# 84232 - Fundamentals of Mechanics of Machines M

### SDGs

This teaching activity contributes to the achievement of the Sustainable Development Goals of the UN 2030 Agenda.

## Learning outcomes

The course aims at strengthening the knowledge of the structure of machines and mechanisms with particular attention to the kinematic, kinetostatic and dynamic analysis of systems with rigid links and to the dynamics of cycle machines. Advanced methods of analysis and synthesis of mechanisms, cams and gears will complement the basic concepts developed at the bachelor level. Elements of machine design and strength of materials are also presented with emphasis to fatigue analysis and structural analysis. At the end of the course students have a deep understanding of all the elements of mechanics that are fundamental for industrial automation, mastering design and construction principles that play a role in modern automatic machines.

## Course contents

Introduction:

• Definition of machines, mechanisms and structures

• Definition of statics and dynamics, kinematics and kinetics

• Definition of links, kinematic pairs and kinematic chains

• Examples of kinematic chains with binary and ternary links

• Lower and higher kinematic pairs: degrees of freedom and construction

• Degrees of freedom of planar and spatial mechanisms: the Grubler and Kutzbach formulas, their applications and limits

Fundamental equations for the study of the mechanics of machines:

• D’Alembert principle

• Virtual Work principle

• Energy equation

• Lagrange equations

Energetics of machines:

• Efficiency of a machines: single machine, machines in series and in parallel, direct and backward motion

• Choice of motor on the bases of useful work

• Mechanical characteristic of machines: definition, measurement, motor-load coupling and its stability

• Start and stop transients of a machine

Tribology:

• Introduction to friction: sliding and rolling

• Analysis of contact between kinematic elements: relative motion, forces and power loss

• Friction: the laws of friction, coefficient of friction, causes of friction, adhesion theory of friction

• Lubrication: introduction to boundary lubrication, hydrodynamic lubrication, hydrostatic lubrication, elasto-hydro-dynamic lubrication and mixed lubrication

• Rolling contact: Hertz theory, rolling friction

• Wear: definitions and types (adhesive, abrasive, corrosive, pitting, fretting)

Functional analysis of kinematic pairs with friction:

• Prismatic pair: introduction, application and realizations; friction cone; balance of forces; efficiency; jamming

• Inclined plane: balance of forces; efficiency for direct and reverse motion

• Revolute pair: introduction, application and realizations; friction circle; balance of forces; efficiency for direct and reverse motion

• Helical pair with friction: introduction, application and realizations; balance of forces; efficiency for direct and reverse motion

Functional analysis of mechanical components with wear:

• Reye's hypothesis

• Planar slot (pad brake): introduction, application and realizations; wear profile and pressure distributions

• Planar clutch (automotive clutch): introduction, application and realizations; wear profile and pressure distributions

• Shoe brake: introduction, application and realizations; wear profile and pressure distributions

Functional analysis components with rolling elements:

• Behavior of single wheel during locomotion: driven wheel, driving wheel, braking wheel

• Equilibrium of a vehicle in straight motion (graphical analysis)

• Rolling bearings with friction: introduction and typologies, calculation of frictional moment

Hydrodynamic lubrication:

• Characteristics and properties of lubricants

• Analysis of hydrodynamic lubricated pairs: Reynolds equations, fluid motion and pressures, resulting forces and moments

• Applications to: planar slots (with infinite and finite length) and axially loaded revolute pairs; radially loaded revolute pairs (with infinite and finite length)

Hydrostatic lubrication:

Analysis of closed chain mechanisms:

• Kinematic analysis via analytical methods

• Kinematic analysis of planar mechanism via graphical methods

• Kinetostatic analysis via analytical methods

• Kinetostatic analysis of planar mechanism via graphical methods

• Applications: the four bar mechanism

• Applications: the single slider crank chain

• Applications: the double slider crank chain (Scotch-Yoke mechanism, Oldham joint)

• Applications: the Cardan joint (single and double)

Analysis of machines with flexible elements:

• Ropes, chains and belts

• Pulley and rope systems (lifting machines): losses, balance of forces and efficiency of systems with fixed and movable pulleys

