Course detail

# Kinematics

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

Learning outcomes of the course unit

The students will be able to analyse the movement from the point of view of kinematics and to carry out its solving. They will be able to analyse mechanisms, and on the basis of a set position determine the rate of change of the position and velocity in arbitrary time of moment. With regard to exploitation of matrix arithmetic, the student will be able to solve kinematic problems with the use of computers.

Prerequisites

Solving of simultaneous linear and quadratic equations. Trigonometry and analytic geometry. Differentiation and integration in one variable. Vector algebra. Matrix algebra. Descriptive geometry.

Co-requisites

Not applicable.

Recommended optional programme components

Not applicable.

Meriam J.L: Engineering Mechanics Vol.2, 2005
Přikryl, K., Malenovský, E., Úlohy z kinematiky, 2005
Přikryl K.: Kinematika, 2005
Brát V.,Rosenberg J., Jáč V.: Kinematika, 2002
Malenovský E.: Kinematika, předřešené úlohy, 2000
Brát V.: Maticové metody, 2001

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 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.

Language of instruction

Czech

Work placements

Not applicable.

Aims

The course “Kinematics” is aimed at proper formulation of setting of motion, 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 solving, other kinematic quantities are to be determined. Determination of the kinematic quantities is necessary for further dynamic solving. Count methods are preferred.

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

Attendance at practical training is obligatory. Head of seminars carry out continuous monitoring of student's presence, their activities and basic knowledge.

Classification of course in study plans

• Programme B3A-P Bachelor's

branch B-MET , 2. year of study, summer semester, 5 credits, compulsory

• Programme B3S-P Bachelor's

branch B-STI , 2. year of study, summer semester, 5 credits, compulsory

• Programme M2I-P Master's

branch M-LPR , 1. year of study, summer semester, 5 credits, compulsory-optional

#### Type of course unit

Lecture

26 hours, optionally

Teacher / Lecturer

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.

Exercise

12 hours, compulsory

Teacher / Lecturer

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 hours, compulsory

Teacher / Lecturer

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.

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