Course detail

Engineering Mechanics

FSI-DTMAcad. year: 2011/2012

The course “Technical mechanics” provides the students with knowledge of basic axioms, laws and principles of theoretical and applied mechanics of moving bodies.
The course “Technical mechanics II” is subdivided into two branches: kinematics and kinetics. Determination of the kinematic quantities is necessary for further dynamic solving. Kinematics is aimed at proper formulation 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. Kinematics of a particle, planar kinematics and a three-dimensional rigid body motion are discussed in the introduction to the course. The graphical and numerical methods of the solution of planar mechanism motion are treated. Step by step the students are led through the following areas of dynamics: basic axioms, general dynamics of a particle, dynamics of a system of particles, dynamics of rigid bodies, moments and products of inertia of rigid bodies and dynamics of a system of rigid bodies. the fundamentals of analytical dynamics, linear vibration of systems. The sequence of presentations is following: work and energy, impulse and momentum and the equations of motion for mechanisms. The methods of vector mechanics as well as the methods of analytical mechanics are considered Finally, description and the fundamental characteristics of linear vibration are treated.

Language of instruction

Czech

Number of ECTS credits

7

Mode of study

Not applicable.

Learning outcomes of the course unit

The course will provide students with knowledge necessary to specify position, velocity and acceleration of any point of the moving bodies, in terms of a fixed coordinate system, as well as in terms of moving coordinate systems. The students will be able to solve the kinematics and kinetics problems of mechanisms.

Prerequisites

Constraints for a rigid body. Resultants of a force and couple system. Further reduction of a force and couple system. Drawing of a free-body diagram. Structural analysis of machines. Equations of equilibrium in two and three dimensions. Characteristics of a dry friction and rolling resistance. Centre of gravity. Definition of work and virtual work for variable force and for variable moment. Principle of work and energy. Conservation of energy theorem. Basic terminology of planar kinematics - radius vector, velocity and acceleration. Curvilinear motion of particle-determination of tangential and normal component of acceleration. Principle of linear impulse and momentum. Conservation of linear momentum and of angular momentum. Statement of Newton’s laws of motion. Relation between moment of a force and angular momentum. Inertial frame of reference.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations.

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 15 ECTS points out of 30 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 70 ECTS points can be reached. Solution of several computational problems is demanded. The problems come from typical profile areas of given subject and can be 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 51 points must be reached.

Course curriculum

Not applicable.

Work placements

Not applicable.

Aims

The course of Technical mechanics II gives to the students the knowledge of basic axioms, laws and principles of theoretical and applied mechanics of moving bodies. 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.

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

Attendance and activity in the seminars are required. One absence can be compensated by attending a seminar with another group in the same week, or by elaboration of substitute tasks. Longer absence can be compensated by elaboration of compensatory tasks assigned by the tutor. The course-unit credit is granted under the condition of active participation in seminars and passing the seminar tests of basic knowledge (at least 15 ECTS points out of 30 must be gained). The points gained in seminar tests are included in the final course evaluation.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Juliš K.,Brepta R. a kol.: Mechanika II.díl-Dynamika,2002 (CS)
Brát V.,Rosenberg J.,Jáč V.: Kinematika, 2005 (CS)

Recommended reading

Přikryl K.: kinematika, 2005
Přikryl, K., Malenovský, E., Úlohy z kinematiky, 2005
Slavík J.,Kratochvíl C.: Mechanika těles-Dynamika, 2000
C. Kratochvíl, E. Malenovský: mechanika těles. Sbírka úloh z dynamiky, 2000

Classification of course in study plans

  • Programme B3A-P Bachelor's

    branch B-PDS , 2. year of study, summer semester, compulsory
    branch B-MTI , 2. year of study, summer semester, compulsory

  • Programme B3S-P Bachelor's

    branch B-AIŘ , 2. year of study, summer semester, compulsory
    branch B-SSZ , 2. year of study, summer semester, compulsory
    branch B-STG , 2. year of study, summer semester, compulsory
    branch B-EPE , 2. year of study, summer semester, compulsory
    branch B-PRP , 2. year of study, summer semester, compulsory

Type of course unit

 

Lecture

52 hours, optionally

Teacher / Lecturer

Syllabus

Lectures:
1. Kinematics of a particle-rectilinear and curvilinear motion. Harmonic motion
2. Kinematics of a body-translational and rotational motion
3. Planar kinematics of a rigid body-graphical analysis.
4. Planar kinematics of a rigid body-numerical analysis
5. Relative motion analysis
6. Kinematics of a rigid body-three-dimensional motion
7. Kinematics of mechanisms
8. Dynamics of particle. Dynamics of a system of particles
9. Planar kinetics of a rigid body. Moment of inertia
10. Three-dimensional kinetics of a rigid body. Balancing of rotors. Gyroscopic motion
11. Planar kinetics of mechanisms. Determination of equations of motion - method of free body diagram
12. Kinetics of a system connected bodies- methods of analytical mechanics. Lagrange equations II
13. Vibrations – single-degree-of - freedom systems

Exercise

14 hours, compulsory

Teacher / Lecturer

Syllabus

Seminars C1:
1. Kinematics of a particle - rectilinear and curvilinear motion. Kinematics of a particle - rectilinear and curvilinear motion. Trajectory, velocity and acceleration determination.
2. Rigid body motion- translation, rotation about fixed axis and general plane motion. Graphical and numerical analysis. Instantaneous centre of zero velocity .
3. Relative motion analysis. Kinematics of mechanisms. Linkages with a cam. Kinematics of planetary and cam gears.
4.Dynamics of particle. Dynamics of a system of particles. Laws of conservation. Planar kinetics of a rigid body. Equations of rigid body motion.
5. Equations of motion of a planar system connected bodies-method of free diagram.
6. Planar kinetics of a planar system connected bodies-methods of analytical mechanics
7. Vibrations of system with one degree of freedom. Undamped and damped free vibration. Forced vibration.

Computer-assisted exercise

12 hours, compulsory

Teacher / Lecturer

Syllabus

Seminars C2A:

1. Rigid body motion. Translation, rotation about fixed axis.
2. General plane motion of a rigid body. Velocity and acceleration of individual points of a rigid body.
3. Relative motion analysis. Kinematics of mechanisms.
4. Planar kinetics of a rigid body.
5. Equations of motion of a planar system connected bodies.
6. Dynamics of vibrations.