# Examination topics in the discipline Mechanical engineering

Mechanics

• Properties of a force couple.
• Cases of reduction of the spatial force systems.
• Equilibrium conditions of a force system.
• Instant center of rotation and acceleration.
• Velocity and acceleration of a point in complex motion.
• The principles of mechanics used in the dynamics of the system of point particles.
• Dynamic equations in translational, rotational, planar and spherical motion of a solid.
• Kinetic energy of a solid in translational, rotational, planar and spherical motion.
• Lagrange equations of the first and second kind.

Strength of materials

• Stress-strain curve, the tensile properties of materials.
• Generalized Hooke’s law for normal and shear strain components.
• Components of stress tensor and strain tensor (special cases: plane stress, plane strain, spatial stress state, spatial strain state), definition of principal stresses.
• Pure bending, internal moment and stress relations, differential equation for the elastic curve of a beam.
• Cylindrical shafts in torsion – distribution of the shear stress, equations for maximum shear stress and angle of twist.
• Material effort, strength theories, equivalent stress.
• Stress concentration phenomenon: stress distribution in notched element,  stress concentration factor definition and variables it depends on.
• Wöhler curve and its description: Basquin equation, concepts of limited fatigue strength and fatigue limit.

Construction and operation of machines:

• Characteristics of belt drives and their application in machine design.
• Problems of transmission shafts design and calculations.
• Design of bolted joints working under static and varying load conditions.
• Construction of bearing systems with application of rolling-element bearings.
• Factors influencing the fatigue strength of machine elements.
• Characteristics of contemporary permanent joints.
• Strength conditions of statically loaded machine elements.
• Clutches – selection criteria, basic calculations, examples.
• Application and functions of lubricants in machine construction. Characteristics of seals used in machine construction.

Drive systems

• Selection criteria of drive systems to various mechanical devices.
• Construction, operation and modelling of electric, hydraulic and pneumatic drives.
• Modern IT tools used to design machine parts and model their movement.

Acoustics:

• The properties of the sound and its sources.
• Contemporary applications of acoustics.
• Methods for conditioning of the acoustics of rooms.
• The purpose of audio engineering.

Robotics:

• The construction and modelling of robots.
• Simple and inverse kinematics task. Statics and dynamics problems.
• Control Systems in Robotics.
• What is the accuracy and repeatability of the manipulator.
• What are the Euler angels and what are the advantages of using them to describe the orientation of the effector of the robot.
• What is the number of degrees of freedom of manipulator.
• What are the holonomic constraints and whether the mobile robot can be a holonomic object.

Modelling:

• Linear and nonlinear models of objects mechanical and electrical and technological processes.
• Classical mechanic, fluid mechanics and thermodynamics problems.
• Static and dynamic characteristics of dynamic objects (time and frequency domain).
• Structural dynamics, partial differential equations usage for object modelling.
• Eigenproblem of the multidimensional objects (mode shapes).