• Block and tackle systems (lifting machines): balance of forces and efficiency

• Belt transmission: introduction, application and realizations; functioning principles (belt deformation, belt speed, belt-pulley sliding, efficiency); calculation of belt tension; balance of forces; dimensioning

Analysis of gear mechanisms:

• introduction, application and realizations

• wheels for the transmission of motion between parallel axes: cylindrical gears with straight and helical teeth; generation of gear profiles; pitch and base circles; rack and pinion; nomenclature; transmission ratio; balance of forces; arc of action (calculation); interference condition (calculation); modular and non-modular wheels

• wheels for the transmission of motion between orthogonal and intersecting axes: bevel gears with straight and helical teeth; generation of gear profiles; pitch cones; transmission ratio; Tredgold’s method for the analysis and design of bevel gears

• wheels for the transmission of motion between skew axes: generalities of worm gears (functioning principles and transmission ratio)

Dynamics of machines:

• Kinetic energy, inertia forces and couples of links moving in space and in plane

• Equivalent masses

• Dynamics of the slider crank mechanism: calculation; methods for the compensation of inertia actions (of both first and second order)

• Mechanics of vibrations of spring-mass-dashpot systems: free vibration response of one degree-of-freedom system (calculation and analysis of the response in time domain); forced vibration response of one degree-of-freedom system (calculation and analysis of the response in frequency domain)

Textbooks:

- lecture notes from the teacher

- E. Funaioli, A. Maggiore e U. Meneghetti, Lezioni di Meccanica Applicata alle macchine – prima parte – Fondamenti di Meccanica delle Macchine, Patron Editore.

- Erdman and Sandor, “Analysis and Synthesis of Mechanisms”, voll. 1 and 2, 1990, Prentice-Hall.

- B. Paul, Kinematics and Dynamics of Planar Machinery, Prentice-Hall.

- S. Doughty, Mechanics of Machines, Wiley & Sons.

- John Uicker, Gordon Pennock, Joseph Shigley, Theory of Machines and Mechanisms, Oxford University Press Canada.

- Kenneth Waldron and Gary Kinzel, “Kinematics, Dynamics, and Design of Machinery 2nd Edition”, John Wiley & Sons, 1999.

- Kolowsky M.Z., Egrafov A.N., Semenov Yu. A., Slousch A.V., “Advanced Theory of Mechanisms and Machines”, Springer, 2000.

- Suh C.H. and Radcliffe C. W., “Kinematics and Mechanisms Design”, John Wiley & Sons, 1978.

- Tsai L.W., “Robot Analysis, The Mechanics of Serial and Parallel Manipulators”, John Wiley & Sons, 1999.

- J-P. Merlet. Parallel robots. Kluwer, Dordrecht, 2000.

- Sandler Ben-Zion, “Robotics: Designing the Mechanisms for Automated Machinery”, Academic Press, 1999.

- Rivin, E. I. “Mechanical design of Robots”, McGraw-Hill, 1988.

## Teaching methods

The course comprises theoretical lectures and classroom exercises.

As for the lectures, the theoretical and analytical aspects of typical problems of Mechanics of Machines are analysed. Basic elements (provided in previous courses) of Physics and Analytical Mechanics are recalled and discussed, then new theoretical tools for modeling and developing functional analysis of machines and mechanisms are provided, with particular emphasis on kinematic, static and dynamic problems.

Exercises are developed as examples of the main methods for the computation of degrees of freedom and for the solution of the kinematic and kinetostatic analysis of mechanisms.

## Assessment methods

Written or oral test, under student request.

The test comprises two exercises, namely on graphical kinematic and on kinetostatic analyses of a mechanism.

Two additional questions are given which are related to the theoretical topics delivered in the course.

## Teaching tools

Blackboard, power point slides, physical models of mechanisms and mechanical systems, in addition to videos on various subiects treated in the lectures, are extensively used.

Most material is made available on the AMS Campus website.

## Office hours

See the website of Vincenzo Parenti Castelli