Course detail
Modeling and Simulations II
FSI-RKD Acad. year: 2025/2026 Winter semester
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
Supervisor
Entry knowledge
Vector algebra. Matrix algebra. Basics of kinematics and dynamics. Newton method, Lagrange equations. Basic of programming.
Rules for evaluation and completion of the course
The evaluation is based on the standard point system 0-100b. The students can get up to 30 points for the individual semestral project and its presentation and up to 70 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.
Attendance at practical training is obligatory. Attendance at exercises is checked.
Aims
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.
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
The study programmes with the given course
Programme N-MET-P: Mechatronics, Master's, compulsory
Type of course unit
Lecture
26 hours, optionally
Syllabus
1. Introduction to kinematics of rigid bodies, forward kinematics
2. Spatial representation of the body in space, their transformation, inverse kinematics – analytical methods
3. Inverse kinematics – numerical methods
4. Optimisation methods – gradient descent
5. Quaternions
6. Trajectory planning
7. D-H parameters
8. Introduction to dynamics of rigid bodies, forward and inverse task
9. Modelling in Matlab/Simulink Multibody
10. Kinematics of wheeled vehicles
11. Linearisation
12. Term project consultations
13. Reserve
Computer-assisted exercise
26 hours, compulsory
Syllabus
1. Forward kinematics of RR manipulator
2. Rotations and transforms
3. Inverse kinematics (analytical and numerical methods)
4. Optimisation tasks
5. Solving sets of nonlinear equations
6. Trajectory planning
7. Robotic toolbox
8. Lagrange equations
9. Basic kinematics and dynamics in Matlab/Simulink Multibody
10. State-space model and discretization
11-12. Work on term project
13. Evaluation