At the end of the course, students will have acquired: • knowledge of the fundamental theory of rigid body kinematics, constraints, and relative motion in articulated mechanical systems; • knowledge of the basic principles governing the dynamics of planar mechanical systems, including force and momentum balance; • understanding of fundamental friction laws and their influence on the behavior of mechanical systems; • ability to construct free-body diagrams and to determine forces and reactions in mechanical systems under equilibrium and dynamic conditions; • ability to apply energy methods and momentum conservation principles for the analysis of mechanical systems; • ability to derive mathematical models of mechanical systems starting from schematic representations, and to formulate the corresponding equations of motion; • basic competence in expressing system models in forms suitable for control-oriented analysis (e.g., state-space representation); • basic competence in numerically integrating equations of motion to simulate the time response of mechanical systems; • ability to interpret simulation results in order to evaluate forces, loads, and operating conditions relevant for design purposes; • understanding of the fundamental principles of stress and strain analysis and of the mechanical behaviour of materials; • knowledge of methodologies for evaluating equivalent stresses and determining appropriate safety factors under static loading; • understanding of the basic principles of fatigue behaviour of materials and their implications for design; • ability to estimate stresses in mechanical components subjected to static and cyclic loading conditions; • basic competence in the static and fatigue analysis of fundamental machine elements used in automated systems; • ability to perform preliminary dimensioning and verification of mechanical components based on loading conditions derived from system-level analysis; • ability to select suitable materials and design parameters to satisfy specified safety and performance requirements.

Basics of Mathematical Analysis, Physics and Technical Drawing.

The course provides an integrated treatment of Applied Mechanics and Machine Design, linking the physical description and modelling of mechanical systems to the analysis of stresses, failure mechanisms, and the preliminary design of components. In the Applied Mechanics part, students develop the ability to model mechanical systems starting from schematic representations, derive the governing equations of motion, and analyse their behaviour using both analytical and numerical methods. These analyses are used to evaluate forces, loads, and operating conditions. In the Machine Design part, these loads are used as input for the verification and dimensioning of components. The course introduces the mechanical behaviour of materials, failure criteria, and fatigue phenomena, providing the tools required for the static and fatigue design of basic machine elements used in automated and mechatronic systems. APPLIED MECHANICS (40 h) • Rigid body kinematics (7 h) Description of rigid body motion, velocity and acceleration fields, and constraints. Representation of mechanical systems through schematic models. • Mechanical couplings (2 h) Bearings, bushings, cams, power screws, and prismatic guides. Functional role within mechanical and mechatronic systems. • Relative motion and articulated mechanisms (6 h) Relative kinematics, mechanism analysis, and examples of transmission systems used in automation. • Planar dynamics of mechanical systems (8 h) Forces and moments, equations of motion, and free-body diagrams. Application to representative systems. • Friction laws (6 h) Static and kinetic friction, rolling resistance, and their influence on system performance and energy dissipation. • Conservation laws and energy methods (2 h) Energy balance, linear and angular momentum equations, with applications to system analysis. • Mathematical modelling and simulation of mechanical systems (integrated within the course) Derivation of equations of motion from schematic models. Introduction to control-oriented representations (e.g., state-space). Numerical time integration methods for the simulation of dynamic response and evaluation of loads. • Introduction to mechanical vibrations (4 h) Basic concepts of vibration in mechanical systems. • Laboratory experience on vibration mechanics (3 h) Experimental analysis and validation of vibration models. • Introduction to machine components (2 h) Overview of components and link between system-level analysis and design requirements. MACHINE DESIGN (40 h) • Stress and strain fundamentals (3 h) Definition of stress and strain tensors and their physical interpretation. • Stress analysis of structures (6 h) Statically determined structures, internal forces, and stress evaluation. • Strain and stress analysis (4 h) Relationships between stress and strain, constitutive behaviour of materials. • Stress analysis in De Saint-Venant problems (8 h) Axial, bending, torsional, and combined loading in prismatic components. • Stress intensity factors and stress concentrations (5 h) Local stress amplification and its role in design and failure. • Failure criteria and static design (6 h) Yielding criteria (e.g., von Mises, Tresca) and definition of safety factors. • Measurement techniques (2 h) Stress and strain measurement methods and sensors. • Fatigue of materials (6 h) Cyclic loading, S–N curves, endurance limits, and fatigue design principles.

