (fkine, ikine)
  2. Denavit-Hartenberg (DH) parameters
  3. Robotic Toolbox and UR5 robot
  4. Practical task on fkine/ikine
  5. Quaternions
  6. Kinematics and dynamics of wheeled vehicles
  7. Dynamics and kinematics of mechanisms (repeat of LR2)
  8. SimScape (repeat)
  9. SimScape Multibody
  10. Solving n equations with m unknowns, ordinary least squares (OLS)
  11. Systems Identification I.
  12. Identification of systems II.
  13. Feedforward control

Computer-assisted exercise

26 hod., compulsory

Teacher / Lecturer

doc. Ing. Robert Grepl, Ph.D.

Syllabus

  1. Direct and inverse kinematics (fkine, ikine)
  2. Denavit-Hartenberg (DH) parameters
  3. Robotic Toolbox and UR5 robot
  4. Practical task on fkine/ikine
  5. Quaternions
  6. Kinematics and dynamics of wheeled vehicles
  7. Dynamics and kinematics of mechanisms (repeat of LR2)
  8. SimScape (repeat)
  9. SimScape Multibody
  10. Solving n equations with m unknowns, ordinary least squares (OLS)
  11. Systems Identification I.
  12. Identification of systems II.
  13. Feedforward control