Course detail

Engineering Mechanics

FSI-DTMAcad. year: 2007/2008

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

6

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, good results in seminar tests of basic knowledge (three written tests during semester are recommended). Solution of additional tasks is required in case of longer justified absence. Seminar tutor will specify these conditions in the first week of a semester. Final evaluation is based on the results of examination, which has a combined form: written part (test of elementary knowledge+computational tasks) and oral part (discussion on written part with supplementary questions). It is necessary to have at least 50% of points in the test to pass the introductory part of exam. The solution of 2-3 computational tasks follows then, the tasks come from typical profile areas of given subject. One of them can be supplied by theoretical question, proof, etc. The result of each task is evaluated from A (excellent) to F (failed). To pass the exam, only one task of all can be evaluated by F (failed), at the most.

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. Credit requirements: active presence in the seminars, - good results in seminar tests testing basic knowledge, - written additional assignments in case of longer excusable absence. Seminar tutor will specify the form of such conditions in the first week of semester. Participation in (???není jasné k čemu se vztahuje, v češtině chybí) theoretical exercises is necessary.

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 B3901-3 Bachelor's

    branch B2379-99 , 2. year of study, summer semester, compulsory
    branch B3942-99 , 2. year of study, summer semester, compulsory

  • Programme B2341-3 Bachelor's

    branch B2370-00 , 2. year of study, summer semester, compulsory
    branch B2324-00 , 2. year of study, summer semester, compulsory
    branch B2307-00 , 2. year of study, summer semester, compulsory
    branch B2323-99 , 2. year of study, summer semester, compulsory
    branch B2330-00 , 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

26 hours, compulsory

Teacher / Lecturer

Syllabus

Seminars:

1. Kinematics of a particle - rectilinear and curvilinear motion
2. Rigid body motion. Translation, rotation about fixed axis
3. Absolute general plane motion of a rigid body- graphical analysis. Instantaneous center of zero velocity
4. Numerical analysis of a general plane motion. Determination of velocity and acceleration of individual points of a body.
5. Relative motion analysis.
6. Three dimensional kinematics of a rigid body. Rotation about fixed point
7. Kinematics of mechanisms. Linkages with a cam. Kinematics of planetary gears
8. Dynamics of particle. Dynamics of a system of particles. Laws of conservation
9. Planar kinetics of a rigid body. Calculation of the moment of inertia
10. Three dimensional kinetics of a rigid body. Equations of motion
11. Equations of motion of a planar system connected bodies-method of free diagram.
12. Planar kinetics of a planar system connected bodies-methods of analytical mechanics
13. Vibrations. Undamped and damped free vibration. Forced vibration