Course detail

Modeling and Simulations II

FSI-RKDAcad. year: 2020/2021

The course deals with the kinematics and dynamics modelling of controlled mechatronic systems. Previous knowledge of mechanics is developed, mainly with focus on numerical solution of problems on computers. Mechanisms are considered as rigid multi body systems. Exercises run on computers using Matlab and Maple. Forward and inverse kinematic model is solved using analytical and numerical methods. Dynamic model is built using Newton's method, Lagrange equations and automatically (Matlab/SimMechanics). Modelling of electrical and regulation structures such as submodels of complex models are also discussed.

Learning outcomes of the course unit

After the course graduation, students will be able to:
- build and solve forward and inverse kinematic model of arbitrary kinematic chain with open topology
- consider the suitability of a particular method in kinematics
- build and solve analytical dynamic models of simple mechanical systems
- be well informed about numerical modelling of complex mechatronics systems


Vector algebra. Matrix algebra. Basics of kinematics and dynamics. Newton method, Lagrange equations. Basic of programming.


Not applicable.

Recommended optional programme components

Not applicable.

Recommended or required reading

Grepl, R. Kinematika a dynamika mechatronických systémů CERM, Akademické nakladatelství, 2007
Spong, M. W.; Hutchinson, S. & Vidyasagar, M. Robot Modeling and Control Wiley, 2005
Grepl, R. Modelování mechatronických systémů v Matlab/SimMechanics BEN - technická literatura, 2007
Sciavicco, L.; Siciliano, B. & Sciavicco, B. Modelling and Control of Robot Manipulators Springer-Verlag New York, Inc., 2000
Valášek M. a kol.: Mechatronika, Vydavatelství ČVUT Praha, 1995
Murray, R. M.; Sastry, S. S. & Zexiang, L. A Mathematical Introduction to Robotic Manipulation CRC Press, Inc., 1994
Kratochvíl, C., Slavík, J.: Mechanika těles-dynamika, PC-DIR, skriptum VUT Brno, 1997
Corke,P.I.: A Robotics Toolbox for Matlab, IEEE Robotics and Automation Magazine, pp.24–32, 1996

Planned learning activities and teaching methods

The course is taught through lectures explaining the basic principles and theory of the discipline. Exercises are focused on practical topics presented in lectures.

Assesment methods and criteria linked to learning outcomes

The evaluation is based on the standard point system 0-100b. The students can get up to 40 points for the individual semestral project and its presentation and up to 60 points for the final test. The final test consists of a theoretical test, assignments in Matlab/Simulink and a discussion. In all cases, especially the fulfillment of functional requirements and the quality of the realization are the evaluation criteria.

Language of instruction


Work placements

Not applicable.


Students are acquainted with modern approaches to solution of kinematic and dynamic problems. The aim of the course is the control of real machines and their simulationg models. The emphasis is given on using of computers. Theoretical information is applied on particular problem solutions in the scope of semestral project.

Specification of controlled education, way of implementation and compensation for absences

Attendance at practical training is obligatory. Attendance at exercises is checked.

Classification of course in study plans

  • Programme N-MET-P Master's, 1. year of study, winter semester, 5 credits, compulsory

Type of course unit



26 hours, optionally

Teacher / Lecturer


1. Introduction to kinematics and dynamics of rigid bodies
2. Spatial representation of body in space, their transformation
3. Forward kinematic model - analytical methods
4. Inverse kinematic model - analytical model, numerical approach
5. Trajectory generation
6. Kinetostatics
7. Analytical methods of dynamics model building
8. Analytical methods of dynamics model building
9. Numerical methods of dynamics model solving
10. Modelling of discontinuities modelling
11. Simulation of dynamic model in Matlab and Matlab/Simulink
12. Modelling of electrical submodels and control structures
13. Automatic building of dynamic model

Computer-assisted exercise

26 hours, compulsory

Teacher / Lecturer


1. Matlab and its usage for kinematic and dynamic modelling. Examples of models.
2. Modelling of kinematics in Matlab and using Robotic Toolbox
3. Modelling of dynamics in Matlabu, examples
4. Modelling of dynamics in Matlabu/Simulink, examples
5. Modelling of dynamics in Matlabu/SimMechanics, examples
6.-12. Semestrer project
13. Presentation of semestrer project, evaluation