Course detail

Technical Mechanics

FEKT-MPC-TMEAcad. year: 2024/2025

„Technical mechanics“ represents the course that gives brief overview of classical mechanics of rigid solid bodies, i.e. statics, kinematics, dynamics and elastostatics. Statics provides discussion from the basic concepts over the classifications of the power systems to the solution of the static equilibrium of bodies and systems in motion with consideration of passive resistances. Kinematics is based on formulation of trajectory, body motion, multi body systems and determination of kinematic quantities, position, velocity and acceleration. For simple mechanical systems, students learn to solve kinematics of mechanisms and analyse the velocity and acceleration of key points of multi body systém. In kinematics (ie, the movement of rigid bodies, regardless of the forces that cause movement), the task of detecting the kinematics of a point body passes to determine the speed and acceleration of individual body points and angular velocity and angular acceleration of bodies. Gradually, the kinematics of the translation, rotation, general plane and spherical movement of the body is discussed. Mechanisms deal with solution of kinematics of complex motion of bodies and kinematic analysis of mechanisms. The dynamics gradually discusses the dynamics of particles and a system of particles, the moments of inertia of the rigid body dynamics of the rigid body and multibody dynamics. The solution of dynamics of rigid bodies is discussed both on the basis of Newton's laws (ie vector mechanics) and on the basis of variational principles (analytical mechanics). The course deals with oscillation with one degree of freedom, and the pitfalls of non-linear dynamics and the fundamentals of the dynamics of pliable bodies are mentioned. The conclusion of the course is devoted to the elasticity and strength (elastostatic) of straight rods and their dimensioning in planar motion.

Language of instruction

Czech

Number of ECTS credits

5

Mode of study

Not applicable.

Entry knowledge

The student should be able to
- to solve the system of linear and nonlinear equations,
- to solve linear differential equations of the second order with constant coefficients,
- apply trigonometry and analytical geometry in space,
- transform Cartesian coordinates into polar, cylindrical and spherical coordinates,
- apply vector and matrix algebra,
- apply physical laws (Newton's laws of motion, momentum of momentum and moments of momentum)
- determine mechanical energy and work/power, force moment and their context, the law of preservation of mechanical energy.

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 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 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 seminars is required. Head of seminars carry out continuous monitoring of student's presence, their activities and basic knowledge. One absence can be compensated for by attending a seminar with another group in the same week, or by elaboration of substitute tasks.

Aims

The aim of the course is to introduce students to the problems of technical mechanics, i.e. statics, kinematics, dynamics and elastostats. The emphasis is placed on students' understanding of the physical principles of movement of rigid bodies and body systems and application of these principles to get solution of a simple problems.
A graduate of the "Technical Mechanics" course will be able to analyze the kinematic and static qualities of placing the bodies and their systems, releasing the bodies and solving their static equilibrium. Student will also be able to describe movement of bodies in terms of kinematics and dynamics. From the kinematic input data (position, speed, acceleration) and the known geometry of the bodies, student will be able to determine the positions, speed and acceleration of any moving parts of the mechanisms. For the specified geometric and material characteristics of the rigid body system,student will be able to analyze the relationship between the external and internal forces effects and the movements induced.

Study aids

Not applicable.

Prerequisites and corequisites

Basic literature

C. Kratochvíl, E. Malenovský: mechanika těles. Sbírka úloh z dynamiky, 2000 (CS)
Florian, Z., Ondráček, E., Přikryl, K.: Mechanika těles - statika, 1995 VUT (CS)
Florian, Z., Suchánek, M.: Mechanika těles - úlohy ze statiky, 1997 VUT (CS)
Janíček P., Florian Z.: Úlohy z pružnosti a pevnosti I, 2. vyd., VUT-FSI, Brno, 1995 (CS)
Janíček P., Ondráček E., Vrbka J., Burša J.: Pružnost a pevnost I, VUT-FSI, Brno, 2004 (CS)
Přikryl K.: kinematika, 2005 VUT (CS)
Přikryl, K., Malenovský, E., Úlohy z kinematiky, 2005 VUT (CS)
Slavík J.,Kratochvíl C.: Mechanika těles-Dynamika, 2000 (CS)

Recommended reading

Not applicable.

Classification of course in study plans

  • Programme MPC-KAM Master's 1 year of study, summer semester, compulsory-optional

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

Syllabus

1. Basic concepts and quantities of mechanics. Force and moment. Force systems and their classification. Center of gravity. 
2. Statics. Static equivalence. Static equilibrium. Static conditions and their substitution. Contact of bodies. Kinematic pairs (couplings). Storage and equilibrium of a body in space. 
3. Kinematics of a mass point. Coordinate systems. Kinematics of translational and rotational motion of a rigid body. 
4. Kinematics of general plane motion of a solid. Kinematics of the compound motion of a solid. (Kinematics of the general spatial motion of a solid) 
5. Dynamics of a mass point.  D'Alambert's principle. Moments of inertia and moments of deviation of a body. 
6. Dynamics of a rigid body. General planar and general spatial motion. 
7. Systems of solids and their static solutions. Composition and formation of plane body systems, kinematic pairs, mobility, static certainty. Static solution of planar systems of bodies by the method of relaxation. 
8. Kinematics of mechanisms and their solutions. 
9. Dynamics of systems of bound bodies. Method of relaxation. Method of reduction . Lagrange's equations. 
10. Free vibration of the system with one degree of freedom. Forced vibration of a system with one degree of freedom. 
11. Internal force effects, stresses, deformations and sizing of straight members in plane bending. 
12. Elastostatics. Uniaxial and planar tension. Deformation energy and Castigliano's theorem. Tensile and compressive stresses on straight members. Simple bending. Simple torsion.

Fundamentals seminar

26 hod., compulsory

Teacher / Lecturer

Syllabus

1. Basic concepts and quantities of mechanics. Force and moment. Force systems and their classification. Center of gravity. 
2. Statics. Static equivalence. Static equilibrium. Static conditions and their substitution. Contact of bodies. Kinematic pairs (couplings). Storage and equilibrium of a body in space. 
3. Kinematics of a mass point. Coordinate systems. Kinematics of translational and rotational motion of a rigid body. 
4. Kinematics of general plane motion of a solid. Kinematics of the compound motion of a solid. (Kinematics of the general spatial motion of a solid) 
5. Dynamics of a mass point.  D'Alambert's principle. Moments of inertia and moments of deviation of a body. 
6. Dynamics of a rigid body. General planar and general spatial motion. 
7. Systems of solids and their static solutions. Composition and formation of plane body systems, kinematic pairs, mobility, static certainty. Static solution of planar systems of bodies by the method of relaxation. 
8. Kinematics of mechanisms and their solutions. 
9. Dynamics of systems of bound bodies. Method of relaxation. Method of reduction . Lagrange's equations. 
10. Free vibration of the system with one degree of freedom. Forced vibration of a system with one degree of freedom. 
11. Internal force effects, stresses, deformations and sizing of straight members in plane bending.