Kinematic Structure of Mechanical Systems
Classification of kinematic pairs and their degrees of freedom. Lower pairs. Higher pairs. Shape and force closure pairs. Kinematic chains and mechanisms. Classical representation of kinematic chains and mechanisms. Introduction to the analysis and synthesis of mechanisms. Topological formulas for calculating the number of degrees of freedom (DoF). Mechanisms with lower pairs only. Correspondence between mechanism graphs. Enumeration of mechanisms with 1 DOF and 4 members.


Geometry of Constrained Systems
Introduction to graphical methods. Representation scales. Classical geometric approach to the problem of initial configuration. Slider-Crank mechanism. Grashof's rule for the planar four-bar linkages. Four-bar parallelogram. anti-parallelogram. Analytical methods for determining the initial configuration. Numerical methods for determining the generic configuration of a mechanism. Dependent and independent coordinates. Solution of the problem of the initial configuration using the numerical method of Newton–Raphson. Application of Dini's theorem to the calculation of degrees of freedom. Graphical method for determining the configuration of an articulated quadrilateral. Methods for determining the configuration of an articulated quadrilateral: analytical and numerical. Technograph. Pantograph. Use of the oscillating slider crank system, Hart's, Peaucellier's straight-line generator.

Geometry of Masses and Moments of Inertia
Static moments or first-order moments. Moments of inertia or second-order moments. Huygens-Steiner theorem. Principal axes and moments of inertia. Moment of inertia of the section about the neutral axis and polar moment of inertia of a shape.

Introduction to Kinematic Analysis of Planar Systems
Review of kinematics of the material point. Review of kinematics of the rigid body. Motion law for a planar system and first-order centrodes. Fundamental formula of kinematics. Velocity center. First-order centrodes. Acceleration field. Euler-Savary formula in the first and second formulations. Inflexion circle. Curvature of trajectories. Null tangential acceleration circle. Review of the theorem of relative motions. Aronhold-Kennedy theorem. Graphical methods of kinematic analysis. Graphical method based on vectors diagrams. Vectors diagrams based on the fundamental formulas of kinematics. Vectors diagrams based on the theorem of relative motions. Graphical determination of K. Center points method. Graphical determination of the center of curvature of the trajectory of a point M of the mobile plane, knowing the centers of curvature of the first-order centrodes. Graphical determination of the first-order centrodes. Kinematic analysis of mechanisms. Kinematic analysis of mechanisms with higher pairs. Construction methods of conjugate profiles. The method of the envelope curve. The method of normal lines. The cycloid curve method with a point trajectory. The cycloid curve method with an auxiliary envelope curve. Assortment profiles. Justification of equivalent mechanisms with the cycloid curve method with a point trajectory. Center of curvature of the trajectory of a point. Kinematic analysis with the method of constraint equations and with complex numbers. General case of a system with rehonomic constraints or time-dependent constraints Kinematic analysis of mechanisms with rolling or sliding bodies. Kinematic analysis of a planar four-bar linkages with numerical method based on constraint equations. Parametric equation of the involute curve. Parametric equation of the cycloid curve.

Recap of Statics
Newton-Euler equations of Statics. Elementary cases of equilibrium. Equivalent force systems. The principle of virtual work. Static equilibrium of mechanisms with one degree of freedom.

Dynamics of Planar Mechanisms
Classifications of dynamic actions. External and internal forces. Driving and resisting forces. Active and reaction forces. Review of the dynamics of the point mass, d'Alembert's principle. Application of d'Alembert's principle to systems of lumped point masses. Review of the dynamics of the rigid body. Equation of motion of a translating body. Equations of motion of a body rotating about an axis. Equivalent force system. Body subjected to generic planar motion. Newto-Euler equations in space. Dynamics of systems through the Principle of the Virtual Work PLV. Direct and indirect dynamic problems. Application of PLV. Scotch-yoke mechanism. Dynamics of the planar four-bar likage. Kinematics and Dynamics of the slider crank mechanism.

Analytical Dynamics
Dynamic analysis with the method of Lagrange multipliers, the role of reactions in the method of Lagrange multipliers. The setting up of the dynamic problem. Integration of equations using initial conditions.

Friction and Wear
Elements of surface mechanics. Ideal and real surfaces. Contact between two real surfaces. Stresses and deformations in surface contacts. Hertz's Formulas. Typology of dissipative phenomena. Types of friction. Types of wear. Models for calculating tangential dissipative forces in direct contacts. Determination of the coefficient of sliding friction in adhesive wear regime. Experimental determination of tribological characteristics of a pair of materials. Models for wear calculation. Axial revolute pair and journal bearings. Friction circle. Classification of friction based on the relative motion between bodies in contact. Rolling friction due to material hysteresis. Rolling friction parameter. Loaded and Unloaded driving wheel. First definition of rolling friction coefficient for material hysteresis. Driven wheel: further definition of rolling friction coefficient for material hysteresis. Rolling friction due to impacts. Rolling bearings. Friction circle for rolling bearings. Design of axial and journal rolling bearings in static and fatigue conditions.