The teaching is structured as follows: • 44 hours of classroom lectures, aimed at developing knowledge and understanding of the kinematics and dynamics of mechanical systems, as well as the mechanical behavior, failure mechanisms, and design of materials and mechanical components (as detailed in the program). Particular emphasis is placed on the modelling of mechanical systems, the derivation of equations of motion, and their role in supporting component design. • 30 hours of classroom exercises, aimed at strengthening the ability to apply the acquired knowledge to practical engineering problems. Activities include numerical exercises on kinematics and dynamics of mechanical systems, modelling and simulation of systems (including 1-degree-of-freedom vibrating systems), and evaluation of stresses and safety factors under different loading conditions. • 6 hours of laboratory activities, divided into: o 3 hours on vibration mechanics (Applied Mechanics): experimental analysis of dynamic behaviour and validation of simplified models; o 3 hours on mechanical behaviour of materials (Machine Design): experimental characterization of material response and observation of phenomena related to stress, deformation, and failure.

Applied Mechanics: C. Ferraresi, T. Raparelli, Applied Mechanics, CLUT, 2017. (in english) J.L. Meriam, LG. Kraige, Engineering Mechanics, Vol I,II, Wiley, 2003. (in english) K. Ogata – System Dynamics (in english) Jacazio, G., & Piombo, B., Meccanica applicata alle macchine (4 volumi). Torino: Ed. Levrotto & Bella. (italiano) Machine Design: 1. Fondamenti di meccanica strutturale G. Curti, F. Curà, CLUT, 2006, 2. Introduzione alla fatica dei materiali e dei componenti meccanici, M; Rossetto, Levrotto & Bella, 2000, 3. Fundamentals of machine component design, R. C. Juvinall, C. Marshek, Wiley, 2006. 4. Mechanics of Materials, 3rd Edition, Roy R. Craig, Wiley ed, 2011 The teaching material will be made available by the class teacher on the didattica web portal.

Lecture slides; Exercises; Exercise with solutions ; Video lectures (previous years);

Exam: Written test;

The exam is aimed at checking the knowledge of the topics listed in the official program of the course and the ability to apply the theory and the relative methods of calculation to the solution of exercises. The final written exam consists of questions and exercises on the content of the course and is made of two parts (duration of one part: 75 minutes), each ranked from 0 to 30: one part concerns the Applied Mechanics and the other one concerns the Machine Design. The Applied mechanics test is composed of two exercises, which require the ability to choose and apply the appropriate method for its resolution, as proposed during the course. They also require theoretical knowledge and the ability of the student to identify the type of technical problem presented and develop it consistently, in particular the first exercise requires the knowledge of the kinematics of rigid bodies and mechanisms, the second the knowledge of various aspects of dynamics and friction. The Machine Design part is composed of one exercise divided in two parts and one theory question. The exercise requires the ability of calcuating the stresses in a simply loaded beam according to de Saint Venant Theory and the calculation of static and fatigue safety factor. The theory question requires to know the basic of simple mechanical components design, working and failure mechanisms. During the exam, students are not allowed to use books, notes or digital tools. They are allowed to use a calculator. In order to consider the exam as passed students must achieve 18 out of 30 for each part. The final grade will be the average of the grades obtained in the two parts. For each part of the exam, an additional point is reserved for notational clarity and expository rigor and allows, if reached for both parts, obtaining "cum laude". The result of the exam is communicated on the portal, together with the date on which the students can view their work and request clarification.

In addition to the message sent by the online system, students with disabilities or Specific Learning Disorders (SLD) are invited to directly inform the professor in charge of the course about the special arrangements for the exam that have been agreed with the Special Needs Unit. The professor has to be informed at least one week before the beginning of the examination session in order to provide students with the most suitable arrangements for each specific type of exam.