Course detail

Engineering Mechanics II

FSI-CTMAcad. year: 2007/2008

The course “Technical mechanics II” 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

5

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

Brát V.,Rosenberg J.,Jáč V.: Kinematika, , 0
Juliš K.,Brepta R. a kol.: Mechanika II.díl-Dynamika, , 0
Hibbeler R.C.: Engineering Mechanics-Statics and Dynamics, , 0

Recommended reading

Přikryl K.: kinematika, , 0
Kolektiv: Úlohy z kinematiky, , 0
Slavík J.,Kratochvíl C.: Mechanika těles-Dynamika, , 0
C. Kratochvíl, E. Malenovský: mechanika těles. Sbírka úloh z dynamiky

Classification of course in study plans

  • Programme B3901-3 Bachelor's

    branch B3942-99 , 3. year of study, winter semester, compulsory

  • Programme B2341-3 Bachelor's

    branch B2379-00 , 3. year of study, winter semester, compulsory

Type of course unit

 

Lecture

26 hours, optionally

Teacher / Lecturer

Syllabus

1. Kinematics of a particle-rectilinear motion.Harmonic motion.
2. Translation and rotation motion about fixed axis.
3. Planar kinematics of a rigid Body. Graphical analysis.
4. Absolute general plane motion analysis.Instantaneous center of zero velocity.
5. Three-Dimensional motion of a rigid Body. Rotation about fixed Point.
6. Relative motion analysis. Simultaneous rotations. Kinematics of planet boxes.
7. Kinematical geometry. Linkages with a cam.
8. Dynamics of particle.Dynamics of a system of particles.
9. Dynamics of rigid body. Moment of inertia
10.Planar kinetics of a rigid body.
11. Planar kinetics of mechanisms - method of free body diagram.
12. Kinetics of a system connected bodies- methods of analytical mechanics. Free and forced vibration of single-degree-of freedom systems.
13. Three-dimensional kinetics of rigid body. Gyroscopic motion. Rotor balancing.

Exercise

26 hours, compulsory

Teacher / Lecturer

Syllabus

1. Kinematics of a particle - rectilinear motion.
2. Kinematics of a particle - curvilinear motion. Normal and tangential components.
3. Rigid body motion. Translation motion and rotation motion about a fixed axis.
4. Planar kinematics of a rigid body-numerical analysis.
5. Planar kinematics of a rigid body-graphical analysis.
6. Three dimensional kinematics of a rigid body.
7. Relative motion analysis.
8. Simultaneous rotations. Kinematics of planetary gears.Two components of an angular acceleration.
9. Kinetics of a particle-equations of motion. Kinetics of a system of particles.
10.Planar kinetics of a rigid body.
11. Equations of motion of a planar system connected bodies-method of free diagram.
12. Planar kinetics of a planar system connected bodies-method of analytical mechanics.
13. Free and forced vibration of single-degree-of freedom systems.