31622 - Mechanics of Machines

Learning outcomes

Basic elements of the functional  analysis of mechanisms and machines are provided. Particular attention is devoted to tribological, kinematic, static and dynamic issues.

Course contents

1. Composition of mechanisms

Definition of machine, mechanisms, link, kinematic element, kinematic pair. Degrees of freedom of a mechanism, constraints. Lower and higher pairs: revolute, prismatic and helical pairs. Plane, spherical and general pairs. Conjugate profiles. Degrees of freedom of a plane and spatial mechanism. Grubler's formula, special cases. Overconstrained mechanisms.

2. Forces acting on machines

General equations of Mechanics. Efficiency. Definition of different types of forces. Fundamental equations of the Dynamics of machines, D'Alembert equation, energy equation, principle of virtual work. Mechanical efficiency of machines in series and in parallel. Inverse motion.

3. Contact forces in solids

Types of contacts among rigid bodies. Friction. Lubrication. Coefficient of friction. Rolling friction. Wear. Prismatic pair, inclined plane. Revolute and helical pairs. Hypothesis of Reye: applications. Friction torque in rolling bearings. Wheels on locomotion.

4. Lubrication of kinematic pairs (basic elements)

Elementary theory of lubrication. Reynolds equation in planar case. Planar bearing, infinite and finite journal bearing. Elastodynamic lubrication (basic elements). Fluidostatic lubrication: thrust and journal bearings.

5. Kinematics of rigid bodies

Center of instantaneous rotation. Trajectory generation. Acceleration of points of rigid bodies in plane motion. Relative motion.

6. Linkages

Four-bar linkage. Grashof formula. Velocity and acceleration analysis of a planar for-bar linkage by graphical methods. Crank and slider mechanism. Analytical methods of kinematic analysis of mechanisms. Kinetostatic analysis of planar systems. Synthesis problems in plane motion. Roberts's theorem. Oldham and Cardan joints.

7. Gears

Transmission by gears. Friction wheels. Generation of conjugate profiles. Sprur gears. Contact line. Interference of profiles. Manufacturing process of gears. Modified gear profiles. Forces and moments in spur, helical and bevel gears. Transmission between skew axis by helical gears. Worm gear transmission.

8. Deformable elements. Lifting machines.

Stiffness of flexible elements. Stationary and mobile pulleys. Burton efficiency. Transmission among parallel shafts by plane and trapezoidal belts.

9. Elements of Dynamics of rigid bodies.

Inertia forces in general motion. Special cases. Kinetic energy. Masses of substitution.

10. Dynamics of the crank and slider mechanism

Dynamic equilibrium of a reciprocating machines. Balancing of inertia forces. Kinetic energy of a reciprocating machine.

11. Mechanical vibrations

Free vibrations of a one degree of freedom system. Forced vibration of a one degree of freedom system. Isolation of vibrations. Balancing of rigid rotors. Balancing machines.

EXERCISES

Exercises are developed on all the basic topics treated in the lectures.

Readings/Bibliography

E. Funaioli – A. Maggiore – U. Meneghetti

Lezioni di MECCANICA APPLICATA ALLE MACCHINE

Prima parte: FONDAMENTI DI MECCANICA DELLE MACCHINE

Pàtron Editore – ISBN 88-555-2829-7

Teaching methods

The deductive approach is mainly adopted for the presentation of the theory. However, also the deductive approach is used in a number of issues.

The basic elements of the main issues are developed by lectures then a complete set of related applications are developed, with the aim of strengthening and further developing the learned theory.

Assessment methods

The final evaluation of the students is performed by a written examination . Oral exam is also allowed upon request of the student.

Teaching tools

The lectures are supported, when necessary, by physical models of mechanisms and part of machines.

Applications accompany the development of the theory by graphical and analytic methods and software tools (CAD systems and computation codes).

Office hours

See the website of Vincenzo Parenti Castelli