Course detail

# Technical Mechanics

FEKT-MPC-TMEAcad. year: 2020/2021

„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.

Supervisor

Department

Learning outcomes of the course unit

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.

Prerequisites

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.

**recommended prerequisite**

Co-requisites

Not applicable.

Recommended optional programme components

Not applicable.

Recommended or required reading

Florian, Z., Ondráček, E., Přikryl, K.: Mechanika těles - statika, 1995 VUT (CS)

Florian, Z., Suchánek, M.: Mechanika těles - úlohy ze statiky, 1997 VUT (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)

C. Kratochvíl, E. Malenovský: mechanika těles. Sbírka úloh z dynamiky, 2000 (CS)

Janíček P., Ondráček E., Vrbka J., Burša J.: Pružnost a pevnost I, VUT-FSI, Brno, 2004 (CS)

Janíček P., Florian Z.: Úlohy z pružnosti a pevnosti I, 2. vyd., VUT-FSI, Brno, 1995 (CS)

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.

Course curriculum

1.Definition of the course content. Basic concepts and quantities of classical mechanics. Coordinate systems. Statics, force systems and their classification, center of gravity, static equilibrium of the body.

2.Effect of passive resistances. Spatial force system replacement and equilibrium conditions. Seating and equilibrium of a rigid body in space.

3.Kinematics of a body - translational, rotational and planar motion. Planar kinematics of rigid body in a mechanism.

4.Dynamics of rigid body. Mass centre, moments of inertia, products of inertia. D´Alembert´s principle.

5.Motion equations of rigid bodies - translation, rotational and planar motion.

6.Mechanics of multibody systems.

7.Kinematics motion analysis of mechanisms - combined motion

8.Dynamics of planar multi body systems. Newton's Law.

9.Dynamics of planar multi body systems. Lagrangian mechanics.

10.Oscillation with 1 DOF. Excited oscillation with 1 DOF. Kinematic excitation.

11.Elasticity. Uniaxial and plane state of stress. Deformation energy and Castigliano´s theorem

12.Tension and compression stress of straight beams. Simple torsion theory

13.Shearing forces and bending moments. Bending stress, reflection and straight beam dimensioning.

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.

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

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.

Classification of course in study plans

- Programme MPC-KAM Master's, 1. year of study, summer semester, 5 credits, compulsory-optional

#### Type of course unit

eLearning

**eLearning:** currently opened course