# 84232 - FUNDAMENTALS OF MECHANICS OF MACHINES M

## Conoscenze e abilità da conseguire

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.

## Contenuti

Mathematical background

• Trigonometry. Vectors. Derivatives.

Kinematics of points and rigid bodies

• Position, velocity and acceleration.
• Instantaneous rigid motions. Finite rigid motions. Planar rigid motion.

Kinematics of multibody systems

• Machines and mechanisms. Kinematic pairs. Degrees of freedom and constraint.
• Kinematics of planar 1-dof mechanisms.
• Graphical kinematic analysis.

Kinetostatics of multibody systems

• Systems of generalized forces. Equilibrium of generalized forces. Constraint reactions.
• Equilibrium of multibody systems.
• Gravitational forces. Inertia forces. Power and Kinetic energy.
• Graphical force analysis.

Dissipative actions in machine components

• Kinetic and static friction. Efficiency. In-series and in-parallel machines.
• Graphical kinetostatic analysis in case of friction.
Power transmission devices with constant transmission ratio
• Ordinary and planetary gear trains: transmission ratio, efficiency, external moments. Differentials.
• Transmissions with flexible elements: lifting devices, power transmission systems.

Power transmission devices with variable transmission ratio

• Motion laws with periodic transmission ratio. The motion law and its properties: velocity, acceleration and torque coefficients. Criteria for the choice of the displacement function: limitation of velocity, acceleration and driving torque. Qualitative comparison between displacement functions.
• Cam mechanisms. Classification. Kinematic and kinetostatic analyses. Force and form joint closure: positive-motion and dual-cam mechanisms.
• Intermittent-motion mechanisms: Geneva mechanisms, indexers.
• Planar linkages. RRRR, RRRP and RRPP kinematic chains. Special positions: stationary and singular configurations. Coupler curves. Dwell mechanisms and force amplifiers. Quick-return mechanisms. Mechanisms for linear and translatory motions.

Dynamics of a single-degree-of-freedom machine.

• Equation of motion. Energetically-equivalent reduced machine. Steady-state operation. Steady-state torque-speed characteristics of driving and operating machines. Speed regulation.

## Testi/Bibliografia

• SLIDES of the course lectures. (required reading)
• MECHANICS OF MACHINES. W.L. Cleghorn, N. Dechev. Oxford University Press, 2016. (supplementary reading)

## Metodi didattici

Classes are based on theoretical lectures with application examples.

## Modalità di verifica e valutazione dell'apprendimento

The examination consists of a written test in two parts: a quiz with questions related to the theoretical topics covered in the course; an exercise focused on graphical kinematic and force analyses.

## Strumenti a supporto della didattica

Students may find the slides of the course lectures on the E-learning Platform.

## Orario di ricevimento

Consulta il sito web di Marco Carricato

Consulta il sito web di Michele Conconi