Course detail

Kinematics

FSI-4KIAcad. year: 2025/2026

Kinematics, as a part of mechanics, is a science that deals with the motion of bodies irrespective of the forces causing the motion. Bodies have only the geometric properties that are constant. In kinematics, the body is immaterial; it is a model solid. The course covers the analysis of motions of a particle and rigid bodies. Topics include kinematics with absolute and relative motions of rigid bodies in translation, rotation, spherical and general planar motion using translating and rotating axes. Gained knowledge is applied to solving the mechanisms in motion. Mechanisms are solved both graphically and numerically. Kinematics geometry is applied as well.

Language of instruction

Czech

Number of ECTS credits

4

Mode of study

Not applicable.

Guarantor

doc. Ing. Jiří Krejsa, Ph.D.

Department

Institute of Solid Mechanics, Mechatronics and Biomechanics (ÚMTMB)

Entry knowledge

The student must be capable of solving the set of linear and quadratic equations. Trigonometry and analytic geometry. Calculus (differentiation and integration) in one variable. Vector algebra. Matrix algebra. Descriptive geometry.

Rules for evaluation and completion of the course

The course-unit credit is granted under the condition of active participation in seminars and passing the seminar tests of basic knowledge (at least 10 ECTS points out of 20 must be gained). The points gained in seminar tests are included in the final course evaluation.
Final examination: Written part of the examination plays a decisive role, where the maximum of 80 ECTS points can be reached. Solution of several computational problems is demanded. The problems come from typical profile areas of given subject and supplied by a theoretical question, proof, etc. The lecturer will specify exact demands like the number and types problems during the semester preceding the examination.
Final evaluation of the course is obtained as the sum of ECTS points gained in seminars and at the examination. To pass the course, at least 50 points must be reached.
Attendance at practical training is obligatory. Head of seminars carry out continuous monitoring of student's presence, their activities and basic knowledge.

Aims

The course is aimed at proper formulation of motion definition, i.e. the students have to be able to determine how to set the position of a point, rigid body, or a system of rigid bodies, in any instant of time. On the basis of a position task solution other kinematic quantities (velocities and accelerations) are to be determined. Determination of the kinematic quantities is necessary for further dynamic solving. Computational methods are preferred.
The students will be able to analyse the movement from the point of view of kinematics and to perform the solution of motion variables determination. They will be able to analyse mechanisms, and on the basis of a set position determine the velocity and acceleration in arbitrary moment of time. As the matrix arithmetic is used during the analysis, the student will be able to solve kinematic problems using the computers.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Brát V.: Maticové metody, 2001
Brát V.,Rosenberg J., Jáč V.: Kinematika, 2002
Meriam J.L: Engineering Mechanics Vol.2, 2005

Recommended reading

Malenovský E.: Kinematika, předřešené úlohy, 2000
Přikryl K.: Kinematika, 2005
Přikryl, K., Malenovský, E., Úlohy z kinematiky, 2005

Classification of course in study plans

  • Programme B-MET-P Bachelor's 2 year of study, summer semester, compulsory

  • Programme B-ZSI-P Bachelor's

    specialization STI , 2 year of study, summer semester, compulsory

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

doc. Ing. Jiří Krejsa, Ph.D.

Syllabus

1. Kinematics of a particle, harmonic motion.
2. Orthogonal transformations of vector quantities.
3. Kinematics of rigid bodies,translational motion.
4. Rotation about a fixed axis.
5. Absolute general plane motion, analytical analysis.
6. Absolute general plane motion, graphical analysis.
7. Kinematics geometry.
8. Three-dimensional motion of a rigid body. Rotation about a fixed point.
9. General three-dimensional motion of a rigid body.Screw motion.
10.Relative motion analysis. Coexistent rotary motion, gears.
11.Kinematics of planar mechanisms. Graphical analysis.
12.Kinematics of planar mechanisms. Analytical analysis.
13.Linkages with a cam. Alternate linkages. Coriolis's method.

Exercise

12 hod., compulsory

Teacher / Lecturer

doc. Ing. Jiří Krejsa, Ph.D.

Syllabus

1. Rectilinear and curvilinear motion of a point.
2. Kinematics of a rigid body. Orthogonal transformations of kinematics quantities.
3. Absolute general plane motion, graphical analysis.
4. Kinematics geometry.
5. Spherical motion of a rigid body. Two components of an angular acceleration.
6.Graphical analysis of planar mechanisms. Linkages with a cams.

Computer-assisted exercise

14 hod., compulsory

Teacher / Lecturer

doc. Ing. Jiří Krejsa, Ph.D.

Syllabus

1. Rectilinear and curvilinear motion of a point.
2. Kinematics of a rigid body. Orthogonal transformations of kinematics quantities.
3. Absolute general plane motion, analytical analysis.
4. General spatial motion of a rigid body. Screw motion.
5.Relative motion analysis.
6.Coeval rotary motion, gears.
7. Analytical analysis of planar mechanisms.