Basics of Lubrication Theory
Viscosity in lubricating fluids. Other characteristics of lubricating oils. Additives for lubricating oils. Classification of lubrication types. Friction in lubricated prismatic pair. Expression of the flow rate of a fluid in a fluid film. Pushing rolling pair. Hydrostatic lubrication with constant flow rate or pressure. Circuits with hydrostatic compensation. Hydrodynamic lubrication: need for a film with variable thickness. Film with constant height in sections: step bearing. Hydrodynamic lubrication in a gap with variable thickness. Film with linearly variable thickness. Effect of lateral leaks. Kingsbury-Michell bearings. Axial revolute pair with lubrication. journal bearing. Half-Somerfield Theory. Geometric meaning of the mediated friction angle in the lubricated rolling pair. Inverse problem. Lubricated flat sliding pair. Direct problem. Michell bearings with self-aligning pads. Direct problem. Michell bearing with fixed orientation.

Work and Energy
Kinetic energy. Variation of kinetic energy. Potential energy. Conservation of mechanical energy. Energy balance and efficiency. Instantaneous and average efficiencies. Backward (reverse) motion efficiency, efficiency of mechanisms. Force and torque reduction. Mass reduction. Reduction of masses in a crank mechanism. Reduction of stiffness. Design of a Flywheel.

Gears
Transmission by higher kinematic pairs. Levers with constant transmission ratio. Friction wheels. Types of gears. Nomenclature of gears. Involute profiles. Line of action and action line. Drawing of the involute profile. Tooth thickness. Calculation of slip between teeth. Specific slips. Interference phenomenon. Methods to overcome interference. Rack-wheel pair with involute profile. Gear cutting. Helical gears for parallel axes. Characteristics of teeth on normal and front planes. Transmission from rotation to translation using gears. Efficiency of gear pair with involute profiles. Worm wheel pair.

Transmission Joints
Analysis of kinematic structure. Homokinetic joints. Oldham joint. Cardanic joints. Cardan joint and double Cardan joint. Overview of other types of joints.

Cam-Follower Mechanisms
Classification of cam-follower mechanisms. Followers. Cam profiling: graphical method. Centric roller follower. Centric plate follower. Eccentric roller follower. Standard motion profiles. Constant velocity profile. Constant acceleration profile (parabolic). Harmonic profile. Cycloidal profile. Polynomial profiles.

Brakes
The dynamic problem of braking. Brake shoe with rigid and free approach motion.

Introduction to Mechanical Vibrations
Preliminary concepts and definitions. Free vibrations of linear systems with one degree of freedom. Equation of motion: Newtonian deduction and energy criterion. Study of undamped free oscillations. Damped free vibrations of linear systems with one degree of freedom. Viscous damping. Logarithmic decrement. Forced and damped vibrations of linear systems with one degree of freedom. Vibration isolation. Transmissibility coefficient. Introduction to systems with multiple degrees of freedom.

Flexural Vibrations and Torsional Pulsations
Flexural vibrations. Self-centering of a rotating shaft with a keyed flywheel in the middle. Torsional pulsations. Elements of rotordynamics: Jeffcott rotor.

Hoists
Lifting organs. Direct and reverse hoist.

Elements of Algebra and Vector and Tensor Calculus
Kinematics of Rigid Bodies
The Rigid Body Model
Rigid Displacements
General Formula for Infinitesimal Rigid Displacement
Planar Rigid Displacements
Systems of Rigid Bodies
Kinematic Characterization of Constraints
Kinematic Characterization of External Constraints
Kinematic Characterization of Internal Constraints
Settlement Constraints
The Kinematic Problem
Kinematic Classification by Analytical Means
Kinematic Classification by Direct Means
Graphical Method for Solving the Kinematic Problem
Definitions. Kinematic Chains.
Statics of Rigid Bodies
Static Characterization of Constraints
Static Characterization of External Constraints
Static Characterization of Internal Constraints
The Static Problem
Cardinal Equations of Statics
Position of the Problem
Static Classification
Static-Kinematic Duality
Kinematics of Beams
The Deformation Process
Displacements and Rotations
Displacement
Rotation of Sections
Small Displacement Assumption
Boundary Conditions on Displacements and Rotations
External Constraints: Kinematic Characterization
Strain Measurements
Axial Strain
Angular Slip
Bending Curvature
Implicit Equations of Compatibility
Timoshenko Model
Euler-Bernoulli Model
Kinematic Problem
Discontinuities in the Kinematic Problem
Statics of Beams

Position of the Problem
External Forces
Internal Actions
Indeterminate Equations of Equilibrium
Static Problem
Laws and Diagrams of Stress Characteristics
Discontinuities in the Static Problem
General Rules for Plotting Stress Characteristic Diagrams

Linear Elastic Link for One-Dimensional Beams
Axial Behavior
Bending Behavior
Shear Behavior
Thermal Distortions
Uniform Thermal Variation
Butterfly Thermal Variation
Linear Thermal Variation
Constitutive Equations for One-Dimensional Beams

