Teaching - Università degli Studi della Tuscia

COMPLEMENTS OF KINEMATICS AND DYNAMICS (objectives)

"Learning objectives (according to the Dublin descriptors): The teaching of ""Complements of Kinematics and Dynamics"" will introduce student engineers to the principles and methods of Applied Mechanics of Machines in order to acquire knowledge of the fundamental laws governing the operation of mechanical devices and machines.
The objective will be to provide students with the ability to decompose machines into elementary components made up of rigid bodies, to give them the tools to be able to describe and critically analyse kinematics, static and dynamic actions acting in mechanical systems and the resulting motion. To provide knowledge of how to test and design plane and space mechanisms for understanding the functioning of the main machine organs. Equip student engineers with the basic elements that constitute the theoretical minimum for modelling and analysing the operation of a machine.
Expected Learning Outcomes - Knowledge and Understanding: The course aims to provide the knowledge of Kinematics and Dynamics aimed at setting up, simulating and evaluating the design and modelling of mechanical systems. - Ability to Apply Knowledge and Understanding: The student will be able to: a) Propose and interpret the results of design solutions. b) Perform the analysis of the kinematic structure and degrees of freedom of mechanisms, identifying the constrained kinematic chains incorporated in larger engineering systems.
c) Calculate velocities and accelerations, by means of kinematic analysis, in articulated mechanisms through analytical and numerical-computational methods recognising direct and inverse problems. d) Apply analytical and numerical-computational procedures in order to solve kinematic design problems (kinematic synthesis) of mechanisms.
e) Set up and simulate mechanical models knowing how to plan, implement and correct computer-aided design tools for the analysis of kinematics and dynamics of constrained mechanical systems using numerical integration and solution methods. f) Know how to synthesise and analyse linear models with multiple degrees of freedom for the analysis of vibrations in mechanical systems.
- Autonomy of Judgement: The student will be able to carry out the setting up and critical examination of models and related simulations. - Communication Skills: To be able to present the results of the development of models and their analysis inherent to mechanical systems using verbal, written and electronic methods (calculation software).
- Learning ability: The learning ability will be developed through the active involvement of students through oral discussions in the classroom and guided design exercises on specific topics inherent to the course. Furthermore, this ability will be stimulated and verified through the assignment of design exercises, to be carried out also through the use of the computer, which will solidify the learning of the fundamental concepts by encouraging student engineers to try their hand at the verification and dimensioning of real mechanical systems."

