B001362 - THEORY OF MACHINES AND MECHANISMS

Italian

Planar and spatial mechanisms.
Friction and wear.
Kinetostatics
Efficiency of machines and group of machines.
Ordinary and differential gearings.
Gears.
Lubrication.
Motion transmission with flexible elements.
Lagrangian Dynamics.
Balancing of alternative mechanisms.

E. Funaioli ed altri, "Meccanica applicata alle macchine", vol. I e II, Ed. Patron Bologna.

S. Falomi, M. Malvezzi, S. Papini, "Esercitazioni di Meccanica Applicata alle Macchine", Volume 1 - Cinematica e Cinetostatica, Esculapio, Bologna.

M. Malvezzi, S. Papini, M.C. Valigi, "Esercitazioni di Meccanica Applicata alle Macchine", Volume 2, Dinamica e Ruotismi, Esculapio, Bologna.

To make the pupils familiar with: kinematic pairs and mechanisms; friction and wear, lubrication; application of Lagrangian dynamics to mechanisms. Make the pupils capable of: performing kinetostatic analysis of planar mechanisms, with and without friction, with graphical and analytical methods; performing the preliminary design of gearings and bearings.

The lecturer assumes as acquired by the students the knowledge and competencies in phisics 1 (mechanics) and analytical dynamics

De visu lectures; class exercise

Oral exam with 3 or 4 questions on theoretical and practical issues, with at least one exercise

1. -Presentation of the course; explanation about examinations
Basic definitions: machine, kinematic chain, mechanism
-Kinematic pairs, elementary kinematic pairs (rotational, helical, prismatic) and higher kinematic pairs in the plane and in three
-dimensional space
-computation of the degrees of freedom (DOFs) of a plane mechanism (Grübler rule) and a spatial mechanism (Kutzbach rule); Bi-dimensional examples: four-bar linkage, crank, cam follower, cam follower with roller, cross connector, cross connector with ineffective auction; spatial examples: spatial four-bar mechanism with 4 revolute pairs, spatial four-bar mechanism with two revolute, a spherical and a cylindrical joint.
2. Sliding friction: Coulomb's law, friction coefficient and friction angle - Definition of boundary lubrication, hydrostatic lubrication (natural and forced) and hydrodynamic lubrication (hard and soft) - Rolling friction: definition of the rolling friction parameter and rolling friction coefficient. Friction between dry surfaces, Reye's hypothesis: push pin, flat sled.
3. Reye hypothesis: brake blocks (only evolution of the pressures on the contact surface, assuming a given direction of approach) - Definition of mechanical efficiency and loss factor – Efficiency of machines in series and in parallel with examples. Efficiency in forward and reverse motion with definition of non back-driveability .
4. Theoretical Treatment of static problems and kinetostatic - Cardinal equations of statics as a result of the dynamic equations - Rigid body subjected to two forces, two forces and a moment, three forces, three forces and a moment, four forces- Examples: four-bar mechanism and crank thrust (only ideal case).
5. Mechanical efficiency of the inclined plane; forces exchanged in a rotational joint in the ideal case, and with friction - definition of the friction circle - efficiency of the rotational joint – efficiency of the prismatic joint - efficiency of the screw-nut pair.
6. Efficiency of the screw-nut torque, direct and reverse motion - relationships between the characteristic angles of the thread - The wheel in locomotion: driven wheel, traction and braking – Example of vehicle moving on a horizontal road.
7. Kinetostatics exercise: crankshaft with friction
8. Recall kinematic circular rigid motions, rolling curve (roulette) and fixed curve in plane motions
9. Kinematic analysis of four-bar mechanisms, analytical formulation for crankshaft
10. Cams and tappets
11. Kinetostatics exercise: ideal case, case with friction.
12. Gearing, introduction to mating profiles
13. Geometry of gears with involute teeth profile
14. Definition of conjugate profiles and methods for their generation; definition of involute and evolute curves; spur gears with involute teeth: basic properties; geometric characteristics and design: pitch, normal pitch (module), etc.; conditions of continuity of the motion and of non-interference; hints on cutting gears; correction of the toothed wheels and mounting of the same; notes on the spur gears with helical teeth.
15. Ordinary and planetary gear trains with 1 DOF
16. Two-DOFs gearing: automotive differential
17. Mechanical systems with flexible organs: transmissions with belts
18. Ordinary and pulley blocks, belt brakes
19. Introduction to the theory of lubrication, deduction of Reynolds’ equation starting from Navier-Stokes’ ones; application to the case of the flat slide: Reynolds’ equation

20. Application to the case of the flat sled: infinitely wide sled, finite width slide, infinitely narrow sled. Reynolds equation
21. Infinitely long rotational joint, finite length rotational joint, infinitely short rotational joint, Reynolds’ equation and examples
22. Lubrication for juxtaposition, Reynolds’ equation and examples
23. Thrust bearing, journal bearing
24. Recalls of Newtonian dynamics. Recalls of Lagrangian dynamics: non-redundant formulation
25. Lagrangian dynamics recalls: redundant formulation and examples
26. Kinematics and dynamics of crankshaft mechanism: equation of motion
27. Dynamic balancing of single-cylinder engines
28. Dynamic balancing multi-cylinder engines