The Elastic Problem for Beams
Euler-Bernoulli Model
Timoshenko Model
Beam Systems
Displacement Method: The Elastic Line
Elastic Line
Axial Problem
Bending Problem: Euler-Bernoulli Model
Elastic Line in Beam Systems
Kinematic and Static Performance of Internal Constraints

Virtual Work Identity. Duality.
Work
Congruent System
Equilibrium System
External Virtual Work
Internal Virtual Work
Virtual Work Theorem
Calculation of Displacements and Rotations in Isostatic Structures

Force Method
Once Hyperstatic Systems
Multiple Hyperstatic Systems
Müller-Breslau Equations

Truss Structures and Continuous Beams.
Truss Structures
Node Method
Ritter's Section Method
Continuous Beams: Three-Moment Equation

Continuum Mechanics: Deformation Analysis
Deformation Process
Deformation Analysis in the Vicinity: Strain Tensor
Mechanical Interpretation of ε Components
Meaning of Diagonal Components εx, εy, εz
Meaning of Off-Diagonal Components γxy, γxz, γyz
Decomposition of the Deformation Process
Volumetric Dilatation
Cauchy's Formula for Deformation - Principal Directions of Deformation
Triaxial Deformation State
Cylindrical Deformation State
Principal Reference - Mohr's Circles
Compatibility Equations

Continuum Mechanics: Stress Analysis
Cauchy Stress
Cauchy's Lemma
Decomposition of the Cauchy Stress Vector
Cauchy's Formula
Indeterminate Equations of Equilibrium
Stresses and Principal Directions
Principal Reference
Stress States
Isostatic Lines
Mean Stress, Deviatoric Stress, and Octahedral Stress
Mohr's Circles
Plane or Biaxial Stress State
Purely Shear Stress State
Monoaxial Stress State
Linear Elastic Link
Isotropic Materials: Generalized Hooke's Law
The Problem of Elastic Equilibrium: Direct Formulation and Energy Aspects

Saint-Venant Problem
Saint-Venant Postulate
Simple and Combined Stresses
Semi-Inverse Method
Indeterminate Equations of Equilibrium
Compatibility and Constitutive Equations
Concentrated Normal Force. Straight Bending
Concentrated Normal Force
Uniform Straight Bending
Deflected Bending. Tensile Bending, Compressive Bending
Uniform Deflected Bending
Compressive (Tensile) Deflected Bending
Eccentric Normal Force
Uniform Torsion
Torsion in Circular Sections
Compact Circular Section
Hollow Circular Section
Torsion in Any Shape Compact Sections
Hydrodynamic Analogy for Shear Stresses
Thin Rectangular Section
Open Sections Made of Thin Rectangles
Thin-Walled Hollow Sections: Bredt's Theory
Composite Thin Sections
Bending and Shear
Distribution of Normal Stresses
Distribution of Shear Stresses: Approximate Treatment by Jourawsky
Problem Equations
Jourawsky's Formula
Applicability of Jourawsky's Formula
Open Thin Sections
Thin Rectangular Section
Thin Double-T Section
Thin U and H Sections
Closed Thin Sections
Symmetrical Hollow Section
Straight Shear according to y
Deflected Shear
Symmetrical Compact Sections
Combined Shear and Torsion Stress
Shear Center
Shear and Torsion Shear Stresses

Strength Criteria and Introduction to Plasticity
Ductile and Brittle Materials
Linear Elastic Model and Plastic Behavior
The Concept of Yielding
Elasto-Plastic Constitutive Relationship
Yielding Mechanisms and Plasticity Criteria
Stress-Strain Diagrams for Elasto-Plastic Materials
Plasticity in Bending: Yield Moments
Effects of Plastic Behavior in Beams and Structural Elements
Calculation of Safety Factors in Plastic Regime
Limit Analysis of Structures
Methods for Determining Plastic Hinges in Hyperstatic Structures
Structural Verification in Plastic Field

The Phenomenon of Structural Instability
Stability Analysis in Rigid Beams with Elastic Constraints
Euler's Column
Stability Curves, Slenderness

Structural Verifications
Verification of Beams under Operating Conditions
Extension of Saint-Venant Theory
Strength Criteria for Saint-Venant Solids
Operational Procedure for Structural Verification

Geometry of Areas
Area and Centroid
Moments of Inertia
Transport Formulas (without Rotation Formulas)
Principal Moments of Inertia
Central Inertia Ellipse
Notable Cases

Recurring Static Schemes
Cantilever
Simply Supported Beam
Fixed-Supported Beam
Beam Fixed at Both Ends
Continuous Beam
Frame

Hibbelet: meccanica dei materiali e delle strutture

Wave loads
Wave structures interaction
Rubble mound breakwaters
Vertical breakwater
Floating breakwater
Ports layout
Offshore platforms

Wave loads
Description and design of rubble mound breakwaters
Description and design of vertical breakwaters
Description and design of pontoons and off-shore platform
Floating breakewaters
harbours layout
Hydro and morpho dynamics of caoastal area

Wave loads
Wave-structure interaction
Rubble mound breakwaters
Vertical breakwaters
Floating breakwaters
Port layouts
Offshore platforms