Università Roma Tre

The variety of the mechanisms in applications. Basic definitions. Degrees of freedom. Classification of the kinematic pairs. Kinematic chains and mechanisms. Kinematic analysis. Plane motion of a rigid body. Velocity and acceleration fields. Kinematic analysis of planar mechanisms. Characteristics of infinitesimal plane motion. Inflection and stationary circles. Euler Savary formula. Planar polodes theory. Pairs with unilateral contacts. Construction of conjugate profiles. Oldham and universal (Cardan) joints. Expression of the transmission ratio. Double cardan joint. Parallel and anti-parallel four bar linkages. Drafting table and pantograph mechanisms. Hart and Peaucellier exact straight lines mechanism generators. Disaggregation principle in statics. Free body static force and torque analysis of complex systems. Applications of the theorem of the virtual works. Basic topics in Tribology. Surface analysis and characterization. Hertz formulae. Friction. An elementary model of adhesive friction. Friction basic mechanisms. Adhesion, abrasion, fretting, surface fatigue. Experimental classification of the worn surfaces: scuffing, scoring, spalling, case crushing, pitting, galling. Predictive models of wear and friction. Energy dissipated “Reye” method, Archard equation. Ball bearings: static force and fatigue modeling, Striebeck formula. Introduction to lubrication. Viscosity and viscosity index. Petroff’s law. One-dimensional Reye theory of hydro-dynamic lubrication. Lubrication of the Rayleigh step bearing. Film with linearly decreasing thickness. Kingsbury – Mitchell bearings. Hydro-static lubrication in the thrust bearing. Hydrostatic compensation. Journal bearings with hydrodynamic lubrication. Work, power and energy. Principles of energy conservation. Power flow analysis in the mechines. Efficiency. Dynamics of the material point. Dynamic of the rigid body. Newton Euler formulation of the dynamic problems. Dynamic analysis by means of the generalized principle of the virtual works. Traction coefficient in transmission. Gearings. The geometrical characteristics of gears with involute profiles. The mechanical interference in gearings. Advanced methods in kinematics: analytical and numerical methods. Dynamic analysis of multibody systems by means of the coordinate partitioning method and the elimination of the Lagrange’s multipliers. Vibration of systems with one degree of freedom. Free oscillation, damped oscillations and excited vibrations. Rayleigh method for the case of the free undamped oscillator. The function of the flywheel in machines. Flexural and torsional vibration in transmission shafts. Vibrations of system with n degrees of freedom. Dynamic problems and wear in breaks. Cams. Construction of cams with prescribed law of motion. Dynamic problems in cams. Constant acceleration cam. Exercises. Kinematic analysis of the slider crank and four bar linkages. Centrodes of the coupler motions. Static balance in different mechanisms. Lubrication. Kingsbury – Michell hydrodynamic bearings. Geometry of involute gearings. Evaluation of the efficiency of simple mechanisms. Analytical and numerical methods in the kinematic analysis of simple mechanisms. Inverse and direct dynamic problems in simple mechanisms. The application of the methods of Lagrange’s multipliers to the solution of direct dynamic analysis of Multibody systems.

Belfiore, N.P., Di Benedetto, A., Pennestrì, E., Fondamenti di meccanica applicata alle macchine, SECONDA
EDIZIONE, CEA Casa Editrice Ambrosiana, Milano, 2011.

Di Benedetto, A., Belfiore, N.P., Fondamenti di Teoria delle vibrazioni meccaniche, CEA Casa Editrice
Ambrosiana, Milano, 2007.