Università Roma Tre

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.