Course detail

Mechanics of Handling Equipment

FSI-GMMAcad. year: 2017/2018

The basic problem of solving the mechanics of manipulators is the kinematic analysis of kinematic chains. Formalized solution is based on the matrix methods. There are two types of problems to be solved. These are the direct and indirect problems of position. Inner forces or moments are solved by kinetostatics. The Lagrange equations of motion and a method of mass and force reduction are used. The area of vibrations concentrates on the specification of modal and spectral characteristics. The finite element method is applied for elastic problems and problems of forced vibrations. Attention is also paid to the positioning and orientation of robots.

Learning outcomes of the course unit

Students will be made familiar with an automated generation of mathematical models of kinematics chains in a matrix form. They will by able to: solve direct and indirect problems of position of robots; analyse the velocities and accelerations; propose propulsion systems in kinematics pairs and determine generalized coordinates for the required position of chosen junctions; use the computer software Maple and Matlab.


Vector algebra. Matrix algebra. Kinematics of kinematic chains. d´Alambert’s principle. Lagrange’s equations. Linear theory of vibration. Differentiation in more variables.


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
Loprais A.: Mechanika manipulačních zařízení, , 0
Schwerin, R. v. MultiBody System SIMulation. Numerical Methods, Algorithms, and Software Springer, 199
Stejskal V.: Mechanika výrobních strojů a zařízení, , 0
Brát V.: Maticové metody v analýze prostorových vázaných mechanických systémů, , 0

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

Course-unit credit is awarded on results in exercises (max. 40 points). The exam has an oral and a written part (max. 60 points).

Language of instruction


Work placements

Not applicable.


The aim of the course is to teach students to create kinematic chains with required properties, create mathematical model by means of computer technology, and to solve the chains from the point of view of kinematics and dynamics. Students will learn how to solve inverse problems of position, propose required energy output of propulsion system units in kinematic pairs.

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

Attendance at practical training is obligatory.

Classification of course in study plans

  • Programme M2I-P Master's

    branch M-VSR , 2. year of study, winter semester, 5 credits, compulsory-optional

Type of course unit



26 hours, optionally

Teacher / Lecturer


1. Creating of kinematic chains.
2. Transformation matrices and their use in mechanics of robots.
3. Direct kinematics. Computation of position and velocity of the tool-center-point.
4. Indirect kinematics. Solving by means of an analytical method.
5. Indirect kinematics. Solving by means of a numerical method.
6. Kinetostatic analysis of mechanism (introduction).
7. Matrix method of kinetostatics. Analysis of robots.
8. Lagrange’s equations of motion.
9. Simulation of dynamic system in Matlab/Simulink
10. Modeling of electrical submodels and control structures
11. Automatical model building
12. Spatial visualization of mechanical systems
13. Introduction to nonlinear control using inverse dynamic model

Computer-assisted exercise

13 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