Code

119628

Language

ITA

Type of certificate

Profit certificate

Credits

Scientific Disciplinary Sector Code

ING-IND/13

Contact Hours

Type of Activity

Related or supplementary learning activities

Teacher	Iandiorio Christian (syllabus) The detailed educational program is organized into the following main sections: - Introduction to Mechanical Systems and Mechanisms: Overview of the historical development of Kinematics and Applied Mechanics. - Recap of Fundamental Aspects of Linear Algebra, Differential Geometry, and Mathematical Analysis: Vector algebra. Solution of vector equations. Vector calculus in Euclidean and curvilinear spaces (non-Euclidean, covariant derivative). Geometry of curves and surfaces. Tensor algebra. Introduction to tensor calculus. Matrix algebra. Eigenvalue/eigenvector problems. Lagrange multipliers method for solving constrained systems. Solution of under- and over-determined linear algebra problems. Analytical solution of linear Ordinary Differential Equations (ODE). - Introduction to Numerical Analysis: Computer arithmetic (floating-point arithmetic). Numerical solutions for large linear systems: Direct Methods (Gauss-Jordan, Cholesky Factorization, QR Decomposition, Singular Value Decomposition-SVD) and an introduction to Iterative Methods. Algorithms for eigenvalue/eigenvector computation in large linear systems using factorization and iterative methods. Numerical methods for solving nonlinear equations and systems of nonlinear equations: Bisection method, Newton-Raphson method. Introduction to solving nonlinear equations and systems as minimization problems using optimization algorithms: Trust-Region, Levenberg-Marquardt. Numerical solution of ODEs with initial value problems (IVP): Explicit and Implicit Integration, Finite Difference Method, Runge-Kutta methods and step size selection, Newmark’s method. - Kinematics of a Point Particle and a Rigid Body: Degrees of freedom of a point particle. Kinematics of a point particle in an inertial reference frame. Kinematics of a point particle in a non-inertial reference frame. Definition of a rigid body. Degrees of freedom of a rigid body. Position and orientation of a rigid body in space. Rotation tensor and its matrix representation. Euler's theorem. Cayley's formula. Rodrigues’ formula. Rodrigues parameters. Euler parameters. Euler angles and Cardan angles. Axis of screw motion (Mozzi’s theorem). Numerical techniques for determining the axis of screw motion. Kinematics of rigid bodies. Axis of instantaneous motion (ISA). Instantaneous centre of accelerations. - Statics and Dynamics of a Point Particle and a Rigid Body: Cardinal equation of the statics of particles. Dynamics equation of particles (Newton's equation). Cardinal equations of statics of rigid bodies. Varignon's theorem. First cardinal equation of rigid body dynamics. Angular momentum. Inertia tensor. Mass geometry. Kinetic energy of a rigid body. Angular momentum. Newton-Euler equations. Important applications in the dynamics of rigid bodies. - Kinematic Structure of Mechanical Systems: Classification of kinematic pairs and their degrees of freedom. Higher pairs. Introduction to Multibody Systems. Kinematic chains, mechanisms, and their graphical representation. Topological formulas for calculating the degrees of freedom of planar and spatial mechanisms. Basic articulated mechanisms. Various types of mechanisms used in industry. - Kinematic Analysis of Mechanisms: Planar motions. Centre of finite rotation. Instantaneous centre of rotation. Aronhold-Kennedy theorem. Graphical methods for kinematic analysis. Kinematic analysis of mechanisms using the constraint equations method. Calculation of a mechanism’s degrees of freedom using the constraint equations method (Hertz-Whittaker formula). Open kinematic chains. Direct and inverse kinematics. Kinematics of infinitesimal motions. Analytical determination of the instantaneous center of rotation. Poles of motion. Flexion circle. Curvature of trajectories (Euler-Savary formula). Stationarity circle. Center of accelerations. Stationary curvature cubic. Burmester points. - Kinematic Synthesis of Mechanisms: Introduction to kinematic synthesis. Kinematic synthesis for trajectory generation. Kinematic synthesis for motion generation. Kinematic synthesis for function generation. Applications of kinematic synthesis in basic mechanisms. Transmission angle. - Introduction to Calculus of Variations: Variational operations. First variation. Second variation. Fundamental lemma of the calculus of variations. Minimization of functionals depending on single or multiple variables, with derivatives of any order. - Statics of Multibody Systems: Static analysis of mechanisms using the cardinal equations of statics. The principle of virtual work in statics (Lagrange's principle). - Dynamics of Multibody Systems: Application of Newton-Euler equations to the dynamics of mechanisms (free-body diagrams). d'Alembert's principle. The principle of virtual work in dynamics (d'Alembert-Lagrange principle). Some variational principles for deriving the dynamics of mechanical systems (Maupertuis, Hamilton). Euler-Lagrange equation. Extension of the Euler-Lagrange equation to constrained mechanical systems. Introduction to dynamic simulation of Multibody Systems. - Mechanical Vibrations: Linear models with one degree of freedom. Free vibrations. Forced vibrations. Experimental determination of the damping coefficient. Vibration isolation. System response to an impulse. Linear models with multiple degrees of freedom. Decoupling the equations of motion via transformation to modal coordinates. Rayleigh damping. Modal superposition method for transient analysis. Modal superposition method for harmonic analysis. Introduction to spectral analysis. Introduction to rotor dynamics. (reference books) For studying the theory, students can refer to one of the following texts, which also include practical examples: - Educational material provided by the instructor (handouts). - N. P. Belfiore, A. Di Benedetto, E. Pennestrì. Fondamenti di meccanica applicata alle macchine. Casa Editrice Ambrosiana (CEA), 2024. ISBN: 9788808220158 - M. Callegari, P. Fanghella, F. Pellicano. Meccanica applicata alle macchine (3rd ed.). CittàStudi, 2022. ISBN: 9788825174397 For practicing the application of theoretical fundamentals of statics and dynamics to practical cases, students can refer to the following text: - G. Figliolini, C. Lanni. Meccanica Applicata alle Macchine. Applicazioni di dinamica dei sistemi meccanici. Società Editrice Esculapio, 2023. ISBN: 9788893854092
Dates of beginning and end of teaching activities	From to
Delivery mode	Traditional
Attendance	not mandatory